<p>Reported are students’ responses to a spatial modelling problem requiring them to think about and manipulate various 2D shapes to meet the goal within constraints. Students were to maximise the number of hermit crabs resting on leaves (represented by different shapes) that could fit into an irregular bounded sea colony. The activity was implemented in two consecutive class periods (90&#xa0;min total) during the 2nd year of a 3-year longitudinal, design research program. Three classes of 2nd-graders from mixed cultural and achievement backgrounds participated (n = 48, 7–8&#xa0;years). Data analysis drew upon video/audio recordings of group interactions and shape manipulations, plus responses to reflective questions. Findings included the efficiency with which students discerned the inverse relationship between the area covered by a shape and the number of crabs that could fit in the colony. Students displayed adaptive expertise as they (a) applied in various ways their knowledge of shape properties and informal knowledge of angles and (b) manipulated shapes to fit along the irregular boundary. Students referred to two key features in shape selections—how effectively a shape would fit along the boundary and whether its properties would enable tessellation. There was a preference for small squares and rectangles over other shapes, and minimal selection of circles. The need to engage young students in challenging spatial problems that extend beyond their regular curriculum experiences and that enable a range of solution approaches is highlighted. Likewise, further theoretical developments on young students’ capabilities in solving challenging spatial problems are needed.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Spatial modelling in second grade: creating crab colonies

  • Lyn D. English

摘要

Reported are students’ responses to a spatial modelling problem requiring them to think about and manipulate various 2D shapes to meet the goal within constraints. Students were to maximise the number of hermit crabs resting on leaves (represented by different shapes) that could fit into an irregular bounded sea colony. The activity was implemented in two consecutive class periods (90 min total) during the 2nd year of a 3-year longitudinal, design research program. Three classes of 2nd-graders from mixed cultural and achievement backgrounds participated (n = 48, 7–8 years). Data analysis drew upon video/audio recordings of group interactions and shape manipulations, plus responses to reflective questions. Findings included the efficiency with which students discerned the inverse relationship between the area covered by a shape and the number of crabs that could fit in the colony. Students displayed adaptive expertise as they (a) applied in various ways their knowledge of shape properties and informal knowledge of angles and (b) manipulated shapes to fit along the irregular boundary. Students referred to two key features in shape selections—how effectively a shape would fit along the boundary and whether its properties would enable tessellation. There was a preference for small squares and rectangles over other shapes, and minimal selection of circles. The need to engage young students in challenging spatial problems that extend beyond their regular curriculum experiences and that enable a range of solution approaches is highlighted. Likewise, further theoretical developments on young students’ capabilities in solving challenging spatial problems are needed.