CAREER: Learning to Make Mathematical Connections

本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，可用于支持中学生绘制数学表示（分数和比率）之间的联系。第三次国际数学和科学研究（TIMSS）视频分析研究的潜在的教学策略被确定为最好的高性能的国家从低性能的国家区分。先前的研究被用来试验研究方法和潜在的结果。问题，预期的解决方案的反应，和教学序列是从一个模型的日本教训。该职业奖将由助理教授Lindsey Richland通过加州大学欧文分校运营。将进行六个实验，每一个策略，旨在帮助开发最佳的教学程序。这六个条件是：1）使学生反应或关键思想可见，2）使比较的学生反应或关键思想同时可见，3）视觉上组织学生反应或关键思想以突出关键连接，4）使用至少一个众所周知的学生反应或关键思想与新事物进行比较，5）在连接的学生反应之间使用手势，以及6）使用视觉图像。五年级和六年级的学生从三个教室将被随机选择参加两个条件之一（高支持和低支持）的六个实验。对于每个实验，每个条件将与30名学生一起研究。所有六个实验的数据将从总共360名学生中收集。所有学生将被给予同样的文字问题，需要比例推理。然后，学生将看到一个教师介绍与问题有关的课程的教学视频。学生将得到前和后测试和一个新的问题，以解决作为措施的效果。将在分析中使用ANOVA（前测/后测），条件作为受试者间变量（高支持/低支持）。另外两个案例研究将调查两位教师在前六个实验中使用最有效的策略的培训。这两个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机构。一项教育计划包括指导研究生和本科生研究人员;教育职前教师;通过在职教师专业发展与区域学校的教师合作;将认知科学应用于数学教学的积极成果将为数学教育领域提供常规实践的信息，这些实践将区分高绩效国家，数学成就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轻可能在学习数学时处理两种语言的学生的认知负担。

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.