CAREER: Learning to Make Mathematical Connections

这个数学教育研究项目的主要目标是通过实验确定具体的教学策略，可以用来支持中学生绘制数学表示（分数和比率）之间的联系。从第三次国际数学和科学研究（TIMSS）视频分析研究中确定了潜在的教学策略，这些策略是最好地区分高绩效国家和低绩效国家的策略。先前的研究被用于试验研究方法和潜在结果。问题、预期的解决方案反应和教学顺序是从日语课程模型中提取的。该职业奖将由加州大学欧文分校助理教授Lindsey Richland负责。将进行六个实验，每个实验采用一种策略，旨在帮助开发最佳的教学程序。这六个条件是：1)使学生的回答或关键观点可见，2)使比较的学生的回答或关键观点同时可见，3)从视觉上组织学生的回答或关键观点以突出关键联系，4)使用至少一个已知的学生的回答或关键观点与新事物进行比较，5)在连接的学生回答之间使用手势，6)使用视觉意象。从三个班级中随机抽取五年级和六年级的学生，在高支持和低支持两种条件下参与六个实验。对于每个实验，每种情况将由30名学生进行研究。所有六个实验的数据将从总共360名学生中收集。所有的学生都会被要求做同样的比例推理题。然后，学生将观看一段教师讲解与问题相关的课程的教学视频。学生将被给予前后测试和一个新的问题来解决，作为衡量效果。方差分析（前测/后测）将条件作为受试者之间的变量（高支持/低支持）用于分析。另外两个案例研究将调查培训两位教师在前六个实验中使用最有效的策略。这两位教师在课堂上使用最佳策略的录像带将使用TIMSS中使用的相同协议进行分析。一个高素质的咨询委员会将作为外部评价。教育计划包括指导研究生和本科生研究人员；培养职前教师；通过在职教师专业发展与地区学校教师合作；并在学术场所传播成果。这种将认知科学应用于数学教学的积极结果，将使数学教育领域了解区分数学成就高的国家的常规实践。这项工作可能对英语学习者和其他代表性不足的群体有最大的好处。如果教学策略是可行的，那么教师将有具体的方法来减少学生在学习数学时可能同时处理两种语言的认知负荷。

The main goal of this mathematics education research project is to determine through experimentation specific teaching strategies that can be used to support middle school students drawing connections between mathematical representations (fractions and ratios). The potential instructional strategies were identified from the Third International Mathematics and Science Study (TIMSS) video analyses study as the ones that best distinguished high performing countries from low performing countries. Prior studies were used to pilot the research approach and potential results. The problem, expected solution responses, and instructional sequences are drawn from a model of a Japanese lesson. This CAREER award will be operated through the University of California-Irvine by Assistant Professor Lindsey Richland. Six experiments will be conducted, each on one strategy and designed to help develop optimal instructional routines. The six conditions are: 1) making student responses or key ideas visible, 2) making compared student responses or key ideas visible simultaneously, 3) visually organizing the student responses or key ideas to highlight key connections, 4) using at least one well-known student response or key idea to compare with something new, 5) using gestures between connected student responses, and 6) using visual imagery. Fifth and sixth grade students from three classrooms will be randomly selected to participate in one of two conditions (high support and low support) for the six experiments. For each experiment, each condition will be studied with 30 students. Data for all six experiments will be collected from a total of 360 students. All students will be given the same word problem requiring proportional reasoning. Then students will be shown an instructional video of a teacher presenting a lesson related to the problem. Students will be given pre- and post-tests and a new problem to solve as measures of effects. An ANOVA (pretest/posttest) with conditions as a between-subjects variable (high support/low support) will be used in the analysis. Two additional case studies will investigate the training of two teachers to use the most effective of the strategies in the first six experiments. Videotapes of these two teachers using the optimal strategies in their classrooms will be analyzed using the same protocol used in TIMSS. A highly qualified advisory board will serve as the external evaluation. An education plan includes mentoring graduate students and undergraduate researchers; educating pre-service teachers; collaborating through in-service teacher professional development with teachers from regional schools; and disseminating results in academic venues.Positive results of this application of cognitive science to the teaching and learning of mathematics will inform the field of mathematics education on routine of practices that distinguish high performing countries in mathematics achievement. The work may be of greatest benefit to English language learners and other under-represented groups. If the instructional strategies are viable, then teachers will have specific ways they can reduce the cognitive load on students who may be processing two languages while trying to learn mathematics.