1. Overview of Cognitively Guided Instruction Research

2. 1970s: Research on Children’s Mathematical Thinking Thomas Carpenter and James Moser research the development of children’s strategies for addition and subtraction problems

4. Children’s Solution Strategies Chart Counting On To Number Facts Flexible Choice of Strategies Direct Modeling Counting Join ( Result Unknown) Part-Part-Whole (Whole Unknown) Separate (Result Unknown) Part-Part- Whole (Part Unknown) Join (Change Unknown) Compare (Difference Unknown) Join/Separate (Start Unknown) Joining All Separating From Joining To Matching Trial and Error Counting On From First Counting On From Larger Counting Down Deriving facts Recalling

5. 1984 - 1988: CGI Experimental Study 40 First grade teachers – 20 Attended Workshop (Treatment) – 20 did not (Control) Treatment and Control group were compared – Teachers’ knowledge – Teachers beliefs – Students’ achievement (problem solving and facts) – Classroom activities (amount of problem solving, type of teacher talk, type of student talk…)

6. 1989-1995:CGI Longitudinal Study Kindergarten through third grade teachers and students in four schools participated in CGI professional development for three years. Assessed over three years: – Teachers’ knowledge and beliefs – Students’ achievement and beliefs – Classroom practice Five years after the workshop ended (2001) teachers’ classroom practice, knowledge and beliefs were assessed

7. 1996-2005: CGI/Algebra Research Program Development : 1996 – 2000 CGI Algebra Professional Development Program was developed by researchers in conjunction with expert CGI teachers. Experimental Research 2000 - 2005 – First – Sixth grade teachers – 90 Treatment Teachers; 90 Control Teachers – Treatment and Control teachers were compared Student Achievement Teacher Knowledge

8. In CGI Professional Development: Teachers learn how children think about mathematics. Teachers are supported in developing their own approach to teaching math for understanding. We focus on number, operation and the algebra underlying number and operation.

9. Summary of CGI Research Results Characteristics of Classrooms Students in CGI Classrooms spend more time engaged in problem solving than students in non-CGI Classrooms. There is a higher ratio of student talk to teacher talk in CGI Classrooms than in non- CGI classrooms.

10. Summary of CGI Research Results Student Achievement CGI students’ achievement on problem solving tasks is higher than non-CGI students’. CGI students’ performance on computation and facts is not significantly different from that of non-CGI students. CGI students are more likely to use strategies that are based on an understanding of mathematical relationships.

11. Strategies that show an understanding of mathematical relationships

12. Summary of CGI Research Results Characteristics of Teachers CGI Teachers have greater knowledge of their students’ thinking than non-CGI teachers. CGI Teachers have greater knowledge of children’s mathematics than non-CGI teachers. CGI Teachers have greater knowledge of mathematics than on-CGI teachers.

13. Good place to include some of your own data – either student test scores and/or number of teachers in your region who have participated in CGI

14. Levels of Teacher Change Level 1: Traditional Level 2: Problem Poser Level 3: Listener Level 4: Knowledge Integrator

15. Level 1: Traditional Provides few, if any, opportunities for children to engage in problem solving or to share their thinking. When problems are presented to children, teachers explain to children how they are to solve them.

16. Level 2: Problem Poser Provides some opportunities for children to engage in problem solving and/or to share their thinking. May show evidence of beginning to attend to children’s thinking and/or using information about children’s thinking to guide instruction.

17. Level 3: Listener Provides opportunities for children to solve problems and share their thinking. May show evidence of beginning to probe for further information when children share their thinking. May show evidence of beginning to use information about children’s thinking to guide instructional decisions.

18. Level 4: Knowledge User; Integrator Provides opportunities for children to solve a variety of problems, elicits children’s thinking, and provides time for children to fully share their thinking. Instructional decisions are driven by general knowledge about his or her students’ thinking, and/or by knowledge of individual children’s thinking.

19. CGI Research Findings: Teacher Change Teachers needed to both learn the CGI framework and use CGI with students. Teachers who began at levels 1 or 2 took at least two and usually three years to achieve levels 3 or 4. Teachers who grew received both professional development and support from teachers at their schools.

20. CGI Research Findings Follow-up Study of Teacher Change All Level 1 or 2 Teachers : were at level 1 five years later. All Level 3 Teachers : sustained their level of implementation or improved to Level 4. (sustained change) All Level 4 Teachers : grew in their ability to teach math for understanding. (generative change)

21. Overview of Cognitively Guided Instruction Research