By Erin Moss, Co-Editor, DUE Point, Millersville University

The Promoting Mathematical Reasoning and Transforming Instruction in College Algebra project helps instructors use digital activities to facilitate a shift in classroom emphasis from simple answer-finding to mathematical reasoning. The project specifically focuses on high-enrollment lower-division undergraduate mathematics courses like college algebra, where such a shift can provide a significant benefit. Below, Principal Investigator Dr. Heather Johnson tells us more about this intervention and the corresponding research that project personnel are conducting.

Please tell us more about the scope and context of your work.

This project establishes a partnership between the University of Colorado Denver, Metropolitan State University of Denver, Santa Fe Community College, and Texas State University. These institutions have a range of size and focus, and serve large populations of students of color and first-generation college students.

We invite college algebra instructors to implement digital activities to foster students’ reasoning around functions and graphs, key ideas in this course. Alongside the implementation, instructors participate in a professional development, in which they examine the place (Where do they fit?), purpose (Why use the activities?), and process (How can we facilitate students’ reasoning?) for the activities. After the professional development, instructors can continue implementation with a community of instructors across institutions.

Can you describe for readers some of the digital activities that have been developed for implementation in college algebra courses?

Project co-investigator Gary Olson blended “technology” and “activities” into the single term “techtivities” to describe what we have created. These are classroom activities created in the freely available Desmos platform. Each Techtivity involves a situation shown in a video animation, such as a toy car moving around a track. Given two attributes in the animation (e.g., a toy car’s total distance traveled and its distance from a stationary object, such as a small shrub), students explore change in each attribute, and then sketch a graph to represent one relationship between those attributes. Next, students sketch a different looking graph to represent the same relationship (with the attributes on different axes). Finally, there is a reflection question, in which students respond to a hypothetical student’s comment about one or more of the graphs in the activity.

There are currently seven Techtivities, housed in a collection called “How Graphs Work.” We are in the process of updating these activities and adding new ones to take advantage of new features available in Desmos, and to include contexts and ideas beyond the current set.

What features of Techtivities are important for helping increase students’ mathematical reasoning?

Working on the Techtivities can help students to form and interpret relationships between variables. They can connect those relationships to graphs in the Cartesian plane, and they can reflect on how they make sense of those graphs. Students encounter graphs that may be different from ones they are familiar with, and this can make room for students to ask their own questions. For example, why does one graph have sharp points while another has smooth curves? In fact, instructors have told us that they explored these questions in their own work with the Techtivities.

A second benefit of the Techtivities is students’ reasoning related to the Cartesian coordinate system. By sketching two different graphs to represent the same relationship, students are more likely to pay attention to the attributes represented on each axis. This can inform their interpretation of graphs in the media, and provide them with tools to critique such graphs as educated citizens.

How do you help faculty learn to engage in instructional practices that allow them to effectively implement Techtivities in their courses?

We know that instructional change requires more than individual efforts. It happens when systems change. Hence, we have designed and are developing project-wide and institution-specific resources. For example, there are facilitation guides to support in-person implementation and modules in a shared learning management system (Canvas) to support asynchronous online implementation. Furthermore, there are local resources in departments across institutions, so instructors can connect around practice.

The resources address instructors’ power in the classroom to promote student reasoning and provide actionable suggestions through which instructors can amplify students’ voices in the classroom. For example, in Desmos, instructors can anonymize students’ responses, which encourages sharing of ideas.

There is a research component to your project as well as the design aspect. Can you share some of your research questions and some preliminary results?

We are investigating how instructors adopt, and later sustain, instructional practices to promote students’ reasoning. To examine this question, we are analyzing data sources at the instructor and project level. These include video recordings of classroom lessons and instructor interviews, student responses to the Techtivities and/or prompts in the online modules, and video recordings/field notes from project and professional development meetings.

The role that the Techtivities play in the classroom matters. It is known that if they are an add-on and instruction remains “business as usual,” they are less likely to make an impact. When instructors legitimize the status of the Techtivities as well as the practices around the Techtivities, their influence is strengthened. This legitimizing can happen when instructors transition meaningfully between students’ work on the Techtivities and other work during the class.

Learn more about NSF DUE 2013186

Full Project Name: Promoting Mathematical Reasoning and Transforming Instruction in College Algebra

Abstract: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2013186

Project Contact: Dr. Heather Johnson, PI; heather.johnson@ucdenver.edu; Twitter: @HthrLynnJ

Project Website: https://itscritical.cu.studio/