AERA 2017 Poster: Teaching and Learning Algebraic Thinking Across the Middle Grades Using PhET Interactive Simulations

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Objectives: This project aims to develop an integration of resources, models, and tools that overcome the tendency for superficial use of computer simulations and enable more mathematics teachers to: (1) Truly leverage the affordances of simulations, (2) Integrate them into their core instruction, and (3) Create learning environments aligned with research-based teaching practices and principles.

Perspective: Tools such as computer simulations mediate how learners engage with and construct their understanding of the mathematics content. These tools also influence how activities can be structured, how teachers interact with students, and how students interact with each other.

Methods: This project asks questions related to both sim design and classroom use. For reasons of length, we focus here on questions regarding classroom use in Year 1: (1) Regarding different possible models of sim-based mathematics instruction, (a) What are the instructional models teachers use to engage students in PhET sims? (b) How do these models align along a continuum from transmissive to ambitious instruction? (c) How does student sim activity map onto these instructional models? (2) Regarding the play phase of sim-based lessons, (a) How do characteristics of play vary across sim-based mathematics lessons? (b) What are the implications of these variations for the competing priorities of valuing students’ thinking and addressing predetermined learning goals? (3) Regarding the positioning of sim use in mathematics lessons, (a) What are the different ways that teachers position sim use in their classrooms? (b) How do these positions relate to the SAMR model of technology integration? (c) How does this positioning relate to teachers’ pedagogical beliefs about sims and content coverage?

Data Sources: The primary data sources for Year 1 are a set of 15 video recordings of sim-based mathematics lessons taught in middle-school classrooms, copies of student activity sheets from those lessons, and video recordings of end-of- year interviews with 3 teachers.

Results: Regarding Research Question 2, we identified and coded for 4 dichotomous characteristics of play, which enabled us to identify 3 distinct profiles of the play phase of sim-based lessons. We analyze these profiles in terms of the competing priorities of valuing student thinking versus keeping pace. We theorize that one of these profiles best achieves a balance between those priorities. We characterize teachers’ facilitation of the play phase as a process consisting of divergent and convergent modes of activity.

Significance: Mathematics education remains a critical challenge in the United States and internationally. Sims offers great promise because they can enhance student interest, provide opportunities for engagement in mathematical practices, and give students more ownership of their learning. PhET sims are already used millions of times per year by teachers and students around the world. Yet little is known about how to effectively teach mathematics with sims. This project will contribute 15 new math sims, together with research-based resources for teachers, and empirical findings and theoretical advances concerning the role of sims in effective mathematics teaching and learning.