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Teaching Mathematics
in the
Visible Learning Classroom
Grades 3–5

Teaching Mathematics
in the
Visible Learning Classroom
Grades 3–5
John Almarode, Douglas Fisher,
Kateri Thunder, Sara Delano Moore,
John Hattie, and Nancy Frey

Copyright © 2019 by Corwin
All rights reserved. Except as permitted by U.S. copyright law, no
part of this work may be reproduced or distributed in any form or
by any means, or stored in a database or retrieval system, without
permission in writing from the publisher.
When forms and sample documents appearing in this work
are intended for reproduction, they will be marked as such.
Reproduction of their use is authorized for educational use by
educators, local school sites, and/or noncommercial or nonprofit
entities that have purchased the book.
All third party trademarks referenced or depicted herein are included
solely for the purpose of illustration and are the property of their
respective owners. Reference to these trademarks in no way indicates
any relationship with, or endorsement by, the trademark owner.
Printed in the United States of America
Library of Congress Cataloging-in-Publication Data
Names: Almarode, John, author.
Title: Teaching mathematics in the visible learning classroom,
grades 3-5 / John Almarode [and five others].
Description: Thousand Oaks, California : Corwin, a Sage Company,
[2019] | Includes bibliographical references and index.
Identifiers: LCCN 2018046544 | ISBN 9781544333243 (pbk. : alk. paper)
Subjects: LCSH: Mathematics teachers—In-service training. |
Mathematics—Study and teaching (Elementary)
Classification: LCC QA10.5 .T433 2019 | DDC 372.7/044—dc23
LC record available at https://lccn.loc.gov/2018046544
This book is printed on acid-free paper.
19 20 21 22 23 10 9 8 7 6 5 4 3 2 1
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sponsor, endorse, verify, or certify such third-party content.

Contents
List of Videos ix
Acknowledgments xi
About the Authors xiii
Introduction 1
What Works Best 3
What Works Best When 8
The Path to Assessment-Capable Visible Learners
in Mathematics 9
How This Book Works 13
Chapter 1. Teaching With Clarity in Mathematics 19
Components of Effective Mathematics Learning 24
Surface, Deep, and Transfer Learning 25
Moving Learners Through the Phases of Learning 30
Surface Learning in the Intermediate Mathematics
Classroom 31
Deep Learning in the Intermediate Mathematics
Classroom 34
Transfer Learning in the Intermediate Mathematics
Classroom 35
Differentiating Tasks for Complexity and Difficulty 37
Approaches to Mathematics Instruction 39
Checks for Understanding 41

Profiles of Three Teachers 42
Beth Buchholz 42
Hollins Mills 43
Katy Campbell 44
Reflection 45
Chapter 2. Teaching for the Application
of Concepts and Thinking Skills 47
Ms. Buchholz and the Relationship Between
Multiplication and Division 48
What Ms. Buchholz Wants Her Students to Learn 50
Learning Intentions and Success Criteria 51
Activating Prior Knowledge 52
Scaffolding, Extending, and Assessing
Student Thinking 56
Teaching for Clarity at the Close 57
Ms. Mills and Equivalent Fractions and Decimals 65
What Ms. Mills Wants Her Students to Learn 67
Scaffolding, Extending, and Assessing Student
Thinking 75
Ms. Campbell and the Packing Problem 85
What Ms. Campbell Wants Her Students to Learn 87
Scaffolding, Extending, and Assessing Student
Thinking 92
Reflection 98
Chapter 3. Teaching for Conceptual
Understanding 101
Ms. Buchholz and the Meaning of Multiplication 102

Scaffolding, Extending, and Assessing Student Thinking 112
Ms. Mills and Representing Division as Fractions 123
Ms. Campbell and the Volume of a Rectangular Prism 138
Reflection 153
Chapter 4. Teaching for Procedural
Knowledge and Fluency 155
Ms. Buchholz and Fluent Division Strategies 156
Ms. Mills and Comparing Fractions 173
Ms. Campbell and Computing Volume 188
Reflection 200

Chapter 5. Knowing Your Impact:
Evaluating for Mastery 201
What Is Mastery Learning? 202
Using Learning Intentions to Define Mastery Learning 203
Establishing the Expected Level of Mastery 207
Collecting Evidence of Progress Toward Mastery 210
Ensuring Tasks Evaluate Mastery 217
Ensuring Tests Evaluate Mastery 218
Feedback for Mastery 222
Task Feedback 222
Process Feedback 223
Self-Regulation Feedback 225
Conclusion 228
Final Reflection 231
Appendices 233
A. Effect Sizes 233
B. Planning for Clarity Guide 238
C. Learning Intentions and Success Criteria Template 243
D. A Selection of International Mathematical
Practice or Process Standards 244
References 247
Index 251

ix
Introduction
Video 1 What Is Visible Learning for Mathematics?
Video 2 Creating Assessment-Capable Visible Learners
Chapter 1. Teaching With Clarity in Mathematics
Video 3
What Does Teacher Clarity Mean in Grades 3–5
Mathematics?
Chapter 2. Teaching for the Application of
Concepts and Thinking Skills
Video 4 Using Self-Reflection to Make Learning Visible
Video 5
Teaching Reflection Skills Starts With Clear
Learning Intentions and Success Criteria
Video 6
Consolidating Prior Learning Before Starting an
Application Task
Chapter 3. Teaching for Conceptual Understanding
Video 7 Choosing a Conceptual Learning Task
Video 8
Making Thinking Visible and Addressing
Roadblocks
Video 9
Learning Intentions and Success Criteria
Throughout a Lesson
Video 10
Questioning and Discourse to Clarify and Deepen
Understanding
Video 11 Practicing Evaluating and Giving Feedback
List of Videos

Chapter 4. Teaching for Procedural Knowledge
and Fluency
Video 12 Setting the Stage for Procedural Learning
Video 13 Direct/Deliberate Instruction in a Procedural Task
Video 14
Direct/Deliberate Instruction to Practice
Mathematical Language and Precision
Video 15
Consolidating Learning Through a Worked
Example and Guided Practice
Chapter 5. Knowing Your Impact: Evaluating
for Mastery
Video 16 Setting the Stage for Transfer
Video 17 Scaffolding Learning in a Transfer Lesson
Note From the Publisher: The authors have provided video
and web content throughout the book that is available to
you through QR (quick response) codes. To read a QR code,
you must have a smartphone or tablet with a camera. We
recommend that you download a QR code reader app that is
made specifically for your phone or tablet brand.
Videos may also be accessed at resources.corwin.com/
vlmathematics-3-5
online
resources

xi
Acknowledgments
We are forever grateful for the teachers and instructional leaders who
strive each and every day to make an impact in the lives of learners.
Their dedication to teaching and learning is evident in the video clips
linked to the QR codes in this book. The teachers in Charlottesville,
Virginia, have graciously opened their classrooms and conversations to
us, allowing us to make mathematics in the Visible Learning classroom
visible to readers. The learners they work with in the Charlottesville
City Public Schools are better simply because they spent time with the
following people:
Mrs. Jenny Isaacs-Lowe, Special Educator, Venable Elementary
School
Mr. Christopher Lorigan, Third Grade Teacher, Burnley-Moran
Elementary School
Ms. Isabel Smith, Fourth Grade Teacher, Burnley-Moran Elementary
School
Mrs. Rachel Caldwell, Fourth Grade Teacher, Burnley-Moran
Elementary School
Mrs. Calder McLellan, Mathematics Specialist, Burnley-Moran
Elementary School
Mr. James Henderson, Assistant Superintendent, Charlottesville
City Schools
We are extremely grateful to Superintendent Dr. Rosa Atkins for
allowing us into the schools and classrooms of Charlottesville, help-
ing to make our work come alive.

xii Teaching Mathematics in the Visible Learning Classroom, Grades 3–5
Ms. Christen Showker is an excellent teacher in Rockingham County
Public Schools in Virginia. Ms. Beth Buchholz, Ms. Hollins Mills,
and Ms. Katy Campbell are excellent teachers in public schools.
They are actively engaged in implementing Visible Learning into
their classrooms. Their contributions to this book provide clear
examples of how they have taken the Visible Learning research and
translated the findings into their teaching and learning. We are for-
ever grateful to these four teachers for sharing their journey with us
so that we could share these examples with you.

xiii
About the Authors
John Almarode, PhD,
has worked with schools,
classrooms, and teach-
ers all over the world.
John began his career in
Augusta County, Virginia,
teaching mathematics and
science to a wide range
of students. In addition
to spending his time in
preK–12 schools and
classrooms, he is an asso-
ciate professor in the
Department of Early,
Elementary, and Reading
Education and the codi-
rector of James Madison University’s Center for STEM Education and
Outreach. In 2015, John was named the Sarah Miller Luck Endowed
Professor of Education. However, what really sustains John—and
what marks his greatest accomplishment—is his family. John lives in
Waynesboro, Virginia, with his wife, Danielle, a fellow educator; their
two children, Tessa and Jackson; and their Labrador Retrievers, Angel
and Forest. John can be reached at www.johnalmarode.com.

xiv Teaching Mathematics in the Visible Learning Classroom, Grades 3–5
Douglas Fisher, PhD, is
Professor of Educational
Leadership at San Diego
State University and a
teacher leader at Health
Sciences High Middle
College. He is the recipi-
ent of a William S. Grey
Citation of Merit and
NCTE’s Farmer Award for
Excellence in Writing, as
well as a Christa McAuliffe
Award for Excellence in
Teacher Education. Doug
can be reached at dfisher@
mail.sdsu.edu.
Kateri Thunder, PhD,
served as an inclusive, early
childhood educator, an
Upward Bound educator, a
mathematics specialist, an
assistant professor of math-
ematics education at James
Madison University, and
site director for the Central
Virginia Writing Project (a
National Writing Project
site at the University of
Virginia). Kateri is a mem-
beroftheWritingAcrossthe
Curriculum Research Team
with Dr. Jane Hansen, co-author of The Promise of Qualitative Metasynthesis
for Mathematics Education, and co-creator of The Math Diet. Currently,
Kateri has followed her passion back to the classroom. She teaches in an
at-risk preK program, serves as the PreK−4 Math Lead for Charlottesville
City Schools, and works as an educational consultant. Kateri is happiest
exploring the world with her best friend and husband, Adam, and her fam-
ily. Kateri can be reached at www.mathplusliteracy.com.

About the Authors xv
Sara Delano Moore,
PhD, is Director of
Professional Learning
at ORIGO Education. A
fourth-generation educa-
tor, her work focuses on
helping teachers and stu-
dents understand math-
ematics as a coherent
and connected discipline
through the power of deep
understanding and mul-
tiple representations for
learning. Sara has worked
as a classroom teacher of
mathematics and science
in the elementary and middle grades, a mathematics teacher educator,
Director of the Center for Middle School Academic Achievement for the
Commonwealth of Kentucky, and Director of Mathematics Science at
ETA hand2mind. Her journal articles appear in Mathematics Teaching in
the Middle School, Teaching Children Mathematics, Science Children, and
Science Scope. Sara can be reached at sara@sdmlearning.com.
John Hattie, PhD, has
been Laureate Professor of
Education and Director of
the Melbourne Education
Research Institute at the
University of Melbourne,
Australia, since March
2011. He was previously
Professor of Education at
the University of Auckland,
as well as in North Carolina,
Western Australia, and New
England. His research inter-
ests are based on applying
measurement models to
education problems. He

xvi Teaching Mathematics in the Visible Learning Classroom, Grades 3–5
has been president of the International Test Commission, has served as
adviser to various ministers, chairs the Australian Institute for Teachers
and School Leaders, and in the 2011 Queen’s Birthday Honours was
made “Order of Merit for New Zealand” for his services to education. He
is a cricket umpire and coach, enjoys being a dad to his young men, is
besotted with his dogs, and moved with his wife as she attained a promo-
tion to Melbourne. Learn more about his research at www.corwin.com/
visiblelearning.
Nancy Frey, PhD, is
Professor of Literacy in the
Department of Educational
Leadership at San Diego
State University. She is the
recipient of the 2008 Early
Career Achievement Award
from the National Reading
Conference and is a teacher
leader at Health Sciences
High Middle College.
She is also a credentialed
special educator, reading
specialist, and administra-
tor in California.

1
Introduction
Dylan is a precocious fourth grader who loves mathematics. One of his
favorite pastimes is playing the 24 Game (Suntex International Inc.,
1988). For those of us not familiar with this particular game, Dylan will
quickly show you that this competitive game involves a card containing
four numbers (e.g., 7, 5, 4, and 3). Once the card is placed on the table,
each player in the game tries to figure out how to make the number 24
using addition, subtraction, multiplication, and division. For the exam-
ple with 7, 5, 4, and 3, Dylan gave the following answer:
7 − 5 = 2
4 × 3 = 12
12 × 2 = 24
In this specific example, Dylan rattled off the difference between seven
and five, the product of four and three, and multiplied those two answers
to get 24. To note, Dylan was able to solve this particular problem before
the teacher had finished placing the card on the table.
Dylan demonstrates a high level of proficiency, or mastery, in proce-
dural knowledge in the area of computation involving the four basic
operations with single-digit whole numbers (e.g., additive thinking and
multiplicative thinking). However, there is more to Dylan’s mathemat-
ics learning than his mastery of number facts. Dylan possesses a balance
of conceptual understanding, procedural knowledge, and the ability
to apply those concepts and thinking skills to a variety of mathemat-
ical contexts. By balance, we mean that no one dimension of math-
ematics learning is more important than the other two. Conceptual
understanding, procedural knowledge, and the application of concepts
Teaching
Takeaway
Procedural
knowledge comes
from balanced
mathematics
teaching and
learning.

2 Teaching Mathematics in the Visible Learning Classroom, Grades 3–5
and thinking skills are each essential aspects of learning mathematics.
Dylan’s prowess in the 24 Game is not the result of his teachers imple-
menting procedural knowledge, conceptual understanding, and appli-
cation in isolation, but through a series of linked learning experiences
and challenging mathematical tasks that result in him engaging in both
mathematical content and processes.
If you were to engage in a conversation with Dylan about mathematics,
you would quickly see that he is able to discuss the concept of multipli-
cation and describe different ways to represent multiplication (i.e., equal
groups, arrays, and number line models). Furthermore, he can articulate
which model he prefers and why: “I sometimes pick the model based
on the type of problem. You know, some ways work better with certain
problems.” Dylan also recognizes that he must apply this conceptual
understanding and thinking to solving problems involving rates and
price. He says, “If a pencil from the school store costs 10 cents and I
want to buy five pencils, I need 50 cents.” Dylan also mentions that he
could easily use this information when he learns about geometric mea-
surements next year. “Well, that is what my teacher tells me,” he adds.
Dylan’s mathematics learning is not by chance, but by design. His pro-
gression in conceptual understanding, procedural knowledge, and the
application of concepts and thinking skills come from the purposeful,
deliberate, and intentional decisions of his current and past teachers.
These decisions focus on the following:
• What works best and what works best when in the teaching and
learning of mathematics, and
• Building and supporting assessment-capable visible learners in
mathematics.
This book explores the components in mathematics teaching and
learning in Grades 3−5 through the lens of what works best in student
learning at the surface, deep, and transfer phases. We fully acknowledge
that not every student in your classroom is like Dylan. Our students
come to our classrooms with different background knowledge, levels of
readiness, and learning needs. Our goal is to unveil what works best so
that your learners develop the tools needed for successful mathematics
learning.
Our Learning
Intention: To
understand what
works best in
the mathematics
classroom,
Grades 3–5.

Introduction 3
What Works Best
Identifying what works best draws from the key findings from Visible
Learning (Hattie, 2009) and also guides the classrooms described in
this book. One of those key findings is that there is no one way to teach
mathematics or one best instructional strategy that works in all situations for
all students, but there is compelling evidence for certain strategies and
approaches that have a greater likelihood of helping students reach their
learning goals. In this book, we use the effect size information that John
Hattie has collected and analyzed over many years to inform how we
transform the findings from the Visible Learning research into learning
experiences and challenging mathematical tasks that are most likely to
have the strongest influence on student learning.
For readers less familiar with Visible Learning, we would like to take
a moment to review what we mean by what works best. The Visible
Learning database is composed of over 1,800 meta-analyses of studies
that include over 80,000 studies and 300 million students. Some have
argued that it is the largest educational research database amassed to
date. To make sense of so much data, John Hattie focused his work on
meta-analyses. A meta-analysis is a statistical tool for combining find-
ings from different studies, with the goal of identifying patterns that
can inform practice. In other words, a meta-analysis is a study of studies.
The mathematical tool that aggregates the information is an effect size
and can be represented by Cohen’s d. An effect size is the magnitude,
or relative size, of a given effect. Effect size information helps readers
understand not only that something does or does not have an influence
on learning but also the relative impact of that influence.
For example, imagine a hypothetical study in which pausing instruction
to engage in a quick exercise or “brain break” results in relatively higher
mathematics scores among fourth graders. Schools and classrooms
around the country might feel compelled to devote significant time
and energy to the development and implementation of brain breaks
in all fourth grade classrooms in a specific district. However, let’s say
the results of this hypothetical study also indicate that the use of brain
breaks had an effect size of 0.02 in mathematics achievement over the
control group, an effect size pretty close to zero. Furthermore, the large
number of students participating in the study made it almost certain
A meta-analysis is
a statistical tool for
combining findings
from different studies,
with the goal of
identifying patterns
that can inform
practice.
Effect size represents
the magnitude of the
impact that a given
approach has.

there would be a difference in the two groups of students (those partic-
ipating in brain breaks versus those not participating in brain breaks).
As an administrator or teacher, would you still devote large amounts
of professional learning and instructional time on brain breaks? How
confident would you be in the impact or influence of your decision on
mathematics achievement in your district or school?
This is where an effect size of 0.02 for the “brain breaks effect” is helpful
in discerning what works best in mathematics teaching and learning.
Understanding the effect size helps us know how powerful a given influ-
ence is in changing achievement—in other words, the impact for the
effort or return on the investment. The effect size helps us understand
not just what works, but what works best. With the increased frequency
and intensity of mathematics initiatives, programs, and packaged curric-
ula, deciphering where to best invest resources and time to achieve the
greatest learning outcomes for all students is challenging and frustrating.
For example, some programs or packaged curricula are hard to imple-
ment and have very little impact on student learning, whereas others
are easy to implement but still have limited influence on student growth
and achievement in mathematics. This is, of course, on top of a literacy
program, science kits, and other demands on the time and energy of ele-
mentary school teachers. Teaching mathematics in the Visible Learning
classroom involves searching for those things that have the greatest
impact and produce the greatest gains in learning, some of which will
be harder to implement and some of which will be easier to implement.
As we begin planning for our unit on rational numbers, knowing the
effect size of different influences, strategies, actions, and approaches to
teaching and learning proves helpful in deciding where to devote our
planning time and resources. Is a particular approach (e.g., classroom
discussion, exit tickets, use of calculators, a jigsaw activity, computer-
assisted instruction, simulation creation, cooperative learning, instruc-
tional technology, presentation of clear success criteria, development
of a rubric, etc.) worth the effort for the desired learning outcomes of
that day, week, or unit? With the average effect size across all influ-
ences measuring 0.40, John Hattie was able to demonstrate that influ-
ences, strategies, actions, and approaches with an effect size greater than
0.40 allow students to learn at an appropriate rate, meaning at least a
year of growth for a year in school. Effect sizes greater than 0.40 mean
Video 1
What Is Visible Learning
for Mathematics?
To read a QR code, you must
have a smartphone or tablet with
a camera. We recommend that
you download a QR code reader
app that is made specifically for
your phone or tablet brand.
Videos can also be accessed at
https://resources.corwin.com/
vlmathematics-3-5

5
THE BAROMETER OF INFLUENCE
–0.20
|
–
0
.1
0
|
0
.
0
0
|
0.10
|
0.20
|
0.30
|
0.40
|
0.50
| 0.60
| 0.70
| 0.80
|
0
.
9
0
|
1
.0
0
|
1
.1
0
|
1.20
|
Zone of
Desired
Effects
HI
G
H
MEDIUM
L
OW
N
E
G
A
T
I
V
E
Reverse
Effects
Develop-
mental
Effects
Teacher
Effects
Source: Adapted from Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Figure 2.4,
page 19. New York, NY: Routledge.
Figure I.1
more than a year of growth for a year in school. Figure I.1 provides a
visual representation of the range of effect sizes calculated in the Visible
Learning research.
Before this level was established, teachers and researchers did not have a way
to determine an acceptable threshold, and thus we continued to use weak
practices, often supported by studies with statistically significant findings.
Consider the following examples. First, let us consider classroom dis-
cussion or the use of mathematical discourse (see NCTM, 1991). Should
teachers devote resources and time into planning for the facilitation
of classroom discussion? Will this approach to mathematics provide
a return on investment rather than “chalk talk,” where we work out
lots of problems on the board for students to include in their notes?
With classroom discussion, teachers intentionally design and purpose-
fully plan for learners to talk with their peers about specific problems
or approaches to problems (e.g., comparing and contrasting strategies
for multiplying and dividing large numbers versus small numbers,
EFFECT SIZE FOR
ABILIT Y GROUPING
(TRACKING/
STREAMING) = 0.12

6
explaining their development of a formula for a three-dimensional
shape) in collaborative groups. Peer groups might engage in working
to solve complex problems or tasks (e.g., determining the equivalent
decimal for a fraction using a number line). Although they are working
in collaborative groups, the students would not be ability grouped.
Instead, the teacher purposefully groups learners to ensure that there is
academic diversity in each group as well as language support and vary-
ing degrees of interest and motivation. As can be seen in the barometer
in Figure I.2, the effect size of classroom discussion is 0.82, which is well
above our threshold and is likely to accelerate learning gains.
Therefore, individuals teaching mathematics in the Visible Learning
classroom would use classroom discussions to understand mathematics
learning through the eyes of their students and for students to see them-
selves as their own mathematic teachers.
Second, let us look at the use of calculators. Within academic circles,
teacher workrooms, school hallways, and classrooms, there have been
Ability grouping,
also referred to as
tracking or streaming,
is the long-term
grouping or tracking
of learners based on
their ability. This is
different from flexibly
grouping students
to work on a specific
concept, skill, or
application or address
a misconception.
THE BAROMETER FOR THE INFLUENCE
OF CLASSROOM DISCUSSION
Classroom Discussion d = 0.82
–0.20
|
–
0
.1
0
|
0
.
0
0
|
0.10
|
0.20
|
0.30
|
0.40
|
0.50
|
0.60
| 0.70
| 0.80
|
0
.
9
0
|
1
.0
0
|
1
.1
0
|
1.20
|
Zone of
Desired
Effects
HI
G
H
MEDIUM
LOW
N
E
G
A
T
I
V
E
Reverse
Effects
Develop-
mental
Effects
Teacher
Effects
Figure I.2

7
many conversations about the use of the calculator in mathematics.
There have been many efforts to reduce the reliance on calculators while
at the same time developing technology-enhanced items on assessments
in mathematics. Using a barometer as a visual representation of effect
sizes, we see that the use of calculators has an overall effect size of 0.27.
The barometer for the use of calculators is in Figure I.3.
As you can see, the effect size of 0.27 is below the zone of desired effects
of 0.40. The evidence suggests that the impact of the use of calcula-
tors on mathematics achievement is low. However, closer examination
of the five meta-analyses and the 222 studies that produced an over-
all effect size of 0.27 reveals a deeper story to the use of calculators.
Calculators are most effective in the following circumstances: (1) when
they are used for computation, deliberate practice, and learners check-
ing their work; (2) when they are used to reduce the amount of cognitive
load on learners as they engage in problem solving; and (3) when there
is an intention behind using them (e.g., generating a pattern of square
numbers, computing multiples of 10, or calculating the area or volume
THE BAROMETER FOR THE INFLUENCE
OF USING CALCULATORS
Using Calculators d = 0.27
–0.20
|
–
0
.1
0
|
0
.
0
0
|
0.10
|
0.20
|
0.30
|
0.40
|
0.50
|
0.60
| 0.70
| 0.80
|
0
.
9
0
|
1
.
0
0
|
1
.1
0
|
1.20
|
Zone of
Desired
Effects
HI
G
H
MEDIUM
L
OW
N
E
G
A
T
I
V
E
Reverse
Effects
Develop-
mental
Effects
Teacher
Effects
Figure I.3
EFFECT SIZE
FOR CLASSROOM
DISCUSSION = 0.82
EFFECT SIZE
OF USE OF
CALCULATORS
= 0.27

of a large space or object). This leads us into a second key finding from
John Hattie’s Visible Learning research: We should not hold any influence,
instructional strategy, action, or approach to teaching and learning in higher
esteem than students’ learning.
What Works Best When
Visible Learning in the mathematics classroom is a continual evaluation
of our impact on student learning. From the above example, the use of
calculators is not really the issue and should not be our focus. Instead,
our focus should be on the intended learning outcomes for that day and
how calculators support that learning. Visible Learning is more than a
checklist of dos and don’ts. Rather than checking influences with high
effect sizes off the list and scratching out influences with low effect sizes,
we should match the best strategy, action, or approach with learning
needs of our students. In other words, is the use of calculators the right
strategy or approach for the learners at the right time, for this specific
content? Clarity about the learning intention brings into focus what the
learning is for the day, why students are learning about this particular
piece of content and process, and how we and our learners will know
they have learned the content. Teaching mathematics in the Visible
Learning classroom is not about a specific strategy, but a location in the
learning process.
Visible Learning in the mathematics classroom occurs when teachers
see learning through the eyes of their students and students see them-
selves as their own teachers. How do teachers of mathematics see mul-
tiplicative thinking, rational numbers, and geometric measurements
through the eyes of their students? In turn, how do teachers develop
assessment-capable visible learners—students who see themselves as
their own teachers—in the study of numbers, operations, and relation-
ships? Mathematics teaching and learning, where teachers see learning
through the eyes of their learners and learners see themselves as their own
teachers, results from specific, intentional, and purposeful decisions
about each of these dimensions of mathematics instruction critical for
student growth and achievement. Conceptualizing, implementing, and
sustaining Visible Learning in the mathematics classroom by identifying
what works best and what works best when is exactly what we set out to
do in this book.
Teaching
Takeaway
Using the right
approach, at
the right time
increases our
impact on student
learning in the
mathematics
classroom.

Introduction 9
Over the next several chapters, we will show how to support mathe-
matics learners in their pursuit of conceptual understanding, procedural
knowledge, and application of concepts and thinking skills through the
lens of what works best when. This requires us, as mathematics teachers,
to be clear in our planning and preparation for each learning experi-
ence and challenging mathematics tasks. Using the guiding questions in
Figure I.4, we will model how to blend what works best with what works
best when. You can use these questions in your own planning. This plan-
ning guide is found also in Appendix B.
Through these specific, intentional, and purposeful decisions in our
mathematics instruction, we pave the way for helping learners see them-
selves as their own teachers, thus making them assessment-capable visi-
ble learners in mathematics.
The Path to Assessment-Capable Visible
Learners in Mathematics
Teaching mathematics in the Visible Learning classroom builds and sup-
ports assessment-capable visible learners (Frey, Hattie, Fisher, 2018).
With an effect size of 1.33, providing a mathematics learning environ-
ment that allows learners to see themselves as their own teacher is essen-
tial in today’s classrooms.
Ava is a bubbly fourth grader who loves school. She loves school for all
of the right reasons—learning and socializing. At times, she confuses the
two, but she quickly engages in the day’s mathematics lesson. During
her review, Ava is engaging in the deliberate practice of adding frac-
tions with unlike denominators. This is a topic that is challenging to her
and is important background or prior knowledge for upcoming learn-
ing. During a discussion with her shoulder partner, Ava discusses her
areas of strength and areas for growth: “I am good at adding fractions
when the bottom numbers—wait, the denominators—are the same. You
know, you just add the top numbers. I need more practice when the
number—I mean, the denominator—is different. I have to slow down
and figure it out.” This is a characteristic of an assessment-capable
learner in mathematics.
EFFECT SIZE FOR
ASSESSMENT-
CAPABLE VISIBLE
LEARNERS = 1.33
Video 2
Creating Assessment-
Capable Visible Learners
vlmathematics-3-5

10
PLANNING FOR CLARITY GUIDE
Rather than what I want
my students to be doing,
this question focuses on
the learning. What do the
standards say my students
should learn? The answer to
this question generates the
learning intentions for this
particular content.
I have to be clear about
what content and practice
or process standards I am
using to plan for clarity. Am
I using only mathematics
standards or am I
integrating other content
standards (e.g., writing,
reading, or science)?
As I gather evidence about
my students’ learning
progress, I need to establish
what they should know,
understand, and be able to
do that would demonstrate
to me that they have
learned the content. This
list of evidence generates
the success criteria for the
learning.
online
resources

This planning guide is available for download at resources.corwin.com/
vlmathematics-3-5.
E S TA B L I S H I N G P U R P O S E
1 What are the key content standards I will focus on in this
lesson?
Content Standards:
2 What are the learning intentions (the goal and why of
learning, stated in student-friendly language) I will focus on
in this lesson?
Content:
Language:
Social:
3 When will I introduce and reinforce the learning intention(s) so
that students understand it, see the relevance, connect it to
previous learning, and can clearly communicate it themselves?
S U C C E S S C R I T E R I A
4 What evidence shows that students have mastered the
learning intention(s)? What criteria will I use?
I can statements:
Once I have clear
learning intentions, I must
decide when and how to
communicate them with
my learners. Where does it
best fit in the instructional
block to introduce the
day’s learning intentions?
Am I going to use guiding
questions?

11
Figure I.4
Now I need to decide
which tasks, activities, or
strategies best support my
learners. Will I use tasks
that focus on conceptual
understanding, procedural
knowledge, and/or the
application of concepts
and thinking skills? What
tools and problem-solving
strategies will my learners
have available?
I need to adjust the tasks
so that all learners have
access to the highest
level of engagement. I can
adjust the difficulty and/
or complexity of a given
task. What adjustments will
I make to ensure all learners
have access to the learning?
I need to create and/or
gather the materials
necessary for the
learning experience (e.g.,
manipulatives, handouts,
grouping cards, worked
examples, etc.).
Finally, I need to decide
how to manage the
learning. How will I
transition learners from
one activity to the next?
When will I use cooperative
learning, small-group, or
whole-group instruction?
How will I group students
for each activity?
Once I have a clear
learning intention and
evidence of success, I
must design my checks
for understanding to
monitor progress in
learning (e.g., observations,
exit tickets, student
conferences, problem sets,
questioning, etc.).
5 How will I check students’ understanding (assess learning)
during instruction and make accommodations?
I N S T R U C T I O N
6 What activities and tasks will move students forward in their
learning?
7 What resources (materials and sentence frames) are needed?
8 How will I organize and facilitate the learning? What questions
will I ask? How will I initiate closure?

Assessment-capable visible mathematics learners are:
1. Active in their mathematics learning. Learners deliberately
and intentionally engage in learning mathematics content and
processes by asking themselves questions, monitoring their
own learning, and taking the reins of their learning. They know
their current level of learning.
Later in the lesson, Ava is working in a cooperative learning group on finding
the area of the school garden. Although the concept of area is a review, her
teacher is using a concept Ava is familiar with to add context to two- by
two-digit multiplication. Her cooperative learning group has encountered a
challenging calculation, 27 × 16. However, they quickly recognize that they
have the tools to solve this problem. One of the group members chimes in,
“To find the product, the answer to the problem, 27 × 16, I am going to use
an open array model. These numbers are unfriendly.” This is a characteristic
of an assessment-capable learner in mathematics.
2. Able to plan the immediate next steps in their mathematics
learning within a given unit of study or topic. Because of
the active role taken by an assessment-capable visible
mathematics learner, these students can plan their next steps
and select the right tools (e.g., manipulatives, problem-solving
approaches, and/or metacognitive strategies) to guide their
learning. They know what additional tools they need to
successfully move forward in a task or topic.
Ava’s teacher, Ms. Christen Showker, takes time to individually conference
with each student at least once a week. This allows the teacher to provide
very specific feedback on each learner’s progress. Ava begins the conference
by stating, “Yesterday’s exit ticket surprised me. You [Ms. Showker] wrote
on my paper that I needed to revisit place value. I think I mixed up the
thousands place. So, tomorrow I am going to work out the entire process
for finding which number is larger in my notebook and not try and do it all
in my head.” This is a characteristic of an assessment-capable learner in
mathematics.

Introduction 13
3. Aware of the purpose of the assessment and feedback
provided by peers and the teacher. Whether the assessment is
informal, formal, formative, or summative, assessment-capable
visible mathematics learners have a firm understanding of
the information behind each assessment and the feedback
exchanged in the classroom. Put differently, these learners
not only seek feedback, but they recognize that errors are
opportunities for learning, monitor their progress, and adjust
their learning (adapted from Frey et al., 2018) (see Figure I.5).
Over the next several chapters, we will explore how to create a classroom
environment that focuses on learning and provides the best environ-
ment for developing assessment-capable visible mathematics learners
who can engage in the mathematical habits of mind represented in one
form or another in every standards document. Such learners can achieve
the following:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
(© Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All
rights reserved.).
How This Book Works
As authors, we assume you have read Visible Learning for Mathematics
(Hattie et al., 2017), so we are not going to recount all of the information

14
ASSESSMENT-CAPABLE VISIBLE LEARNERS
ASSESSMENT-CAPABLE LEARNERS:
KNOW THEIR CURRENT LEVEL OF UNDERSTANDING
KNOW WHERE THEY’RE GOING AND ARE CONFIDENT
TO TAKE ON THE CHALLENGE
SELECT TOOLS TO GUIDE THEIR LEARNING
SEEK FEEDBACK AND RECOGNIZE THAT ERRORS ARE
OPPORTUNITIES TO LEARN
MONITOR THEIR PROGRESS AND ADJUST THEIR
LEARNING
RECOGNIZE THEIR LEARNING AND TEACH OTHERS
FEEDBACK
AHEAD
Source: Adapted from Frey, Hattie, Fisher (2018).
Figure I.5

Introduction 15
contained in that book. Rather, we are going to dive deeper into aspects
of mathematics instruction in Grades 3–5 that are critical for students’
success, helping you to envision what a Visible Learning mathematics
classroom like yours looks like. In each chapter, we profile three teach-
ers who have worked to make mathematics learning visible for their
students and have influenced learning in significant ways. Each chapter
will do the following:
1. Provide effect sizes for specific influences, strategies, actions,
and approaches to teaching and learning.
2. Provide support for specific strategies and approaches to teach-
ing mathematics.
3. Incorporate content-specific examples from third, fourth, and
fifth grade mathematics curricula.
4. Highlight aspects of assessment-capable visible learners.
Through the eyes of third, fourth, and fifth grade mathematics teach-
ers, as well as the additional teachers and the instructional leaders in
the accompanying videos, we aim to show you the mix and match of
strategies you can use to orchestrate your lessons in order to help your
students build their conceptual understanding, procedural knowledge,
and application of concepts and thinking skills in the most visible ways
possible—visible to you and to them. If you are a mathematics specialist,
mathematics coordinator, or methods instructor, you may be interested
in exploring the vertical progression of these content areas across preK–12
within Visible Learning classrooms and see how visible learners grow
and progress across time and content areas. Although you may identify
with one of the teachers from a content perspective, we encourage you
to read all of the vignettes to get a full sense of the variety of choices you
can make in your instruction, based on your instructional goals.
In Chapter 1, we focus on the aspects of mathematics instruction that
must be included in each lesson. We explore the components of effec-
tive mathematics instruction (conceptual, procedural, and application)
and note that there is a need to recognize that student learning has
to occur at the surface, deep, and transfer levels within each of these

components. Surface, deep, and transfer learning served as the organiz-
ing feature of Visible Learning for Mathematics, and we will briefly review
them and their value in learning. This book focuses on the ways in
which teachers can develop students’ surface, deep, and transfer learn-
ing, specifically by supporting students, conceptual understanding, pro-
cedural knowledge, and application whether with comparing fractions
or geometric measurement. Finally, Chapter 1 contains information
about the use of checks for understanding to monitor student learning.
Generating evidence of learning is important for both teachers and stu-
dents in determining the impact of the learning experiences and chal-
lenging mathematical tasks on learning. If learning is not happening,
then we must make adjustments.
Following this introductory chapter, we turn our attention, separately,
to each component of mathematics teaching and learning. However, we
will walk through the process starting with the application of concepts
and thinking skills, then direct our attention to conceptual understand-
ing, and finally, procedural knowledge. This seemingly unconventional
approach will allow us to start by making the goal or endgame visible:
learners applying mathematics concepts and thinking skills to other sit-
uations or contexts.
Chapter 2 focuses on application of concepts and thinking skills.
Returning to our three profiled classrooms, we will look at how we plan,
develop, and implement challenging mathematical tasks that scaffold
student thinking as they apply their learning to new contexts or situa-
tions. Teaching mathematics in the Visible Learning classroom means
supporting learners as they use mathematics in a variety of situations.
In order for learners to effectively apply mathematical concepts and
thinking skills to different situations, they must have strong conceptual
understanding and procedural knowledge. Returning to Figure I.4, we
will walk through the process for establishing clear learning intentions,
defining evidence of learning, and developing challenging tasks that,
as you have already come to expect, encourage learners to see them-
selves as their own teachers. Each chapter will discuss how to differenti-
ate mathematical tasks by adjusting their difficulty and/or complexity,
working to meet the needs of all learners in the mathematics classroom.
Chapters 3 and 4 take a similar approach with conceptual understanding
and procedural knowledge, respectively. Using Chapter 2 as a reference

Introduction 17
point, we will return to the three profiled classrooms and explore the
conceptual understanding and procedural knowledge that provided
the foundation for their learners applying ideas to different mathemat-
ical situations. For example, what influences, strategies, actions, and
approaches support a learner’s conceptual understanding of multiplica-
tion and division, rational numbers, or geometric measurement? With
conceptual understanding, what works best as we encourage learners
to see mathematics as more than a set of mnemonics and procedures?
Supporting students’ thinking as they focus on underlying conceptual
principles and properties, rather than relying on memory cues like
PEMDAS, also necessitates adjusting the difficulty and complexity of
mathematics tasks. As in Chapter 2, we will talk about differentiating
tasks by adjusting their difficulty and complexity.
In this book, we do not want to discourage the value of procedural
knowledge. Although mathematics is more than procedural knowledge,
developing skills in basic procedures is needed for later work in each
area of mathematics from the area and circumference of a circle to linear
equations. As in the previous two chapters, Chapter 4 will look at what
works best when supporting students’ procedural knowledge. Adjusting
the difficulty and complexity of tasks will once again help us meet the
needs of all learners.
In the final chapter of this book, we focus on how to make mathematics
learning visible through evaluation. Teachers must have clear knowl-
edge of their impact so that they can adjust the learning environment.
Learners must have clear knowledge about their own learning so that
they can be active in the learning process, plan the next steps, and under-
stand what is behind the assessment. What does evaluation look like so
that teachers can use it to plan instruction and to determine the impact
that they have on learning? As part of Chapter 5, we highlight the value
of feedback and explore the ways in which teachers can provide effec-
tive feedback to students that is growth producing. Furthermore, we will
highlight how learners can engage in self-regulation feedback and pro-
vide feedback to their peers.
This book contains information on critical aspects of mathematics
instruction in Grades 3–5 that have evidence for their ability to influ-
ence student learning. We’re not suggesting that these be implemented
in isolation, but rather that they be combined into a series of linked

learning experiences that result in students engaging in mathematics
learning more fully and deliberately than they did before. Whether
finding equivalent fractions or calculating volume, we strive to create a
mathematics classroom where we see learning through the eyes of our
students and students see themselves as their own mathematics teach-
ers. As learners progress from simplifying rational expressions to using
ratios and proportions, teaching mathematics in the Visible Learning
classroom should build and support assessment-capable visible mathe-
matics learners.
Please allow us to introduce you to Christen Showker, Beth Buchholz,
Hollins Mills, and Katy Campbell. These four elementary school teachers
set out each day to deliberately, intentionally, and purposefully impact
the mathematics learning of their students. Whether they teach third,
fourth, or fifth grade, they recognize that:
• They have the capacity to select and implement various teach-
ing and learning strategies that enhance their students’ learning
in mathematics.
• The decisions they make about their teaching have an impact
on students’ learning.
• Each student can learn mathematics, and they need to take
responsibility to teach all learners.
• They must continuously question and monitor the impact of
their teaching on student learning. (adapted from Hattie
Zierer, 2018)
Through the videos accompanying this book, you will meet addi-
tional elementary teachers and the instructional leaders who support
them in their teaching. Collectively, the recognitions above—or their
mindframes—lead to action in their mathematics classrooms and
their actions lead to outcomes in student learning. This is where we
begin our journey through Teaching Mathematics in the Visible Learning
Classroom.
Mindframes are
ways of thinking
about teaching and
learning. Teachers
who possess certain
ways of thinking have
major impacts on
student learning.

1
TEACHING WITH CLARITY
IN MATHEMATICS
CHAPTER 1 SUCCESS CRITERIA:
(1) I can describe teacher clarity and the
process for providing clarity in my
classroom.
(2) I can describe the components of
effective mathematics instruction.
(3) I can relate the learning process to my
own teaching and learning.
(4) I can give examples of how to
differentiate mathematics tasks.
(5) I can describe the four different
approaches to teaching mathematics.

In Ms. Showker’s fourth grade mathematics class, students are learning
to collect, organize, and represent data using line graphs or bar graphs.
Ms. Showker starts the math block by walking her learners through the
learning intention and success criteria.
Learning Intention: I am learning that the type of data and the way
I display that data are connected.
Success Criteria:
1. I can describe why I would use a graph.
2. I can compare and contrast a line graph with a bar graph.
3. I can explain why I would use each type of graph.
4. I can construct a line graph and a bar graph from data.
There are many different approaches for engaging learners in data, line
graphs, and bar graphs. Given that the specific standard associated with
today’s learning emphasizes questions and investigations related to stu-
dents’ experiences, interests, and environment, Ms. Showker uses data
collected during their unit on weather and an earlier unit on measure-
ment. During these two units, Ms. Showker’s learners collected weather
data (i.e., sky cover and precipitation type) and kept those observations
in their interactive notebooks. She introduces today’s lesson as follows:
Over the past several weeks, we have recorded weather
observations in your interactive notebooks. We used tally
marks to record the sky cover for the day (for example, cloudy
or sunny). We also used tally marks to record the type of
precipitation (for example, rain, snow, or none). When I say
“go,” please get out your interactive math notebooks and
make your way to your assigned tables.
Learners are flexibly grouped based on the previous day’s exit ticket.
There are learners who demonstrate surface knowledge about the nec-
essary parts of graphs (e.g., axes, labels, and key). Furthermore, previ-
ous checks for understanding provided evidence about her learners’
understanding and use of skip counting, an important piece of prior
A learning intention
describes what it
is that we want our
students to learn.
Success criteria
specify the necessary
evidence students will
produce to show their
progress toward the
learning intention.
EFFECT SIZE
FOR LEARNING
INTENTION = 0.68
EFFECT SIZE FOR
SUCCESS CRITERIA
= 1.13
EFFECT SIZE FOR
COOPERATIVE
LEARNING = 0.40
EFFECT SIZE FOR
COOPERATIVE
LEARNING
COMPARED TO
COMPETITIVE
LEARNING = 0.53

CHAPTER 1. Teaching With Clarity in Mathematics 21
knowledge for this particular content. Ms. Showker provides each table
with a folder of resources that will support students in accomplishing
today’s mathematics task. Each folder contains several examples of line
graphs and several examples of bar graphs.
Favorite Sport
Number
of
People
9
8
7
6
5
4
3
2
1
0
Soccer Basketball Tennis Hockey Baseball
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Apples Sold
January February March April
Ms. Showker deliberately informs her learners that their folders con-
tain examples of two types of graphs: line graphs and bar graphs. She
does not want vocabulary or terminology to distract from today’s
learning. She says, “With your fellow mathematicians, please sort the
examples into two groups—line graphs and bar graphs.” As she moni-
tors her learners during this sorting task, Ms. Showker is making note
of the specific mathematical discussions around the sorting of the

examples. She notices some students are focusing on essential char-
acteristics (e.g., bar graphs contain vertical or horizontal bars with a
separate bar for each category, or line graphs include a key to identify
what each line represents), whereas others are basing their sorts on
irrelevant characteristics (e.g., this graph is about sports, and this one
is not about sports). Ms. Showker uses the evidence gathered during
these discussions to provide direct/deliberate instruction through a
mini-lesson for specific learners who need additional instruction to
master the concept.
The challenging task during today’s mathematics block is for each group
to construct a line graph and a bar graph using the weather data in
their interactive notebooks. Learners have to first decide which type of
graph best fits the two different types of data (i.e., type of sky cover
and precipitation). They will then create graphs, using the examples
in the folder as a model. Anticipating that learners would be at differ-
ent places in the learning progression associated with data and graphs,
Ms. Showker prepared different levels of support for each group. In addi-
tion to the examples provided for the sorting task, she provides groups
the following different levels of support:
• Graph paper with rows or columns drawn for each category, and
options for values of pictures
• Stamps or stickers to use in constructing the graphs
• Graph paper with the axes drawn and scaled (learners need to
graph the data, label the axes, provide a key if necessary, and
add a title)
• Graph paper with the axes drawn, but not scaled
• Graph paper with a checklist of the components needed for each
type of graph
• A blank sheet of paper
Throughout the task, Ms. Showker monitors her learners’ progress, ask-
ing guiding questions and providing feedback and additional support
as needed. She wants to give her learners an opportunity for productive
struggle, but she carefully monitors this struggle to ensure her students
do not get frustrated.
EFFECT SIZE
FOR DIRECT/
DELIBERATE
INSTRUCTION
= 0.60
EFFECT SIZE
FOR FINDING THE
“RIGHT” LEVEL OF
CHALLENGE = 0.74
EFFECT SIZE FOR
SCAFFOLDING
= 0.82
EFFECT SIZE FOR
QUESTIONING
= 0.48

Before Ms. Showker collects the graphs from each group, she asks them
to complete an individual writing prompt.
As you wrap up today’s task, I want you to summarize your
learning on the left side of your interactive mathematics notebook
by responding to the following writing prompt: What informed
your decisions about how to best represent each type of data?
Ms. Showker is implementing the principles of Visible Learning in her
fourth grade mathematics classroom. Our intention is to help you imple-
ment these principles in your own classroom. By providing learners with
a challenging task, a clear learning intention and success criteria, and
direct/deliberate instruction where and when needed, Ms. Showker’s
cooperative learning teams are developing conceptual understanding,
gaining procedural knowledge, and applying their learning. She holds
high expectations for her students in terms of both the difficulty and
complexity of the task, as well as her learners’ ability to deepen their
mathematics learning by making learning visible to herself and each
individual learner. As Ms. Showker monitors the learning progress in
each team, holding all students individually accountable for their own
learning, she takes opportunities to provide additional instruction when
needed. Although her learners are engaged in cooperative learning with
their peers, she regularly assesses her students to identify gaps in their
learning that she can address with additional instruction or interven-
tion. Ms. Showker is mobilizing principles of Visible Learning through
her conscious awareness of her impact on student learning, and her stu-
dents are consciously aware of their learning through challenge tasks.
Ms. Showker works to accomplish this through these specific, inten-
tional, and purposeful decisions in her mathematics instruction. She
had clarity in her mathematics teaching, allowing her learners to have
clarity and see themselves as their own teachers (i.e., assessment-capable
visible mathematics learners). This came about from using the following
guiding questions in her planning and preparation for learning:
1. What do I want my students to learn?
2. What evidence shows that the learners have mastered the learn-
ing or are moving toward mastery?
EFFECT SIZE FOR
TEACHER CLARIT Y
= 0.75
Video 3
What Does Teacher Clarity
Mean in Grades 3–5
Mathematics?
vlmathematics-3-5

24
3. How will I check learners’ understanding and progress?
4. What tasks will get my students to mastery?
5. How will I differentiate tasks to meet the needs of all learners?
6. What resources do I need?
7. How will I manage the learning?
Ms. Showker exemplifies the relationship between Visible Teaching and
Visible Learning (see Figure 1.1).
Now, let’s look at how to achieve clarity in teaching mathematics by
first understanding how components of mathematics learning interface
with the learning progressions of the students in our classrooms. Then,
we will use this understanding to establish learning intentions, identify
success criteria, create challenging mathematical tasks, and monitor or
check for understanding.
Components of Effective Mathematics Learning
Mathematics is more than just memorizing formulas and then work-
ing problems with those formulas. Rather than using a compilation of
Visible Teaching Visible Learning
Clearly communicates the learning
intention
Understands the intention of the learning
experience
Identifies challenging success criteria Knows what success looks like
Uses a range of learning strategies Develops a range of learning strategies
Continually monitors student learning Knows when there is no progress and
makes adjustments
Provides feedback to learners Seeks feedback about learning
Figure 1.1
online
resources

This figure is available for download at resources.corwin.com/
vlmathematics-3-5.
HOW VISIBLE TEACHING AND
VISIBLE LEARNING COMPARE
Clarity in learning
means that both
the teacher and the
student know what
the learning is for
the day, why they are
learning it, and what
success looks like.

procedures (memorizing mnemonics for the different types of polygons,
labeling place value, or multiplying two whole numbers), mathematics
learning involves an interplay of conceptual understanding, procedural
knowledge, and application of mathematical concepts and thinking
skills. Together these compose rigorous mathematics learning, which
is furthered by the Standards for Mathematical Practice that claim stu-
dents should:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
(© Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All
rights reserved).
Teaching mathematics in the Visible Learning classroom fosters student
growth through attending to these mathematical practices or processes.
As highlighted by Ms. Showker in the opening of this chapter, this
comes from linked learning experiences and challenging mathematics
tasks that make learning visible to both students and teachers.
Surface, Deep, and Transfer Learning
Each school year, regardless of the grade level, students develop their
mathematics prowess through a progression that moves from understand-
ing the surface contours of a concept into how to work with that concept
efficiently by leveraging procedural skills as well as applying concepts
and thinking skills to an ever-deepening exploration of what lies beneath
mathematical ideas. For example, third graders transition from an empha-
sis on number sense involving whole numbers to a focus on decimals

26
THE RELATIONSHIP BETWEEN SURFACE, DEEP, AND
TRANSFER LEARNING IN MATHEMATICS
Transfer: Apply conceptual
understanding and skills—with little
teacher assistance—to new and
parallel contexts and scenarios and
future units of study
In any given unit of
study, your ongoing,
continuous assessment
will tell you that your
learners are in various
places in their learning
along this path and will
sometimes move back
and forth between
surface and deep as
they build understanding.
Transfer happens when
students apply what
they know to new
situations or new
concepts. It is your
goal to provide the
interventions and
strategies they need at
the right time for the
right reason.
Leverage prior knowledge from
previous unit
Deep: Deepen understanding by
making conceptual connections
between and among concepts and
applying and practicing procedural
skills
Surface: Build initial understanding
of concepts, skills, and vocabulary on
a new topic
Source: Hattie et al. (2017). Spiral Image copyright EssentialsCollection/iStock.com
Figure 1.2
and fractions. As another example, learners progress in their mathemat-
ics learning from third to fifth grade through an increased emphasis on
using different representations of numbers to engage in problem solving.
Understanding these progressions requires that teachers consider the lev-
els of learning expected from students. We think of three levels, or phases,
of learning: surface, deep, and transfer (see Figure 1.2).
Learning is a process, not an event. With some conceptual understand-
ing, procedural knowledge, and application, students may still only
understand at the surface level. We do not define surface-level learn-
ing as superficial learning. Rather, we define surface learning as the
initial development of conceptual understanding and procedural skill,
with some application. In other words, this is the students’ initial, often
Surface learning is
the phase in which
students build
initial conceptual
understanding of
a mathematical
idea and learn
related vocabulary,
representations, and
procedural skills.

foundational, learning around what a fraction is, the various represen-
tations of fractions (e.g., region or area model, set models, or length
models), and fundamental ideas about how to use fractions to solve
problems. Surface learning is often misrepresented as rote rehearsal or
memorization and is therefore not valued, but it is an essential part of
the mathematics learning process. Students must understand how to
represent fractions with manipulatives, in words or sketches, in context,
and in real-world applications to be able to connect these representa-
tions and use them in an authentic situation.
With the purposeful and intentional use of learning strategies that
focus on how to relate and extend ideas, surface mathematics learning
becomes deep learning. Deep learning occurs when students begin
to make connections among conceptual ideas and procedural knowledge
and apply their thinking with greater fluency. As learners begin to mon-
itor their progress, adjust their learning, and select strategies to guide
their learning, they more efficiently and effectively plan, investigate,
elaborate on their knowledge, and make generalizations based on their
experiences with mathematics content and processes.
If learners are to deepen their knowledge, they must regularly encoun-
ter situations that foster the transfer and generalization of their learn-
ing. The American Psychological Association (2015) notes that “student
transfer or generalization of their knowledge and skills is not sponta-
neous or automatic” (p. 10) and transfer learning requires intention-
ally created events on the part of the teacher.
Figure 1.3 contains a representative list of strategies or influences orga-
nized by phase of learning. This is an updated list from Visible Learning
for Mathematics (Hattie et al., 2017). Notice how many of these strategies
and influences—clarity of learning goals, questioning, discourse, and
problem solving—align with the Effective Teaching Practices outlined
by the National Council of Teachers of Mathematics (2014) in Principles
to Actions: Ensuring Mathematical Success for All (see Figure 1.4).
For the influences from the Visible Learning research, we placed them in
a specific phase based on the evidence of their impact and the outcomes
that researchers use to document the impact each has on students’
learning. For example, we have included concept maps and graphic
organizers under deep learning. Learners will find it hard to organize
EFFECT SIZE FOR
PRIOR ABILITY = 0.94
EFFECT SIZE
FOR PRIOR
ACHIEVEMENT
= 0.55
Deep learning is a
period when students
consolidate their
understanding and
apply and extend
some surface learning
knowledge to support
deeper conceptual
understanding.
EFFECT SIZE FOR
ELABORATION AND
ORGANIZATION
= 0.75
Transfer learning is the
point at which students
take their consolidated
knowledge and
skills and apply what
they know to new
scenarios and different
contexts. It is also a
time when students
are able to think more
metacognitively,
reflecting on their
own learning and
understanding.

28
HIGH-IMPACT APPROACHES
AT EACH PHASE OF LEARNING
Surface Learning Deep Learning Transfer Learning
Strategy ES Strategy ES Strategy ES
Imagery 0.45 Inquiry-based teaching 0.40 Extended writing 0.44
Note taking 0.50 Questioning 0.48 Peer tutoring 0.53
Process skill: record keeping 0.52 Self-questioning 0.55 Synthesizing information across
texts
0.63
Direct/deliberate instruction 0.60 Metacognitive strategy
instruction
0.60 Problem-solving teaching 0.68
Organizing 0.60 Concept mapping 0.64 Formal discussions (e.g., debates) 0.82
Vocabulary programs 0.62 Reciprocal teaching 0.74 Organizing conceptual knowledge 0.85
Leveraging prior knowledge 0.65 Class discussion:
discourse
0.82 Transforming conceptual
knowledge
0.85
Mnemonics 0.76 Outlining and
transforming notes
0.85 Identifying similarities and
differences
1.32
Summarization 0.79 Small-group learning 0.47
Integrating prior knowledge 0.93 Cooperative learning 0.40
Teacher expectations 0.43
Feedback 0.70
Teacher clarity 0.75
Integrated curricula programs 0.47
Assessment-capable visible learner 1.33
Source: Adapted from Almarode, Fisher, Frey, Hattie (2018).
Figure 1.3
mathematics information or ideas visually or graphically if they do not
yet understand that information. Without a conceptual understanding
of the properties of the operations, fourth grade mathematics students
may approach single-step and multistep problems based on surface-level
features (e.g., this problem involves money or addition) instead of deep-
level features (e.g., this problem requires me to use the distributive
EFFECT SIZE FOR
METACOGNITIVE
STRATEGIES = 0.60
AND EVALUATION
AND REFLECTION
= 0.75

29
EFFECTIVE MATHEMATICS
TEACHING PRACTICES
Establish mathematics goals to focus learning. Effective teaching of mathematics
establishes clear goals for the mathematics that students are learning, situates goals
within learning progressions, and uses the goals to guide instructional decisions.
Implement tasks that promote reasoning and problem solving. Effective teaching
of mathematics engages students in solving and discussing tasks that promote
mathematical reasoning and problem solving and allow multiple entry points and varied
solution strategies.
Use and connect mathematical representations. Effective teaching of mathematics
engages students in making connections among mathematical representations to
deepen understanding of mathematics concepts and procedures and as tools for
problem solving.
Facilitate meaningful mathematical discourse. Effective teaching of mathematics
facilitates discourse among students to build shared understanding of mathematical
ideas by analyzing and comparing student approaches and arguments.
Pose purposeful questions. Effective teaching of mathematics uses purposeful
questions to assess and advance students’ reasoning and sense making about
important mathematical ideas and relationships.
Build procedural fluency from conceptual understanding. Effective teaching
of mathematics builds fluency with procedures on a foundation of conceptual
understanding so that students, over time, become skillful in using procedures flexibly
as they solve contextual and mathematical problems.
Support productive struggle in learning mathematics. Effective teaching of
mathematics consistently provides students, individually and collectively, with
opportunities and supports to engage in productive struggle as they grapple with
mathematical ideas and relationships.
Elicit and use evidence of student thinking. Effective teaching of mathematics uses
evidence of student thinking to assess progress toward mathematical understanding
and to adjust instruction continually in ways that support and extend learning.
Source: NCTM. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA:
NCTM, National Council of Teachers of Mathematics. Reprinted with permission.
Figure 1.4
property). When students have sufficient surface learning about specific
content and processes, they are able to see the connections between
multiple ideas and connect their specific knowledge of properties to ana-
lyze problems based on these deep-level features (i.e., the distributive

property is applicable across multiple contexts), which allow for the
generalization of mathematics principles. As a reminder, two key find-
ings from the Visible Learning research are as follows:
1. There is no one way to teach mathematics or one best instruc-
tional strategy that works in all situations for all students; and
2. We should not hold any influence, instructional strategy, action,
or approach in higher esteem than students’ learning.
As teachers, our conversations should focus on identifying where stu-
dents are in their learning journey and moving them forward in their
learning. This is best accomplished by talking about learning and mea-
suring the impact that various approaches have on students’ learning.
If a given approach is not working, change it. If you experienced suc-
cess with a particular strategy or approach in the past, give it a try but
make sure that the strategy or approach is working in this context. Just
because we can use PEMDAS to support computation, for example, does
not mean those mnemonics will work for all students in your mathe-
matics classroom—particularly if they lack understanding of the con-
ceptual underpinnings of those procedures. Teachers have to monitor
the impact that learning strategies have on students’ mathematics learn-
ing and how they are progressing from surface, to deep, to transfer.
Moving Learners Through the
Phases of Learning
The SOLO Taxonomy (Structure of Observed Learning Outcomes)
(Biggs Collis, 1982) conceptualizes the movement from surface to
deep to transfer learning as a process of first branching out and then
strengthening connections between ideas (Figure 1.5).
As you reflect on your own students, you can likely think of learners
who have limited to no prior experiences with certain formal math-
ematics content. They do, however, have significant informal prior
knowledge. Take, for example, perimeter and area. Although learners
have likely encountered real-world uses of these concepts (e.g., how
many laps around the track equals a mile in physical education, a fence
As teachers, our
conversations
should focus on
identifying where
students are in
their learning
journey and
moving them
forward in their
learning.
The SOLO Taxonomy
is a framework
that describes
learners’ thinking
and understanding
of mathematics.
The taxonomy
conceptualizes the
learning process from
surface, to deep, and
then to transfer.

31
around the garden or yard), many have had no experience with the for-
mal mathematics behind those real-world applications. Thus, they have
no formal, relevant structure to their thinking. This means they likely
struggle to articulate a single idea about the perimeter or area of a given
shape using mathematical language or notation.
Another example of this occurs with the equations or formulas for area
and perimeter. Learners may recognize that letters represent specific
items in an equation, say A = l × w or P = l + l + w + w for a rectangle,
but they are not able to identify these features in a rectangle or find the
perimeter or area of a square when they are given only one side. This
part of the SOLO Taxonomy is referred to as the prestructural level or
prestructural thinking. At the prestructural level, learners may focus on
irrelevant ideas, avoid engaging in the content, or not know where to
start. In some cases, learners may ask for a ruler. This requires the teacher
to support the learner in acquiring and building background knowledge.
When teachers clearly recognize that a learner or learners are at the pre-
structural level, the learning experience should aim to build surface
learning around concepts, procedures, and applications.
Surface Learning in the Intermediate
Mathematics Classroom
As learners progress in their thinking, they may develop single ideas
or a single aspect related to a concept. Learners at this level can iden-
tify and name shapes or attributes, follow simple procedures, highlight
single aspects of a concept, and solve one type of problem (Hook
Mills, 2011). They know that A = l × w calculates the area of a rectangle
THE SOLO TAXONOMY
One
idea
Many
ideas
Related
ideas
Extended
ideas
Source: Adapted from Biggs Collis (1982).
Figure 1.5
Teaching
Takeaway
We must
preassess our
learners to
identify their
prior knowledge
or background
knowledge in
the mathematics
content they
are learning.
We should use
informal language,
little notation,
and familiar
contexts in our
preassessments to
allow all students
to show what they
know.

and that l represents the length and w represents the width. They can
only solve problems involving the exact type of rectangle provided in an
in-class example, such as in Figure 1.6.
EXAMPLES OF DIFFERENT AREA AND PERIMETER
PROBLEMS INVOLVING QUADRILATERALS
Find the area and perimeter area of the following squares and rectangles.
Perimeter:
Area:
Perimeter:
Area:
Perimeter:
Area:
Perimeter:
Area:
Perimeter:
Area:
Perimeter:
Area:
Perimeter and Area
10
8
9
5
5
7
13
9
Figure 1.6
For example, let’s say a learner can calculate the area of a rectangle
where the length and width are labeled on the diagram and the length
is greater than the width. Any variation to the problem will pose a signif-
icant challenge to this learner, requiring additional instruction (e.g., the
width is the larger number, the rectangle is rotated, or the dimensions
are merely provided without a diagram). With the right approach at the
right time, learners will continue to build surface learning by acquiring
multiple ideas about concepts, procedures, and applications. Learners
can then solve area problems involving different variations of rectan-
gles or from different perspectives, and they describe coherently how to
calculate the area of any rectangle instead of simply executing the algo-
rithm. However, at this phase of their thinking and learning, learners
see each variation of an area of a rectangle problem as a distinct scenario
that is not connected to the other variations of rectangles.

Like Ms. Showker, all teachers should establish learning intentions and
success criteria based on where students are in their learning progression.
Moving away from perimeter and area and back to Ms. Showker’s classroom,
let us look at how we can develop learning intentions and success criteria
for conceptual understanding, procedural knowledge, and application for
learners at these two levels (one idea and many ideas) (Figures 1.7 and 1.8).
SURFACE-PHASE LEARNING INTENTIONS FOR EACH
COMPONENT OF MATHEMATICS LEARNING
Learning
Intentions
Conceptual
Understanding Procedural Knowledge
Application of Concepts
and Thinking Skills
Unistructural
(one idea)
I am learning that the purpose
of a graph is to represent data
gathered to answer a question.
I am learning that there
are ways to represent data
using graphs.
I am learning that I can use
data to answer questions
that I want to investigate.
Multistructural
(many ideas)
I am learning that different
questions produce different
types of data.
I am learning that there are
multiple ways to represent
data using graphs.
I am learning that there are
specific characteristics of my
graph that represent my data.
Figure 1.7
SURFACE-PHASE SUCCESS CRITERIA FOR EACH
COMPONENT OF MATHEMATICS LEARNING
Success
Criteria
Conceptual
Understanding Procedural Knowledge
Application of Concepts
and Thinking Skills
Unistructural
(one idea)
I can describe how a graph
represents data.
I can describe the parts of
a graph.
I can create a question that
generates data.
Multistructural
(many ideas)
I can identify specific questions
and data that are represented
by different types of graphs.
I can give examples of
different types of graphs.
I can list the characteristics
of a graph that would answer
my question.
Figure 1.8

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“Meg.”
“Will you go?” and Mr. Bhaer looked at the lads, who were greatly
touched by Mrs. Brooke’s kind words and wishes.
“Yes,” they answered, like one boy; and an hour later they went
away with Franz to bear their part in John Brooke’s simple funeral.
The little house looked as quiet, sunny, and home-like as when
Meg entered it a bride, ten years ago, only then it was early summer,
and roses blossomed everywhere; now it was early autumn, and
dead leaves rustled softly down, leaving the branches bare. The
bride was a widow now; but the same beautiful serenity shone in
her face, and the sweet resignation of a truly pious soul made her
presence a consolation to those who came to comfort her.
“O Meg! how can you bear it so?” whispered Jo, as she met them
at the door with a smile of welcome, and no change in her gentle
manner, except more gentleness.
“Dear Jo, the love that has blest for ten happy years supports me
still. It could not die, and John is more my own than ever,”
whispered Meg; and in her eyes the tender trust was so beautiful
and bright, that Jo believed her, and thanked God for the immortality
of love like hers.
They were all there—father and mother, Uncle Teddy, and Aunt
Amy, old Mr. Laurence, white-haired and feeble now, Mr. and Mrs.
Bhaer, with their flock, and many friends, come to do honor to the
dead. One would have said that modest John Brooke, in his busy,
quiet, humble life, had had little time to make friends; but now they
seemed to start up everywhere,—old and young, rich and poor, high
and low; for all unconsciously his influence had made itself widely
felt, his virtues were remembered, and his hidden charities rose up
to bless him. The group about his coffin was a far more eloquent
eulogy than any Mr. March could utter. There were the rich men
whom he had served faithfully for years; the poor old women whom
he cherished with his little store, in memory of his mother; the wife
to whom he had given such happiness that death could not mar it

utterly; the brothers and sisters in whose hearts he had made a
place for ever; the little son and daughter, who already felt the loss
of his strong arm and tender voice; the young children, sobbing for
their kindest playmate, and the tall lads, watching with softened
faces a scene which they never could forget. A very simple service,
and very short; for the fatherly voice that had faltered in the
marriage-sacrament now failed entirely as Mr. March endeavored to
pay his tribute of reverence and love to the son whom he most
honored. Nothing but the soft coo of Baby Josy’s voice up-stairs
broke the long hush that followed the last Amen, till, at a sign from
Mr. Bhaer, the well-trained boyish voices broke out in a hymn, so full
of lofty cheer, that one by one all joined in it, singing with full hearts,
and finding their troubled spirits lifted into peace on the wings of
that brave, sweet psalm.
As Meg listened, she felt that she had done well; for not only did
the moment comfort her with the assurance that John’s last lullaby
was sung by the young voices he loved so well, but in the faces of
the boys she saw that they had caught a glimpse of the beauty of
virtue in its most impressive form, and that the memory of the good
man lying dead before them would live long and helpful in their
remembrance. Daisy’s head lay in her lap, and Demi held her hand,
looking often at her, with eyes so like his father’s, and a little gesture
that seemed to say, “Don’t be troubled, mother; I am here;” and all
about her were friends to lean upon and love; so patient, pious Meg
put by her heavy grief, feeling that her best help would be to live for
others, as her John had done.
That evening, as the Plumfield boys sat on the steps, as usual, in
the mild September moonlight, they naturally fell to talking of the
event of the day.
Emil began by breaking out, in his impetuous way, “Uncle Fritz is
the wisest, and Uncle Laurie the jolliest, but Uncle John was the
best; and I’d rather be like him than any man I ever saw.”
“So would I. Did you hear what those gentlemen said to Grandpa
to-day? I would like to have that said to me when I was dead;” and

Franz felt with regret that he had not appreciated Uncle John
enough.
“What did they say?” asked Jack, who had been much impressed
by the scenes of the day.
“Why, one of the partners of Mr. Laurence, where Uncle John has
been ever so long, was saying that he was conscientious almost to a
fault as a business man, and above reproach in all things. Another
gentleman said no money could repay the fidelity and honesty with
which Uncle John had served him, and then Grandpa told them the
best of all. Uncle John once had a place in the office of a man who
cheated, and when this man wanted uncle to help him do it, uncle
wouldn’t, though he was offered a big salary. The man was angry
and said, ‘You will never get on in business with such strict
principles;’ and uncle answered back, ‘I never will try to get on
without them,’ and left the place for a much harder and poorer one.”
“Good!” cried several of the boys warmly, for they were in the
mood to understand and value the little story as never before.
“He wasn’t rich, was he?” asked Jack.
“No.”
“He never did any thing to make a stir in the world, did he?”
“No.”
“He was only good?”
“That’s all;” and Franz found himself wishing that Uncle John had
done something to boast of, for it was evident that Jack was
disappointed by his replies.
“Only good. That is all and every thing,” said Mr. Bhaer, who had
overheard the last few words, and guessed what was going on in the
minds of the lads.
“Let me tell you a little about John Brooke, and you will see why
men honor him, and why he was satisfied to be good rather than
rich or famous. He simply did his duty in all things, and did it so

cheerfully, so faithfully, that it kept him patient, brave, and happy
through poverty and loneliness and years of hard work. He was a
good son, and gave up his own plans to stay and live with his
mother while she needed him. He was a good friend, and taught
Laurie much beside his Greek and Latin, did it unconsciously,
perhaps, by showing him an example of an upright man. He was a
faithful servant, and made himself so valuable to those who
employed him that they will find it hard to fill his place. He was a
good husband and father, so tender, wise, and thoughtful, that
Laurie and I learned much of him, and only knew how well he loved
his family, when we discovered all he had done for them,
unsuspected and unassisted.”
Mr. Bhaer stopped a minute, and the boys sat like statues in the
moonlight until he went on again, in a subdued, but earnest voice:
“As he lay dying, I said to him, ‘Have no care for Meg and the little
ones; I will see that they never want.’ Then he smiled and pressed
my hand, and answered, in his cheerful way, ‘No need of that; I
have cared for them.’ And so he had, for when we looked among his
papers, all was in order, not a debt remained; and safely put away
was enough to keep Meg comfortable and independent. Then we
knew why he had lived so plainly, denied himself so many pleasures,
except that of charity, and worked so hard that I fear he shortened
his good life. He never asked help for himself, though often for
others, but bore his own burden and worked out his own task
bravely and quietly. No one can say a word of complaint against him,
so just and generous and kind was he; and now, when he is gone,
all find so much to love and praise and honor, that I am proud to
have been his friend, and would rather leave my children the legacy
he leaves his than the largest fortune ever made. Yes! Simple,
genuine goodness is the best capital to found the business of this
life upon. It lasts when fame and money fail, and is the only riches
we can take out of this world with us. Remember that, my boys; and
if you want to earn respect and confidence and love follow in the
footsteps of John Brooke.”

When Demi returned to school, after some weeks at home, he
seemed to have recovered from his loss with the blessed elasticity of
childhood, and so he had in a measure; but he did not forget, for his
was a nature into which things sank deeply, to be pondered over,
and absorbed into the soil where the small virtues were growing
fast. He played and studied, worked and sang, just as before, and
few suspected any change; but there was one—and Aunt Jo saw it—
for she watched over the boy with her whole heart, trying to fill
John’s place in her poor way. He seldom spoke of his loss, but Aunt
Jo often heard a stifled sobbing in the little bed at night; and when
she went to comfort him, all his cry was, “I want my father! oh, I
want my father!”—for the tie between the two had been a very
tender one, and the child’s heart bled when it was broken. But time
was kind to him, and slowly he came to feel that father was not lost,
only invisible for a while, and sure to be found again, well and
strong and fond as ever, even though his little son should see the
purple asters blossom on his grave many, many times before they
met. To this belief Demi held fast, and in it found both help and
comfort, because it led him unconsciously through a tender longing
for the father whom he had seen to a childlike trust in the Father
whom he had not seen. Both were in heaven, and he prayed to
both, trying to be good for love of them.
The outward change corresponded to the inward, for in those few
weeks Demi seemed to have grown tall, and began to drop his
childish plays, not as if ashamed of them, as some boys do, but as if
he had outgrown them, and wanted something manlier. He took to
the hated arithmetic, and held on so steadily that his uncle was
charmed, though he could not understand the whim, until Demi said
—
“I am going to be a bookkeeper when I grow up, like papa, and I
must know about figures and things, else I can’t have nice, neat
ledgers like his.”
At another time he came to his aunt with a very serious face, and
said—

“What can a small boy do to earn money?”
“Why do you ask, my deary?”
“My father told me to take care of mother and the little girls, and I
want to, but I don’t know how to begin.”
“He did not mean now, Demi, but by and by, when you are large.”
“But I wish to begin now, if I can, because I think I ought to make
some money to buy things for the family. I am ten, and other boys
no bigger than I earn pennies sometimes.”
“Well, then, suppose you rake up all the dead leaves and cover the
strawberry bed. I’ll pay you a dollar for the job,” said Aunt Jo.
“Isn’t that a great deal? I could do it in one day. You must be fair,
and not pay too much, because I want to truly earn it.”
“My little John, I will be fair, and not pay a penny too much. Don’t
work too hard; and when that is done I will have something else for
you to do,” said Mrs. Jo, much touched by his desire to help, and his
sense of justice, so like his scrupulous father.
When the leaves were done, many barrow loads of chips were
wheeled from the wood to the shed, and another dollar earned.
Then Demi helped cover the school-books, working in the evenings,
under Franz’s direction, tugging patiently away at each book, letting
no one help, and receiving his wages with such satisfaction that the
dingy bills became quite glorified in his sight.
“Now, I have a dollar for each of them, and I should like to take
my money to mother all myself, so she can see that I have minded
my father.”
So Demi made a duteous pilgrimage to his mother, who received
his little earnings as a treasure of great worth, and would have kept
it untouched, if Demi had not begged her to buy some useful thing
for herself and the women-children, whom he felt were left to his
care.

This made him very happy, and, though he often forgot his
responsibilities for a time, the desire to help was still there,
strengthening with his years. He always uttered the words “my
father” with an air of gentle pride, and often said, as if he claimed a
title full of honor, “Don’t call me Demi any more. I am John Brooke
now.” So, strengthened by a purpose and a hope, the little lad of ten
bravely began the world, and entered into his inheritance,—the
memory of a wise and tender father, the legacy of an honest name.

CHAPTER XX
ROUND THE FIRE
With the October frosts came the cheery fires in the great
fireplaces; and Demi’s dry pine-chips helped Dan’s oak-knots to blaze
royally, and go roaring up the chimney with a jolly sound. All were
glad to gather round the hearth, as the evenings grew longer, to
play games, read, or lay plans for the winter. But the favorite
amusement was story-telling, and Mr. and Mrs. Bhaer were expected
to have a store of lively tales always on hand. Their supply
occasionally gave out, and then the boys were thrown upon their
own resources, which were not always successful. Ghost-parties
were the rage at one time; for the fun of the thing consisted in
putting out the lights, letting the fire die down, and then sitting in
the dark, and telling the most awful tales they could invent. As this
resulted in scares of all sorts among the boys, Tommy’s walking in
his sleep on the shed roof, and a general state of nervousness in the
little ones, it was forbidden, and they fell back on more harmless
amusements.
One evening, when the small boys were snugly tucked in bed, and
the older lads were lounging about the school-room fire, trying to
decide what they should do, Demi suggested a new way of settling
the question.

All were glad to gather round the hearth, as the
evenings grew longer. Page 312.
Seizing the hearth-brush, he marched up and down the room,
saying, “Row, row, row;” and when the boys, laughing and pushing,
had got into line, he said, “Now, I’ll give you two minutes to think of
a play.” Franz was writing, and Emil reading the Life of Lord Nelson,
and neither joined the party, but the others thought hard, and when
the time was up were ready to reply.

“Now, Tom!” and the poker softly rapped him on the head.
“Blind-man’s Buff.”
“Jack!”
“Commerce; a good round game, and have cents for the pool.”
“Uncle forbids our playing for money. Dan, what do you want?”
“Let’s have a battle between the Greeks and Romans.”
“Stuffy?”
“Roast apples, pop corn, and crack nuts.”
“Good! good!” cried several; and when the vote was taken,
Stuffy’s proposal carried the day.
Some went to the cellar for apples, some to the garret for nuts,
and others looked up the popper and the corn.
“We had better ask the girls to come in, hadn’t we?” said Demi, in
a sudden fit of politeness.
“Daisy pricks chestnuts beautifully,” put in Nat, who wanted his
little friend to share the fun.
“Nan pops corn tip-top, we must have her,” added Tommy.
“Bring in your sweethearts then, we don’t mind,” said Jack, who
laughed at the innocent regard the little people had for one another.
“You shan’t call my sister a sweetheart; it is so silly!” cried Demi,
in a way that made Jack laugh.
“She is Nat’s darling, isn’t she, old chirper?”
“Yes, if Demi don’t mind. I can’t help being fond of her, she is so
good to me,” answered Nat, with bashful earnestness, for Jack’s
rough ways disturbed him.
“Nan is my sweetheart, and I shall marry her in about a year, so
don’t you get in the way, any of you,” said Tommy, stoutly; for he
and Nan had settled their future, child-fashion, and were to live in

the willow, lower down a basket for food, and do other charmingly
impossible things.
Demi was quenched by the decision of Bangs, who took him by
the arm and walked him off to get the ladies. Nan and Daisy were
sewing with Aunt Jo on certain small garments for Mrs. Carney’s
newest baby.
“Please, ma’am, could you lend us the girls for a little while? we’ll
be very careful of them,” said Tommy, winking one eye to express
apples, snapping his fingers to signify pop-corn, and gnashing his
teeth to convey the idea of nut-cracking.
The girls understood this pantomime at once, and began to pull
off their thimbles before Mrs. Jo could decide whether Tommy was
going into convulsions or was brewing some unusual piece of
mischief. Demi explained with elaboration, permission was readily
granted, and the boys departed with their prize.
“Don’t you speak to Jack,” whispered Tommy, as he and Nan
promenaded down the hall to get a fork to prick the apples.
“Why not?”
“He laughs at me, so I don’t wish you to have any thing to do with
him.”
“Shall, if I like,” said Nan, promptly resenting this premature
assumption of authority on the part of her lord.
“Then I won’t have you for my sweetheart.”
“I don’t care.”
“Why, Nan, I thought you were fond of me!” and Tommy’s voice
was full of tender reproach.
“If you mind Jack’s laughing I don’t care for you one bit.”
“Then you may take back your old ring; I won’t wear it any
longer;” and Tommy plucked off a horse-hair pledge of affection
which Nan had given him in return for one made of a lobster’s feeler.

“I shall give it to Ned,” was her cruel reply; for Ned liked Mrs.
Giddy-gaddy, and had turned her clothes-pins, boxes, and spools
enough to set up housekeeping with.
Tommy said, “Thunder-turtles!” as the only vent equal to the pent-
up anguish of the moment, and, dropping Nan’s arm, retired in high
dudgeon, leaving her to follow with the fork,—a neglect which
naughty Nan punished by proceeding to prick his heart with jealousy
as if it were another sort of apple.
The hearth was swept, and the rosy Baldwins put down to roast. A
shovel was heated, and the chestnuts danced merrily upon it, while
the corn popped wildly in its wire prison. Dan cracked his best
walnuts, and every one chattered and laughed, while the rain beat
on the window-pane and the wind howled round the house.
“Why is Billy like this nut?” asked Emil, who was frequently
inspired with bad conundrums.
“Because he is cracked,” answered Ned.
“That’s not fair; you mustn’t make fun of Billy, because he can’t hit
back again. It’s mean,” cried Dan, smashing a nut wrathfully.
“To what family of insects does Blake belong?” asked peacemaker
Franz, seeing that Emil looked ashamed and Dan lowering.
“Gnats,” answered Jack.
“Why is Daisy like a bee?” cried Nat, who had been wrapt in
thought for several minutes.
“Because she is queen of the hive,” said Dan.
“No.”
“Because she is sweet.”
“Bees are not sweet.”
“Give it up.”
“Because she makes sweet things, is always busy, and likes
flowers,” said Nat, piling up his boyish compliments till Daisy blushed

like a rosy clover.
“Why is Nan like a hornet?” demanded Tommy, glowering at her,
and adding, without giving any one time to answer, “Because she
isn’t sweet, makes a great buzzing about nothing, and stings like
fury.”
“Tommy’s mad, and I’m glad,” cried Ned, as Nan tossed her head
and answered quickly—
“What thing in the china-closet is Tom like?”
“A pepper pot,” answered Ned, giving Nan a nut meat with a
tantalizing laugh that made Tommy feel as if he would like to bounce
up like a hot chestnut and hit somebody.
Seeing that ill-humor was getting the better of the small supply of
wit in the company, Franz cast himself into the breach again.
“Let’s make a law that the first person who comes into the room
shall tell us a story. No matter who it is, he must do it, and it will be
fun to see who comes first.”
The others agreed, and did not have to wait long, for a heavy step
soon came clumping through the hall, and Silas appeared, bearing
an armful of wood. He was greeted by a general shout, and stood
staring about him with a bewildered grin on his big red face, till
Franz explained the joke.
“Sho! I can’t tell a story,” he said, putting down his load and
preparing to leave the room. But the boys fell upon him, forced him
into a seat, and held him there, laughing and clamoring for their
story, till the good-natured giant was overpowered.
“I don’t know but jest one story, and that’s about a horse,” he
said, much flattered by the reception he received.
“Tell it! tell it!” cried the boys.
“Wal,” began Silas, tipping his chair back against the wall, and
putting his thumbs in the arm-holes of his waistcoat, “I jined a
cavalry regiment durin’ the war, and see a consid’able amount of

fightin’. My horse, Major, was a fust-rate animal, and I was as fond
on him as ef he’d ben a human critter. He warn’t harnsome, but he
was the best-tempered, stiddyest, lovenest brute I ever see. The
fust battle we went into, he gave me a lesson that I didn’t forgit in a
hurry, and I’ll tell you how it was. It ain’t no use tryin’ to picter the
noise and hurry, and general horridness of a battle to you young
fellers, for I ain’t no words to do it in; but I’m free to confess that I
got so sort of confused and upset at the fust on it, that I didn’t know
what I was about. We was ordered to charge, and went ahead like
good ones, never stoppin’ to pick up them that went down in the
scrimmage. I got a shot in the arm, and was pitched out of the
saddle—don’t know how, but there I was left behind with two or
three others, dead and wounded, for the rest went on, as I say. Wal,
I picked myself up and looked round for Major, feeling as ef I’d had
about enough for that spell. I didn’t see him nowhere, and was
kinder walking back to camp, when I heard a whinny that sounded
nateral. I looked round, and there was Major stopping for me a long
way off, and lookin’ as ef he didn’t understand why I was loiterin’
behind. I whistled, and he trotted up to me as I’d trained him to do.
I mounted as well as I could with my left arm bleedin’ and was for
going on to camp, for I declare I felt as sick and wimbly as a
woman; folks often do in their fust battle. But, no, sir! Major was the
bravest of the two, and he wouldn’t go, not a peg; he jest rared up,
and danced, and snorted, and acted as ef the smell of powder and
the noise had drove him half wild. I done my best, but he wouldn’t
give in, so I did; and what do you think that plucky brute done? He
wheeled slap round, and galloped back like a hurricane, right into
the thickest of the scrimmage!”
“Good for him!” cried Dan excitedly, while the other boys forgot
apples and nuts in their interest.
“I wish I may die ef I warn’t ashamed of myself,” continued Silas,
warming up at the recollection of that day. “I was as mad as a
hornet, and I forgot my waound, and jest pitched in, rampagin’
raound like fury till there come a shell into the midst of us, and in
bustin’ knocked a lot of us flat. I didn’t know nothin’ for a spell, and

when I come-to, the fight was over jest there, and I found myself
layin’ by a wall with poor Major long-side wuss wounded than I was.
My leg was broke, and I had a ball in my shoulder, but he, poor old
feller! was all tore in the side with a piece of that blasted shell.”
“O Silas! what did you do?” cried Nan, pressing close to him with a
face full of eager sympathy and interest.
“I dragged myself nigher, and tried to stop the bleedin’ with sech
rags as I could tear off of me with one hand. But it warn’t no use,
and he lay moanin’ with horrid pain, and lookin’ at me with them
lovin’ eyes of his, till I thought I couldn’t bear it. I give him all the
help I could, and when the sun got hotter and hotter, and he began
to lap out his tongue, I tried to get to a brook that was a good piece
away, but I couldn’t do it, being stiff and faint, so I give it up and
fanned him with my hat. Now you listen to this, and when you hear
folks comin’ down on the rebs, you jest remember what one on ’em
did, and give him the credit of it. A poor feller in gray laid not fur off,
shot through the lungs, and dying fast. I’d offered him my
handkerchief to keep the sun off his face, and he’d thanked me
kindly, for in sech times as that men don’t stop to think on which
side they belong, but jest buckle-to and help one another. When he
see me mournin’ over Major and tryin’ to ease his pain, he looked up
with his face all damp and white with sufferin’, and sez he, ‘There’s
water in my canteen; take it, for it can’t help me,’ and he flung it to
me. I couldn’t have took it ef I hadn’t had a little brandy in a pocket
flask, and I made him drink it. It done him good, and I felt as much
set up as if I’d drunk it myself. It’s surprisin’ the good sech little
things do folks sometimes;” and Silas paused as if he felt again the
comfort of that moment when he and his enemy forgot their feud,
and helped one another like brothers.
“Tell about Major,” cried the boys, impatient for the catastrophe.
“I poured the water over his poor pantin’ tongue, and ef ever a
dumb critter looked grateful, he did then. But it warn’t of much use,
for the dreadful waound kep on tormentin’ him, till I couldn’t bear it

any longer. It was hard, but I done it in mercy, and I know he
forgive me.”
“What did you do?” asked Emil, as Silas stopped abruptly with a
loud “hem,” and a look in his rough face that made Daisy go and
stand by him with her little hand on his knee.
“I shot him.”
Quite a thrill went through the listeners as Silas said that, for
Major seemed a hero in their eyes, and his tragic end roused all their
sympathy.
“Yes, I shot him, and put him out of his misery. I patted him fust,
and said, ‘Good-by;’ then I laid his head easy on the grass, give a
last look into his lovin’ eyes, and sent a bullet through his head. He
hardly stirred, I aimed so true, and when I see him quite still, with
no more moanin’ and pain, I was glad, and yet—wal, I don’t know as
I need be ashamed on’t—I jest put my arms raound his neck and
boo-hooed like a great baby. Sho! I didn’t know I was such a fool;”
and Silas drew his sleeve across his eyes, as much touched by
Daisy’s sob, as by the memory of faithful Major.
No one spoke for a minute, because the boys were as quick to feel
the pathos of the little story as tender-hearted Daisy, though they
did not show it by crying.
“I’d like a horse like that,” said Dan, half-aloud.
“Did the rebel man die too?” asked Nan, anxiously.
“Not then. We laid there all day, and at night some of our fellers
came to look after the missing ones. They nat’rally wanted to take
me fust, but I knew I could wait, and the rebel had but one chance,
maybe, so I made them carry him off right away. He had jest
strength enough to hold out his hand to me and say, ‘Thanky,
comrade!’ and them was the last words he spoke, for he died an
hour after he got to the hospital-tent.”
“How glad you must have been that you were kind to him!” said
Demi, who was deeply impressed by this story.

“Wal, I did take comfort thinkin’ of it, as I laid there alone for a
number of hours with my head on Major’s neck, and see the moon
come up. I’d like to have buried the poor beast decent, but it warn’t
possible; so I cut off a bit of his mane, and I’ve kep it ever sence.
Want to see it, sissy?”
“Oh, yes, please,” answered Daisy, wiping away her tears to look.
Silas took out an old “wallet” as he called his pocket-book, and
produced from an inner fold a bit of brown paper, in which was a
rough lock of white horse-hair. The children looked at it silently, as it
lay in the broad palm, and no one found any thing to ridicule in the
love Silas bore his good horse Major.
“That is a sweet story, and I like it, though it did make me cry.
Thank you very much, Si,” and Daisy helped him fold and put away
his little relic; while Nan stuffed a handful of pop-corn into his
pocket, and the boys loudly expressed their flattering opinions of his
story, feeling that there had been two heroes in it.
He departed, quite overcome by his honors, and the little
conspirators talked the tale over, while they waited for their next
victim. It was Mrs. Jo, who came in to measure Nan for some new
pinafores she was making for her. They let her get well in, and then
pounced upon her, telling her the law, and demanding the story. Mrs.
Jo was very much amused at the new trap, and consented at once,
for the sound of the happy voices had been coming across the hall
so pleasantly that she quite longed to join them, and forget her own
anxious thoughts of Sister Meg.
“Am I the first mouse you have caught, you sly pussies-in-boots?”
she asked, as she was conducted to the big chair, supplied with
refreshments, and surrounded by a flock of merry-faced listeners.
They told her about Silas and his contribution, and she slapped
her forehead in despair, for she was quite at her wits’ end, being
called upon so unexpectedly for a bran new tale.
“What shall I tell about?” she said.

“Boys,” was the general answer.
“Have a party in it,” said Daisy.
“And something good to eat,” added Stuffy.
“That reminds me of a story, written years ago, by a dear old lady.
I used to be very fond of it, and I fancy you will like it, for it has
both boys, and ‘something good to eat’ in it.”
“What is it called?” asked Demi.
“‘The Suspected Boy.’”
Nat looked up from the nuts he was picking, and Mrs. Jo smiled at
him, guessing what was in his mind.
“Miss Crane kept a school for boys in a quiet little town, and a
very good school it was, of the old-fashioned sort. Six boys lived in
her house, and four or five more came in from the town. Among
those who lived with her was one named Lewis White. Lewis was
not a bad boy, but rather timid, and now and then he told a lie. One
day a neighbor sent Miss Crane a basket of gooseberries. There
were not enough to go round, so kind Miss Crane, who liked to
please her boys, went to work and made a dozen nice little
gooseberry tarts.”
“I’d like to try gooseberry tarts. I wonder if she made them as I
do my raspberry ones,” said Daisy, whose interest in cooking had
lately revived.
“Hush,” said Nat, tucking a plump pop-corn into her mouth to
silence her, for he felt a peculiar interest in this tale, and thought it
opened well.
“When the tarts were done, Miss Crane put them away in the best
parlor closet, and said not a word about them, for she wanted to
surprise the boys at tea-time. When the minute came and all were
seated at table, she went to get her tarts, but came back looking
much troubled, for what do you think had happened?”
“Somebody had hooked them!” cried Ned.

“No, there they were, but some one had stolen all the fruit out of
them by lifting up the upper crust and then putting it down after the
gooseberry had been scraped out.”
“What a mean trick!” and Nan looked at Tommy, as if to imply that
he would do the same.
“When she told the boys her plan and showed them the poor little
patties all robbed of their sweetness, the boys were much grieved
and disappointed, and all declared that they knew nothing about the
matter. ‘Perhaps the rats did it,’ said Lewis, who was among the
loudest to deny any knowledge of the tarts. ‘No, rats would have
nibbled crust and all, and never lifted it up and scooped out the fruit.
Hands did that,’ said Miss Crane, who was more troubled about the
lie that some one must have told than about her lost patties. Well,
they had supper and went to bed, but in the night Miss Crane heard
some one groaning, and going to see who it was she found Lewis in
great pain. He had evidently eaten something that disagreed with
him, and was so sick that Miss Crane was alarmed, and was going to
send for the doctor, when Lewis moaned out, ‘It’s the gooseberries; I
ate them, and I must tell before I die,’ for the thought of a doctor
frightened him. ‘If that is all, I’ll give you an emetic and you will
soon get over it,’ said Miss Crane. So Lewis had a good dose, and by
morning was quite comfortable. ‘Oh, don’t tell the boys; they will
laugh at me so,’ begged the invalid. Kind Miss Crane promised not
to, but Sally, the girl, told the story, and poor Lewis had no peace for
a long time. His mates called him Old Gooseberry, and were never
tired of asking him the price of tarts.”
“Served him right,” said Emil.
“Badness always gets found out,” added Demi, morally.
“No, it don’t,” muttered Jack, who was tending the apples with
great devotion, so that he might keep his back to the rest and
account for his red face.
“Is that all?” asked Dan.

“No, that is only the first part; the second part is more interesting.
Some time after this a peddler came by one day and stopped to
show his things to the boys, several of whom bought pocket-combs,
jew’s-harps, and various trifles of that sort. Among the knives was a
little white-handled penknife that Lewis wanted very much, but he
had spent all his pocket-money, and no one had any to lend him. He
held the knife in his hand, admiring and longing for it, till the man
packed up his goods to go, then he reluctantly laid it down, and the
man went on his way. The next day, however, the peddler returned
to say that he could not find that very knife, and thought he must
have left it at Miss Crane’s. It was a very nice one with a pearl
handle, and he could not afford to lose it. Every one looked, and
every one declared they knew nothing about it. ‘This young
gentleman had it last, and seemed to want it very much. Are you
quite sure you put it back?’ said the man to Lewis, who was much
troubled at the loss, and vowed over and over again that he did
return it. His denials seemed to do no good, however, for every one
was sure he had taken it, and after a stormy scene Miss Crane paid
for it, and the man went grumbling away.”
“Did Lewis have it?” cried Nat, much excited.
“You will see. Now poor Lewis had another trial to bear, for the
boys were constantly saying, ‘Lend me your pearl-handled knife,
Gooseberry,’ and things of that sort, till Lewis was so unhappy he
begged to be sent home. Miss Crane did her best to keep the boys
quiet, but it was hard work, for they would tease, and she could not
be with them all the time. That is one of the hardest things to teach
boys; they won’t ‘hit a fellow when he is down,’ as they say, but they
will torment him in little ways till he would thank them to fight it out
all round.”
“I know that,” said Dan.
“So do I,” added Nat, softly.
Jack said nothing, but he quite agreed; for he knew that the elder
boys despised him, and let him alone for that very reason.

“Do go on about poor Lewis, Aunt Jo. I don’t believe he took the
knife, but I want to be sure,” said Daisy, in great anxiety.
“Well, week after week went on and the matter was not cleared
up. The boys avoided Lewis, and he, poor fellow, was almost sick
with the trouble he had brought upon himself. He resolved never to
tell another lie, and tried so hard that Miss Crane pitied and helped
him, and really came at last to believe that he did not take the knife.
Two months after the peddler’s first visit, he came again, and the
first thing he said was—
“‘Well, ma’am, I found that knife after all. It had slipped behind
the lining of my valise, and fell out the other day when I was putting
in a new stock of goods. I thought I’d call and let you know, as you
paid for it, and maybe would like it, so here it is.’
“The boys had all gathered round, and at these words they felt
much ashamed, and begged Lewis’ pardon so heartily that he could
not refuse to give it. Miss Crane presented the knife to him, and he
kept it many years to remind him of the fault that had brought him
so much trouble.”
“I wonder why it is that things you eat on the sly hurt you, and
don’t when you eat them at table,” observed Stuffy, thoughtfully.
“Perhaps your conscience affects your stomach,” said Mrs. Jo,
smiling at his speech.
“He is thinking of the cucumbers,” said Ned, and a gale of
merriment followed the words, for Stuffy’s last mishap had been a
funny one.
He ate two large cucumbers in private, felt very ill, and confided
his anguish to Ned, imploring him to do something. Ned good-
naturedly recommended a mustard plaster and a hot flat iron to the
feet; only in applying these remedies he reversed the order of
things, and put the plaster on the feet, the flat iron on the stomach,
and poor Stuffy was found in the barn with blistered soles and a
scorched jacket.

“Suppose you tell another story, that was such an interesting one,”
said Nat, as the laughter subsided.
Before Mrs. Jo could refuse these insatiable Oliver Twists, Rob
walked into the room trailing his little bed-cover after him, and
wearing an expression of great sweetness as he said, steering
straight to his mother as a sure haven of refuge,—
“I heard a great noise, and I thought sumfin dreffle might have
happened, so I came to see.”
“Did you think I would forget you, naughty boy?” asked his
mother, trying to look stern.
“No; but I thought you’d feel better to see me right here,”
responded the insinuating little party.
“I had much rather see you in bed, so march straight up again,
Robin.”
“Everybody that comes in here has to tell a story, and you can’t,
so you’d better cut and run,” said Emil.
“Yes, I can! I tell Teddy lots of ones, all about bears and moons,
and little flies that say things when they buzz,” protested Rob, bound
to stay at any price.
“Tell one now, then, right away,” said Dan, preparing to shoulder
and bear him off.
“Well, I will; let me fink a minute,” and Rob climbed into his
mother’s lap, where he was cuddled, with the remark—
“It is a family failing, this getting out of bed at wrong times. Demi
used to do it; and as for me, I was hopping in and out all night long.
Meg used to think the house was on fire, and send me down to see,
and I used to stay and enjoy myself, as you mean to, my bad son.”
“I’ve finked now,” observed Rob, quite at his ease, and eager to
win the entrée into this delightful circle.
Every one looked and listened with faces full of suppressed
merriment as Rob, perched on his mother’s knee and wrapped in the

gay coverlet, told the following brief but tragic tale with an
earnestness that made it very funny:—
“Once a lady had a million children, and one nice little boy. She
went up-stairs and said, ‘You mustn’t go in the yard.’ But he wented,
and fell into the pump, and was drowned dead.”
“Is that all?” asked Franz, as Rob paused out of breath with this
startling beginning.
“No, there is another piece of it,” and Rob knit his downy
eyebrows in the effort to evolve another inspiration.
“What did the lady do when he fell into the pump?” asked his
mother, to help him on.
“Oh, she pumped him up, and wrapped him in a newspaper, and
put him on a shelf to dry for seed.”
A general explosion of laughter greeted this surprising conclusion,
and Mrs. Jo patted the curly head, as she said, solemnly,—
“My son, you inherit your mother’s gift of story-telling. Go where
glory waits thee.”
“Now I can stay, can’t I? Wasn’t it a good story?” cried Rob, in
high feather at his superb success.
“You can stay till you have eaten these twelve pop-corns,” said his
mother, expecting to see them vanish at one mouthful.
But Rob was a shrewd little man, and got the better of her by
eating them one by one very slowly, and enjoying every minute with
all his might.
“Hadn’t you better tell the other story, while you wait for him?”
said Demi, anxious that no time should be lost.
“I really have nothing but a little tale about a wood-box,” said Mrs.
Jo, seeing that Rob had still seven corns to eat.
“Is there a boy in it?”
“It is all boy.”

“Is it true?” asked Demi.
“Every bit of it.”
“Goody! tell on, please.”
“James Snow and his mother lived in a little house, up in New
Hampshire. They were poor, and James had to work to help his
mother, but he loved books so well he hated work, and just wanted
to sit and study all day long.”
“How could he! I hate books, and like work,” said Dan, objecting
to James at the very outset.
“It takes all sorts of people to make a world; workers and students
both are needed, and there is room for all. But I think the workers
should study some, and the students should know how to work if
necessary,” answered Mrs. Jo, looking from Dan to Demi with a
significant expression.
“I’m sure I do work,” and Demi showed three small hard spots in
his little palm, with pride.
“And I’m sure I study,” added Dan, nodding with a groan toward
the blackboard full of neat figures.
“See what James did. He did not mean to be selfish, but his
mother was proud of him, and let him do as he liked, working away
by herself that he might have books and time to read them. One
autumn James wanted to go to school, and went to the minister to
see if he would help him, about decent clothes and books. Now the
minister had heard the gossip about James’s idleness, and was not
inclined to do much for him, thinking that a boy who neglected his
mother, and let her slave for him, was not likely to do very well even
at school. But the good man felt more interested when he found
how earnest James was, and being rather an odd man, he made this
proposal to the boy, to try how sincere he was.
“‘I will give you clothes and books on one condition, James.’
“‘What is that, sir?’ and the boy brightened up at once.

“‘You are to keep your mother’s wood-box full all winter long, and
do it yourself. If you fail, school stops.’ James laughed at the queer
condition and readily agreed to it, thinking it a very easy one.
“He began school, and for a time got on capitally with the wood-
box, for it was autumn, and chips and brush-wood were plentiful. He
ran out morning and evening and got a basket full, or chopped up
the cat sticks for the little cooking stove, and as his mother was
careful and saving, the task was not hard. But in November the frost
came, the days were dull and cold, and wood went fast. His mother
bought a load with her own earnings, but it seemed to melt away,
and was nearly gone, before James remembered that he was to get
the next. Mrs. Snow was feeble and lame with rheumatism, and
unable to work as she had done, so James had to put down his
books, and see what he could do.
“It was hard, for he was going on well, and so interested in his
lessons that he hated to stop except for food and sleep. But he knew
the minister would keep his word, and much against his will James
set about earning money in his spare hours, lest the wood-box
should get empty. He did all sorts of things, ran errands, took care of
a neighbor’s cow, helped the old sexton dust and warm the church
on Sundays, and in these ways got enough to buy fuel in small
quantities. But it was hard work; the days were short, the winter
was bitterly cold, the precious time went fast, and the dear books
were so fascinating, that it was sad to leave them, for dull duties
that never seemed done.
“The minister watched him quietly, and seeing that he was in
earnest helped him without his knowledge. He met him often driving
the wood sleds from the forest, where the men were chopping, and
as James plodded beside the slow oxen, he read or studied, anxious
to use every minute. ‘The boy is worth helping, this lesson will do
him good, and when he has learned it, I will give him an easier one,’
said the minister to himself, and on Christmas eve a splendid load of
wood was quietly dropped at the door of the little house, with a new
saw and a bit of paper, saying only—

“‘The Lord helps those who help themselves.’
“Poor James expected nothing, but when he woke on that cold
Christmas morning, he found a pair of warm mittens, knit by his
mother, with her stiff painful fingers. This gift pleased him very
much, but her kiss and tender look as she called him her ‘good son,’
was better still. In trying to keep her warm, he had warmed his own
heart, you see, and in filling the wood-box he had also filled those
months with duties faithfully done. He began to see this, to feel that
there was something better than books, and to try to learn the
lessons God set him, as well as those his school-master gave.
“When he saw the great pile of oak and pine logs at his door, and
read the little paper, he knew who sent it, and understood the
minister’s plan; thanked him for it, and fell to work with all his
might. Other boys frolicked that day, but James sawed wood, and I
think of all the lads in the town the happiest was the one in the new
mittens, who whistled like a blackbird as he filled his mother’s wood-
box.”
“That’s a first rater!” cried Dan, who enjoyed a simple matter-of-
fact story better than the finest fairy tale; “I like that fellow after all.”
“I could saw wood for you, Aunt Jo!” said Demi, feeling as if a new
means of earning money for his mother was suggested by the story.
“Tell about a bad boy. I like them best,” said Nan.
“You’d better tell about a naughty cross-patch of a girl,” said
Tommy, whose evening had been spoilt by Nan’s unkindness. It
made his apple taste bitter, his pop-corn was insipid, his nuts were
hard to crack, and the sight of Ned and Nan on one bench made him
feel his life a burden.
But there were no more stories from Mrs. Jo, for on looking down
at Rob he was discovered to be fast asleep with his last corn firmly
clasped in his chubby hand. Bundling him up in his coverlet, his
mother carried him away and tucked him up with no fear of his
popping out again.

“Now let’s see who will come next,” said Emil, setting the door
temptingly ajar.
Mary Ann passed first, and he called out to her, but Silas had
warned her, and she only laughed and hurried on in spite of their
enticements. Presently a door opened, and a strong voice was heard
humming in the hall—
“Ich weiss nicht was soll es bedeuten
Dass ich so traurig bin.”
“It’s Uncle Fritz; all laugh loud and he will be sure to come in,”
said Emil.
A wild burst of laughter followed, and in came Uncle Fritz, asking,
“What is the joke, my lads?”
“Caught! caught! you can’t go out till you’ve told a story,” cried the
boys, slamming the door.
“So! that is the joke then? Well, I have no wish to go, it is so
pleasant here, and I pay my forfeit at once,” which he did by sitting
down and beginning instantly—
“A long time ago your Grandfather, Demi, went to lecture in a
great town, hoping to get some money for a home for little orphans
that some good people were getting up. His lecture did well, and he
put a considerable sum of money in his pocket, feeling very happy
about it. As he was driving in a chaise to another town, he came to
a lonely bit of road, late in the afternoon, and was just thinking what
a good place it was for robbers when he saw a bad-looking man
come out of the woods in front of him and go slowly along as if
waiting till he came up. The thought of the money made Grandfather
rather anxious, and at first he had a mind to turn round and drive
away. But the horse was tired, and then he did not like to suspect
the man, so he kept on, and when he got nearer and saw how poor
and sick and ragged the stranger looked, his heart reproached him,
and stopping, he said in his kind voice—

“‘My friend, you look tired; let me give you a lift.’ The man seemed
surprised, hesitated a minute, and then got in. He did not seem
inclined to talk, but Grandfather kept on in his wise, cheerful way,
speaking of what a hard year it had been, how much the poor had
suffered, and how difficult it was to get on sometimes. The man
slowly softened a little, and, won by the kind chat, told his story.
How he had been sick, could get no work, had a family of children,
and was almost in despair. Grandfather was so full of pity that he
forgot his fear, and, asking the man his name, said he would try and
get him work in the next town, as he had friends there. Wishing to
get at pencil and paper, to write down the address, Grandfather took
out his plump pocket-book, and the minute he did so, the man’s eye
was on it. Then Grandfather remembered what was in it and
trembled for his money, but said quietly—
“‘Yes, I have a little sum here for some poor orphans. I wish it was
my own, I would so gladly give you some of it. I am not rich, but I
know many of the trials of the poor; this five dollars is mine, and I
want to give it to you for your children.’
“The hard, hungry look in the man’s eyes changed to a grateful
one as he took the small sum, freely given, and left the orphans’
money untouched. He rode on with Grandfather till they approached
the town, then he asked to be set down. Grandpa shook hands with
him, and was about to drive on, when the man said, as if something
made him, ‘I was desperate when we met, and I meant to rob you,
but you were so kind I couldn’t do it. God bless you, sir, for keeping
me from it!’”
“Did Grandpa ever see him again?” asked Daisy, eagerly.
“No; but I believe the man found work, and did not try robbery
any more.”
“That was a curious way to treat him; I’d have knocked him
down,” said Dan.
“Kindness is always better than force. Try it and see,” answered
Mr. Bhaer, rising.

“Tell another, please,” cried Daisy.
“You must, Aunt Jo did,” added Demi.
“Then I certainly won’t, but keep my others for next time. Too
many tales are as bad as too many bonbons. I have paid my forfeit
and I go,” and Mr. Bhaer ran for his life, with the whole flock in full
pursuit. He had the start, however, and escaped safely into his study,
leaving the boys to go rioting back again.
They were so stirred up by the race that they could not settle to
their former quiet, and a lively game of Blind-man’s Buff followed, in
which Tommy showed that he had taken the moral of the last story
to heart, for, when he caught Nan, he whispered in her ear, “I’m
sorry I called you a cross-patch.”
Nan was not to be outdone in kindness, so, when they played
“Button, button, who’s got the button?” and it was her turn to go
round, she said, “Hold fast all I give you,” with such a friendly smile
at Tommy, that he was not surprised to find the horse-hair ring in his
hand instead of the button. He only smiled back at her then, but
when they were going to bed, he offered Nan the best bite of his
last apple; she saw the ring on his stumpy little finger, accepted the
bite, and peace was declared. Both were sorry for the temporary
coldness, neither was ashamed to say, “I was wrong, forgive me,” so
the childish friendship remained unbroken, and the home in the
willow lasted long, a pleasant little castle in the air.

CHAPTER XXI
THANKSGIVING
This yearly festival was always kept at Plumfield in the good old-
fashioned way, and nothing was allowed to interfere with it. For days
beforehand, the little girls helped Asia and Mrs. Jo in store-room and
kitchen, making pies and puddings, sorting fruit, dusting dishes, and
being very busy and immensely important. The boys hovered on the
outskirts of the forbidden ground, sniffing the savory odors, peeping
in at the mysterious performances, and occasionally being permitted
to taste some delicacy in the process of preparation.
Something more than usual seemed to be on foot this year, for the
girls were as busy up-stairs as down, so were the boys in school-
room and barn, and a general air of bustle pervaded the house.
There was a great hunting up of old ribbons and finery, much cutting
and pasting of gold paper, and the most remarkable quantity of
straw, gray cotton, flannel, and big black beads, used by Franz and
Mrs. Jo. Ned hammered at strange machines in the workshop, Demi
and Tommy went about murmuring to themselves as if learning
something. A fearful racket was heard in Emil’s room at intervals,
and peals of laughter from the nursery when Rob and Teddy were
sent for and hidden from sight whole hours at a time. But the thing
that puzzled Mr. Bhaer the most was what became of Rob’s big
pumpkin. It had been borne in triumph to the kitchen, where a
dozen golden-tinted pies soon after appeared. It would not have
taken more than a quarter of the mammoth vegetable to make
them, yet where was the rest? It disappeared, and Rob never
seemed to care, only chuckled, when it was mentioned, and told his
father, “To wait and see,” for the fun of the whole thing was to
surprise Father Bhaer at the end, and not let him know a bit about
what was to happen.

He obediently shut eyes, ears, and mouth, and went about trying
not to see what was in plain sight, not to hear the tell-tale sounds
that filled the air, not to understand any of the perfectly transparent
mysteries going on all about him. Being a German, he loved these
simple domestic festivals, and encouraged them with all his heart,
for they made home so pleasant that the boys did not care to go
elsewhere for fun.
When at last the day came, the boys went off for a long walk, that
they might have good appetites for dinner; as if they ever needed
them! The girls remained at home to help set the table, and give last
touches to various affairs which filled their busy little souls with
anxiety. The school-room had been shut up since the night before,
and Mr. Bhaer was forbidden to enter it on pain of a beating from
Teddy, who guarded the door like a small dragon, though he was
dying to tell about it, and nothing but his father’s heroic self-denial
in not listening, kept him from betraying the grand secret.
“It’s all done, and it’s perfectly splendid,” cried Nan, coming out at
last with an air of triumph.
“The——you know—goes beautifully, and Silas knows just what to
do now,” added Daisy, skipping with delight at some unspeakable
success.
“I’m blest if it ain’t the ’cutest thing I ever see, them critters in
particular,” and Silas, who had been let into the secret, went off
laughing like a great boy.
“They are coming; I hear Emil roaring ‘Land lubbers lying down
below,’ so we must run and dress,” cried Nan, and up-stairs they
scampered in a great hurry.
The boys came trooping home with appetites that would have
made the big turkey tremble, if it had not been past all fear. They
also retired to dress; and for half-an-hour there was a washing,
brushing, and prinking that would have done any tidy woman’s heart
good to see. When the bell rang, a troop of fresh-faced lads with
shiny hair, clean collars, and Sunday jackets on, filed into the dining-

room, where Mrs. Jo, in her one black silk, with a knot of her
favorite white chrysanthemums in her bosom, sat at the head of the
table, “looking splendid,” as the boys said, whenever she got herself
up. Daisy and Nan were as gay as a posy bed in their new winter
dresses, with bright sashes and hair ribbons. Teddy was gorgeous to
behold in a crimson merino blouse, and his best button boots, which
absorbed and distracted him as much as Mr. Toot’s wristbands did on
one occasion.
As Mr. and Mrs. Bhaer glanced at each other down the long table,
with those rows of happy faces on either side, they had a little
thanksgiving, all to themselves, and without a word, for one heart
said to the other,—“Our work has prospered, let us be grateful and
go on.”
The clatter of knives and forks prevented much conversation for a
few minutes, and Mary Ann with an amazing pink bow in her hair
“flew around” briskly, handing plates and ladling out gravy. Nearly
every one had contributed to the feast, so the dinner was a
peculiarly interesting one to the eaters of it, who beguiled the
pauses by remarks on their own productions.
“If these are not good potatoes I never saw any,” observed Jack,
as he received his fourth big mealy one.
“Some of my herbs are in the stuffing of the turkey, that’s why it’s
so nice,” said Nan, taking a mouthful with intense satisfaction.
“My ducks are prime any way; Asia said she never cooked such fat
ones,” added Tommy.
“Well, our carrots are beautiful, ain’t they, and our parsnips will be
ever so good when we dig them,” put in Dick, and Dolly murmured
his assent from behind the bone he was picking.
“I helped make the pies with my pumpkin,” called out Robby, with
a laugh which he stopped by retiring into his mug.
“I picked some of the apples that the cider is made of,” said Demi.
“I raked the cranberries for the sauce,” cried Nat.

“I got the nuts,” added Dan, and so it went on all round the table.
“Who made up Thanksgiving?” asked Rob, for being lately
promoted to jacket and trousers he felt a new and manly interest in
the institutions of his country.
“See who can answer that question,” and Mr. Bhaer nodded to one
or two of his best history boys.
“I know,” said Demi, “the Pilgrims made it.”
“What for?” asked Rob, without waiting to learn who the Pilgrims
were.
“I forget,” and Demi subsided.
“I believe it was because they were not starved once, and so
when they had a good harvest, they said, ‘We will thank God for it,’
and they had a day and called it Thanksgiving,” said Dan, who liked
the story of the brave men who suffered so nobly for their faith.
“Good! I didn’t think you would remember any thing but natural
history,” and Mr. Bhaer tapped gently on the table as applause for his
pupil.
Dan looked pleased; and Mrs. Jo said to her son, “Now do you
understand about it, Robby?”
“No, I don’t. I thought pil-grins were a sort of big bird that lived
on rocks, and I saw pictures of them in Demi’s book.”
“He means penguins. Oh, isn’t he a little goosey!” and Demi laid
back in his chair and laughed aloud.
“Don’t laugh at him, but tell him all about it if you can,” said Mrs.
Bhaer, consoling Rob with more cranberry sauce for the general
smile that went round the table at his mistake.
“Well, I will;” and, after a pause to collect his ideas, Demi
delivered the following sketch of the Pilgrim Fathers, which would
have made even those grave gentlemen smile if they could have
heard it.

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