Adapting Tasks That Assess Understanding of the Function Concept for Use in a Collaborative Platform

• In Event: The Design of Collaborative Activities Across Disciplines to Promote Student Learning and Agency

Abstract

The concept of function is both central to the study of mathematics and challenging for students to understand (e.g., Sfard, 1992; Vinner & Dreyfus, 1989). Prior research suggests that while many students are comfortable with the notion of using a function to express a pattern, the set-theoretic definition of a function as a mapping between sets is less tractable (Sfard, 1992; Kalchman et al., 2001). In other words, the idea that a function is a relation that maps each element of the domain to a single element of the range is very abstract. For example, many-to-one functions are often rejected as functions (Leinhardt et al., 1990).
The Algebra Project (Moses & Cobb, 2001) is an organization committed to supporting the mathematics literacy of students from historically marginalized communities. The Algebra Project’s Road Coloring curriculum (Budzban & Moses, 2017) emphasizes the concept of function by offering students practice with translating among equivalent function representations such as directed graphs, arrow diagrams, ordered pairs, and matrices.
An important aspect of the implementation of the Road Coloring curriculum is that students typically work on the activities cooperatively in small groups, following a period of individual reflection. The groups then present their results to the class and discussion ensues. The goal of this model is to support the learning of challenging ideas such as the concept of function through collaborative discourse and critique.
ETS and the Algebra Project collaborated to develop a paper-and-pencil assessment consisting of short multiple-choice and constructed response items based on the Algebra Project’s Road Coloring Curriculum. The assessment was originally designed for administration to individuals, however we observed that some of the items lent themselves to collaboration and were ideally suited for administration in EPCAL (Hao et al., 2017). EPCAL is an online collaborative assessment and learning platform that allows students to work together on items in pairs or small groups. Administration of the items within EPCAL is more consistent with the intended implementation of the Road Coloring curriculum activities.
We selected six items from the assessment that appeared most suitable for collaboration. We selected items that 1) involved challenging mathematical reasoning, such as explaining why a particular relation is not a function, or 2) had the potential to be adapted so that some information was unshared (Stasser & Titus, 1985). In the unshared format, each student on a team only has access to a subset of the given item information. However, the union of these subsets provides the necessary information to respond to the item. The unshared item format is used to encourage collaboration.
Prior to administering the items to students via EPCAL, we wish to elicit expert feedback from mathematics teachers on both the items and their instantiation in EPCAL. We have scheduled meetings with five teachers to gather this feedback. This presentation will focus on design considerations in preparing the items for use in an online collaborative platform, suggestions made by the teachers for item and/or platform revision, and how we plan to address these suggestions.

Authors

• Edith Aurora Graf, ETS

• William Crombie, The Algebra Project