A Quantitative Reasoning Approach to Algebra Using Inquiry-Based Learning
A Quantitative Reasoning Approach to Algebra Using Inquiry-Based Learning
复制标题
使用基于探究的学习的代数定量推理方法
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发表时间：
2017
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通讯作者：
Victor I. Piercey
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文献类型：
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作者：
Victor I. Piercey
在这篇文章中，我分享了一个混合的定量推理/代数两门课程序列，它挑战了量化素养和推理是代数的不那么严格的数学替代这一普遍假设，并说明量化推理框架可以用于教授传统代数。演讲分为两个部分。在第一部分中，我解释了我个人对“代数”和“做代数”的看法，这部分有点哲学和理论性。我认为，代数是一种交流形式，它的价值是精确，它允许我们以简化和求解动作的形式执行代数操作。传统代数处理的定量推理方法依赖于有意和有目的地使用简化和解决上下文情景中的动作。在第二部分中，我描述了一个为期6周的教学模块，面向商科本科生，提供给那些已经开始学习代数的学生。第1部分中描述的透视图在很大程度上影响了本模块的设计。这些课程材料涉及在多种真实环境中使用Excel，围绕研究性学习的使用而构建。在完成本单元后，在评估中成功完成模型问题的学生的百分比与接受调查的学生在微积分预科和微积分方面的百分比相同，大约比他们的安排提前两个“年级水平”。
In this paper, I share a hybrid quantitative reasoning/algebra two-course sequence that challenges the common assumption that quantitative literacy and reasoning are less rigorous mathematics alternatives to algebra and illustrates that a quantitative reasoning framework can be used to teach traditional algebra. The presentation is made in two parts. In the first part, which is somewhat philosophical and theoretical, I explain my personal perspective of what I mean by “algebra” and “doing algebra.” I contend that algebra is a form of communication whose value is precision, which allows us to perform algebraic manipulations in the form of simplification and solving moves. A quantitative reasoning approach to traditional algebraic manipulations rests on intentional and purposeful use of simplification and solving moves within contextual situations. In part 2, I describe a 6-week instructional module intended for undergraduate business students that was delivered to students who had placed into beginning algebra. The perspective described in part 1 heavily informed the design of this module. The course materials, which involve the use of Excel in multiple authentic contexts, are built around the use of inquiry-based learning. Upon completion of this module, the percentage of students who successfully complete model problems in an assessment is in the same range as surveyed students in precalculus and calculus, approximately two “grade levels” ahead of their placement.