**ERIC Number:**EJ907315

**Record Type:**Journal

**Publication Date:**2010-Nov

**Pages:**10

**Abstractor:**ERIC

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**ISSN-1073-5836

What Math Knowledge Does Teaching Require?

Thames, Mark Hoover; Ball, Deborah Loewenberg

Teaching Children Mathematics, v17 n4 p220-229 Nov 2010

No one would argue with the claim that teaching mathematics requires mathematics knowledge. However, a clear description of such knowledge needed for teaching has been surprisingly elusive. To differentiate teachers' levels of mathematical knowledge, numerous studies have examined whether a teacher has a certification in math or a degree as well as the number of math courses taken. But analyses of the correlations between these indicators and students' achievement gains reveal no advantage at the grades K-8 level and only slight advantage at the secondary level. These studies, carried out over the past forty years, do not contradict the assertion that mathematical knowledge matters for teaching math, but they do suggest that conventional content knowledge is insufficient for skillfully handling the mathematical tasks of teaching. Although it seems that majoring in math should provide an edge in teachers' capacity, it simply does not at the grades K-8 level, and it is an uneven predictor at the high school level. So what "do" teachers need? Intrigued by the problem of identifying the mathematical knowledge and skill that actually contribute to student learning, the authors and their colleagues at the University of Michigan directly studied the work of teaching to uncover the mathematical issues that arise in practice. They found out that teaching is not merely about doing math oneself, but about helping students learn to do it. This is challenging and requires specialized, skilled ways of knowing the domain. Examining practice itself--from planning lessons to using textbooks, leading a discussion, using the board carefully, and choosing examples--reveals the mathematical demands of the work, which are often overlooked. Identifying these demands allows the identification of the mathematical knowledge needed for teaching. Mathematical knowledge does matter for teaching. But it is not a mathematical expertise like that required for research in mathematics or for other kinds of quantitative work. Instead, mathematical knowledge for teaching is a kind of complex mathematical understanding, skill, and fluency used in the work of helping others learn mathematics. (Contains 5 figures and a bibliography.)

Descriptors: Mathematics Education, Textbooks, Achievement Gains, Mathematics Instruction, Mathematics, Academic Achievement, Higher Education, Pedagogical Content Knowledge, Faculty Development

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers - Location:**Michigan