Scholarlink

<p>In addition to basic calculation skills, mathematical competencies that focus on understanding relationships and structures are also gaining importance in primary school education. Functional relationships are a&#xa0;key component of this. Currently, in Germany only proportional relationships are routinely addressed. The project presented in this paper investigates a&#xa0;possible approach to non-proportional linear functions via figural growing patterns. The approach used here is to directly prompt the children to colour an additive constant in the pattern in order to make the rate of change visible at the same time. Although colouring approaches are worked on in previous studies, the colouring of a&#xa0;constant approach is novel and, moreover, primary school children have not been engaged with it before now. The results of an exploratory study with over 200 third and fourth graders indicate that the approach can be fruitful and that highly significant correlations and medium size effects between colouring and functional thinking strategies can be revealed. However, the children’s functional thinking strategies demonstrate that the project approach of colouring a&#xa0;constant does not necessarily result in explicit functional thinking. It may therefore be worthwhile to pursue the approach in more depth in follow-up studies.</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

Colouring a Constant in Figural Growing Patterns as an Approach to Understanding the Structure of Linear Functions: an Exploratory Study with German Primary School Children

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月14日

查看全文
  • Anna Susanne Steinweg,
  • Aisling Twohill,
  • Sharon Mc Auliffe

摘要

In addition to basic calculation skills, mathematical competencies that focus on understanding relationships and structures are also gaining importance in primary school education. Functional relationships are a key component of this. Currently, in Germany only proportional relationships are routinely addressed. The project presented in this paper investigates a possible approach to non-proportional linear functions via figural growing patterns. The approach used here is to directly prompt the children to colour an additive constant in the pattern in order to make the rate of change visible at the same time. Although colouring approaches are worked on in previous studies, the colouring of a constant approach is novel and, moreover, primary school children have not been engaged with it before now. The results of an exploratory study with over 200 third and fourth graders indicate that the approach can be fruitful and that highly significant correlations and medium size effects between colouring and functional thinking strategies can be revealed. However, the children’s functional thinking strategies demonstrate that the project approach of colouring a constant does not necessarily result in explicit functional thinking. It may therefore be worthwhile to pursue the approach in more depth in follow-up studies.