Professor Dawn Teuscher recently published an article titled “Geometric Reflections: Why Not a Flip?” in the journal Mathematics Teacher: Learning and Teaching PK-12. Dawn has answered a few questions about this article below:
Who were your co-authors on this article?
Shannon Dingman, Travis Olson, and Lisa Kasmer
Who would you say is the target audience for this article?
Middle grade (8th grade) teachers.
What is the big problem you hoped to address with this article?
Many students and teachers think about reflections visually and not mathematically.
What are some of the key ideas in the article?
Teachers need to bring out the mathematics behind reflections, specifically that reflections require a line of reflection that is in the middle of the two figures, but the line segments that connect corresponding points must be perpendicular to the line of reflection. That students need to explore more with reflections that are not on a coordinate grid and that are not over vertical and horizontal lines. This is because the perpendicularity is implicit when the line of reflection is horizontal or vertical. Many students do not see the perpendicularity.
What are some of the main ideas you hope your audience will take away from this article?
We hope that teachers will modify how they teach geometric reflections, they will begin to have students think about reflections off of a coordinate plane, and they will have them work with reflections over oblique lines of reflections.