who had taught at least one course in mathematics in grades 6-12, participated in the seven-month study. One group consisted of teachers who held either subject area certification or endorsement in mathematics (“in-field teachers”), and the other group consisted of teachers who lacked these credentials (“out-of-field teachers). Both groups of teachers taught the same mathematics course in the same school to students of the same general ability. Pretest scores of students across the different groups did not differ significantly from each other. Researchers proceeded to examine comparative teacher effectiveness by looking at student achievement,2 teacher professional skills,3 and teacher knowledge of the subject field.4

Students taught by in-field teachers scored significantly higher on general mathematics (p< .001) and algebra (p<.01) tests than did students taught by out-of-field teachers. In-field teachers scored significantly higher (p<.001 ) on the test of teachers’ subject matter knowledge than did out-of-field teachers. In-field teachers also scored significantly higher (p<. 001) on the Carolina Teacher Performance Assessment System than did their out-of-field counterparts. No significant differences were observed between the two groups based on years of teaching experience, years of experience teaching mathematics, or level of degree earned. Overall, in-field mathematics teachers knew more mathematics and showed evidence of using more effective teaching practices than did their out-of-field counterparts. Hawk et al. (1985) concluded that certification requirements are an effective mechanism to assure higher student achievement in mathematics.

Also important to this discussion are Ingersoll’s (1999) findings that, nationwide, approximately one third of all secondary school teachers of mathematics have neither a major nor a minor in mathematics, mathematics education, or in such related disciplines as engineering or physics. Similarly, about 20 percent of science teachers lack even a minor in science or science education, and “over half of teachers teaching physical sciences classes (chemistry,


Student achievement was measured with the Stanford Achievement Test (general mathematics) and the Stanford Test of Academic Skills (algebra).


Teacher professional skills were observed for an entire class period twice during the seven-month period by trained observers who used the Carolina Teacher Performance Assessment System (CTPAS). This instrument focuses on five teaching characteristics: management of instructional time, management of student behavior, instructional presentation, instructional monitoring, and instructional feedback. The inter-rater reliability exceeded 90 percent.


Descriptive Tests of Mathematics Skills (arithmetic and elementary algebra skills) were used to measure teachers’ subject matter knowledge.

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