- Title: Learning about Functions through Learner-Generated Examples
- Authors: Martha O. Dinkelman and Laurie O. Cavey
- Access the original paper here
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Paper summary
This article from The Mathematics Teacher explores the use of learner-generated examples (LGEs) in teaching functions in an introductory Algebra 2 course. Researchers Dinkelman and Cavey detail fourteen LGE tasks designed to assess student understanding of functions and their various representations (numerical, graphical, symbolic, and narrative). Analysis of student responses reveals that while students initially favored numerical representations, their use of multiple representations improved throughout the unit. The study demonstrates LGEs’ effectiveness as a formative assessment tool, highlighting students’ evolving understanding and identifying areas needing further instruction. The authors conclude that LGEs promote deeper engagement with mathematical concepts and improve students’ mathematical writing skills.
What are the key implications for teachers in the classroom?
The authors suggest learner-generated examples (LGEs) offer teachers an effective strategy to understand student thinking about a mathematical concept and to determine if they grasp the important ideas. The use of LGEs may reveal student misconceptions more effectively than traditional methods like worksheets or homework assignments.
Here are some key implications for using LGEs in the classroom:
- Provide information to inform instruction: LGEs can reveal areas where students need more experience and support, such as using different representations of functions. For instance, the authors found that students initially relied heavily on numerical representations of functions and needed more exposure to graphical, symbolic, and narrative representations.
- Encourage student engagement with mathematical thinking: While students may initially struggle with generating their own examples, this process can be valuable for promoting mathematical thinking and discussion. Over time, students may become more comfortable with LGEs and require less coaching.
- Assess students’ ability to adapt to new learning approaches: Asking students to think for themselves and generate their own examples can be a new experience, requiring them to adapt to different ways of doing mathematics.
- Improve students’ ability to write mathematically: Using LGEs can help students develop their ability to write about mathematics, which may be a new and challenging skill for some. As students engage in LGEs throughout a unit, they may become more comfortable and proficient in expressing mathematical ideas in writing.
In summary, the authors suggest that using LGEs can be a valuable formative assessment tool for teachers, providing insights into student understanding, promoting mathematical thinking, and supporting the development of mathematical writing skills.
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