1.
Pickover, Clifford. The Math Book. Sterling.
2012.
2.
The text describes the history, gives a
definition, and some examples of the Pythagorean Theorem.
3.
The text is pretty simple if you have a
background in mathematics. There are some nice historical comments. The hardest
part to understand is probably the part where Fermat asks for the hypotenuse
and the sum of a and b be perfect squares. That is a bit tricky to understand,
especially because the answers are such large numbers. The text’s word choice
do not include longer words, and there isn’t excessive sentence length.
4.
If someone wants to know the history of the
Pythagorean Theorem, this is a great place to start.
5.
If you were mathematician Pierre de Fermat, what
question would you pose to other mathematicians?
1.
Sultan, Alan and Artzt, Alice. The Mathematics
That Every Secondary School Math Teacher Needs To Know. New York and London: Routledge. 2011.
2.
Although the very beginning and very end are
missing, this text contains all the meat of the proof. It is a beautiful proof,
simple and elegant, but if math isn’t your strong suit I could see this being
difficult to follow.
3.
The text is filled with math specific
terminology. And if you don’t know math vocabulary very well, you won’t
understand the text. The sentences aren’t excessively long and are usually to
the point. This makes the text pretty dense though. For example, it’s hard to
make sense of the definition and formula for the trapezoid. And other parts of
the text. This is because the text requires you to look back and forth at the
picture, the written text, and the equation. This requires work and if you don’t
know what you’re doing it is tough stuff. Although, the text does make it
possible to do the work step by step.
4.
If you want learn a cool proof of the
Pythagorean Theorem, here one is.
5.
Why is the picture drawn as such for this proof?
1.
Berlinghoff, William. Gouvea Fernando. Math
through the Ages: A Gentle History for Teachers and Others. Farmington, Maine:
Oxton House Publishers. 2002.
2.
This text include various proofs of the
Pythagorean Theorem, its history, and its use.
3.
The text isn’t overly complex. In fact, it’s
quite simple, you just need to know a little math, such as squaring a length
gives you the area of a square composed of the length you squared. On the page
I copied, there are 2 proofs without words, so considering the text to be just
the written words will miss out on a lot of the information on the page. The proofs
without words require a knowledge of geometry, specifically how to find area of
different parts of the pictures and then to string it all together so that it
is understandable. That’s the main thing with these math texts: you have to look
back and forth between the text and the pictures to glean an understanding.
4.
If you want to know purely visual proofs of the
Pythagorean Theorem, this is a good place to do it.
5.
Can you think of a different proof of the
Pythagorean Theorem other than what’s given?
1.
Angie Head. Pythagorean Theorem. 1997. http://jwilson.coe.uga.edu/EMT668/emt668.student.folders/HeadAngela/essay1/Pythagorean.html
2.
This is a really nice short essay on the history
of Pythagorean Theorem and various proofs of it.
3.
The complexity isn’t very high, especially for
the history part which reads well. The texts of the proofs themselves are
difficult because one has to repeatedly look back and forth between the picture
and the text, so that they may have a visual representation of the proof as it
goes on. There aren’t words of excessive complexity and the sentences are kept
short.
4.
This would be a good place to go for a brief
history and list of some of the simpler proofs the Pythagorean Theorem.
5.
Are there proofs of PT that you don’t understand
but would like to? See if anyone close to you understands the proof you would
like to understand.
2.
This webpage has 103 unique proofs of the PT.
3.
The complexity is somewhat high because many of
the proofs are not given full explanation but rather are left implicit for the
reader to deduce for him or herself. Again, it is hard to look back and forth
between the picture and the text to construct the meaning of the text for him
or herself. The sheer complexity of some of the proofs make this text a
difficult read. One definitely must be an active reader to understand what is
being said in these proofs.
4.
This read would be good for you if you wanted to
collect the various proofs of the PT.
5.
Are any of the 103 proofs incorrect?
1.
Math is Fun. Pythagorean Theorem Algebra Proof. 2013.
http://www.mathsisfun.com/geometry/pythagorean-theorem-proof.html
2.
This website is simple and gives a nice, easy proof
of the Pythagorean Theorem.
3.
This website is pretty simple to understand and
requires little mathematical knowledge to understand the proof because they
explain it all thoroughly. The words were not obscure and the sentences were
short. Everything is well organized, making it easy to understand overall.
4.
If you just want one simple proof of the
Pythagorean Theorem, this is the place to go.
5.
Could this proof be made easier to understand?
Overall, these texts can be used in combination to yield the best communication possible. Using the easy to understand ways of writing along with well-described pictures with necessary arrows of reference would give the reader the best understanding.
Overall, these texts can be used in combination to yield the best communication possible. Using the easy to understand ways of writing along with well-described pictures with necessary arrows of reference would give the reader the best understanding.
Michael,
ReplyDeleteGreat resources and nice range of text complexity. My question to you would be how are you going to address the areas of difficulty in your first two texts in terms of vocabulary knowledge needed and confusing wording? You highlight a lot of different proof examples which would provide students with repeated access to the knowledge in different ways which is great for learning! Could you have students design proofs in class to display their understanding of the Pythagorean theorem?
I don't think I will use the more complex text directly in class. They will be for my own knowledge to inform the class.
DeleteI could have the students design their own proofs of the Pythagorean Theorem in class, but to come up with a proof independently is surprisingly difficult. At least, it was for me when I first learned of the Pythagorean theorem. I just believed it because it worked, not because of any proof I could come up with.
Michael, I really enjoyed looking at your text set on the Pythagorean Theorem. You did a wonderful job assessing the complexity of each text. I really liked how you took the perspective of a student or other outsider to the massive mathematical knowledge you know. For me, this really made me think about the text and how complex it was in another light, a much more realistic light. Going along with Ashley, how do you plan on addressing the complex vocabulary? I think your last question, "could this be made easier to understand" is definitely getting at this idea. What would you do with those responses then? I love this question. What a great way to assess the student's understanding from a new direction!
ReplyDeleteHey Michael, nice job creating this blog with all the various texts. I had to laugh to myself because I too used the text from our 675 class together. It was such a great and useful text wasn't it!! But I agree with your text complexity explanations. It is a very difficult text to comprehend if you don't already have a good basis of mathematics knowledge. I wanted to give you one idea that you could use to teach your students about the Pythagorean theorem and its' proof. I learned that it took several hundreds of years to come up with the first proof for the Pythagorean theorem. You can find images of early proofs on google to show your students. I think that they would find it interesting how the first proofs came about and how it was so difficult to create that first proof but now today we have what??....like a hundred or so proofs for this theorem! Just an idea. Nice job on this post =)
ReplyDeleteI really like, especially with math, when they use examples and I believe the second and third text you used gave more than the others, I would love to find out more bout the Pythagorean theorem!
ReplyDeleteIt's interesting how there are so many proofs to the Pythagorean theorem! I like how you include texts of the same kinds of things each with a different level of complexity and different voice. It is definitely helpful to see different styles of writing applied to something.
ReplyDelete