Cognitively Guided Instruction

1. Cognitively Guided Instruction Gwenanne Salkind Mathematics Education Leadership Research Expertise Presentation December 11, 2004

2. Addition & Subtraction • Problem Types • Joining or separating actions • Comparing situations • Part-whole relations • Combined with what is unknown • Carpenter, T. P., & Moser, J. M. (1983) • Riley, M. S., Greeno, J. G., & Heller, J. K. (1983) • Carpenter, T. P. (1985)

3. Classification of Word Problems Connie had 5 red marbles and 8 blue marbles. How many marbles does she have? Connie has 13 marbles. Five are red and the rest are blue. How many blue marbles does Connie have?

4. Development of Problem-Solving Strategies • Direct Modeling • Counting • Derived Facts • Recall Facts

5. CGI Framework • Analysis of problem types and solution strategies provides a framework for analyzing teachers’ pedagogical content knowledge. • Will providing research-based knowledge to teachers influence their instruction?

6. Researchers • Thomas P. Carpenter, University of Wisconsin • Elizabeth Fennema, University of Wisconsin • Penelope L. Peterson, Michigan State University • Deborah A. Carey, University of Wisconsin • Megan L. Franke, UCLA • Nancy Knapp, University of Georgia

7. CGI Workshops • 40 first-grade teachers • 4-week summer workshops • 1986 and 1987 • Familiarize teachers with the findings of the research on the learning and development of addition and subtraction concepts in young children • Provide teachers with an opportunity to think about and plan instruction on the basis of this knowledge

8. Measures of Teachers’ Knowledge • Knowledge of problem types • General knowledge of strategies • Teachers’ knowledge of their own students Measures of Student Performance • Number Facts • Problem Solving (Carpenter, Fennema, Peterson, & Carey, 1988)

9. Results • Teachers could distinguish between major problem types and were capable of identifying student strategies • Teachers were able to predict the success of their own students. • Most teachers did not have a coherent framework for classifying problems. • Many teachers did not recognize that problems that can be directly modeled are easier than problems that cannot. (Carpenter et al., 1988)

10. Another Study • 20 of the original 40 teachers • Case studies of two of the teachers • Compared a knowledgeable teacher with a less knowledgeable teacher (Peterson, Carpenter, & Fennema, 1989)

11. Data Collection • Classroom observations • Teachers’ Belief Questionnaire • Teachers’ knowledge of their own students • Student Measures of Achievement • ITBS pretest/posttest • Interviews (Peterson et al., 1989)

12. Teachers’ Knowledge & Beliefs • Teachers’ knowledge of their students’ problem-solving abilities was the best predictor of students’ problem-solving achievement. • Teachers’ beliefs were significantly positively correlated with students’ mathematics achievement. (Peterson et al., 1989)

13. More Knowledgeable Questioned and listened to students Believed that students construct their own knowledge Believed that children came to school with a lot of knowledge Believed that the role of teacher is as facilitator Less Knowledgeable Explained how to solve the problem Believed that children receive knowledge Skeptical of students’ entering knowledge Focused on knowledge that her children did not have Believed that role of teacher is to present knowledge. Difference between More Expert Teachers and Less Expert Teachers (Peterson et al., 1989)

14. A Case Study • Ms. J • First grade teacher • Participated in the CGI studies • Four years (Fennema, Franke, Carpenter, & Carey, 1993)

15. Data Collection • Year 1 • Interviews • CGI Belief Instrument • Year 2 • Classroom observations • CGI Belief Instrument • Year 3 (Case Study) • Group discussion • Interviews • Classroom observations • Student Interviews • Year 4 • Interviews • Knowledge assessment (Fennema et al., 1993)

16. Ms. J • Ranked near the top of her experimental group on knowledge of CGI framework • High score on CGI Belief Instrument • Students learned mathematics at a higher level than most first grade children (Fennema et al., 1993)

17. Ms. J’s Instruction • Frequently questioned her students about their thinking • Listened to her students more than the other teachers • Expected multiple solution strategies at a higher level than most of the other teachers • Expected students to persist in their work, share strategies, and reflect on their own thinking (Fennema et al., 1993)

18. Results • Ms. J had research-based knowledge of children’s thinking and was able to use it to make instructional decisions. • Study shows evidence that teachers can use CGI research to inform their instruction and increase learning of children. (Fennema et al., 1993)

19. CGI After Four Years • 20 of original 40 participants • All 40 were contacted and asked to participate • Phone interviews • Interviews collected detailed descriptions of the participants’ teaching practices. • Teachers varied widely in degree of CGI use and beliefs (Knapp & Peterson, 1995)

20. CGI After Four Years • Three groups of teachers emerged • Ten teachers used CGI as the main basis for their teaching. • Four teachers had never used CGI more than supplementally. • Six teachers had used CGI more extensively in earlier year, but now were using it only occasionally. (Knapp & Peterson, 1995)

21. CGI After Four Years • Researchers did, as they had hoped, develop an intervention that could result in significant changes in elementary teachers’ practices and beliefs about mathematics. • The positive effects of CGI intervention seem to have been most pervasive and long lasting in teachers who constructed for themselves more conceptual and flexible meanings for CGI rather than adopting means that were tied to specific procedures from the CGI training. (Knapp & Peterson, 1995)

22. Other Studies • Four year longitudinal study • 21 teachers • Workshops & Support • Classroom observations • Interviews • CGI Belief Scale • Student Interviews • Student computation tests Fennema, Carpenter, Franke, Levi, Jacobs, & Empson, 1996)

23. Levels of CGI Instruction

24. Teachers’ Beliefs • The beliefs of 18 teachers in the final year were more cognitively guided than were their beliefs in the initial year. • Beliefs were characterized by the acceptance of the idea that children can solve problems without direct instruction and that the mathematics curriculum should be based on children’s abilities. ( Fennema et al., 1996)

25. Student Achievement • Student achievement in problem solving was higher at the end of the study than at the beginning • There was no change in computation skills. ( Fennema et al., 1996)

26. Three Case Studies • Three teachers chosen from the original 21 • Interviews • Classroom observations • Looked at teacher change • Only one teacher showed self-sustaining, generative change. Frank, Carpenter, Fennema, Ansell, & Behrend, 1998)

27. Kindergarten Children’s Problem-Solving Processes • Carpenter, Ansell, Franke, Fennema, and Weisbeck, 1993 • 70 kindergarten children • Teachers participated in CGI course • Student interviews • Children can solve a wide range of problems, including multiplication and division situations, much earlier than generally presumed.

28. Other Researchers • Villasenor & Kepner, 1993 • Used a control group • Urban district with significant minority population • CGI students scored significantly better on number facts and problem solving tests • CGI students used advanced strategies significantly more often than non-CGI students

29. Other Researchers • Vacc & Bright, 1999 • Thirty-four preservice teachers • Two case studies (Helen and Andrea) • University of North Carolina • Two years of professional coursework • Student teaching • Observations • CGI Belief Instrument • Interviews

30. Other Researchers • Warfield, 2001 • Case study of one kindergarten teacher • Sixth year as CGI teacher • Classroom observations • Interviews • Looked at beliefs, knowledge, and instruction • Teacher used CGI framework to learn about individual children’s mathematical thinking and used that knowledge to make instructional decisions

31. Summary • Evidence that knowledge of CGI framework changed teachers’ instructional practices and beliefs • Evidence that CGI instruction increased student performance in problem-solving and computation.

32. CGI in FCPS • Have trained about 70 teachers • Support from instructor/coach • Share research with CGI Instructor • Consider using CGI Instructional Levels and CGI Belief Instrument