MLCS packet ICTCM 2013 ( with sampler pages)
- 1. Mathematical Literacy for College Students (MLCS) 3 – 6 semester hours (depending on depth and breadth desired) Prerequisite: Appropriate placement or prealgebra with a grade of “C” or better One goal of developmental mathematics education is to provide students with the necessary skills and understanding required to be successful in college level mathematics. Mathematical Literacy for College Students (MLCS) is a new course being developed at the national level by AMATYC’s New Life for Developmental Mathematics. Its origins are related to Quantway, funded by the Carnegie Foundation. MLCS is an alternative path to certain college level math courses or further algebra. It integrates numeracy, proportional reasoning, algebraic reasoning, and functions with statistics and geometry as recurring course themes. Throughout the course, college success components are integrated with the mathematical topics. The course focuses on developing mathematical maturity through problem solving, critical thinking, writing, and communication of mathematics. Content is developed in an integrated fashion, increasing in depth as the course progresses. Upon completion of the course, students will be prepared for a statistics course or a general education mathematics course. Students may also take traditional intermediate algebra upon completion if they choose to pursue STEM courses. MLCS provides an alternative to beginning algebra, creating multiple pathways for the developmental students. However, it is more difficult than beginning algebra to ensure students are prepared for a college level math course upon successful completion. It allows students to potentially complete their developmental math and college level math requirement for an Associate in Arts degree in one year total (one semester each), working toward the goal of improving college completion rates. It promotes 21st century skills to prepare students for both the workplace and future coursework. Further, it does not diminish requirements for non-STEM college level math courses but instead creates appropriate paths to these courses with the same level of intensity and complexity as the current path through intermediate algebra. The course has college level expectations and coursework but with a pace and instructional design intended for the adult, developmental learner. This strategy emulates the approach taken by the Common Core Standards and aligns with them as well. For more information on MLCS Contact: Kathleen Almy, Heather Foes (Rock Valley College) Emails: kathleenalmy@gmail.com heather.foes@gmail.com Blog: http://almydoesmath.blogspot.com Blog contains video, pilot updates, presentations, and more. 1|Page
- 2. MLCS Course Description and Objectives Mathematical Literacy for College Students is a one semester course for non-math and non-science majors integrating numeracy, proportional reasoning, algebraic reasoning, and functions. Students will develop conceptual and procedural tools that support the use of key mathematical concepts in a variety of contexts. Throughout the course, college success content will be integrated with mathematical topics. Prerequisite: Appropriate placement or prealgebra with a grade of “C” or better COURSE OUTCOMES 1. Apply the concepts of numeracy in multiple contexts. 2. Recognize proportional relationships and use proportional reasoning to solve problems. 3. Use the language of algebra to write relationships involving variables, interpret those relationships, and solve problems. 4. Interpret and move flexibly between multiple formats including graphs, tables, equations, and words. 5. Demonstrate student success skills including perseverance, time management, and appropriate use of resources. 6. Develop the ability to think critically and solve problems in a variety of contexts using the tools of mathematics including technology. COURSE OBJECTIVES Upon successful completion of this course, the student will be able to: Numeracy 1. Demonstrate operation sense and the effects of common operations on numbers in words and symbols. 2. Demonstrate competency in the use of magnitude in the contexts of place values, fractions, and numbers written in scientific notation. 3. Use estimation skills. 4. Apply quantitative reasoning to solve problems involving quantities or rates. 5. Demonstrate measurement sense. 6. Demonstrate an understanding of the mathematical properties and uses of different types of mathematical summaries of data. 7. Read, interpret, and make decisions based upon data from line graphs, bar graphs, and charts. Proportional reasoning 8. Recognize proportional relationships from verbal and numeric representations. 9. Compare proportional relationships represented in different ways. 10. Apply quantitative reasoning strategies to solve real-world problems with proportional relationships. Algebraic reasoning 11. Understand various uses of variables to represent quantities or attributes. 12. Describe the effect that changes in variable values have in an algebraic relationship. 13. Construct and solve equations or inequalities to represent relationships involving one or more unknown or variable quantities to solve problems. 2|Page
- 3. Functions 14. Translate problems from a variety of contexts into a mathematical representation and vice versa. 15. Describe the behavior of common types of functions using words, algebraic symbols, graphs, and tables. 16. Identify the reasonableness of a linear model for given data and consider alternative models. 17. Identify important characteristics of functions in various representations. 18. Use appropriate terms and units to describe rate of change. 19. Understand that abstract mathematical models used to characterize real-world scenarios or physical relationships are not always exact and may be subject to error from many sources. Student success 20. Develop written and verbal skills in relation to course content. 21. Evaluate personal learning style, strengths, weaknesses, and success strategies that address each. 22. Research using print and online resources. 23. Apply time management and goal setting techniques. Mathematical success 24. Develop the ability to use mathematical skills in diverse scenarios and contexts. 25. Use technology appropriately including calculators and computers. 26. Demonstrate critical thinking by analyzing ideas, patterns, and principles. 27. Demonstrate flexibility with mathematics through various contexts, modes of technology, and presentations of information (tables, graphs, words, equations). 28. Demonstrate and explain skills needed in studying for and taking tests. 3|Page
- 4. Implementation Options MLCS is a 3 – 6 credit hour course depending on the depth and breadth desired. 1. Replacement Model: Use MLCS to replace beginning algebra. 2. Augmented Model: Use MLCS to create a non-STEM alternative to beginning algebra that provides sufficient preparation for statistics or liberal arts math. 3. Supplemental Model: Use MLCS lessons for problem solving sessions in an Emporium model (lab-based traditional redesign.), engaging all students and moving beyond skills alone. 4. High School Model: Use MLCS lessons for 4th year high school course to develop college readiness and help students place into college level math. 4|Page
- 5. Sample lesson from the text Math Lit, by Kathleen Almy and Heather Foes. 5|Page
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- 11. Solutions for Acceleration, Redesign, and Readiness Math Lit, by Kathleen Almy and Heather Foes, provides a one-semester alternative to the traditional two-semester developmental algebra sequence. This new approach offers an accelerated pathway to college readiness through developmental math, allowing non-STEM (Science, Technology, Engineering, and Math) students to move directly into liberal arts math or introductory statistics. Through its emphasis on contextual problem-solving, the Almy/Foes text and its accompanying MyMathLab® course help students understand and practice the major themes of numeracy, proportional reasoning, algebraic reasoning, and functions. The textbook and MyMathLab content are organized into cycles (rather than linear chapters) that take a spiral approach to covering topics that relate to four thematic strands—numeracy, proportional reasoning, algebraic reasoning, and functions. Once introduced, these thematic topics are revisited several times as appropriate, going into a little more detail each time. • ach cycle is divided into three parts: E • End-of-lesson homework begins with skills-based assignments in MyMathLab® and the worktext. ˚ Gear Up—introduces key ideas for the content Shift Gears—contains the bulk of the cycle. Students are also asked to complete conceptual and ˚ and skills for the cycle. application-based problems in the text to expand their understanding beyond a procedural level. ˚ Wind Down—connects the main ideas and wraps things up. • End-of-Cycle Wrap Ups provide a five-step action • ycles are composed of activity-based lessons that C plan to help students study and prepare for the Cycle include carefully designed tasks, explorations, and test. A Cycle Profile gives a brief overview of important instruction—all paced for the developmental learner. topics, and a Self Assessment asks students to indicate Most lessons are divided into 4 segments: their level of expertise with each topic. ˚ Explore—offers an interesting problem or group activity opens the lesson and sets the stage for the new material Discover—presents a new theory with examples and ˚ practice problems. Connect—connects content to past or future lessons ˚ through a group or class problem. Reflect—provides an opportunity to look back at ˚ what has been learned. continued on reverse
- 12. Math Lit Cycle Overview Cycle Question Goal Focus Problem Topics Developed in Depth 1 What can be Establish foundation Explore a situation involving Graphs (Venn diagrams, pie graphs, bar graphs, scatterplots), learned? skills used in all cycles medical error to understand percent skills (increase/decrease, percent of change), as well as skills necessary the role of error, technology, fraction review, rates/ratios, function basics, proportionality, to make the course rates, units, and open-ended reasoning and conjectures, types of change (linear/exponen- operate well problem solving tial), types of graphs (non-linear), concepts of area/ perimeter/volume, similarity 2 Why does it matter? Develop understanding Explore the magic number Signed number concepts and operations, means, exponent of numbers and in baseball to understand properties with whole number exponents, polynomial basics, operations that will integers, expressions, and order of operations, FOIL, polynomial multiplication, be used in cycle 3 order of operations properties of real numbers (distributive, commutative, with equations associative), geometric and other formulas, Pythagorean Theorem, slope, distance formula 3 When is it worth it? Build on cycle 2’s skills to Determine when it is worth it to Theory, creation, and solving of equations (both linear develop understanding buy print copies of a book or an and some basic non-linear situations), median, weighted of building, solving, and e-reader to develop graphical, averages, correlation, standard deviation, volume and surface graphing equations, both numerical, and algebraic area calculations, Pareto charts, slope-intercept form, linear and non-linear comparison skills graphing linear equations, variation, rational function modeling with a basic situation 4 How big is big? Understand large and Make sense of the national Proportionality, dimensional analysis, exponential vs. linear small numbers and debt in terms of height, weight, revisited with modeling, scientific notation, exponent quantities in absolute and area, time, and relationship properties with negative exponents, solving a formula for relative contexts through to other countries’ debts to a variable, factoring the GCF, probability concepts, solving numerical and functional develop understanding of size, proportions algebraically, writing equations of lines, 2x2 means scale, scientific notation, and systems of equations, compound inequalities, quadratic measurement modeling with a basic situation, z-scores, Golden ratio, order of magnitude About the authors Kathleen Almy has been a professor of Heather Foes is a professor of mathematics at Rock Valley College for Mathematics at Rock Valley College in over 10 years and has taught high school Rockford, Illinois and has also taught at and college level math for 15 years. She Illinois State University, Northern Illinois has a bachelor’s degree in mathematics University and the University of Illinois. education from Southern Illinois University Heather has a bachelor’s degree in chemistry and master’s degree in pure mathematics and mathematics and a master’s degree in from Northern Illinois University. As her department’s mathematics from Illinois State University. She has written developmental math coordinator, she has organized and led solution manuals and other supplemental materials over the a successful comprehensive redesign of the program over the last ten years, as well as algorithmic questions for test-generator past 5 years. As a result of giving talks about the redesign, software and conceptual questions for MyStatLab for Pearson. she has been consulting with colleges throughout Illinois and across the country to improve their developmental math programs. Since 2009, she has been a member of AMATYC’s Quantway project which is affiliated with the Carnegie Foundation. She was AMATYC’s Developmental Math Committee chair and serves on several state committees on developmental education. © 2013 Pearson Education, Inc. All rights reserved. Printed in the U.S.A. DEVMATH2696/0113