Promoting Achievement, Motivation, and
Strategic Learning in Math Contexts
West Texas Middle School Math Partnership
Spring 2010
Timothy J. Cleary
Associate Professor
University of Wisconsin-Milwaukee
tcleary@uwm.edu
414-229-4053
Dan, a 12 year old student in the 6th grade at an urban
middle school, has been reported by his teachers to exhibit
academic and motivational difficulties. More specifically a
few of his teachers expressed concern about his poor test
performance and inconsistent homework completion, his
tendency to give up easily when attempting to complete
topics, and his overall negative attitudes about school. Math
is particularly difficult for Dan as he fails most tests and
rarely participates in class activities. His parents revealed
that Dan is a “poor studier” and over the past couple of
years has developed a sense of helplessness about his
school because he does not really understand why things
are so difficult.
Maladaptive
behaviors
Maladaptive beliefs
and attitudes
Poor academic performance
Intervention
Baseline
Strategy
Plan
- Looked
over stuff
-Read
my notes
Strategy
Plan
Same
Strategy
Plan
Strategy
Plan
-Index
-cards
- Study
plan
- Graphic
organizer
- Index
cards
- Study
plan
Strategy
Plan
- Study
Strategy plan
Plan
- Graphic
Read
notes
organizer
- Mother
quizzed
him
Link between self-regulation and math
performance
Poor performance in math could be attributed to
ineffective prior math instruction, but also often involves:
deficiencies in SRL skills such as:
- overestimating their math proficiency, which may
result in “under” preparation for exams
- failing to self-evaluate their efforts to learn accurately
- failing to attribute errors to shortcomings in strategy
- failing to adapt their maladaptive approaches to
subsequent math problems
…how we can cultivate adaptive regulatory thoughts and
actions that promote motivation and achievement in math
Primary Objectives of Lecture
1. To briefly describe a three-phase cyclical model of
self-regulation
2. To highlight a couple of instructional tactics to enhance
student motivation and math achievement
- type of feedback
- graphing/progress monitoring
- attribution training
- forethought training
- error analysis
- cognitive modeling
- self-monitor
- guided practice
Thinking in the language of strategies
Characteristics of a self-regulated learner? 1,2
• Highly self-motivated, proactive
• Set goals and develop/use strategic plans
• Monitoring strategies and performance
• Frequent self-reflection and analysis
ADJUST or CHANGE strategies and goals
To optimize future performance
Cycle of Self-Regulatory Thought and Action
1
Performance Phase
Self-Control
Self-Instruction
Imagery
Attention Focusing
Task Strategies
Forethought Phase
Self-Observation
Self-recording
Metacognitive Monitoring
Self-Reflection Phase
Task Analysis
Goal Setting
Strategic Planning
Self-Judgment
Self-Evaluation
Causal Attributions
Self-Motivational Beliefs
Self-efficacy
Outcome expectations
Intrinsic Interest
Goal Orientation
Self-Reaction
Self-satisfaction/affect
Adaptive Inferences
Developing strategic reflective thinkers
1. Attributions following failure 3
Has there been any activity or experience which proved
to be especially challenging or difficult for you?
(something you were not very good at doing). What
types of thoughts did you have immediately following
poor performance? What did you think was the reason
for your performance and how did you feel?
Can be categorized across three broad dimensions:
a)Internal/External
- is the cause a personal or environmental phenomenon?
b) Controllable/Uncontrollable
- is the cause under a person’s control or not?
c) Stable/Unstable
- is the cause easily modified or changeable?
Types of attributions we make following failure impacts
our subsequent behaviors and affect
Attribution
What is the main
reason why you failed
your last math test?
Adaptive Inference
What do you need to
do to improve your
next test grade?
Attributions not under student control
“The Cowboys lost again last night”
“Test was too hard”
“The teacher is not any good”
“The teacher does not like me”
“I don’t know”
Uncontrollable
Now what???
Under student control/internal/unstable
“I did not try hard enough”
“I did not use the correct STRATEGY”
Attribution
What is the main
reason why you failed
your last math test?
Strategy
Adaptive Inference
What do you need to
do to improve your
next test score?
Change my strategy
I forgot how to do the step
for getting all variables on
one side of the equation
Ask the teacher or classmates
about this method
I did not think about the
type of problem before
trying to solve it
Use the math strategy that
my teacher taught me
Cycle of Self-Regulatory Thought and Action
2
Performance Phase
Self-Control
Self-Instruction
Imagery
Attention Focusing
Task Strategies
Forethought Phase
Self-Observation
Self-recording
Metacognitive Monitoring
Self-Reflection Phase
Task Analysis
Goal Setting
Strategic Planning
Self-Judgment
Self-Evaluation
Causal Attributions
Self-Motivational Beliefs
Self-efficacy
Outcome expectations
Intrinsic Interest
Goal Orientation
Self-Reaction
Self-satisfaction/affect
Adaptive Inferences
2) Error Analysis – A self-regulation perspective
• Problem solving errors are not signs of imperfection
but rather are essential sources of guidance for SRL
• Students should be taught to reflect carefully upon
the errors they make because such errors reveal
alternative ways to solve math problems
• Enhanced efficacy and SRL behaviors occur when
students make successful adaptations from errors
• Students should be praised and graded favorably for
recognizing and overcoming errors rather than
criticized and penalized for making them.
Zimmerman, Hudesman, Flugman & Moylan (2010)
• The goal of this project was to prepare students to
respond to their academic grades as sources of selfregulated learning rather than as indices of personal
limitation.
• Examine the efficacy of an SRL intervention
involving strategic instruction (classroom level) and
self-reflection training (individuals) on student
motivation, self-regulation and math achievement
What was the nature of the SRL intervention?
Classroom-based strategy instruction
• strategic instruction in error analysis
• coping modeling techniques and guided practice
Focus on self-reflection following quiz performance
• frequent math quizzes (every 2-3 days)
• an SRL Math Self-Assessment Form designed to
guide students’ self-reflection processes during
math problem corrections
Classroom-based strategy instruction
A. Strategic Instruction
• Teacher models specific strategies at each step of
the problem – use of think alouds
– teacher makes deliberate errors during presentation
– teacher models identifying errors and coping tactics
– math solution errors are used as a departure point for
analysis, i.e. teachers don’t just start over or quickly
correcting errors themselves
•
Teacher writes down strategies clearly on the board
in words
B. Increased Practice and Feedback
• Teacher sets aside time for students to engage in
individual practice of strategies for problem solving
and error detection
• Teacher asks students to verbalize error detection/
problem solving strategies while reviewing or
working through practice problems
• Teacher asks students to check their understanding
(discuss answers to problems and errors) with peers
in pairs or groups
Self-regulation instruction following performance
a) Math quizzes (4-5 problems) every 2 to 3
classes (returned that day or the following day)
b) Following each quiz, students were instructed to
complete a Self-assessment Form
a) Compare self-efficacy and self-evaluation estimates with
actual quiz performance (calibration accuracy)
b) Explain their ineffectual strategies (attributions)
c) Establish new effective strategies (adaptive inferences)
Quiz Reflection Form: Error Analysis
PLAN IT
1 a. How much time did you spend studying for this quiz? _______
b. How many practice problems did you do in this topic area __________in
preparation for this quiz?
(circle one) 0 – 5 / 5 – 10 / 10+
c. What did you do to prepare for this quiz? (use study strategy list to
answer this question)
2. After you solved this problem, was your confidence rating too high (i.e. 4 or
5)? Yes/no
3. Explain what strategies or processes went wrong on the quiz problem.
Quiz Reflection Form: Strategic Practice
PRACTICE IT
4. Now re-do the original quiz problem and write the strategy you are
using on the right.
2x  7 x  9
x2
2
Quiz Reflection Form: Transfer of Knowledge
5. How confident are you now that you can correctly solve this similar item?
6. Now use the strategy to solve the alternative problem.
x  4x  8
x3
2
7. How confident are you now that you can correctly solve a similar problem
on a quiz or test in the future?
Who was the target population?
• Student population 13,370
-
37.1% Black (non-Hispanic)
28.6% Hispanic
15.9% Asian/Pacific Islander
11.6% White (non-Hispanic)
0.3% Native American
7% Other
• 80% of incoming freshmen receive need-based aid
• Graduation rate for associate degree students
averages 21% after six years
• Only 38% of entering freshmen pass the entrance
exam in mathematics
Research Design
• This study involves a developmental math course
and an introductory college-level math course. In
both course levels, students are randomly
assigned to either the SRL or control classroom.
• Control classrooms received traditional remedial
or college-level math instruction plus the quizzes.
• The two groups were compared using multiple
examination measures and course-related selfregulatory measures.
Math Achievement Measures
• Math periodic exams. Three uniform, cumulative math
tests that were administered during the semester were
used as problem-solving performance measures.
• Math final exam. Comprehensive, department-wide
final exam scores were used as another achievement
measure.
Self-Evaluation Measures
• Self-evaluation. To measure post-performance selfevaluative judgments, students rated their
confidence that their responses were correct using
the same scale as for the self-efficacy measure.
• Self-evaluation bias. Bias calibration of postperformance self-evaluative judgments was
assessed similarly to self-efficacy bias.
Math Exam Results
80
70
Math Grades
60
50
Intervention
40
Control
30
20
10
0
Periodic Math Exam
Final Math Exam
Types of Math Exams
Self-Regulation Results
4
3.5
Self-Ratings
3
Intervention
Control
2.5
2
1.5
1
0.5
0
Self-Efficacy Self-Evaluation
Self-Efficacy
Bias
Self-Evaluation
Bias
Self_Regulation Measures
Self-Reflectors’ Math Exam Results
80
70
Exam Grades
60
50
High Self-Reflectors
40
Low Self-Reflectors
30
20
10
0
Periodic
Final
Type of Math Exams
Self-Reflectors’ Self-Regulation Results
4
3
High Self-Reflectors
2.5
Low Self-Reflectors
2
1.5
1
0.5
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Self-Ratings
3.5
Self-Regulation Measures
Conclusions
• SRL students surpassed control students on periodic
exams as well final exams – greater reflection
opportunities and strategic liearning led to higher
performance
• SRL students reported less over-confidence than control
students in both their math self-efficacy beliefs and selfevaluative judgments
• SRL students who engaged in greater error correction and
self-reflection displayed higher math exam grades and
calibration than students who were low in error correction
• Although self-efficacy and self-evaluation measures were
correlated positively with periodic and final math exam
performance, the SRL intervention did not influence these
self- beliefs
How can we create a shift in students’ strategic
thinking?
Talking in the language of strategies
• interpret failure/mistakes in terms of strategies
• link errors to strategies
• model and allow practice for error correction
• set strategic goals and strategic plans
• self-monitoring strategy use link