Cognitively Guided Instruction

Guide to Effective Programs
for Children and Youth

COGNITIVELY GUIDED INSTRUCTION

OVERVIEW

The Cognitively Guided Instruction program was a four-week workshop for 1^st grade teachers, intended to provide insight on how children develop addition and subtraction concepts. The workshop did not prescribe specific teaching strategies, but instead gave teachers the opportunity to explore how they might use research on children’s mathematical development to guide their mathematics instruction.

In an experimental assignment study which 40 teachers were randomly assigned to the treatment or control group, the workshop was found to have significant impacts on treatment teachers’ mathematics instruction. The workshop also had impacts for these teachers’ students. Compared with students taught by teachers who did not receive the workshop, students taught by teachers who did receive the workshop were significantly better at solving complex addition and subtraction problems and were more likely to employ appropriate problem-solving strategies when presented with word problems.

DESCRIPTION OF PROGRAM

Target population: 1^st grade teachers

The first half of the CGI workshop was devoted to giving teachers access to knowledge about addition and subtraction word problems and how children think about them. Teachers learned to classify problems and to identify the processes that children use to solve different types of problems.

The remainder of the workshop was devoted to discussing principles of instruction that might be derived from research on children’s problem-solving styles. Teachers were provided with broad principles to guide discussion and questions to consider when planning lessons. They were also familiarized with curricular materials available and were encouraged to evaluate these materials on the basis of knowledge gained at the workshop.

Workshop activities included reading syntheses of research on children’s problem-solving strategies, discussing readings, watching videotapes of children solving problems, and interviewing children. Teachers were given a great deal of freedom to focus on those activities important to them and to plan for future instruction.

EVALUATION(S) OF PROGRAM

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C., & Loef, M. (1989). Using Knowledge of Children’s Mathematical Thinking in Classroom Teaching: An Experimental Study. American Educational Research Journal, 26(4), 499-531.

Evaluated population: 40 1^st grade teachers and their students served as the study sample for this investigation. Teachers came from 24 schools in the Madison, Wisconsin area. 22 of the schools were public; 2 were Catholic. On average, participating teachers had been teaching for 11 years and had been teaching 1^st grade for 6 years. None of the teachers had received any prior training on addition and subtraction problem-solving research. 12 students were selected at random from each teacher’s class to serve in the study sample. Students with special learning needs were not selected to be a part of the sample.

Approach: Teachers were randomly assigned, by school, to either the treatment group or the control group.

Teachers assigned to the treatment group took part in the Cognitively Guided Instruction workshop. The workshop was run during teachers’ summer vacations and was taught by the two program developers and three of their graduate students. It involved five hours of participation each day, four days a week, for four weeks. Treatment group teachers were provided with a program contact person with whom they could discuss questions that developed over the course of the school year.

Teachers assigned to the control group received four hours of instruction on non-routine problem solving. Instruction occurred at the beginning of and midway through the school year. Instruction did not deal with how children think when they solve problems.

Math instruction in study classrooms was observed throughout the school year. Students completed standardized mathematics assessments at the beginning and end of the school year. Teachers also completed a series of measures at these timepoints.

Results: Teachers assigned to receive the Cognitively Guided Instruction workshop spent significantly more time teaching word problems than did control teachers. CGI teachers also spent significantly less time on number facts. CGI teachers were more likely to pose problems to students and focused more on students’ problem-solving processes and less on their answers than did control teachers. CGI teachers also allowed their students to employ a greater variety of problem-solving strategies than did control teachers.

Students in CGI classrooms did not perform better than students in control classrooms on a standardized test of computational abilities; however, they did have a higher level of recall of number facts when interviewed. Students in CGI classrooms did not perform significantly better than students in control classrooms on a test of simple addition and subtraction problems (perhaps because scores were near the ceiling. An interaction analysis found CGI in low-achieving classrooms did gain more by the post-test), they did perform better on a test of complex addition and subtraction problems. Additionally, CGI students more frequently employed correct problem-solving strategies when given word problems in interviews.

Students in CGI classrooms reported greater confidence in their ability to solve math problems than did students in control classrooms. CGI students did not significantly differ from control students in reports of how often they paid attention during math class.

SOURCES FOR MORE INFORMATION

Curriculum materials available for purchase at:

http://my.nctm.org/ebusiness/ProductCatalog/product.aspx?ID=706

References:

Program categorized in this guide according to the following:

Evaluated participant grades: 1^st

Program age ranges in the guide: Middle Childhood

Program components: School-Based

Measured outcomes: Educational Achievement

Program information last updated on 11/15/07.