How Much Math Does a Teacher Need to Know to Teach Math?
I once asked a colleague if he’d read a particular book. “Read it?” he replied incredulously. “I haven’t even taught it!” A former college English professor, he came by the joke honestly. The first time I taught a course that I had never taken myself, I acknowledged the absurdity, at least to myself. I stayed about a week ahead of my students. Out-of-field teaching? Not exactly. I was teaching a course that was in my field, but outside of my immediate area of expertise. The teaching assignment was justified on the grounds that, as a Ph.D.-holder, I was deeply grounded in the core theoretical perspectives and research traditions in my discipline, and that I could therefore pick up the literature in a subfield quickly and accurately, and teach that literature competently. (At the time, no one was concerned with pedagogical content knowledge, the idea that there is practical knowledge of how to teach a subject that differs from mastery of the subject itself.)
Last week, the National Council on Teacher Quality released a report on the mathematics preparation of elementary school teachers who teach mathematics. The report indicts education schools for failing to select and prepare elementary teachers who have an adequate mastery of mathematics. Singling out algebra as a topic that is shortchanged in preparation programs, the authors offer a number of sensible recommendations for states, education schools, textbook publishers, and institutions of higher education.
The Teacher Education and Development Study in Mathematics (TEDS-M), a comparative study of how 18 countries, including the U.S., prepare mathematics teachers at the primary and lower secondary grades, is currently underway under the auspices of the International Association for the Evaluation of Educational Achievement. We’ll learn a great deal from this study that will complement the NCTQ recommendations.
It seems obvious that teachers must have knowledge of the subject matter they will actually teach. But how much more knowledge should a teacher have than what she or he is seeking to assist students in learning? The case of secondary school mathematics is instructive. Is it enough for a high school trigonometry teacher to know trigonometry cold – but not, say, real analysis, or ordinary differential equations?
In the US, many states have content specialty tests that prospective teachers must pass prior to assuming full-time teaching positions; presumably these tests tell us something about the mathematical content that states think is important for teachers to master. The four-hour Massachusetts test covers number sense and operations; pattern relations, and algebra; geometry and measurement; data analysis, statistics, and probability; trigonometry, calculus, and discrete mathematics; and integration of knowledge and understanding. Approximately 23% of the test is devoted to patterns, relations, and algebra, and there are 100 multiple-choice items and two constructed-response items. From tests such as these, we can infer that some states do not demand that high school math teachers have an extensive understanding of the discipline of mathematics.
One of the reasons I was unhappy with much of the press reporting on the Urban Institute’s study of Teach for America teachers’ effects on end-of-course tests in Algebra I, Algebra II, and Geometry (among other subjects) in North Carolina is that it shifted the locus of policy discussion to whether to expand alternate routes to teacher certification, without addressing the more challenging questions about what knowledge about subject matter and about how to teach it is optimal for student learning in particular subjects in high school. The reality is that even if we could count on the incremental achievement observed in the Urban Institute study, lots of other countries would still be kicking our butts in international assessments of mathematics and other subjects. I think we’d be better off examining how these countries prepare secondary math teachers – and teachers in other subjects – to see if there are approaches that we can adapt to the U.S. context. One thing that we might learn is that other countries demand much higher levels of subject matter competence from their elementary and secondary school teachers than we do.