Overcoming Self-Regulatory Deficits of At-Risk Math Students at an Urban Technical College: A Self-Regulated Learning (SRL) Intervention

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Overcoming Self-Regulatory Deficits of At-Risk
Math Students at an Urban Technical College A
Self-Regulated Learning (SRL) Intervention

• Barry J. Zimmerman, Adam Moylan, John Hudesman,
  and Bert Flugman
• Graduate School and University CenterCity
  University of New York

Project funded by a Grant from the Institute for
Educational Sciences
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Setting New York City College of Technology

• 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

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Why are many minority students in a urban
technical college at-risk in math?

• In addition to ineffective prior math
  instruction, these students are often deficient
  in key SRL skills, such as
• They often overestimate their math proficiency
  metacognitively and under-prepare for exams.
• They fail to self-evaluate their efforts to learn
  accurately.
• They fail to attribute errors to shortcomings in
  strategy.
• They fail to adapt their erroneous approaches to
  subsequent math problems.

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Cyclical Self-Regulatory Phases
Performance Phase Self-Control Self-instruction Im
agery Attention focusing Task strategies Self-Obse
rvation Metacognitive Monitoring Self-recording

Forethought Phase Task Analysis Goal
setting Strategic planning Self-Motivation
Beliefs Self-efficacy Outcome expectations Intrins
ic interest/value Goal orientation
Self-Reflection Phase Self-Judgment Self-evaluatio
n Causal attribution Self-Reaction Self-satisfacti
on/affect Adaptive/defensive
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A SRL perspective on errors in math

• Problem solving errors are not signs of
  imperfection but rather are essential sources of
  guidance for SRL.
• Errors should be reflected upon carefully because
  they reveal alternative ways to solve math
  problems.
• SRL occurs when students make successful
  adaptations from personal errors.
• Students should be praised and graded favorably
  for recognizing and overcoming errors rather than
  criticized and penalized for making them.

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Present Study

• Semester-long classroom intervention for
  undergraduates (N 496) in challenging math
  courses (developmental math introductory
  college math).
• Particular focus was placed on enhancing
  self-reflection processes to improve students
  responses to academic feedback
• Random assignment of Ss to SRL or control
  classrooms

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Strategic Instruction

• Teacher models specific strategies at each step
  of the problem
• Teacher writes down strategies clearly on the
  board in words
• Teacher explains to the students that they need
  to write down strategies
• Students encouraged to monitor strategy use
  during math problem solving

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Increased Practice and Feedback

• Teacher sets aside time for students 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.

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Quiz
Use the following rating scale to answer the
questions before and after each problem
Definitely not Not confident Undecided
Confident Very confident
confident 1 2
3 4
5
Before solving each problem, circle the number that represents how confident you are that you can solve it correctly. After you have solved each problem, circle the number that represents how confident are you that you solved it correctly.
1 2 3 4 5 1 2 3 4 5

1. Divide by long division
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Quiz Reflection Form Error Analysis
Revision Sheet, MA175 Quiz ____ Item ____
Now that you have received your corrected quiz,
you have the opportunity to improve your score.
Complete all sections thoroughly and
thoughtfully. Use a separate revision sheet for
each new problem.

• PLAN IT
• 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.

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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.

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Quiz Reflection Form Transfer of Knowledge


Definitely not Not confident Undecided
Confident Very confident
confident
5. How confident are you now that you
1 2 3
4 5 can correctly solve this
similar item?
6. Now use the strategy to solve the alternative
problem. 7. How confident are you now
that you 1 2
3 4 5 can
correctly solve a similar problem on a quiz or
test in the future?
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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.
• The sample involved a total of 496 students in
  remedial and college-level mathematics courses.
• There were 4 experimental teachers and 9 control
  teachers
• Control classrooms receive traditional remedial
  or college-level math instruction.
• The two groups are compared using multiple
  examination measures and course-related
  self-regulatory measures.

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Self-Regulation Intervention

• Train instructors to become coaches of SRL
• 1. Trained over 3 days before semester
• 2. Weekly meetings to review implementation by
  instructors
• 3. Classroom component (modeling, emulation,
  strategy charts, focus on errors as sources of
  understanding)
• B. Instructors trained to use Self-Reflection
  forms with math quizzes
• 1. Correcting errors on quizzes
• 2. Solving alternative problems
• 3. Gaining points on quiz for self-reflection

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Math Achievement Measures

• Math periodic exams. Three uniform, cumulative
  math tests that were administered during the
  semester were used as problem solving performance
  measures. Students were required to fully write
  out their problem solving processes. This exam is
  developed jointly by SRL and control teachers.
• Math final exam. Comprehensive, department-wide
  final exam scores were used as another
  achievement measure.

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Self-Efficacy Measures

• Self-efficacy. As a measure of task-specific math
  self-efficacy, before solving each problem,
  students rated their confidence in their ability
  to solve the problem correctly using a 5-point
  scale (1 definitely not confident, 2 not
  confident, 3 undecided, 4 confident, 5
  very confident).
• Self-efficacy accuracy. The accuracy calibration
  or magnitude of error between students
  self-efficacy beliefs and their actual
  performance was assessed by subtracting the
  absolute value of the bias score (if problem was
  correct, then the bias score was 5 minus the
  self-efficacy rating if there was an error, then
  the self-efficacy score was subtracted from 1)
  from 4, with 0 being completely inaccurate and 4
  completely accurate.

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Self-Evaluation Measures

• Self-evaluation. To measure post-performance
  self-evaluative judgments, students rated their
  confidence that their responses were correct
  using the same scale as for the self-efficacy
  measure.
• Self-evaluation accuracy. Accuracy calibration of
  post-performance self-evaluative judgments was
  assessed similarly to self-efficacy accuracy.

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Correlations among Measures (Combined Math
Courses)
Measure 1 2 3 4 5 6
1. Self-Efficacy 1. Self-Efficacy 0.91 0.50 0.43 0.43 0.33
2. Self-Evaluation 2. Self-Evaluation 2. Self-Evaluation 0.43 0.49 0.45 0.34
3. Self-Efficacy Bias 3. Self-Efficacy Bias 3. Self-Efficacy Bias 0.93 -0.46 -0.34
4. Self-Evaluation Bias 4. Self-Evaluation Bias 4. Self-Evaluation Bias 4. Self-Evaluation Bias -0.46 -0.37
5. Periodic Math Exam 5. Periodic Math Exam 5. Periodic Math Exam 5. Periodic Math Exam 0.71
6. Final Math Exam 6. Final Math Exam 6. Final Math Exam
All correlation coefficients ps gt,01 All correlation coefficients ps gt,01
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Developmental Math Performance
? ?
?
p lt .05 p lt .01. Error bars are standard
errors of the mean.
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Introductory Math Performance
? ?
? ?
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Self-efficacy and Self-Evaluation Results

• There were no significant differences between SRL
  and control group students in their self-efficacy
  or self-evaluation judgments.
• The mean for the self-efficacy belief was 3.43
  for Controls and 3.39 for SRL on a 5-point scale
• The means for the self-evaluation belief was
• 3.58 for controls and 3.45 for SRL
• These means fall between confident and undecided.

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Developmental Math Calibration
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Introductory Math Calibration
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Within SRL Group Analyses

• Self-reflection rate of self-reflection
  forms / of quiz errors
• Formula adjusts for differences in Ss
  opportunities to use the form because students
  who made fewer errors would have fewer chances to
  self-reflect
• A median split of the self-reflection rate was
  used to compare performance of high
  self-reflectors with low self-reflectors

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Self-Reflectors Math Exam Results(Combined Math
Courses)
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Self-Reflectors Math Calibration(Combined Math
Courses)
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Conclusions

• SRL students surpassed control students on
  periodic exams as well final exams
• SRL students reported less over-confidence than
  control students in both their math
  self-efficacy beliefs and self-evaluative
  judgments.
• SRL students who engaged in greater error
  correction 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.