Abstract

Productive learning of algebra is supported when students reflect on multiple strategies, compare them and discuss the rationale behind and relative merits of particular strategies. Comparison and Discussion of Multiple Strategies (CDMS) is an instructional approach designed to support these processes in math classrooms. In the current study, 16 Algebra I teachers received professional development and supplemental materials to support CDMS when teaching a unit on linear equation solving and 475 of their students completed assessments of their linear equation solving knowledge before and after the unit. Thirteen Algebra I teachers and their 359 students were the business-as-usual control group. CDMS increased how often teachers engaged their students in comparison of multiple strategies, sustained small group work, and sustained mathematical discussions. Students in CDMS classrooms also had higher knowledge of linear equations on the posttest, particularly procedural flexibility, even after controlling for pretest knowledge and school demographic differences. Thus, encouraging teachers to regularly compare and discuss multiple strategies increases students’ algebra learning. Findings highlight the need to expand theories of algebra learning to include attention to procedural flexibility, illustrate an instructional theory and method to promote broader learning about algebra, and provide evidence for effective instructional practices.

摘要

当学生反思多种策略、比较它们并讨论特定策略背后的基本原理和相对优点时，可以支持高效的代数学习。多种策略的比较和讨论 (CDMS) 是一种教学方法，旨在支持数学课堂中的这些过程。在当前的研究中，16 名代数 I 教师在教授线性方程求解单元时获得专业发展和补充材料以支持 CDMS，并且他们的 475 名学生在单元前后完成了对线性方程求解知识的评估。13 名代数 I 老师和他们的 359 名学生是一切照旧的对照组。CDMS 增加了教师在多种策略、持续的小组工作、和持续的数学讨论。即使在控制了前测知识和学校人口统计差异之后，CDMS 课堂上的学生在后测中也对线性方程有更高的了解，尤其是程序灵活性。因此，鼓励教师定期比较和讨论多种策略可以增加学生的代数学习。调查结果强调需要扩展代数学习理论以包括对程序灵活性的关注，说明教学理论和方法以促进更广泛的代数学习，并为有效的教学实践提供证据。鼓励教师定期比较和讨论多种策略可以增加学生的代数学习。调查结果强调需要扩展代数学习理论以包括对程序灵活性的关注，说明教学理论和方法以促进更广泛的代数学习，并为有效的教学实践提供证据。鼓励教师定期比较和讨论多种策略可以增加学生的代数学习。调查结果强调需要扩展代数学习理论以包括对程序灵活性的关注，说明教学理论和方法以促进更广泛的代数学习，并为有效的教学实践提供证据。