2.  Constructed response scores on MCA’s?  The use of differentiated instruction in the area of mathematics?

4.  Cognitively Guided Instruction is a professional development program based on over 20 years of research. Developed by education researchers Thomas Carpenter, Elizabeth Fennema, Penelope Peterson, Megan Loef Franke, and Linda Levi. Using this program teachers learn how children develop knowledge of number sense, operations, and algebra. CGI teachers study how their children think about mathematics and how children, in general, understand mathematics.

5.  Children bring an intuitive knowledge of mathematics to the classroom. This knowledge should serve as the basis for developing formal mathematics instruction and the assessment of the processes students use to solve problems.  Mathematics instruction should be based on the relationship between computational skills and problem solving. This idea leads to an emphasis on problem solving in the classroom instead of the repetition of number facts.

6.  Step One: › Write a problem that has relevance to your students

7. The School Board Conference Room has 13 types of ice cream cones. They also have 24 flavors of ice cream cones. How many different combinations of ice cream cones can you get at your next school board work session?

8.  Provide materials for recording thinking and manipulatives for counting.  Have students attempt to solve the problem. Encourage them to use pictures, tallies, number lines, 100’s charts, equations and graphs to solve the problem.  While students are working, walk around the room observing and questioning.

9.  SHARE, SHARE, SHARE!!! Record student solutions on white board, or use an ELMO and LCD projector.  Emphasize that different methods of finding an answer are positive, and that there is no RIGHT way if students arrive at the same answer.

10.  Students work at their level of understanding.  Students are not restricted to one method of problem solving.  Students learn peers methods of problem solving and implement them in their own work.

11.  The Carpenter et al. (1989) study of 20 CGI teachers and 20 control teachers found the following: › CGI students scored significantly higher than control students on the complex mathematics addition and subtraction portion of the ITBS; with a mean score of 8.6, compared with 7.8, out of a possible score of 12. › Similarly, CGI students scored significantly higher than control students on the ITBS problem-solving interview, with an average score of 5.61 versus 5.38, out of a possible score of 6. › CGI students also significantly outscored controls on the ITBS number-facts problem scale, with a mean score of 2.26 versus 0.78, out of a possible score of 5. http://www.promisingpractices.net/program.asp?progr amid=114#findings

12.  Villasenor and Kepner's (1993) study of 144 CGI students and 144 control students reported: › CGI students scored significantly higher than control students on the written problem-solving test (9.41 versus 3.18, out of a possible score of 14). › CGI students significantly outscored control students on the word problems portion of the interview (5.44 versus 2.93, out of a possible score of 6). › The CGI students also scored significantly higher than control students on the number-facts section of the interview (4.68 versus 3.00, out of a possible score of 5).

13.  Increased Scantron Scores  Improved Constructed Response Scores  Creative Problem Solving Skills  Student Confidence  Verbal Skills  Computation