This project will compare the effects on algebraic learning when using the Connected Math Program to the effects of using other (non-NSF supported) middle school mathematics curriculum materials at the middle school level. The research questions to be addressed by the project are:
What are the similarities and differences between the intended treatment of algebra in the CMP curriculum and in the non-CMP curricula?
What are the key features of the CMP and non-CMP experience for students and teachers, and how might these features explain performance differences of CMP and non-CMP students?
What are the similarities and differences in performance between CMP students and a comparable group of non-CMP students on tasks measuring a broad spectrum of mathematical thinking and reasoning skills, with a focus on algebra?
The algebra focus skills/concepts to be assessed are: conceptual understanding and problem solving; algebraic manipulative skills; solution strategies, representations and mathematical justifications.
The LieCal Project investigated not only the ways and circumstances under which the Connected Mathematics Program (CMP) curriculum can or cannot enhance middle school students’ learning of algebra-related mathematics, but also the characteristics of the curriculum and implementation that lead to student achievement gains in middle school. CMP is a complete, Standards-based, middle school mathematics program, which was developed with funding from the National Science Foundation. The first three years of the LieCal project were conducted in 14 middle schools of an urban school district serving a diverse student population. The school district had 51 schools that housed grades 6-8, of which 24 were using the CMP curriculum and 27 were using non-CMP curricula. Seven schools were randomly selected from the 24 CMP schools, and then seven of the non-CMP schools were matched to the selected CMP schools on the basis of achievement, SES, and ethnicity. Initially, about 700 sixth grade CMP students in 25 classes and 600 non-CMP students in 22 classes participated in the study. We followed these students as they progressed to 7th and 8th grade. During the fourth year of the project, we continued to follow about 1000 of the 1300 students who had enrolled in 10 of the high schools in the original urban school district. In high school, these CMP and non-CMP students were mixed together in the same mathematics classrooms, and they used the same curricula. The LieCal project was designed to answer the following three sets of research questions. 1. What are the similarities and differences between the intended treatment of algebra in the CMP curriculum and in the non-CMP curricula? 2. What are key features of the CMP and non-CMP experience for middle school students and teachers, and how might these features explain performance similarities and differences between CMP and non-CMP students? 3. What are the similarities and differences in performance between CMP students and a comparable group of non-CMP students on tasks measuring a broad spectrum of mathematical thinking and reasoning skills, with a focus on algebra? Question 1: We found that the CMP and non-CMP curricula are very different. Our analyses of the algebra strands of the CMP and non-CMP curricula used in the LieCal project revealed fundamental differences between the CMP and non-CMP curricula. Overall, we found that CMP curriculum takes a functional approach to the teaching of algebra, while the non-CMP curricula take a structural approach to the teaching of algebra. CMP’s functional approach is built upon the important ideas of change and variation that are inherent in situations and contexts. The structural approach of the non-CMP curricula, on the other hand, moves away from contextual problems and develops students’ ability to generalize, work abstractly with symbols, and follow procedures in a systematic way. Our analysis of the cognitive demand of the algebra problems in the two types of curricula revealed that 71% of the tasks in the CMP curriculum make high-level demands on students’ thinking, but only 21% of the non-CMP make similar high-level demands on students’ thinking. Question 2: We found that the instruction conducted in the CMP classrooms was quite different than the instruction conducted in the non-CMP classrooms. We observed 579 mathematics lessons of more than 50 grades 6-8 LieCal teachers. Approximately half of the observations were of classes using the CMP curriculum and half were of non-CMP classes. We found a significant difference between the percentage distributions of the cognitive demand of the instructional tasks as implemented in the CMP and non-CMP classrooms. We found that the CMP teachers implemented 45% of their classroom tasks in such a way as to make high cognitive demands on their students, but the non-CMP teachers only implemented 10% of their tasks in this way. In addition, we found that CMP teachers emphasized the conceptual aspects of learning significantly more often than the non-CMP teachers. On the other hand, non-CMP teachers emphasized the procedural aspects of learning significantly more often than the CMP teachers. Question 3: We found significantly higher CMP growth on conceptual understanding and problem solving. We administered both multiple choice and open-ended tasks to the students at the beginning of 6th grade, and at the ends of grades 6, 7, and 8. On the open-ended tasks, which assessed conceptual understanding and problem solving, the growth rate for CMP students over the three years was significantly greater than that for non-CMP students. On the multiple-choice tasks assessing computation and equation solving skills, however, the CMP and non-CMP students showed similar growth over the three middle school years. High School Achievement: On the 10th grade state test, high school students who had used the CMP curriculum in middle school performed significantly better than students who had used more traditional curricula in middle school.
