CAREER: Learning to Make Mathematical Connections

职业：学习建立数学联系

• 批准号: 1313531
• 负责人: Lindsey Richland
• 金额: $ 53.85万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-03-01 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1313531&HistoricalAwards=false
• 关键词: CAREER; Learning; Make; Mathematical; Connections

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.

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，以支持中学生在数学表示(分数和比例)之间建立联系。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战略，这些战略是最能区分表现良好的国家和表现不佳的国家的战略。先前的研究被用来试验研究方法和潜在的结果。问题、预期的解决方案和教学顺序来自一节日语课的模型。这个职业奖项将由助理教授林赛·里奇兰通过加州大学欧文分校运营。将进行六个实验，每个实验都针对一种策略，旨在帮助制定最佳的教学程序。这六个条件是：1)让学生的反应或关键想法可见，2)让比较的学生反应或关键想法同时可见，3)视觉上组织学生的反应或关键想法以突出关键联系，4)使用至少一个众所周知的学生反应或关键想法来与新事物进行比较，5)在相连的学生反应之间使用手势，以及6)使用视觉图像。来自三个教室的五年级和六年级学生将被随机选择参加六个实验的两个条件(高支持和低支持)之一。对于每个实验，每个条件都将与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。所有学生都将被要求进行比例推理的同一道应用题。然后，将向学生播放一段教师讲授与问题相关的课程的教学视频。学生们将接受前后测试和一个新问题的解决，作为效果的衡量标准。分析中将使用以条件为受试者间变量(高支持度/低支持度)的ANOVA(前测/后测)。另外两个案例研究将调查两名教师如何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估。教育计划包括指导研究生和本科生研究人员；培训职前教师；通过在职教师专业发展与地区学校的教师合作；以及在学术场所传播结果。将认知科学应用于数学教与学的积极结果将向数学教育领域的常规做法提供信息，这些做法在数学成就方面表现优异。这项工作可能对英语学习者和其他代表性不足的群体最有好处。如果教学策略是可行的，那么教师将有具体的方法来减轻学生在试图学习数学的同时处理两种语言的认知负担。