Promoting Achievement, Motivation, and Strategic Learning in Math Contexts Timothy J. Cleary Associate Professor University of Wisconsin-Milwaukee West Texas Middle School Math Partnership Spring 2010

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 Maladaptive beliefs behaviors and attitudes Poor academic performance

Baseline Intervention - Looked over stuff -Read my notes Same -Index -cards - Study plan - Graphic organizer - Index cards - Study plan Read notes - Study plan - Graphic organizer - Mother quizzed him Strategy Plan Strategy Plan Strategy Plan Strategy Plan Strategy Plan Strategy Plan

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 Monitoring strategies and performance ADJUST or CHANGE strategies and goals Set goals and develop/use strategic plans Frequent self-reflection and analysis To optimize future performance

Cycle of Self-Regulatory Thought and Action 1 Forethought Phase Task Analysis Goal Setting Strategic Planning Self-Motivational Beliefs Self-efficacy Outcome expectations Intrinsic Interest Goal Orientation Performance Phase Self-Control Self-Instruction Imagery Attention Focusing Task Strategies Self-Observation Self-recording Metacognitive Monitoring Self-Reflection Phase Self-Judgment Self-Evaluation Causal Attributions Self-Reaction Self-satisfaction/affect Adaptive Inferences

1. Attributions following failure 3 Developing strategic reflective thinkers 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? 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?

What is the main reason why you failed your last math test? UncontrollableNow what??? AttributionAdaptive Inference What do you need to do to improve your next test grade? Types of attributions we make following failure impacts our subsequent behaviors and affect “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” Attributions not under student control

Strategy Under student control/internal/unstable “I did not try hard enough” “I did not use the correct STRATEGY” What is the main reason why you failed your last math test? What do you need to do to improve your next test score? Attribution Adaptive Inference 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

Forethought Phase Task Analysis Goal Setting Strategic Planning Self-Motivational Beliefs Self-efficacy Outcome expectations Intrinsic Interest Goal Orientation Cycle of Self-Regulatory Thought and Action 2 Performance Phase Self-Control Self-Instruction Imagery Attention Focusing Task Strategies Self-Observation Self-recording Metacognitive Monitoring Self-Reflection Phase Self-Judgment Self-Evaluation Causal Attributions Self-Reaction Self-satisfaction/affect Adaptive Inferences

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. 2) Error Analysis – A self-regulation perspective

Zimmerman, Hudesman, Flugman & Moylan (2010) The goal of this project was to prepare students to respond to their academic grades as sources of self- regulated 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

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 Classroom-based strategy instruction

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 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?

Student population 13, % Black (non-Hispanic) % 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 Who was the target population?

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 self- regulatory 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-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 = confident, 3 = undecided, 4 = confident, & 5 = very confident). Self-efficacy bias. Measures of accuracy calibration or magnitude of error between students’ self-efficacy beliefs and their actual performance - range from being completely accurate and 4 completely inaccurate.

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 bias. Bias calibration of post- performance self-evaluative judgments was assessed similarly to self-efficacy bias.

Math Exam Results

Self-Regulation Results

Self-Reflectors’ Math Exam Results

Self-Reflectors’ Self-Regulation Results

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 self- evaluative 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