Supporting Mathematics Teachers in Integrating Rigor Into Assessment Items or Tasks

• In Event: Innovations in Designing, Implementing, and Evaluating Classroom Assessments Based on Learning Theories

Abstract

With the implementation of college and career ready standards, increasing emphasis is being placed on mathematics teachers to increase the level of rigor in both their lessons and assessments. In alignment with the Standards for Mathematical Practice and the NCTM Principles to Actions, this involves a movement from simply asking students to use a correct procedure to get a correct answer to a focus on the solving of complex problems that elicit mathematical reasoning. An emphasis on reasoning is thought to provide multiple benefits to students including helping them to focus on process, building greater confidence in their ability to think mathematically, and preparing them to engage in greater abstraction as they progress through their coursework (Charles & Lester, 1984; McLeod, 1989; Russell, 1999).

A common challenge that teachers face with increasing rigor involves developing an understanding of what features of mathematical items or tasks contribute to reasoning. Especially in recent years, a strong emphasis has been placed on using hierarchical frameworks, such as Webb’s (2005) Depth-of-Knowledge (DOK), for integrating rigor. Despite this, DOK can be difficult to reliably use (see La Torre, 2017, 2018) and is not designed to provide teachers with diagnostic information about student skills and knowledge. Despite this, some recent studies have explored how certain features contribute to the rigor (including cognitive complexity) and difficulty of mathematics items (see Embretson & Daniel, 2008; Peterson & Braeken, 2019).

This presentation will focus on a component of a larger study exploring features of mathematics items that contribute to increased rigor in mathematics items or tasks. It will begin with a discussion of the features of mathematics items and the empirical backings for their inclusion in the study. After that we will briefly present results from the explanatory item response theory models and diagnostic classification models used to assess the contributions of the features to measuring achievement. This analysis uses an empirical data set gathered from a study of formative assessment in 638 students in 36 eighth-grade mathematics classes in Southern California. Finally, we will discuss how the results of this study can be used to help guide the development of classroom or common assessments, and the types of diagnostic information they can provide.

Author

• Deborah M. La Torre, University of California - Los Angeles