On Twitter, Nick Corley writes: Students were SUPPOSED to use the distance formula, but look at the response in the pic. How do you grade????? This is a great discussion starter! Here are my thoughts. Assessment Should the student be penalized for finding the correct answer, using a correct method? That would be particularly egregious… Continue reading An Assessment Conundrum
Tag: Geometry
Seen Elsewhere
Today, I share some materials not from my website — though not unrelated! Robert Wirtz As a young elementary school teacher and math specialist in the 1970’s I came across Robert Wirtz’s materials, and was inspired by them. Here is an example, the one I call “Wirtz’s flags": The idea is to draw vertical lines,… Continue reading Seen Elsewhere
Polyarcs in the Classroom
You may be familiar with polyominoes, the figures that can be made by connecting unit squares, edge to edge. For example, these are the tetrominoes, each one made of four unit squares: Polyominoes are an example of polyforms. I discussed polyforms in this article: Geometric Puzzles in the Classroom. In particular, this is where I… Continue reading Polyarcs in the Classroom
No Best Way
In 2020, I wrote No One Way, a blog post which I used to explain my website’s motto (“There is no one way.”) I argued that it is the math itself that demands that we approach important topics in multiple ways. As it turns out, this is a favorite topic of mine: in 2016, I… Continue reading No Best Way
Geometric Puzzles Unit
The Geometric Puzzles home page on my website contains many links, and it is organized reasonably well. Still, someone who is not familiar with all these puzzles may need help in turning them into a curriculum unit. This is what I hope to do in this post. (I will try to not duplicate the overview of… Continue reading Geometric Puzzles Unit
Transformational Geometry for Teachers
I taught geometry for decades, starting in the 1980’s, and loved it. I’m reasonably good at manipulating algebraic symbols, but I don’t especially enjoy it. In contrast, I am happy to spend plenty of time on visual puzzles, and I am enthusiastic about sharing that passion with colleagues and with students. Early in my high… Continue reading Transformational Geometry for Teachers
Tiling in GeoGebra
In my last two posts, I promoted the idea of using tiling (tessellation) as an interesting context in geometry class, especially for the introduction of some basic ideas of transformational geometry. One reason this works is the connection with art, including the abstract patterns in Islamic art and the mind-bending creations of M.C. Escher. John Golden is a connoisseur of… Continue reading Tiling in GeoGebra
Tiling and Transformations
In my last post, I argued that tiling is a good topic to include in a geometry program. Students find it engaging: on the one hand, it connects with art and culture; on the other hand, it provides a context for student creativity. At the same time, it presents many connections with the geometry curriculum in middle school and high… Continue reading Tiling and Transformations
Tiling
Covering the plane with an unlimited supply of identical tiles is called tiling the plane, or tessellation. Over the years, I’ve developed a number of classroom activities about tiling. You can find links to those on the Tiling home page on my website. In a conversation with a teacher a few months ago, I realized… Continue reading Tiling
Virtual Manipulatives: Part 2
In the previous post, I discussed virtual manipulatives in general, and a particular implementation for algebra, using a Google Drawings representation of the Lab Gear. In this post, I will explore GeoGebra as a platform for virtual manipulatives. Pattern Blocks Virtual pattern blocks are not hard to find on the Web. One good implementation is on the Math… Continue reading Virtual Manipulatives: Part 2
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