Measuring Knowledge and Motivation for Teaching Multidigit Arithmetic: Evidence of Elemental, Structural, and Ecological Validity

• In Event: Argument-Based Approaches to Measure Validation Situated in Mathematics Education

Abstract

Purpose
The mathematical proficiency for teaching framework (Author, 2013) identifies a multifaceted goal for elementary preservice teacher education: integrated knowledge and productive disposition for teaching. Research on how teacher education influences mathematical proficiency for teaching is difficult because existing measures differ in focus and scope. The purpose of the study was to develop a coordinated measure of knowledge and motivation for teaching multidigit arithmetic. We report validity evidence for the novel measure.

Framework
In an argument-based approach to validity, various forms of evidence are used to support argument-based inferences regarding score interpretation and use. Specifically, we address three aspects of validity: elemental, structural, and ecological (Schilling & Hill, 2007). The elemental aspect concerns the items (i.e., content validity); the structural aspect concerns how items are combined in subscales; and the ecological aspect concerns how the measure is related to the context of use. For each aspect, we discuss theory-based assumptions, articulate inferences based on these assumptions, and assess empirical evidence to support the inferences.

Methods, Data, and Results
Elemental. We assumed the items reflected the target constructs, not extraneous factors. We inferred that knowledge would correspond with item responses, and used 60-minute think-aloud interviews (n = 15) to confirm. We also inferred that experts would judge the knowledge and motivation items to be consistent with the construct, and surveyed 8 experts to assess this inference.
Structural. We assumed items would form unidimensional scales for each construct, and furthermore that the motivation items would be more closely related with each other than with the knowledge items. Therefore, we inferred that the items for each scale were unidimensional. We also inferred that a model with the hypothesized structure would better fit the data than competing models. We used data from two survey administrations (n = 169) to confirm these inferences.
Ecological. We assumed that the measure was sensitive teacher education and appropriately related to other constructs. Thus, we inferred PSTs knowledge and motivation would increase during a methods class, and used pre-post surveys of 33 PSTs to confirm. We also inferred that knowledge was correlated with conceptions of multidigit number (Thanheiser, 2009) and that motivation was correlated with teaching self-efficacy beliefs (Tschannen-Moran & Hoy, 2001), and used survey data (n = 114) to confirm.

Significance
The validity evidence for the novel measure suggests that it accurately reflects the intended constructs for the intended use. Thus, continued use of the measure to investigate teacher education within the MPT framework is justified.

Authors

• Erik D. Jacobson, Indiana University - Bloomington

• Dubravka Svetina, Indiana University - Bloomington