A 3D Visualization Teaching-Learning Trajectory for by Jacqueline Sack, Irma Vazquez

By Jacqueline Sack, Irma Vazquez

This monograph describes the advance and use of a 3D visualization teaching-learning trajectory for ordinary age novices. utilizing layout learn ideas, the authors built this trajectory utilizing the NCTM options and the Spatial Operational means (SOC) theoretical framework to steer lesson improvement. The SOC framework makes use of real 3D types, 2nd and summary representations of the particular versions, and, a dynamic laptop interface, the Geocadabra development field, which integrates those representations dynamically in genuine time. The paintings starts off with describing the theoretical SOC frameworks that guided the research, the inquiry-based studying concentration, the study approach used, and casual pre-program interviews with player young ones. the following bankruptcy describes introductory actions used to orient the kids to the 3D items that they used during the software. The booklet then specializes in the advance of summary top-view numeric plan representations resulting in representations of oblong prisms, by means of front-side-top view representations. The final bankruptcy exhibits how numeracy was once built-in into this system to help the not easy reputable arithmetic curriculum.

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Additional info for A 3D Visualization Teaching-Learning Trajectory for Elementary Grades Children

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3 Conclusions It is remarkable that the children were able to move from the abstract top plan numeric view and front, side and top views representations to the 3D models inde‐ pendently of the computer interface. The research team considered this to be evidence of the children’s growing ability to visualize, abstract and generalize as they moved between abstract and 3D assembly models. Actions on objects (Connell 2001) occured concretely with the 3D models, virtually through the Geocadabra Construction Box interface and ultimately as mental imaging through the powerful problem-solving approaches developed by the research team.

After pointing out the combination sequence on her cake pattern: 7–6–5–1, she started to write another random combination, starting with 1—… We suggested she keep the 7 and the 6 in place and think about another arrangement. She immediately wrote 7–6–5–1, and then 7–6–1–5 and continued until she had all 6 arrangements beginning with 7. She then proceeded to write down all six combi‐ nations beginning with 6—and had no trouble suggesting that there would be six more that began with 5 and six more that began with 1 for a total of 24 different combinations (See Fig.

In the left figure, the child was able to calculate 9 × 27 = 243; then, multiplied 243 × 3, an extension of 1-digit by 2-digit multiplication that is in the 3rd grade curriculum. In the lower right example, the child knew that each of six Soma figures contained four 27-cubes or 108 small unit cubes (from the previous week), plus Soma #1, with three 27-cubes. This learner-generated problem provided the children an opportunity to apply their developing multiplication skills to a much more difficult problem than they were expected to compute during their regular mathematics classes.

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