Cognitively Guided Instruction in Mathematics

1. Cognitively Guided Instruction in Mathematics Presented to the Oelwein CSD Board of Education by the Harlan 2nd Grade Team.

2. What is CGI? • CGI focuses on developing students’ mathematical thinking skills through instruction. • Instruction is based on each teacher’s understanding of her students’ mathematical thinking skills. • The goal is to move students through a hierarchy of cognitive development through the use of a variety of strategies.

3. Professional Development • Teachers attend various meetings throughout the summer and school year. • Teachers are learning different strategies, as well as how to challenge students without frustrating them. • Harlan teachers applied and were chosen to participate in CGI, which is funded completely by the AEA.

4. Training • Original training was presented by Annie Keith, a co-author of the book used for this course. • AEA sends a representative to Harlan school twice a month to provide support and observe teacher implementation of CGI. • A total of 32 teachers were accepted from Northeast Iowa to participate. 6 teachers are from Harlan Elementary School.

5. Why CGI? • Teachers gain understanding of students’ cognitive abilities. • Students learn a variety of problem-solving strategies from other students. • Students are actively engaged in exploring various strategies. • Even struggling students are beginning to look forward to math class.

6. The Process • Students are given a story problem to solve. • They solve the problem using any strategy. Students are encouraged to think of more than one strategy. • Several students are chosen to share their solutions and strategies with the class. • Sometimes differentiated instruction is utilized in creating story problems to meet the individual needs of each student.

7. CGI involves a “sharing out process”, where students become teachers.

8. Students are motivated by the desire to be involved in the sharing out process. They attempt to come up with different strategies for each problem, instead of just one “right” strategy.

9. Solution Strategies Chart

10. Student Work Sample This student began with direct modeling, by drawing tens and ones cubes. The second strategy involved an addition sentence, which required the student to count by tens to find an answer. The third strategy allowed the student to use number facts and basic knowledge of Base 10 to quickly and easily solve the problem. This student’s overall cognitive abilities would be classified as “average.”

11. Student Work Sample This student used direct modeling by drawing a picture to illustrate the four groups of ten and the extra five cookies. The second explanation describes counting by tens to solve the problem. This student’s overall cognitive ability would be classified as high-average.

12. Student Work Sample This student used the direct modeling strategy to draw a picture of five groups of ten and six extra pieces. This student’s overall cognitive ability would be classified as low. This work sample also illustrates differentiated instruction, as each student is often able to choose his/her own numbers to use in the problem.

13. Data • We collected baseline data from the students and analyzed it at our first CGI training session of the school year. • We will collect and compare data on the same problems to analyze at our May session. • We also expect to see improvements in the problem solving section of ITBS.

14. Conclusion • We believe that CGI has been beneficial for both students and teachers in the classroom. • Teachers have raised expectations for all students in math problem solving. • We believe that students in Oelwein Community School district would benefit from 2-3 consecutive years of CGI, perhaps in grades 1-3.