Characterizing prospective secondary teachers’ foundation and contingency knowledge for definitions of transformations

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in the work of teaching. We argue that the dimensions of Rowland's (2013) Knowledge Quartet, especially Foundation and Contingency, form a fruitful framework for this purpose. We contribute an analytic framework to characterize the quality of mathematical knowledge observed in the Foundation and Contingency dimensions, developed using a purposive sampling from over 300 representations. These representations all featured geometry teaching. We showcase the framework with examples of "high" and "developing" Foundation and Contingency.Then, we compare our coding along these dimensions with performance on a measure of mathematical knowledge for teaching geometry. Finally, we describe the potential for generalizing this framework to other domains, such as algebra and mathematical modeling.     

基于知识图谱和GPT模型的可靠性代码自动生成方法

工程结构服役中广泛使用可靠性分析进行结构安全评估,但可靠性分析方法种类多、分析程序代码自动化程度低且复用难,需要研究可靠性代码自动生成方法。生成式预训练转换器GPT(Generative Pre-trained Transformer)模型已经在大量替代编程手工作业,进行代码自动生成。但是,其在工程领域中的应用受限于可学习数据量小和问题匹配度不高。本文提出了一种结合多种类可靠性知识图谱、基于GPT的代码自动完成模型进行Matlab可靠性代码预测的方法,使用精心设计的源代码预处理降噪策略,以及知识图谱传播模拟密集型任务解释意图;采用条件代码生成训练,有效提升了小数据样本量的学习性能,实现高准确率、问题匹配的可靠性代码自动生成。最后通过三个可靠性知识图谱案例验证了所提方法的有效性。