Post #2: Where I Am, and Where I Want To Go
For my Inquiry Blog, I would like to focus on the math topic of the Pythagorean Theorem. This topic is interesting to me because it is first seen by students in 8th grade, and then is used for the rest of their math career. While that use of scaffolding is not unique to just the Pythagorean Theorem, I think that there is often a lack of quality understanding of this concept when it is first taught that affects how well students can implement and apply it in later grades. In 8th grade, when the theorem is first introduced, the students are supposed to be shown a proof of the theorem and its converse. From talking with fellow math education majors about our past secondary math experiences, it seems that this step of truly understanding the proof of the theorem and where it comes from is missed by a lot of students. I hope to find texts that help me teach that aspect of this topic.
There are a couple aspects of this topic that I already understand. I understand that there are many ways to solve the proof of this theorem, and different versions use different methods of thinking and levels of background knowledge. I also know that the use of Pythagorean Theorem goes on to help solve for unknown lengths and distances in triangles and coordinate systems and relates to many future geometric concepts.
When thinking of what I would like to know about this topic, my main goal is to find ways to help my students, especially those with ASD (Autism Spectrum Disorder), understand where the Pythagorean Theorem comes from and how it relates to different concepts. Students with ASD have unique struggles with executive functioning, theory of mind, and central coherence that affect their math achievement. If I can understand what teaching strategies support their learning needs, then I can find texts that can help them understand this topic.
*I really like this picture of the for the Pythagorean Theorem because it touches on the vocabulary of the concept: a number squared, such as x^2, represents an area in the shape of a square with sides that are length x.*
Here are some links about not only how ASD students learn or struggle in math but also websites that show different ways of understanding and applying the Pythagorean Theorem that can help me understand the different perspectives that my students may have about the content.
https://www.exinn.net/autism-math-word-problem-solving/
http://www.corestandards.org/Math/Content/8/G/
Great intro to your topic, I feel it's something everyone has used and heard about but don't know everything about it or how it came to be used so frequently. I also like the lens of using this as a tool to teach ASD students rather than the whole student population.
ReplyDeleteHello Eleanora,
ReplyDeleteWhen I was introducued to a^2+b^2=c^2 maybe in the 8th grade or prior, I remember being taught the simple principles behind the theorem. I don't remember walking through the proof, and in most cases math teachers aren't effective explaining how or why, just methods to solving the specific problem. In addition, I think all professionals should learn techniques to help students with ASD, ADHD, and other "disabilities" because those techniques could also help students who don't have those disabilities as well.
The pythagorean theorem is certainly among one of the more popular ideas people tend to remember about math. However, I think many miss the beauty of how it works, and the numerous ways we can show this. It is also cool to see how you want to focus on how to present the material to students with ASD and helping them understand given some of their challenges.
ReplyDeleteI agree with your assessment that it is not taught thoroughly or well enough to give reason for learning it. I remember learning to solve it for the sake of solving it. I would like to learn more about it myself.
ReplyDeleteThis visual of the three squares has been very helpful in explaining the concept behind Pythagorean theorem. I look forward to seeing what you create for your visualization project.
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