Splitting, Similarity and Rate of Change: New Approaches to Multiplication and Exponential Functions

这个项目考察了学生乘法和乘法变化率计划的发展，这将使学生能够理解指数增长的关键社会和环境问题。通过使用教学实验、历史分析和结合新的表现形式和视觉形式的软件设计，研究小组试图调查如何提高学生对规模、功能、乘性变化率和生物生长形式等问题的洞察力。为了促进对中学生的研究，将对幼儿关于乘法、相似和增长的概念进行初步研究，这些概念与被标记为“分裂”的原始结构有关，该结构被推测为独立于计数的乘法方法的基础。初步研究还将包括对科学家和社会科学家使用指数函数的民族数学调查。根据访谈研究，将对整个课堂实施情况进行研究，以编制应用研究产品，包括课程、教师发展案例研究和软件产品。

This project examines the development of students' schemes for multiplication and multiplicative rate of change that will enable students to understand the crucial societal and environmental issues of exponential growth. Through the use of teaching experiments, historical analysis and the design of software incorporating new representational and visual forms, the research team seeks to investigate how to improve students' insight in issues of scale, functions, multiplicative rate of change and biological forms of growth. To facilitate the research on secondary students, preliminary work will be undertaken into young children's concepts of multiplication, similarity and growth in relation to a primitive construct labelled "splitting" which is conjectured to be the basis of an approach to multiplication independent of counting. Initial studies will also include an ethnomathematical investigation of scientists' and social scientists' use of exponential functions. Informed by the interview studies, research on whole classroom implementation will be undertaken towards the preparation of applied research products including curricula, case studies of teacher development and software products.