The Mathematical Transitions Project, based at Michigan State University, has closely followed 93 high school and college students for 2.5 years as they moved from a traditional to a Standards -based mathematics or reform calculus program (or vice versa).
We began our work with a weakly conceived central notion: A mathematical transition was a "bump in the road" caused by a mismatch between the student's expectations from past mathematical experience and his/her current experience in a "new" program. "Transition" became our conceptual vehicle for studying the impact of Standards -based curricula.
Given our intent to locate and analyze mathematical transitions, we needed sites where relatively abrupt shifts between reform and more traditionally structured programs took place. We sought these curricular shifts at two major junctures in students' experience (junior high to high school and high school to college). We chose not to examine the elementary to junior high juncture for logistical and pragmatic reasons: We lacked the means to "cover" all three junctures at the same time and focused instead on the high school and college years where the controversy about reform was the most intense.
At the two junctures in our design, we sought schools and colleges with a solid history of using reform materials. At the K-12 level, our search was aided by numerous (though still very spotty) implementations of two Standards -based curricula written in our region--the Connected Mathematics Project materials (CMP) (Lappan, Fey, Friel, Fitzgerald, & Phillips, 1995) for grades 6-8 and the Core-Plus Mathematics Project materials (CPMP) (Hirsch, Coxford, Fey, & Schoen, 1995) for grades 9-12. We located a nearby district where CMP graduates moved into a relatively traditional high school program and another where high school students used the CPMP materials after a relatively traditional junior high program. Two local universities provided complementary college sites. One used materials developed by the Harvard Calculus Consortium (HCC) for all sections of Pre-Calculus, Calculus I, and Calculus II (Connally, et al., 1998; Hughes-Hallett, et al., 1994); the other a more traditional set of texts for these courses (e.g., Thomas & Finney, 1996). At the HCC site we recruited graduates of traditional programs; at the traditional college site, we recruited from a smaller pool of CPMP graduates and also added graduates of a nearby high school that had developed its own mathematics program based on the Standards . Because we wanted to understand these students' mathematical experiences in some depth and over a relatively long period of time, we limited our research design to a single site per cell. These choices produced the following site design matrix (Table 1).
Table 1: Site Design Matrix
| Educational Level |
Type of Curricular Shift |
| Reform to Traditional |
Traditional to Reform |
| Junior high to High school |
HS 1: From CMP to traditional |
HS 2: From traditional to CPMP |
| High school to College |
U1: From CPMP to traditional |
U2: From traditional to HCC |
This curricular shift by educational level design facilitated the exploration of questions and issues as yet unexamined in the impact literature. First, we could analyze the impact of reform on students leaving as well as entering those programs and contrast the resulting patterns. We could also identify factors that could be conflated with impact, but were relatively independent of the reforms. For example, it is reasonable to expect that mathematics becomes more difficult at each successive educational level. If most students at the same educational level (e.g., at both HS1 and HS2) report that mathematics is more difficult after the curricular shift, that would indicate that the difficulty of new content has an impact on students, but not one due to either curricular tradition.
In designing our student sample, other conceptual and methodological decisions (e.g., breadth and depth of our assessment) limited the number of students we could effectively track. We settled on a target 25 students per site, thinking this was large enough to explore both diversity and substantial commonality in students' experience within and across sites. We recruited students in the first semester of their freshman years (9th grade or first year of college). We also systematically observed instructional practice at the two sites where reform curricula were currently being used (HS2 and U2, Table 1) to assess their implementation.
