ABSTRACT

Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical concepts. We note that geometry is an area particularly neglected. In an innovative year-long project, a group of university-based mathematicians and early years teachers collaborated on a child-led exploration of ‘patterns in nature.’ The early years teachers ran the project within the setting, meeting regularly with the mathematicians to discuss potential areas of interest, and to highlight the children’s mathematical thinking. We found that, with the appropriate environment and guidance, the children naturally displayed deep levels of geometrical thinking and found enjoyment and satisfaction in the exploration of mathematical ideas. We define what we mean by the term ‘deep geometrical thinking’ and demonstrate this by looking at three excerpts through the lens of the van Hiele levels of geometric thought, finding that the children are capable of exhibiting thought at level 3 (abstraction), more advanced than previously thought of children of this age. Using a second taxonomy we also assess the range of skills across which they are demonstrating such geometric thought.

摘要

早年的数学通常仅限于学习计算和识别简单的形状。这部分是由于许多早期课程的范围狭窄以及教师培训不足以探索更深层次的数学概念。我们注意到几何是一个特别被忽视的领域。在一个为期一年的创新项目中，一群大学数学家和早教教师合作开展了以儿童为主导的“自然模式”探索。早年的老师们在这个环境中运行这个项目，定期与数学家会面，讨论潜在的兴趣领域，并突出孩子们的数学思维。我们发现，在适当的环境和指导下，孩子们自然而然地表现出深层次的几何思维，并在探索数学思想中找到了乐趣和满足感。我们定义了“深度几何思维”一词的含义，并通过 van Hiele 几何思维水平的镜头观察三个节选来证明这一点，发现孩子们能够在 3 级（抽象）展示思维，更多这个年龄的孩子比以前想象的要先进。使用第二种分类法，我们还评估了他们展示这种几何思想的技能范围。发现孩子们能够表现出 3 级（抽象）的思想，比以前认为的这个年龄段的孩子更先进。使用第二种分类法，我们还评估了他们展示这种几何思想的技能范围。发现孩子们能够表现出 3 级（抽象）的思想，比以前认为的这个年龄段的孩子更先进。使用第二种分类法，我们还评估了他们展示这种几何思想的技能范围。