Co-Principal Investigators: Mitchell Nathan, Voicu Popescu, Nicoletta Adamo-Villani (Purdue University); Susan Cook (University of Iowa)

Purpose: Mathematical ideas are connected to and build upon other mathematical ideas. Understanding these connections is fundamental to having a deep conceptual understanding of mathematics. This project will build on previous IES-funded research (Does Visual Scaffolding Facilitate Students' Mathematics Learning? Evidence From Early Algebra) that focused on exploring how mathematics teachers make connections between ideas during middle school lessons in beginning algebra. The purpose of this current project is to test hypotheses about how to most effectively link ideas in algebra instruction. The research team will use GALE (Gesturing Avatar for Learning and Education), a software-based system that includes a human-like avatar teacher who can speak, gesture, and write, as a test bed for understanding which ways of communicating about connections among ideas are most effective for fostering student learning in mathematics.

Project Activities: The research plan has three aims. Aim 1 will be to adapt an existing software system/avatar (GALE) to serve as a test bed for hypotheses about linking mathematical ideas in early algebra. To accomplish this, the researchers will adapt GALE, originally developed  to create elementary mathematics learning activities for deaf children. After implementing the new system, the researchers will conduct a system usability study and will make any necessary revisions and improvements. The researchers will address Aims 2 and 3 with a series of experiments where students will learn about linear equations and polynomial multiplication. Aim 2 will be to determine how to most effectively use gestures and speech to link ideas in early algebra instruction. Aim 3 will be to test whether avatar-based linking instruction can be used as a tool to help teachers improve their algebra instruction.

Products: The products of this project will be the preliminary identification of effective ways of linking ideas in instruction, which can be used in the development of future interventions.  Peer-reviewed publications will also be produced.

Structured Abstract

Setting: Participating middle schools will be located in towns in Wisconsin and Iowa. Research will also be conducted at the researchers’ laboratories at the University of Wisconsin, Madison and the University of Iowa.

Sample: Participants will be recruited for five pairs of experiments. For each pair of experiments, participants will be between 90-180 sixth- or rising seventh-grade students and 90-180 seventh- or rising eighth-grade students. In addition, two experiments will also include six pre-service teachers recruited from the mathematics teacher education program at University of Wisconsin, Madison.

Intervention: This work investigates the malleable factor of making connections through multimodal instruction, and explores its relation to learning outcomes in algebra. The findings from these studies will inform the development of future interventions to improve curriculum design, teacher education, and instructional practices.

Research Design and Methods: The researchers will accomplish three aims.  For Aim 1, the research team will adapt the GALE system so that it can be used to conduct experiments in which mathematics lessons are presented by an animated teacher avatar. They will test the system through expert guideline-based evaluation, formative user-centered evaluation, and iterative intervention refinement. After successfully accomplishing Aim 1, the researchers will address Aims 2 and 3. Under Aim 2, the researchers will conduct experiments to determine how to most effectively use gestures and speech to link ideas in early algebra instruction. Under Aim 3, the researchers will evaluate whether avatar-based linking instruction can be used as a tool to help teachers improve their algebra instruction. Within Aims 2 and 3, the researchers will conduct a pair of experiments to address each research question: one experiment will use linear equations and sixth- or rising seventh-grade students and one will use polynomial multiplication and seventh or rising-eighth grade students. All experiments conducted under Aims 2 and 3 will use a between-subjects design, where each student will be randomly assigned to only one learning condition, and will use the pretest-lesson-posttest method.

Control Condition: The control or comparison condition will vary across experiments as a function of the research question being addressed.

Key Measures: The key measures will be researcher-designed pre-tests and post-tests, which will be designed to assess students’ knowledge of the target concepts. Researcher-designed questionnaires will be used to measure other aspects of the instructional conditions. Think-aloud data will be collected during pre-tests and post-tests for a subset of participants.

Data Analytic Strategy: Across all experiments, individual students’ pre-test and post-test performance will be compared. The pre-test will be used as a covariate to account for the different baselines of individuals before instruction. The data will be analyzed using multi-level logistic models. The researchers will also use a structural equation modeling framework to look for potential mediators and moderators of student learning.

Related IES Projects: Does Visual Scaffolding Facilitate Students' Mathematics Learning? Evidence From Early Algebra (R305H060097)

Products and Publications

Proceeding

Anasingaraju, S., Wu, M.L., Adamo-Villani, N., Popescu, V., Cook, S.W., Nathan, M., and Alibali, M. (2016). Digital Learning Activities Delivered by Eloquent Instructor Avatars: Scaling With Problem Instance. In SIGGRAPH ASIA 2016 Symposium on Education. Macao, Macao: Association for Computing Machinery (ACM).