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 Center City University of New York Project funded by a Grant from the Institute for Educational Sciences

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

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.

Cyclical Self-Regulatory Phases Forethought Phase Task Analysis Goal setting Strategic planning Self-Motivation Beliefs Self-efficacy Outcome expectations Intrinsic interest/value Goal orientation Self-Reflection Phase Self-Judgment Self-evaluation Causal attribution Self-Reaction Self-satisfaction/affect Adaptive/defensive Performance Phase Self-Control Self-instruction Imagery Attention focusing Task strategies Self-Observation Metacognitive Monitoring Self-recording

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.

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

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

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.

Quiz Use the following rating scale to answer the questions before and after each problem Definitely not Not confident Undecided Confident Very confident confident Divide by long division 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

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 1a. 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.

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. 7. How confident are you now that you can correctly solve a similar problem on a quiz or test in the future? Definitely not Not confident Undecided Confident Very confident confident

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.

Self-Regulation Intervention A.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

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.

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.

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.

Correlations among Measures (Combined Math Courses) Measure Self-Efficacy Self-Evaluation Self-Efficacy Bias Self-Evaluation Bias Periodic Math Exam Final Math Exam ** All correlation coefficients ps >,01

Developmental Math Performance * p <.05; ** p <.01. Error bars are standard errors of the mean.    

Introductory Math Performance     

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.

Developmental Math Calibration

Introductory Math Calibration

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

Self-Reflectors’ Math Exam Results ( Combined Math Courses)

Self-Reflectors’ Math Calibration (Combined Math Courses)

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.