在聚焦本质的活动中感悟模型思想——以“认识方程”一课为例

Perception of Model Thinking in Activities Focusing on Essence

模型思想是重要的数学思想之一。由于小学生数学思维特征的局限,学生很难有机会经历严格意义的、完整的建模活动,但教师在教学中聚焦知识本质设计活动,引导学生在活动中感悟模型思想,有助于学生理性精神的形成和可持续发展。一元一次方程的核心在于内在的"等价关系"模型,在这一内容教学中借助有效直观、给予建模"拐杖",引发认知冲突、跨越建模障碍,遴选结构性素材、引导感悟模型结构,有助于学生感悟模型思想,提升数学素养。

Model thinking is one of the important mathematics ideas. Because of the limitation of children’s mathematics thinking features, it is difficult for them to experience the modeling activities rigorously and completely. Yet, teachers may focus on the design activity on the knowledge essence in teaching and guide students to perceive the model thinking in activities, which can help students to form and sustainably develop their rational spirit. The core of the equation lies in its internal equivalence model, which can be taught by effective intuition and the walking stick of modeling so that it can trigger cognitive conflicts and overcome the modeling barriers. Meanwhile, teachers should select structural materials and guide students to perceive the model structure, helping them understand the modeling idea and improve their mathematics accomplishments.