ABSTRACT

The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the perspective of experiencing the mathematics curriculum as a coherent story, and neither seems likely to take best advantage of the accumulated body of knowledge in the education research literature about effective didactics for mathematics. In this position paper, as we embark on the collaborative, research-informed design of a complete, fully-resourced, free-to-access mathematics curriculum for students aged 11–14, we use the conceptual framework of mathematics curriculum as a story to draw out five key curriculum design principles. A mathematics curriculum should harness and develop the skills and expertise of teachers; balance the teaching of fluency, reasoning and problem solving; give explicit attention to important errors and misconceptions; compare and contrast alternative methods; and engineer coherence through strategic use of consistent representations and contexts. We use these five principles to set out our vision for the next step in research-informed mathematics curriculum design.

摘要

用于中学数学教学的课程资源因学校而异。一些学校的教学主要基于单一的已发布方案，而另一些学校则设计自己的学习方案，从一系列（通常是免费的）在线资源中挑选资源。从体验数学课程作为一个连贯的故事的角度来看，这两种方法似乎都有问题，而且似乎都不太可能充分利用教育研究文献中关于有效数学教学法的知识体系。在这份立场文件中，当我们着手为 11-14 岁的学生设计一个完整的、资源充足的、免费访问的数学课程时，我们使用数学课程的概念框架作为一个故事制定五个关键的课程设计原则。数学课程应该利用和发展教师的技能和专业知识；平衡流利度、推理和解决问题的教学；明确关注重要的错误和误解；比较和对比替代方法；通过战略性地使用一致的表示和上下文来设计一致性。我们使用这五个原则来制定我们对研究型数学课程设计下一步的愿景。