2_Sigma_Problem_Mick_Wood

Michael Wood (EH4102 – Assignment 1)
1
Teaching Large Groups: Revisiting Bloom’s 2-Sigma Problem
Part 1 - What keeps me awake at night?
I remember a presentation at the 2007 ALT Conference in Nottingham delivered by Dr Peter Norvig, the
Director of Research at Google. Norvig captured my attention as he discussed the problems faced when
teaching large groups and, in particular, the 2-Sigma Problem (see Bloom, 1984). Norvig showed the
following painting1
which sums up life in a lecture theatre.
The painting is circa 1530 and shows that little has changed during the last 500 years. A lecturer is
speaking to a group of students. One student can clearly be seen to be asleep; others are talking
amongst themselves; some are paying attention. Why Universities continue to teach large groups in
lecture theatres is another question but how could I efficiently and successfully teach large groups, thus
solving the 2-Sigma Problem?
How do I know that learning has taken place? How do I know that the students are listening? If students
are listening do they understand what I am talking about? As someone who has seen life in a lecture
theatre, both as a student and as a lecturer, I am interested in the answers to these questions. Is good
1
“Liber ethicorum des Henricus de Alemannia, Einzelblatt, Szene: Henricus de Alemannia vor seinen Schülern” by
Laurentius de Voltolina (see http://en.wikipedia.org/wiki/File:Laurentius_de_Voltolina_001.jpg)

2
teaching totally dependent on good teachers or is it possible to factor out the lecturer? I know from my
own experience how variable the standard of teaching is.
As a mature student I was totally focused and determined to work hard and do well. I remember many
times thinking some lectures added no value to my learning experience and having to self-learn.
As a lecturer / trainer I am keen on doing all I can to help students / delegates learn. People have chosen
to attend my sessions, not been forced or coerced to do so, and deserve to get fully recompensed for
their time and effort.
Part 2 - Summary of Bloom’s Original Paper
In 1984 Benjamin Bloom published a landmark paper entitled ‘The 2-Sigma Problem: The Search for
Methods of Group Instruction as Effective as One-to-One Tutoring’. The paper was a response to two
student dissertations 2
which compared student learning under three different instructional methods.
1: Conventional – Large groups of students were taught in a lecture theatre with regular tests
and assessments given to assess them. This traditional University model was the control method
in the study.
2: Mastery Learning 3
– Large groups of students were taught in a lecture theatre with regular
formative 4
tests and assessments. The testing was used to identify any topic difficulties which
were then re-taught and re-tested until the students had mastered the material. The students
could not move on to the next topic until they had demonstrated mastery of the current topic.
Mastery Learning requires more teacher involvement and time and is more expensive than
conventional teaching. Guskey (2007, p8) argues that, initially, Mastery Learning takes longer
but this time can be recovered as students learn the principles.
3: Tutoring – One-to-one student instruction was followed by formative assessment. Feedback
was given with remedial actions if required and simultaneous formative testing. Remedial work
is generally minor when students are tutored. Obviously this is expensive and not sustainable in
a University.
Students were randomly allocated to one of the three groups. The students were a homogenous group
with similar test scores, interests, attitudes and knowledge. The amount of teaching time was the same
in each group apart from the remedial work in the mastery learning and tutor groups. The study was
repeated with four groups of students at different ages and taking two different subjects.
2 See Anania (1982, 1983) and Burke (1984)
3 See Guskey (2005, 2007)
4 See Boston (2002)

3
The results of the study highlighted the large variations in achievement amongst the three groups of
students. Using the standard deviation (sigma) 5
of the control group as a base it was found that the
average student taught in the tutoring group was approximately two standard deviations (2-sigma)
above the average student in the control group. In other words the average student in the tutored
group was above 98% of the students in the control group. Likewise the average student taught in the
mastery learning group was approximately one standard deviation (1-sigma) above the average student
in the control group. In other words the average student in the mastery learning group was above 84%
of the students in the control group.
An alternative interpretation is that 90% of the tutored students and 70% of the mastery learning
students reached a level of achievement only attained by the top 20% of the control group.
The study showed that most students have the potential to do well if they are tutored. Unfortunately
individual tutoring is not a viable solution, either practically or financially, to the problem of successfully
teaching large groups of students. This is the 2-sigma problem. Can educators come up with methods of
teaching large groups of students in such a way as to enable them to reach the levels currently only
attainable to students who are tutored?
Bloom began his search for solutions by looking at research which contrasted a number of educational
variables, both alterable and constant. Alterable variables included the quality of teaching, the use of
time by teachers and students, student ability at course entry, formative testing, learning rates and the
student’s home environment. Constant or static variables included the personal qualities of the
teachers, summative testing and the socio-economic status of the student’s family.
Many of these variables affect learning but not all necessarily in the same way or to the same degree.
Bloom tried to focus on the variables which had the most impact. The results tried to take into account
the gender and age of the students, the sample size, and so on. Bloom produced a table summarising
the effects of the key alterable educational variables in order of significance. It is a matter for debate
whether Bloom’s numbers are accurate but the principle is certainly valid. The ‘Alterable Variable’ table
on the following page is adapted from Bloom’s table which was itself adapted from work done by
Walberg (1984).
To explain the data in the table you can see that the first entry refers to instruction by a tutor. The effect
size is 2.00 (i.e. 2-sigma) and the percentage equivalent of 98% shows that a student who has been
tutored will do better than 98% of the students in the control group.
The table also indicated the change driver - in other words who or what changed. The options are the
student (S), teacher (T), course material (M), home environment (H), or student peers (P).
5 The standard deviation measures the spread of the data about the mean.

4
Table 1: Alterable Variables
Change
Driver
Alterable Variable
Effect
Size
Percentage
Equivalent
T Tutorial Instruction 2.00 98
T Positive Reinforcement & Praise 1.20 88
S Feedback-Corrective (Mastery Learning) 1.00 84
T Teaching Cues and Explanations 1.00 84
S / T Student Classroom Participation 1.00 84
S Student time on task 1.00 84
S Improved reading / study skills 1.00 84
H Cooperative / Group Learning 0.80 79
T Graded Homework 0.80 79
T Classroom Morale 0.60 73
S Initial Cognitive Pre-Requisites 0.60 73
H Home Environment Intervention 0.50 69
P / T Peer and Cross-Age Remedial Tutoring 0.40 66
T Assigned Homework 0.30 62
T Higher Order Questions 0.30 62
M / T New Course Materials 0.30 62
T Teacher Expectancy 0.30 62
P Peer Group Influence 0.20 58
Socio-Economic Status (Static Variable for contrast) 0.25 60
Having obtained this data Bloom assumed that two or three variables, with a different change driver,
would be required to solve the 2-sigma problem. These variables, when implemented simultaneously,
could have a cumulative effect on the learning experience. For example, Mastery Learning, which has

5
the biggest affect on the learner, and changes in the Teaching Process, which have the greatest affect
on the teacher, does have a cumulative effect. Bloom also recognised that variables with the same
change driver would probably not have a cumulative effect.
Bloom assumed that Mastery Learning would be one of the variables and systematically tried other
variables in combination. However Bloom could not solve the 2-sigma problem using mastery learning
combined with just one of the other variables.
Bloom suggested that students could improve, irrespective of the teacher, by developing good study
habits, improving their reading skills, and allocating more time to their studies.
Improving Student Cognition
Mastery Learning improves student cognition by its very nature. Students cannot proceed to the next
topic until they have ‘mastered’ the current topic. As previously stated the average student taught in
the Mastery Learning group was approximately one standard deviation (1-sigma) above the average
student in the control group even when both groups were taught by the same teacher using the same
course materials. The key feature is that the students, by mastering a topic, have the cognitive
prerequisites for the next learning task. This leads to improved student confidence and more active
learning time.
Leyton (1983) suggested enhancing the students’ initial cognitive entry prerequisites at the start of a
program of study. In effect, diagnostic testing with remedial work using the Mastery Learning process.
Students who undertook this prerequisite work performed better than the control class by 0.7 sigma.
Those students who were also taught using Mastery Learning enjoyed a cumulative improvement of 1.6
sigma over the control class. There were also qualitative student improvements including a greater
interest in, and a desire to learn, the subject.
Other studies have indicated that peer support and study groups provide student encouragement and
help and are beneficial and effective (Slavin, 1980). Special study programs aimed at improving reading,
writing and study skills enable students to learn more effectively. (Pflaum et al, 1980).
Improving Teaching Materials
Improvements in course textbooks may have a marginal effect of 0.3. The improvements mainly relate
to the organisation of the material, chapter summaries, learning aids, etc. This change should add to the
overall cumulative improvement and can easily be implemented by the tutor.
Bloom would have been unaware of the plethora of online Computer Based Tools that are now available
at little or no cost. Motivated or interested students could take advantage of this material to reinforce
their learning. There is no data to quantify the effect of online materials but I estimate a cumulative
effect of 0.5 if improved teaching materials AND online testing are used.

6
Home Life and Peer Groups
A number of studies6
have found that a good home life, coupled with encouragement and support from
family and friends, can have a positive impact on student achievement. The opposite is also true.
The key factors (in 1984) included:-
• Family stability with good routines in the home.
• Priority being given to homework.
• Academic help, guidance and support from the parents.
Recent data7
paints a different picture of family life.
• There are many single parent families, often with the lone parent at work.
• Students have more distractions (and possessions) – computers, TV’s, Mobile Phones, etc. Some
students are often left alone with little or no interaction with their parent(s).
• Widening Participation can mean that some parents cannot offer academic help. Many parents
do not have sufficient knowledge to help their children having never been to University.
The issue is how the current home life can be changed, if necessary, for the benefit of the student. I do
not propose to deal with the home-life factors but the creation of a study and / or a peer support group
is easy to implement although the effect is marginal at 0.2 sigma.
Improving Teaching
Having observed many teachers in the classroom Bloom wrote that some students were treated
differently to other students by some teachers. Bloom surmised that some teachers:-
• direct their teaching to some students and ignore others
• encourage some students more than others
• encourage active participation from some students and discourage others
• give more time and attention to the best students
This means that some students get more / better opportunities to learn than other students.8
This could
account for the fact that only 20% of students in the control group do as well as tutored students
despite the fact that most students have the potential to do well. In effect the top 20% are actually
receiving a form of tutoring despite being in a large class situation.
Bloom stated that many teachers were simply unaware of these findings and felt that they treated all
students the same. Reflection by the teacher, or lack of it, is a key factor here. Bloom finishes his paper
by discussing a number of studies aimed at improving teaching standards.
6
See Dave (1963)
7
For example see Gallop (2005)
8
See Brophy & Good (1970)

7
Part 3 - Post-Bloom Literature
There are few articles offering solutions to the 2-sigma problem but numerous articles concerning the
learning environment variables highlighted by Bloom have been written.
Teacher Education
Matthew (2003) wonders whether I should be concerned with being an excellent teacher or concentrate
on creating excellent learners? Korthagen (2004) asks two key questions concerning teachers:-
1. What are the essential qualities of a good teacher?
2. How can we help teachers to become good teachers?
Am I a good teacher? How do I know? Korthagen argues that there are no definitive answers to these
questions - the answers differ according to context.
The qualities of a good teacher are often listed as a series of competencies (Brown 2003). Matthew
(2003) stated that good teaching ‘encourages high quality student learning. It discourages the superficial
approach to learning and encourages active engagement with the subject matter.’ Does my teaching
fall in line with this definition?
The Minus 2-Sigma Problem
Vockell (1994) wrote that bad teaching can have a negative effect on student learning just as good
teaching can have a positive effect. He produced a table of negative teaching strategies and their
effects. The data is hypothetic but does make a point. The percentile column shows the score of a
student who would normally score 50%.
Table 2: Effects of Negative Teaching Strategies
Strategy Effect Size Percentile
No sensible teaching at all -2.00 2
No corrective feedback -1.00 16
Making students think only when it is their turn to answer -1.00 16
Promoting rote learning -0.80 22
Not making subject matter interesting -0.80 22
Discouraging higher order thinking -0.80 22
Giving punishments unrelated to offenses -0.60 30

8
Constructive Alignment
The principle behind ‘Constructive Alignment’ (Biggs, 1999) is that “the curriculum is designed so that the
learning activities and assessment tasks are aligned with the learning outcomes that are intended in the
course.” (Houghton, 2004) In summary:-
1. Students construct meaning from what they do to learn.
2. The teacher aligns the planned learning activities with the learning outcomes.
Houghton (2004) states that there are 3 steps to 'Constructively Aligning' a course:
1. Define the learning outcomes.
2. Select learning and teaching activities likely to enable the students to attain the outcomes.
3. Assess the students' outcomes and grade the students learning.
Cohen (1987) pointed out that alignment is more important to lower aptitude students than to higher
aptitude students. When undertaking difficult aligned tasks lower aptitude students performed better
than higher aptitude students undertaking non-aligned tasks. This indicates that lower aptitude
students can successfully perform highly cognitive tasks when instruction is aligned.
Cohen concludes his paper by stating; “Teaching what we assess, or assessing what we teach seems
embarrassingly obvious. The fundamental issue is: What’s worth teaching? ... What’s worth assessing?”
Mastery Learning
Benjamin Bloom observed that teachers tended to teach all their students in the same way, giving them
all the same amount of time to learn (Guskey 2007, p10). Teachers did not appear to take account of the
different ways that students learned. Some students did well because the teaching methodology suited
them but many did less well as the teaching methods were inappropriate. Bloom went on to say that
teachers must vary their teaching methods to suit more individual students’ learning styles. The
challenge is how to do this in a large group setting so that all students learn well.
Bloom (1968) suggested that course materials should be grouped into instructional units and each unit
assessed at the end of the unit rather than at the end of the academic year. The classroom would be
used as a place to provide feedback on learning progress and guidance on how to correct learning
errors. The assessments become part of the learning process rather than an end-of-year scorecard.
Bloom recommended that students undertake a second, slightly different, formative assessment
following any corrective work. This would confirm whether any corrective work has been successful and
also, assuming students pass this second assessment, provides students with encouragement and
motivation.
Bloom also recognised that that some students do really well at the first assessment and do not require
corrective help. Bloom suggested that ‘special enrichment activities’ be provided to broaden the
knowledge of these students.

9
Bloom believed that this methodology would provide the stimulus required to enable all students to
master course material and simultaneously reduce the variations in student learning achievement levels.
Class Sizes
Oestmann and Oestmann (2005) were interested in the relationship between (online) class sizes and
learning outcomes. This research looked at the effectiveness of online Social Network Tools, in
particular threaded discussion type tools. Vygotsky’s (1987) Socio-Cultural Cognitive Theory claims that
increased social interaction between students increases cognitive development. Therefore, larger
(online) classes lead to more threaded discussions which facilitate improved learning. The fact that this
research is based on online teaching is largely irrelevant. Glahn and Gen (2002, p777) state that “Online
teaching is not better than face-to-face teaching, nor is it worse. It is simply different.”
Course Design: Student Learning Outcomes (SLO’s)
SLO’s describe the knowledge, skills, abilities and attitudes that students will possess at the end of a
particular course/module/assignment etc. The key focus is on what students can do with their
knowledge. At the end of the course students should possess integrated, higher learning skills which
they can demonstrate to others.
Teachers have to identify the specific SLO’s for their program and then design assessments which give
students an opportunity to demonstrate what they have learned. These assessments will also provide
the evidence necessary for course evaluation.
The theory is that students perform better when they know what is expected of them and this includes
knowledge of how they will be assessed. This is known as transparency and the students should have
the opportunity to practice these skills before they are formally assessed.
Employing the SLO method integrates course activities with what the students are actually learning,
their outcomes, and their assessments leading to a balanced and focused course.
Part 4 – A Suggested Solution to the 2-Sigma Problem
We know the simplest answer to the 2-Sigma Problem but we cannot afford it. As one-to-one tutoring is
not a realistic option one possible route that lecturers could implement is my proposed 6-Stage Model.
This Model alters at least 6 key variables with 4 different change drivers. I conservatively estimate that
fully implementing all six of these changes will have a cumulative effect in excess of 2-Sigma and
therefore ‘solve’ the 2-Sigma problem.
Having previously outlined Bloom’s original 2-sigma paper and then looked at the literature concerning
the alterable variables highlighted by Bloom the next question is ‘how do I apply this knowledge to my
own working practices?’
My problem is that I don’t personally teach a full module or course. However, I can apply this knowledge
vicariously as I am involved in course development and resource creation for other lecturers. I do teach

10
occasionally and facilitate a variety of workshops and I can thus apply my findings to those sessions that
I do teach.
One of the key issues concerns resources. James, McInnis and Devlin (2002, p31) addressed the
challenges and solutions faced by teachers of large groups. Reducing workload is a key factor but many
of the 6-stages require an initial investment of time and potentially have cost implications. Creating
these resources should reduce marking time in the long run and produce consistency in the marking
process, especially when multiple markers are used.
My suggested solution to the 2-sigma problem is underpinned by Race (2006) who highlighted five
factors which are needed to optimise learning:
1. We can try to get our learners to want to learn.
2. We can help them learners the point, and take ownership of the need to learn.
3. We can keep learners busy, learning by doing, practice, trial and error, repetition.
4. We can help learners to make sense of what they are learning…
5. …particularly by making sure that learners get feedback on what they are doing and thinking.
Table 3: 6-Stage Solution to the 2-Sigma Problem
The ‘Change Driver’ options are the student (S), teacher (T), course material (M), or student peers (P).
Stage
Change
Driver
Alterable Variable
Estimated
Effect Size
1 S Initial Cognitive Pre-Requisites
0.60
2 S Improved reading / study skills
3 M / T
New Course Materials
0.80New Online Materials
(Auto) Graded Homework
4 S / T Feedback-Corrective (Mastery Learning)
1.00
5 S / T Student Classroom Participation
6 P Peer Tutoring/Support using Social Network Tools 0.40
Estimated Cumulative Effect 2.80

11
For lecturers who want to implement this model there are many free online resources available which
can simply be ‘dropped’ into their course. Of course some resources will need to be created but these
resources could also potentially be free of charge if the lecturer chooses to seek help from centrally
available technical staff such as myself in the Learning Development Unit.
Time is always an issue but the long-term saving needs to be kept in mind and the lecturer may need to
‘bite the bullet’. I also believe that implementing this model can have positive effects on student
satisfaction and retention which, from a personal point of view, are unlikely to harm future job
prospects or security.
Stage 1 - Initial Cognitive Pre-Requisites
I suggest the use of QuestionMark Perception to provide diagnostic testing of the initial cognitive entry
prerequisites. The School of Built & Natural Environment at UCLan has successfully implemented this
strategy for students enrolled on different modules. Students undertook diagnostic Mathematics and
English tests and the majority of students passed both tests. For students who failed the School
arranged for ‘futures’9
to provide compulsory remedial help.10
Stage 2 - Improved reading / study skills
Lecturers should include special workshops which improve reading, writing and study skills such as those
provided by WISER11
. WISER facilitate a variety of workshops, one-to-one tutorials and bespoke
workshops for students.
It makes sense to take advantage of this type of expertise. I would envisage offering bespoke workshops
during the first few tutorial sessions or organize a specific ‘study skills development day’ for students.
The effect of implementing the first two stages is conservatively set at 0.60 as the students are seen to
be the main change driver in both stages. I see this as giving the students a massive confidence boost in
the early stages of their study program as well as providing them with a variety of transferable key skills.
Stage 3 – New Course & Online Materials and (Auto) Graded Homework
Lecturers should spend some time identifying good (or better) course materials and online resources
and then create resources to fill any gaps. Although this can be time consuming the benefits (0.80
sigma) are well worth the time outlay. Research shows that two thirds of academics do not take
advantage of this opportunity.
A recent ‘Digitally Enhanced Survey’12
highlighted the fact that approximately one third of respondents13
have no online assessment activities although they have made basic course information available online.
9
https://staff.uclan.ac.uk/12998.htm
10
Futures have also development of a series of psychometric tests to help with employability.
11
http://www.uclan.ac.uk/information/services/wiser/index.php
12
Undertaken by P Mahoney & M Wood, Learning Development Unit, UCLan, Summer 2010 (Data unpublished)
13
110 Course leaders completed the survey out of a possible 400+ who were invited.

12
Another third said that they have some simple basic online activities such as the WebCT Assessment
Tool. The final third claimed to have significant online activities which the students must complete to
pass the module. This would include wikis, blogs, audio, video, and other interactive tools.
Using Questionmark Perception it is relatively easy to add graded (0.30 sigma) or auto-graded (0.80
sigma) homework assignments. I have not added the benefits of adding graded homework to the
cumulative score for this stage but expect empirical evidence to be forthcoming shortly as I am applying
this stage to a CEPS14
Statistics module which has a failure rate in excess of 50%.
Specifically I have, in partnership with a lecturer, created a bank of questions for each of eight topics.
Ten questions are randomly selected from the bank by Questionmark Perception and students are
tested online. Feedback for each wrong answer directs students to a PDF and a Video. Those students
who fail the test, having looked at the feedback resources, are then directed to a second quiz in line with
Bloom’s previously mentioned recommendations. The second quiz randomly selects another ten
questions from the bank. It is worth noting that each student is provided with a different random
selection of questions to prevent copying / cheating.
Stage 4 - Feedback-Corrective (Mastery Learning)
Lecturers should create corrective resources for each learning concept within an assessment. Students
only need to work on those skills which they haven’t mastered. The corrective resources can range from
something as simple as a web link, or a reference in a text book, to a DVD, video, or computerized
course. Other resources may include study guides, group / peer activities and so on. This is de facto
individual learning because each student knows what he or she needs to do to obtain the requisite skills
in a particular unit. This method also allows teachers to vary how they present material, thus appealing
to a variety of student learning styles.
The previously mentions CEPS Statistics module fits in perfectly with this stage. This also highlights how
resources can be used for multiple purposes within a course.
I need to create some additional resources for my Turnitin training course to reinforce the correct way
to interpret reports, particularly in the case of collusion.
Stage 5 - Student Classroom Participation
Microsoft Mouse Mischief15
or IML QuestionWizard16
are two excellent examples of technology which
the lecturer can use to promote active participation / learning and deliver lecture based formative
testing in the classroom.
14
Computing, Engineering & Physical Sciences – MS1063 Statistics
15
http://www.microsoft.com/uk/multipoint/mouse-mischief/default.aspx
16
http://www.iml.co.uk/default.asp

13
Mouse Mischief integrates with PowerPoint enabling you to insert questions, polls and activity slides
directly into your presentations. Each student has their own mouse meaning they can actively
participate in the lessons. Students click, circle, cross out or draw answers directly on to the screen.
Question Wizard is a Student Interactive Response System (SIRS) enabling staff to:-
• Encourage group discussion
• Obtain simultaneous feedback / responses from a group
• Record and immediately display group feedback
• Actively engage every participant
• Combine real-time assessment, dynamic presentation options, and enjoyable learning activities.
Lecturers can use these technologies to ask effective revision questions before the lecture (for example,
to ascertain if mastery learning of prior topics has taken place) AND ask questions or create scenarios
during the lecture to check understanding of the new topic.
SIRS has been available for many years at UCLan but I need to promote it, and use it, much more than I
currently do. My experience with SIRS is very positive, staff and students universally enjoy using this
type of technology and it can be used to facilitate different student learning styles.
Stage 6 - Peer Tutoring/Support using Social Network Tools
Vygotsky’s research suggests that lecturers should at least consider Social Network Tools but at least
two thirds of lecturers do not use them. These tools focus on building up social networks and/or social
relations among people who share interests and activities. Facebook17
, Bebo18
and Twitter19
are popular
tools and most Virtual Learning Environments include a (threaded) discussion tool. There is no shortage
of tools available for lecturers to choose from.
A blog, such as Wordpress20
, can be used to enable students to share problems, ask for help, and pass
on news and other success stories. Posts are rather like diary entries and other students can comment
and offer help and support.
Lecturers can easily use one or more of these tools. Setup is really quick and relatively easy; the majority
of students are already using these types of tools so minimal student support is required. The potential
benefit of 0.4 sigma should encourage lecturers to at least try these tools but the best way to use these
tools is a subject of further research. 21
17
http://www.facebook.com
18
http://www.bebo.com
19
http://twitter.com
20
http://wordpress.org
21
See Alexander (2008)

14
Again, I should definitely add the WebCT discussion tool to my Turnitin and Website Marketing training
courses.
Assessment
Having made all these changes I need to be able to measure student learning and achievement. Having
defined SLO’s for my courses / programmes I need to assess whether my students have achieved their
SLO’s, see if I have met my own targets, and provide evidence based data to back up my claims.
I have therefore developed a whole pack of assessment resources including question and assessment
templates, assessment evaluation forms, anti-plagiarism strategies and a ‘high level ’mind map of the
topic.
If the learning process is sound and student learning can be assessed and proven, a strong argument can
be made that my 6-stage process is indeed a solution to the 2-sigma problem.
Part 5 – Personal Reflection
If I was to become a lecturer in the future this is the model I would follow when developing my own
course material.
I have to say that I have been quite stressed at times with the whole process of producing this report. I
find academic writing to be difficult and tend to read far too much. The first draft of this report was
more than 9000 words and severe editing has been undertaken.
An increase in my workload limits my time to reflect on academic matters and implement changes
highlighted by my research. Which of the plethora of models, plans, and ideas should I implement?
Assuming I want to implement them all, which do I implement first?
I feel that, for the first time, I have really researched a topic thoroughly and been able to create a
structured, flowing narrative with a cohesive plan of action which others could follow.
Even though I have been stressed I have thoroughly enjoyed the process and have learned lots of things.
I feel that should I, or anyone else, implement my 6-stage plan students would be given an excellent
chance to fulfil their potential - they will have improved by a minimum of 2-sigma.

15
Bibliography
Alexander, B. (2008) Social Networking in Higher Education. In: Katz, R. (ed.) The Tower and the Cloud.
EduCause: Available from: http://net.educause.edu/ir/library/pdf/PUB7202s.pdf [Accessed 13th
December 2010]
Anania, J. (1982) The effects of quality of instruction on the cognitive and affective learning of students.
Dissertation Abstracts International, 42, 4269A.
Anania, J. (1983) The influence of instructional conditions on student learning and achievement.
Evaluation in Education: An International Review Series, 7(1), 1 – 92
Biggs, J. (1999) Teaching for Quality Learning at University. SRHE and Open University Press,
Buckingham
Bloom, B. (1968) Learning for mastery. Evaluation Comment, 1(2), 1–12. (ERIC Document Reproduction
No. ED053419)
Bloom, B. (1984) The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-
to-One Tutoring. Educational Researcher, 13(6), 4 – 16
Boston, C. (2002) The Concept of Formative Assessment. Practical Assessment, Research & Evaluation;
8(9). Available from: http://PAREonline.net/getvn.asp?v=8&n=9 [Accessed 21st
July 2010]
Brophy, J. & Good, T. (1970) Teachers’ communication of differential expectations for children’s
classroom performance: Some behavioural data. Journal of Educational Psychology, 61, 365 – 374
Brown, S. (2003) Differentiating good and excellent teaching: is it possible? Exchange 5, 32. Available
from: http://www.exchange.ac.uk [Accessed 4th
November 2010]
Burke, A. (1984) Students’ potential for learning under tutorial and group approaches to instruction.
Dissertation Abstracts International, 44, 2025A.
Cohen, S. (1987) Instructional Alignment: Searching for a Magic Bullet. Educational Researcher, 16(8) 16
– 20
Combs, A., Blume, R., Newman, A., and Wass, H.; (1974) The professional education of teachers: A
humanistic approach to teacher preparation. Boston: Allyn & Bacon
Dave, R. (1963) The identification and measurement of environment process variables that are related to
educational achievement. Unpublished Thesis, University of Chicago

16
Gallop, A (2005) Ageing Population Conference 2005: Sixty-Five and Not Out! An Age of Opportunity or
Limitation? Demographic Data Pack - 7-9 September 2005, St Anne’s College, Oxford, UK
Glahn, R. and Gen, R. (2002) Progenies in education: The evolution of internet teaching. Community
College Journal of Research and Practice. 26, 777 – 785
Guskey, T. (2005) Formative Classroom Assessment and Benjamin S. Bloom: Theory, Research, and
Implications. Paper presented at the Annual Meeting of the American Educational Research Association
(Montreal, Canada, April 11-15, 2005) Available from: http://www.eric.ed.gov/ (ERIC # ED490412),
[Accessed 10th
June 2010]
Guskey, T. (2007) Closing the achievement gap: Revisiting Benjamin S. Bloom’s “learning for mastery”.
Journal of Advanced Academics, 19(1), 8 – 31
Houghton, W. (2004) Constructive Alignment - and why it is important to the learning process.
Engineering Subject Centre Guide: Learning and Teaching Theory for Engineering Academics.
Loughborough: HEA Engineering Subject Centre. (Available from: http://www.engsc.ac.uk/learning-and-
teaching-theory-guide/constructive-alignment [Accessed 26th November 2010]
James, R., McInniss, I. and Devlin, M. (2002) Assessing Learning in Australian Universities. Centre for the
Study for Higher Education. Available from:
http://www.cshe.unimelb.edu.au/assessinglearning/docs/AssessingLearning.pdf [Accessed 18th
November 2010]
Korthagen, F. (2004) In search of the essence of a good teacher: towards a more holistic approach in
teacher education. Teaching and Teacher Education, 20, 77 – 97
Leyton, F. (1983) The extent to which group instruction supplemented by mastery of the initial cognitive
prerequisites approximates the learning effectiveness of one-to-one tutorial methods. Dissertation
Abstracts International, 44, 974A.
Lowyck, J. (1978) Process Analysis of Teaching Behaviour. Leuven: Leuven University
Matthew, R. (2003) Excellent Teaching or Excellent Learning? Exchange, 5, 30 – 31. Available from:
http://www.exchange.ac.uk [Accessed 4th
November 2010]
Oestmann, E. & Oestmann, J. (2005) Significant Differences in Learning Outcomes and Online Class Size.
Journal of Online Educators, 2(1). Available from:
http://www.oeinet.org/LEARNING%20OUTCOMES%20&%20CLASS%20SIZE.doc [Accessed 10th
June
2010]
Pflaum, S., Walberg, H., Karegianes, M., & Rasher, S. (1980) Reading instruction: A Quantitative
Synthesis. Educational Researcher. 9, 12 – 18

17
Race, P. (2006) Making Teaching Work; Presentation made at Tralee Institute. Available from:
http://www.ittralee.ie/en/InformationFor/Staff/TeachingandLearningUnit/WorkshopandReports/PhilRa
cePresentation/filedownload,10961,en.pdf [Accessed 17th
November 2010]
Slavin, R. (1980) Cooperative Learning; Review of Educational Research, 50, 315 – 342
Vockell, E.(1994) The Minus Two-Sigma Problem: Correcting Defective Instruction. Contemporary
Education, 65(4), 185 – 190
Vygotsky, L.; (1987) Thinking and Speech: The Collected Works of L. S. Vygotsky. New York: Plenum
Walberg, H. (1984) Improving the Productivity of America's Schools. Educational Leadership, 41(8). 19 –
27

2_Sigma_Problem_Mick_Wood

More Related Content

What's hot (20)

Viewers also liked (11)

Similar to 2_Sigma_Problem_Mick_Wood (20)

2_Sigma_Problem_Mick_Wood