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Names and Affiliations of Presenters: • Paul Goldenberg, Education Development Center (EDC) • June Mark, EDC • Deborah Spencer, EDC • Kristen Reed, EDC • Kate Coleman, EDC • Katie Chiappinelli, EDC • Zachary Kolar, Waltham Public Schools

Significance and Relevance of the Topic: The Math+C project at Education Development Center (EDC) is developing microworlds that integrate programming into elementary mathematics as a language to help children express and explore mathematical ideas. Our broad hypothesis is that programming, suitably designed, can change how children learn mathematics and help to develop and reveal children's computational thinking (in particular, abstraction, precision of specification, and algorithm). Embedding programming into the core mathematics instruction for grades 2–5 ensures that all children gain experience with programming, in developmentally appropriate ways – and it increases access to mathematical ideas by providing an engaging approach to learning critical mathematics content that offers different affordances than pencil-and-paper activities. This NSF-funded early-stage design and development project is investigating what features of a programming environment best supports this kind of work for elementary-aged children.

Programming gives children a language with which to express their thinking precisely and have that thinking enacted by the computer, allowing them to assess, refine, and extend their thinking with greater ease. Each microworld challenges children to build and debug their own scripts to solve a series of highly engaging mathematical puzzles. This approach takes advantage of children’s natural way of learning: doing, getting feedback, building experience, then naming and systematizing. This epistemological principle of experience before formality guides our approach to curriculum development in both mathematics and in programming.

We will share several examples of microworlds we have designed in Snap! for grades 2–5 with a particular emphasis on our newest microworlds, focused on decimals on the number line, angles, and the coordinate plane. For each, we will show how the microworld environment preserves the power of Snap! but tailors the options to present only what initially children need, gradually revealing more features as they need them.

Decimal number line. In our decimals microworld, children “zoom in” on the number line to add and subtract tenths and hundredths by programming combinations of ±0.3 and ±0.5 and ±0.03 and ±0.05. Children also explore magnitude and distance as it relates to integers and decimals on the number line. This is an extension of our number line microworld where children program combinations of ±3 and ±5 to build fluency within 20 and later 1000. Children explore fractions in a similar way by programming combinations of ±3/8 and ±5/8 in our fractions number line microworld.

Angles. In the angles microworld, children explore angle measures by drawing line segments to make angles on an isometric grid. They start by making simple shapes and eventually move to creating complex shapes. Children experiment with moving and turning on the grid by changing aspects of their scripts, such as the angle size (60°, 120°, 180°) and length of line segments. Children can customize color of their pen as well as the fill used within their shapes.

Coordinate Plane/Town Map. The coordinate plane microworld builds on our earlier work on a “town map” microworld where children move on a map and compare distances. In this latest version, upper-elementary children work on a coordinate plane to plot points of ordered pairs using point of origin, the X and Y axis and directionality on a grid. They continue to compare distances between various points on the grid.

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, including technological advancements made over the past year. Participants will watch video of elementary students developing both mathematical and CS concepts within our newest microworlds environments and will also be invited to explore these microworlds themselves.

*Rough Agenda for the Workshop: * • Introduction (5 minutes) • Preview of Math+C microworlds (15 minutes) • Exploration of the Math+C microworlds (20 minutes) • Using Math+C microworld environment tools to build other microworlds, and technological updates (10 min) • Questions (10 minutes)

Expected Audience: Our examples are from grades 1–5, but easily extend higher and lower. We anticipate that the workshop would be of interest to K–12 teachers, particularly elementary teachers, as well as developers of learning environments for K–12 students.

Participant Equipment Requirements: Equipment recommended—a computer that can run Snap!, and preferably Chrome or Firefox as a browser.