Post #4: Disciplinary Text Set
When investigating my inquiry topic, the Pythagorean Theorem, I went about finding texts for a specific group of students. I imagine to be teaching an 8th grade classroom of math students, since that is when the Pythagorean Theorem is first introduced and used. I also picture the group of students to be wonderfully diverse! This means a couple different things. Not only would the students be culturally diverse, but also very neurologically diverse. I wanted texts that would support the learning needs of students with nuero-diversity, specifically thinking of students with Autism Spectrum Disorder (ASD)- to match my certificate in ASD. I think these texts work really well together. I have a couple texts, such as the Interactive GeoGebra activity and the Math is Fun website's explanation of the Pythagorean Theorem's proof, that are great for introducing the topic. I then would use my Cut-The-Knot website article to help students dive deeper into different versions of the proof that supports understanding. The next two texts, the VoiceThread I created and the Math is Fun website's article on applications of the theorem to help my students understand applications and uses of the content. I would show my students the culturally relevant videos, one that explains the theorem in a song and one that explains the theorem and how to use it in a rap, to engage my students in the content and provide ways to remember the content. I think that one video could be shown in the middle of learning the content- possibly as a class opener- and the other could be shown closer to the end of the topic. The following are my text descriptions for the content I found.
Text 1 (Print):
Pythagoras' Theorem. (n.d.). Retrieved from https://www.mathsisfun.com/pythagoras.html
The first text I will be talking about falls into the print category of text. It is a website article from the website Math Is Fun that explains Pythagorean Theorem and its applications beautifully. The text starts off by explaining and defining the Pythagorean Theorem and then shows students a way to check and see if it really works. The site goes on to answer questions that students often have about content such as: "Why is this useful?" and "How do I use it?". The article ends with a couple videos and bullet points on how to prove the theorem very simply.
I used the StoryToolz website to investigate this text's quantitative measures. The article was given an Average Grade Level of grade 5.3. This would be a fairly low reading level for an average 8th grader, however it supports my goal of finding texts that are accessible to nuero-diverse students- as harder text can keep those students from understanding the math concept at hand. The text had a only 561 total words, with 50% of the sentences being 7 words or less. The article also had very small paragraphs with an average of 1.2 sentences per paragraph. I agree with all of these qualitative descriptions. The article uses many qualitative aspects of the text help support the reading grade level. The text is broken up into short chunks of text with images and visuals embedded in the text constantly that supports student understanding of the words. This makes harder parts of text or harder words easier to understand because the student immediately has a visual example. There is a very small amount of background knowledge that this text requires. For example, I think it would be helpful for students to understand what a "theorem" is to truly understand the content surrounding the Pythagorean Theorem. The text does a great job of explaining every term they use before using it.
Now let's talk about task and reader complexity. This text would be used right after introducing the topic of Pythagorean Theorem. The great part about this text is that it doesn't assume the reader remembers everything so it almost is a review of the introduction and an introduction to the applications of the topic. This means that it summarizes concepts and rules learned the class or a couple classes before, and then teaches students how to apply them. I have found that the one culturally relevant aspect that this text applies to is frequency. I think that the way the article uses a small amount of text and matches it with a picture is similar to how students learn to read picture books. This means that the text is familiar to students and similar to texts they have read before. The text helps students remember content, understand concepts, and apply the new concept. I feel as thought the lower reading level helps all students access this information and content the task requires.
Vocabulary terms to support:
Theorem
Proof
x, y, z triangles (ex: 3, 4, 5 triangle)
Text 2 (Multimedia):
Pythagoras Theorem (GGB). (n.d.). Retrieved from https://www.interactive-maths.com/pythagoras-theorem-ggb.html
The second text I will talk about falls into the multimedia category. This text is an interactive activity that allows students to explore how the Pythagorean Works. The website presents an image (as shown above) and allows students to drag points N and B along the lines they are on the change the shape of the triangle and thus the areas of the squares. The website includes thought provoking questions for the students to think about while they investigate such as: "What happens to the areas of the squares if you change one of the side lengths?", "How are the three areas related?", and "Is this always the case?". It is a great text to create student-led investigation and discussion in a math classroom. It also supports those nueor-diverse students who benefit from using visuals and manipulatives to understand math.
I again used StoryToolz to check out the quantitative measures of my text. Since this is an interactive activity, there is very little text on the page- about a paragraph's worth really. The average grade level for the text on the page is 6.5, which is again slightly below 8th grade (the grade of the students using it). There are only 6 total sentences, most of which explain how to use the interactive image, with a couple thought-provoking questions as well (like I mentioned above). Overall, the text doesn't seem too difficult for students to read. The qualitative measures of this text are different than the last. The text doesn't require much background knowledge. Students, at most, have to understand area and shapes. Since the purpose of the text is to introduce and explore the topic, students don't have to know too much in-depth background information.
As for task and reader complexity, the purpose of the task is to introduce a topic and motivate interest. The student only needs to interact with the image and make observations. The text itself doesn't seem to be very culturally relevant. It doesn't help relate students to the topic and probably isn't similar to many other texts they have seen. The complexity of the task seems low. The students are given straightforward instruction with very little expectations. As I mentioned before, students are simply asked to make observations- no matter how simple or complex- there is no right or wrong answer.
Vocabulary to support:
Right-angled triangles
Area
Related area
Point
Investigate
Side lengths
Text 3 (Culturally Relevant):
Text 1 (Print):
The first text I will be talking about falls into the print category of text. It is a website article from the website Math Is Fun that explains Pythagorean Theorem and its applications beautifully. The text starts off by explaining and defining the Pythagorean Theorem and then shows students a way to check and see if it really works. The site goes on to answer questions that students often have about content such as: "Why is this useful?" and "How do I use it?". The article ends with a couple videos and bullet points on how to prove the theorem very simply.
I used the StoryToolz website to investigate this text's quantitative measures. The article was given an Average Grade Level of grade 5.3. This would be a fairly low reading level for an average 8th grader, however it supports my goal of finding texts that are accessible to nuero-diverse students- as harder text can keep those students from understanding the math concept at hand. The text had a only 561 total words, with 50% of the sentences being 7 words or less. The article also had very small paragraphs with an average of 1.2 sentences per paragraph. I agree with all of these qualitative descriptions. The article uses many qualitative aspects of the text help support the reading grade level. The text is broken up into short chunks of text with images and visuals embedded in the text constantly that supports student understanding of the words. This makes harder parts of text or harder words easier to understand because the student immediately has a visual example. There is a very small amount of background knowledge that this text requires. For example, I think it would be helpful for students to understand what a "theorem" is to truly understand the content surrounding the Pythagorean Theorem. The text does a great job of explaining every term they use before using it.
Now let's talk about task and reader complexity. This text would be used right after introducing the topic of Pythagorean Theorem. The great part about this text is that it doesn't assume the reader remembers everything so it almost is a review of the introduction and an introduction to the applications of the topic. This means that it summarizes concepts and rules learned the class or a couple classes before, and then teaches students how to apply them. I have found that the one culturally relevant aspect that this text applies to is frequency. I think that the way the article uses a small amount of text and matches it with a picture is similar to how students learn to read picture books. This means that the text is familiar to students and similar to texts they have read before. The text helps students remember content, understand concepts, and apply the new concept. I feel as thought the lower reading level helps all students access this information and content the task requires.
Vocabulary terms to support:
Theorem
Proof
x, y, z triangles (ex: 3, 4, 5 triangle)
Text 2 (Multimedia):
The second text I will talk about falls into the multimedia category. This text is an interactive activity that allows students to explore how the Pythagorean Works. The website presents an image (as shown above) and allows students to drag points N and B along the lines they are on the change the shape of the triangle and thus the areas of the squares. The website includes thought provoking questions for the students to think about while they investigate such as: "What happens to the areas of the squares if you change one of the side lengths?", "How are the three areas related?", and "Is this always the case?". It is a great text to create student-led investigation and discussion in a math classroom. It also supports those nueor-diverse students who benefit from using visuals and manipulatives to understand math.
I again used StoryToolz to check out the quantitative measures of my text. Since this is an interactive activity, there is very little text on the page- about a paragraph's worth really. The average grade level for the text on the page is 6.5, which is again slightly below 8th grade (the grade of the students using it). There are only 6 total sentences, most of which explain how to use the interactive image, with a couple thought-provoking questions as well (like I mentioned above). Overall, the text doesn't seem too difficult for students to read. The qualitative measures of this text are different than the last. The text doesn't require much background knowledge. Students, at most, have to understand area and shapes. Since the purpose of the text is to introduce and explore the topic, students don't have to know too much in-depth background information.
As for task and reader complexity, the purpose of the task is to introduce a topic and motivate interest. The student only needs to interact with the image and make observations. The text itself doesn't seem to be very culturally relevant. It doesn't help relate students to the topic and probably isn't similar to many other texts they have seen. The complexity of the task seems low. The students are given straightforward instruction with very little expectations. As I mentioned before, students are simply asked to make observations- no matter how simple or complex- there is no right or wrong answer.
Vocabulary to support:
Right-angled triangles
Area
Related area
Point
Investigate
Side lengths
Text 3 (Culturally Relevant):
Scott, J. (Producer). (2012, August 24). The Best Pythagorean Theorem Rap Ever [Video file]. Retrieved from https://www.youtube.com/watch?v=nbopLhP4kpo
The last text I will break down today is a YouTube video titled The Best Pythagorean Theorem Rap Ever and falls under the culturally relevant category of text. This video is a rap song written by a math teacher to teach his students about the Pythagorean Theorem. The rap hits on the equation for the theorem, how and when to use the theorem, and the parts of a triangle needed to apply the theorem. This text is greatly accessible to a variety of students as it provides audio, visual, closed captioning, and written lyrics. It is also a fun way to present the concept and engage students.
When using StoryToolz to investigate the quantitative measures of my text (using the lyrics of the song), I got very interesting results. I discovered that the average reading level for the lyrics of the video is 11.8. However, once I looked more closely at all the reading level scores, I found that the text got a couple scores of grades 6-7 and a couple scores of grades 12, 14-15. This seems like very contradictory results, and the average doesn't help. I think that the format of the text plays a big part in these results. Since it is a rap song and the writer is striving for flow and rhyme, the sentences don't follow usual sentence structure which could be seen as confusing to some students. This could be why certain scores are so high. However, when paired with the visuals, captions, and written lyrics, I think that the reading level goes down. The quantitative measures are unique as well since, as I just mentioned, the text structure is not conventional. However, the text doesn't require tons of knowledge demands, especially when considering the purpose and task of the text.
The purpose of this text is definitely to motivate students interest. It is a very engaging way to present the concept. I think that this video would best be used as a way to start class. It would engage students and introduce them to that day's lesson and could also be used to spark discussion. Students could be asked what they heard in the rap about the Pythagorean Theorem and a class discussion could be formed. This is definitely my most culturally relevant piece of text. Many students would be find the people/characters in the video as relatable. They also would recognize the type of text. Many students would be fans of rap music and would find the format of the audio familiar. This makes the text more culturally relevant. As I mentioned before, the task for this text would be to discuss what students heard or saw. This task is not very challenging and doesn't rely on background information, which helps make the text and task more accessible.
Vocabulary to support:
Logic
Proof
Unknown values
Theorem
Square root
Disciplined min
The following is the bibliography for the remaining four texts I found for this project. It includes two more printed text, one more multimedia text, and one more culturally relevant text. The web pages in the citation include links to the texts.
Bibliography
Bogomolny, A. (n.d.). Pythagorean Theorem. Retrieved from http://www.cut-the-knot.org/pythagoras/index.shtml
Dodds, C., Mr (Producer). (2012, April 22). Colin Dodds- Pythagorean Theorem (Math Song) [Video file]. Retrieved from https://www.youtube.com/watch?v=l8-bnZh8Zuc
(2020, July 19). Retrieved July 25, 2020, from https://voicethread.com/share/14879246/
Pythagorean Theorem Algebra Proof. (n.d.). Retrieved from https://www.mathsisfun.com/geometry/pythagorean-theorem-proof.html
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