A Computer-enhanced Package for Learning School Algebra

这项建议是为了推广ESRC/EPSRC资助的MiGen项目的成果，以加强中学早期代数的教学，从而提高整个英格兰的数学成绩。具体地说，我们建议根据MiGen项目的成果，为学生和教师收集和传播一套精美的计算机和基于文本的材料，并向一系列受众传播。总体目标是支持早期代数的学习，其方式明确和明确地与国家课程和教师在关键阶段3的实践相一致。MiGen专注于一个普遍存在的阻碍学生在中学学习数学的困难：即他们经常没有看到代数的意义，这一发现在文献中已经得到了彻底的讨论(例如，KüChemann，2010；Mason等人，2009；Nunes&Bryant，2010)。因此，他们不能使用代数作为数学思维的工具，这反过来又阻碍了他们对STEM科目的学习和更广泛的参与。MiGen通过建立一个具有教学理论基础和支持的技术环境以及相关的活动来应对这些挑战，以便11-14岁的学生从一开始就认识到代数是关于建立和表达结构和概括性的，而符号规则是这种表达的语言。这种环境的一个独特特点是，计算机系统为学生提供支持，源于人工智能(AI)技术，根据学生的行动向他们提供及时和有针对性的反馈。第一条线将汇集在一个连贯的包中，MiGen项目的输出包括学生活动、教师指导和帮助过渡到纸和铅笔的“桥梁活动”。第二部分包括一系列针对教师和教师教育社区以及政策和商业利益攸关方的知识交流活动。

This proposal is to roll out the outcomes of the ESRC/EPSRC-funded MiGen project, in order to enhance the teaching of early algebra in the secondary school, and thus improve mathematics achievement throughout England. Specifically, we propose to assemble and disseminate to a range of audiences, a polished package of computer and text-based materials for students and teachers based on the MiGen project outputs. The overarching aim is to support the learning of early algebra, in ways that are clearly and explicitly aligned to the National Curriculum and to teachers' practice at Key Stage 3. MiGen focused on a widespread difficulty that impedes students' ability to learn mathematics in secondary school: namely that they routinely fail to see the point of algebra, a finding that has been discussed thoroughly in the literature (e.g. Küchemann, 2010; Mason et al., 2009; Nunes & Bryant, 2010). As a result, they cannot use algebra as a tool for thinking mathematically, which in turn obstructs their learning about and engagement with STEM subjects more generally. MiGen addressed these challenges by building a technical environment with pedagogical rationale and support, as well as associated activities, so that 11-14 year-old students could appreciate from the outset that algebra is about building and expressing structure and generality and that symbolic rules are the language of this expression. A unique feature of this environment is that the computer system provides support to the students, derived from AI (Artificial Intelligence) techniques, which offer timely and targeted feedback to students on the basis of their actions.The proposed project has two strands. The first strand will assemble in a coherent package, the outputs of the MiGen project to include student activities, teacher guidance, and 'bridging activities' to assist the transition to paper and pencil. The second strand comprises a series of knowledge-exchange activities, targeted at the teacher and teacher education communities, as well as policy and commercial stakeholders.