When teachers know what students know: integrating mathematics assessment

Theory Into Practice, Autumn, 2004 by Maryl Gearhart, Geoffrey B. Saxe

3. Developing Mathematical Ideas (DMI) is a professional development seminar program that has a solid mathematics core, while emphasizing action research in the classroom (www.edc.org/ MLT/CDT/DMIcur.html). The program objectives and activities are similar to IMA's, although the program is not linked to specific curriculum, because DMI participants come from a wide range of school settings. The professional development materials are available for purchase on the website. In addition, the project has produced three volumes of action research cases authored by DMI teachers, each case providing a detailed analysis of a teacher's strategy for supporting children's mathematical learning (Schifter, 1996a, 1996b; Schifter & Fosnot, 1993).

The teachers, researchers, and professional developers whose work we just described view 'knowing what students know' as a critical component of effective classroom practice. The core assumption underlying this body of work is that students benefit when their teacher understands the mathematics they are teaching and the sense their students are making of the mathematics. For these educators, assessment is not a particular technology, like end-of-chapter tests, but rather an orientation to instructional practice. The IMA study provides important evidence that, when professional development programs help teachers build the necessary knowledge and a commitment to ongoing assessment, teachers will teach effectively and students will learn.

Notes

(1.) IMA also supported My Travels With Gulliver (Kleiman & Bjork, 1991), a unit on measurement and scale.

(2.) We also provided background on children's academic motivation. See Stipek, Givvin, Salmon, and MacGyvers, (1998) for a description of that component of the IMA program.

(3.) To confirm that we had constructed a test that captured both procedural skill and conceptual understanding, we used statistical techniques (confirmatory factor analysis) to produce two separate scales.

(4.) We analyzed changes in classroom level performance rather than individual student level performance. We took this approach because subsets of children were in the same classrooms and instructed by the same teachers. Thus, student posttest performances within classrooms should be correlated. Therefore, we calculated the classroom means for the two scales for conceptual and procedural understanding. Note that we also used statistical procedures to control for students' primary language.

References

Ball, D.L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90, 449-466.

Ball, D.L. (1992). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 157-195). Hillsdale, NJ: Erlbaum.

Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L., & Empson, S.B. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, N J: Heinemann.