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The Math+C project at Education Development Center (EDC) is developing a coherent integration of CS ideas and skills into elementary mathematics. Our broad hypothesis is that programming, suitably designed, can be an optimal language for children to express and explore mathematical ideas, changing how children learn mathematics and helping develop and reveal children's computational thinking (in particular, abstraction, precision of specification, and algorithm). Programming is thus seen as both a medium and language for children’s mathematical and computational thinking and a new and useful window into that thinking for teachers and children. We are investigating that hypothesis in grades 2–5 and also looking more broadly at what features of a programming environment best supports this kind of work.
We will share several samples of microworlds we have designed in Snap! for grades 2–5 classrooms and share ideas for other extensions and microworlds appropriate for grades 2–5, with one goal being to encourage others to develop and investigate other such microworlds.
Number line, Fraction number line, Decimal number line: Second graders start by programming combinations of ±3 and ±5 to see what numbers they can make, and build fluency adding and subtracting within 20 predicting results mentally. Later, they extend that through 1000. Students in later grades explore fractions and decimals in a similar way.
Multiplication, Arrays: In the Multiplication microworld, children build multiplication expressions using only the factors 2, 3, 5, and 7, exploring what numbers they can and can’t make, and in what ways they can make them. Children use lists to track their explorations and are introduced to ideas of sorting and eliminating duplicates. In the Arrays microworld, children build small arrays anticipating simple multiplication.
Additional microworlds focus on building ideas about place value, and moving on a coordinate grid and comparing distances.
Introducing programming to children this young—especially ones who’ve had no prior programming experience—and doing that in service of the core mathematics they are learning in school requires the entry to programming to focus on the mathematics and create no overhead. This ease is also critical for teachers. For this reason, we have developed a microworld environment that lets us preserve all the power of Snap! but tailor the options to present all, but only, what the children initially need, and gradually reveal greater power and more features as children need them.
This session will include discussion of the rationale and need for microworld environments, the design of the environments and supporting instructional materials, and how these microworlds are implemented in SnapI. We will share video of elementary students developing both mathematical and CS concepts and some of our learnings about how children operate within these environments. Participants will be invited to explore the microworld environments themselves. In addition, we will discuss how the tools and design of the Math+C microworlds can be used by others to create their own microworlds for children’s learning in other contexts.
For more information, see https://elementarymath.edc.org/programming/