Validating Measures of Algebra Teacher Subject Matter Knowledge and Pedagogical Content Knowledge

Abstract

The purpose of this study was to validate inferences about scores of one task designed to measure subject matter knowledge and three tasks designed to measure aspects of pedagogical content knowledge. Evidence for the validity of inferences was based on two expectations. First, if tasks were sensitive to expertise, we would find group differences. Second, tasks that measured similar types of knowledge would correlate strongly, and tasks that measured different types of knowledge would correlate weakly. We recruited and assessed 4 groups of participants including 46 experienced algebra teachers (2+ years experience), 17 novice algebra teachers (0–2 years experience), 10 teaching experts, and 13 subject matter experts. Results indicate that one task differentiated among levels of expertise and measured several aspects of knowledge needed to teach algebra. Results also highlight that future studies should use a combination of tasks to accurately measure different aspects of teacher knowledge.

Notes

^a n = 13.

^b n = 10.

^c n = 17.

^d n = 46.

^a n = 13.

^b n = 10.

^c n = 17.

^d n = 46.

^a n = 13.

^b n = 10.

^c n = 17.

^d n = 46.

^a n = 13.

^b n = 10.

^c n = 17.

^d n = 46.

^eGroup differences between subject matter experts and nonexperts (experienced teachers and novice teachers) exist at p > .05 (two-tailed).

^fGroup differences between pedagogical content expert experts and nonexperts (experienced teachers and novice teachers) exist at p > .05 (two-tailed).

**p > .01 (two-tailed).

*p > .05 (two-tailed).

**p > .01 (two-tailed).

*p > .05 (two-tailed).

**p > .01 (two-tailed).