Academic journal article The Mathematics Enthusiast

Assessing Mathematical Knowledge for Teaching: The Role of Teaching Context

Academic journal article The Mathematics Enthusiast

Assessing Mathematical Knowledge for Teaching: The Role of Teaching Context

Article excerpt

Introduction

Mathematical Knowledge for Teaching (MKT) is the content knowledge used in recognizing, understanding, and responding to the mathematical problems and tasks encountered in teaching the subject (Ball & Bass, 2002; Ball, Thames & Phelps, 2008). Assessments of MKT are designed to measure the mathematical knowledge that teachers use in these teaching practices. A number of practice-based assessments of MKT have recently been developed for teachers of K-12 grades (Herbst & Kosko, 2014; Hill, Ball, & Schilling, 2008; Hill, Schilling, & Ball, 2004; Kersting, 2008; Krauss, Baumert, & Blum, 2008; McCrory, Floden, Ferrini-Mundy, Reckase, & Senk, 2012; Phelps, Weren, Croft, & Gitomer, 2014; Tatto et al., 2008).

We follow Ball, Thames, and Phelps (2008) in defining MKT to include the full range of mathematics content knowledge used in teaching. The most widely assessed component of MKT is the common content knowledge that is taught and learned as part of regular schooling and is familiar to most adults. There is a long history of assessing teachers' common mathematical knowledge (Hill, Sleep, Lewis, & Ball, 2007). Often these assessment tasks look identical to those on student assessments because the construct is essentially the content of the student curriculum, either at grade level or at a level above the assigned grade (Phelps, Howell, & Kirui, 2015).

MKT assessments have generally focused, however, on the specialized forms of content knowledge that only teachers need to use in the course of their day-to-day work (Ball et al., 2008). While definitions and focus vary in the literature, and the mapping of the MKT construct is likely somewhat dependent on curriculum and culture, most studies share a focus on MKT as a form of applied knowledge that goes beyond common content knowledge (Krauss et al., 2008; McCrory et al., 2012; Thompson, 2015; Turner & Rowland, 2008). MKT assessments typically present teachers with content tasks that are encountered in teaching, such as interpreting student thinking and work, selecting materials for instruction, explaining concepts and procedures, or evaluating whether to use a representation for a particular instructional purpose (Ball & Bass, 2002; Hill et al., 2004). And since these tasks often occur in complex instructional contexts, MKT assessments typically also provide key information about the teaching context, such as the learning goals that direct the teaching, details about a student's prior academic work, or how students are grouped and organized (Phelps et al., 2015). Assessments of MKT differ in how teaching practice is represented. Some provide written descriptions, while others incorporate video or animations depicting mathematics teaching (see, for example, Herbst & Kosko, 2014; Hill et al., 2004; Kersting, 2008). These features of context support test takers in recognizing the relevant aspects of the content task, understanding the content problem, or providing a response to the assessment question.

This contextualization of MKT assessment tasks is in part theoretically motivated. Ball and Bass (2002) argue that how teachers encounter mathematics in their teaching directly shapes the nature of the mathematical knowledge that is needed. The context used in many MKT assessment tasks defines both what kinds of content knowledge teachers need to use and how they use this knowledge. Largely missing, however, from the current literature on MKT assessment are well-articulated design arguments that make clear the links between the construct and assessment task design (Mislevy & Haertel, 2006). Given the central role of teaching in MKT, it seems likely that any endeavor to assess MKT would require consideration of how context functions in the design of MKT tasks (Phelps et al., 2015).

In this study, we take the first steps in this direction by presenting arguments and illustrations for how context functions in a set of elementary-level MKT assessment tasks, with a particular focus on how context enables tasks to measure MKT that goes beyond common content knowledge. …

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