Understanding and supporting teacher horizon knowledge around limits: a framework for evaluating textbooks for teachers

ABSTRACT

As part of recent scrutiny of teacher capacity, the question of teachers’ content knowledge of higher level mathematics emerges as important to the field of mathematics education. Elementary teachers in North America and some other countries tend to be subject generalists, yet it appears that some higher level mathematics background may be appropriate for teachers. An initial examination of a small sample of textbooks for teachers suggested the existence of a wide array of treatments and depth and quality of mathematics coverage. Based on the literature, a new framework was created to assess the mathematical quality of treatments for both specialized knowledge and horizon knowledge in mathematics textbooks for teachers. The framework was tested on a sample topic of the circle area formula derivation, chosen because it draws heavily on both specialized and horizon knowledge. The framework may contribute to similar analyses of other topics in a broader range of resources, in the overall quest to better describe the details of what constitutes appropriate mathematics horizon knowledge for teachers.

KEYWORDS:

• Textbooks for teachers
• teacher horizon knowledge
• evaluating textbooks for teachers

Acknowledgments

The authors are most grateful to Jennifer Holm for her assistance with this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The expression ‘area of a circle’ is inaccurate, since a circle is a curve and has no area (it has length however, and thus the phrases ‘circumference of a circle’ or ‘perimeter of a circle’ are mathematically accurate). It is correct to say ‘area of a disk’ and ‘area of the region bounded by a circle.’ However, since the phrase ‘area of a circle’ is very often used both in written and oral communication, including in the curriculum in question, we continue to use this phase here, given the disclaimer just noted.