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Using comparison to develop flexibility for teaching algebra

机译：使用比较来发展代数教学的灵活性

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In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students’ flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent student discussion of these multiple solution methods to highlight the similarities and differences among problem-solving techniques. The goals of the professional development activity were to make teachers aware of how to use comparison effectively in their instruction, as well as to impact teachers’ own flexibility in algebra by using comparison instructionally during the professional development. Our analysis of teachers’ experiences in the professional development activity suggests that when teachers were presented with techniques for effective use of comparison, their own understanding of multiple solution methods was reinforced. In addition, teachers began to question why they relied exclusively on one familiar method over others that are equally effective and perhaps more efficient and started to draw new connections between problem-solving methods. Finally, as a result of experiencing instructional use of comparison, teachers began to see value in teaching for flexibility and reported changing their own teaching practices.
机译：在本文中，我们描述了为期一天的数学教师专业发展活动，该活动促进了将比较作为一种教学工具，以提高学生在代数中的灵活性。在数学教学中有效地使用比较包括涉及问题和解决方法的并排介绍，以及随后的学生对这些多种解决方法的讨论，以突出解决问题的技术之间的异同。专业发展活动的目标是使教师意识到如何在他们的教学中有效地使用比较，以及在专业发展过程中通过教学中的比较来影响教师自己的代数灵活性。我们对教师在专业发展活动中的经验的分析表明，当向教师介绍有效使用比较的技术时，他们对多种解决方法的理解就会增强。此外，教师开始质疑为什么他们只依靠一种熟悉的方法，而不是同样有效甚至更高效率的方法，并开始在解决问题的方法之间建立新的联系。最后，由于经历了比较教学的使用，教师开始看到教学在灵活性方面的价值，并报告了他们自己的教学实践的变化。

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