Exploring Student Response and Chat Data Through the Lens of the Function Concept Learning Progression

• In Event: Advancing Equity in Assessment Through Small-Team Collaboration in Mathematics

Abstract

Objectives
A learning progression (LP) is usually empirically validated by examining the alignment between the observed difficulties of items and the ordering of levels proposed by the LP (e.g., Confrey et al., 2009; Deane et al., 2012; Duschl et al., 2011). In addition to looking at the alignment between items and levels, our objective is to analyze process-level data through an LP lens; specifically, we are interested in how student’s text-based chats about mathematics tasks provide evidence on the development of thinking with respect to an LP.
Theoretical Framework
A learning progression is a model of how student thinking about a particular topic develops, from early intuitions to the target understanding (e.g., Smith et al., 2004; Corcoran et al., 2009). The purpose of an LP is not to sort students into ability groups. Rather, the purpose is to acknowledge what students already know with the goal of supporting further learning. In earlier work, we developed a LP for the concept of function (Authors, 2021; Authors, 2021), which guided the development of tasks that students respond to and discuss in a text-based chat.
Methods
On Days 1, 2, and 4, students responded individually to their assigned pair of tasks. The small team collaboration took place on Day 2. On Day 2, 12 facilitated teams and 8 unfacilitated teams participated.
Data Sources
Our data sources consist of 1) response data to three pairs of near-transfer tasks from Days 1,2, and 4 focused on the concept of function, and 2) chat log data reflecting the small-team discussion about the same tasks for which we collected responses.
Analysis
Rubrics were created that map possible student responses to levels of the LP. The next steps are that two members of the research team will independently 1) score the response data with respect to the rubrics, and 2) code the chat text through the lens of the LP by using a coding framework adapted from the rubrics. We will compare performance with respect to the LP between the two individual phases and the small-team collaborative phase; in addition, we will compare LP performance between facilitated and unfacilitated teams on each of Days 1,2, and 4. Finally, we will qualitatively examine how student ideas evolve with respect to the LP in the chat.
Scholarly Significance
To our knowledge, there is little scientific work about the application of LPs to student group work, and how student thinking with respect to an LP develops as students engage in mathematical discourse in text chat. Offering students the opportunity to discuss mathematics tasks and to learn from each other supports student agency in the doing of mathematics. Traditional assessments may not adequately elicit evidence for what students know and can do, especially when they collaborate. Through this work, we hope to elevate the voices of all students, especially students who may not have demonstrated the full depth of their understanding on traditional assessments.

Authors

• Edith Aurora Graf, Educational Testing Service

• Cheryl L. Lizano, Southern Illinois University - Edwardsville