Mathematics through Programming in the Elementary Grades

Education Development Center, Waltham MA

Investigators

Abstract

Working with children and their teachers in grades 3-5, this 3-year project investigates the idea that expressing and exploring mathematics through an appropriate programming language may make it easier for children to engage fully and enjoy and learn that mathematics. Children need their natural language to talk about the contexts in which mathematics gets used - far more than just word problems - and also their reasoning when solving problems. Over the years, they learn a second language, that is, the mathematical symbols needed for expressing arithmetic and algebraic statements. Both are needed, but neither is optimal for expressing a process - showing the way a calculation is performed (think of explaining how to multiply 37 x 43 or add 3/4 + 1/2), or encoding the method for solving a word problem in a way that can be repeated with different starting values. For that, a third language is needed. In an earlier exploratory work conducted with second grade students, the research team investigated the use of a child-friendly but very rich programming language (Snap!) as the third language. When children are provided with an opportunity to explain a process to a machine - that is, by describing the process as a small program, they develop clearer and more concise ways to explain the process in their natural language. Expressing the process as a small program helps children not only experiment and generalize but gives them a "runnable" notation for their thinking. Unlike writing on paper, which just sits there, correct or incorrect, a runnable piece of code lets children get immediate feedback on their work and helps their mathematical learning long before career or college. Building the program, articulating the methods, and generalizing are all key elements of computational thinking (CT), which is increasingly a national, state, and school priority, because it is now so necessary both for careers and for modern college study. This project extends the investigation to grades 3-5, seeking new opportunities in the more advanced mathematics of those grades and seeking clearer data on the effects on both mathematical learning and CT. This project is funded by the STEM + Computing (STEM+C) program that supports research and development to understand the integration of computing and computational thinking in STEM learning. The goal of the project is to understand how programming, integrated with elementary students' regular mathematics study, influences mathematical and computational thinking, and to determine whether, and under what conditions, it enhances thinking. This early-stage design and development study explores both the promise of materials that integrate programming into the mathematics curriculum to extend students' learning opportunities in the elementary math classroom, and the feasibility of the implementation of these materials. The project will (1) investigate a model that integrates programming into elementary mathematics and builds foundational CT ideas; (2) develop programming microworlds and other instructional resources (e.g., print materials and teacher guides) for grades 3-5 to support teachers and students; (3) pilot the materials in 48 classrooms, testing for feasibility and usability; (4) explore how the modules influence student learning and identify design features that help or interfere with learning; (5) describe challenges to broader use and identify potential solutions; and (6) provide greater opportunities for a wide range of students to learn in these domains. A design experiment methodology will be used to develop, test, and refine the microworlds and modules. Teacher interviews and classroom and student observation tools will be used to collect data, and a pilot study will be conducted using a mixed-methods approach that will compare the computational and mathematical thinking of students who experience the integrated modules with a comparison group in similar classrooms in the same school. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.