False Position

My word problem: Two of a number and its square root are equaled to 36.




2x + √x = 36

Try 4: 2(4) + √4 =

8 + 1 = 9

36/9 = 4, therefore multiple 4 by 4

2(16) + √16 =

32 + 4 = 36




It worked!

Was Pythagoras Chinese?

Does it make a difference to our students learning if we acknowledge (or don't acknowledge) that non-European sources of Mathematics? Why, or how?

I think that it is important to study the history of math in a fully holistic manner. It doesn't make any sense to me why someone would study Greek math history but not Chinese? Are their discoveries any less impressive or important? I would think not. The arguments behind teaching math history as part of the curriculum; understanding the trial-and-error aspect of math, understanding that math is always evolving, would surely also apply to Chinese math history. I guess it is true what they say, history is written by those that create it and in our western world we are more attuned to the western history of math, I think that should change though. 

What are your thoughts on the naming of the Pythagorean Theorem, and other named mathematical theorems and concepts (for example, Pascal's triangle)

The naming of proofs and math concepts is a complicated subject. On one hand, the Babylonians and Egyptians understood the relationship between sides of a triangle prior to Pythagoras, so why should he go down in history as the master of the triangle? Is it because his way of thinking was very western? Prior generations had possibly placed less importance on individual fame and recognition, placed less importance on a formal proof process and Pythagoras has reaped the rewards of such. On the other hand, where do you draw the line? If not the Pythagoras Triangle then what? The Egyptian triangle? But then the Babylonians would be up-in-arms. I think that there is no solution to this problem and if Pythagoras was the one that made the theory famous, I'm fine with that.       

Why Teach Math History?

Pre-reading ideas about whether, why, and how math history should or could be incorporated into math teaching. 

As one of the few non-education majors, I am not sure I can say how I would implement it into "my own" math teaching. I can, however, put myself into the shoes of a high school student and think about what I would want to learn about. That being said, I see math history playing a minimal role in high school math education. I think that the history of math can be helpful if it provides context to complicated techniques, showing how a certain type of math was discovered could create real-world applications for math in the minds of students. Other than that though, I think it would just confuse kids and overload them with information that they don't necessarily need. 

Things that made me "stop and wonder"

"History can be torturous and confusing, rather than enlightening", this is exactly what I was trying to say, this has been phrased a lot more eloquently than I could ever say it, but I 100% agree. "Lack of time", I also agree with this, highschool math already has a ton of concepts packed into it, I feel that adding the history of math would increase that "knowledge overload" that I discussed above. "The active predisposition towards mathematics", I agree that this point is interesting. Math should be seen as ever-evolving and should inspire students to question everything and maybe even discover new are better ways to approach math. A few hundred years ago math looked a lot different than it does now and in a few hundred years with will look different again.  

Conclusion

I think that some very valid points were made for both sides and I now definitely now see the benefits of teaching the history of math to students more than I did prior to reading this. However, my main doubts remain and I think some of them were even strengthened and confirmed by the article. 

Alice Major on Mayan and Other Numbers

Is this something that you might want to introduce to your secondary math students? Why or why not?

I likely would not teach this to secondary math students. My reasoning is, although this is interesting, I'm not sure it would help the students understand math better. In high school, when students are learning concepts like pre-calculus and calculus, math can be very hard to grasp. I wouldn't want to complicate things any further

If you would use these ideas in your math class, how might you do so?

I think that these concepts can be applied and useful to a different age group. For example, in primary school when students are first learning to use addition and subtraction I could see this playing a role. The concepts and personalities of the numbers would obviously be simplified from what the Mayans used, to apply to primary students. I think that a video, showing numbers as personalities and how they interact could be extremely fun and useful to these primary school students. For example, showing a pair of fives as young and energetic twins, then showing a ten as a more mature and larger version of those fives, showing that two of those fives equal to that ten. This is a very rough example, but hopefully, you get the point. 

Do numbers have particular personalities for you? Why, how, or why not? What about letters of the alphabet, days of the week, months of the year, etc?

I have never thought about it like this, but now that I am thinking about it, definitely. I saw a meme a while back that said "I can't explain why, but the number eight, the day Thursday, and the month October all are the same", and I couldn't agree more. I tried dissecting the reason for it and I think it's all about being an even number and being close to the end of their respective spectrums. Eight is an even number and is very close to ten, October is an even-numbered month (tenth) and is close to the end of the year. I know technically Thursday is the fifth day of the week, with Sunday being the first but I think most people think of Thursday as the fourth day of the week and Monday as the first, which would make it an even-numbered day and close to the end of the week. Additionally, I see five and ten as being preppy and perfect, likely because of being seen as "round numbers". I see numbers 2,4,6 and 8 as being related because they are even. Three and nine are seen as the "rebels" to me, somewhat related to six, but a little rough around the edges. Then that leaves one and seven, I see one as being the baby of the group (self-explanatory) and I see seven as being the hipster. I think this personality comes from people choosing a number between one and ten, somehow seven is always the most common choice. This is likely because it doesn't fit into any of the usual categories (even numbers, multiples of five, multiple of three, close to zero, or close to ten), it is just kind of its own thing and I respect seven for that. After reading this story, I will definitely look at numbers differently. 

Assignment 1 Reflection

 Pythagorean Triples have been a favourite of mine for many years, since we learned about them in high school. It just seemed to be an incredibly simplistic solution. In high school, we didn't learn anything about the history of Pythagorean Triples though, so this was a cool opportunity to dive deeper. For example, I didn't know that Pythagorean Triples went as far back as Babylonia, this shows the depth and complexity that the Babylonians were able to accomplish, very impressive. It was discovered that the Babylonians knew a form of this theorem because it was found on a tablet and the numbers were so large that it stands to reason that trial and error could not have been used. It is a shame that one side of the tablet was cut off however, it would provide great context on how and why this tablet was used. Aside from the history of Pythagorean triples, this assignment was also a fantastic opportunity to put myself in the shoes of a teacher. I am one of the few non-teaching majors in the class so this experience likely taught me more than it did most of the other students. I was able to learn about a subject, then think about how it could be most effectively taught, which was a lot of fun for me. Being a finance major, excel is always my go-to-method, but this also made me think about how other students would want to solve the equations. Overall, working with my teammates on this assignment was an extremely fulfilling experience, and one I hope to have again (excited for assignment 2!). 

Dancing Euclid Proofs

Euclid is iconic not only for the collection of proofs that he has combined into a series of textbooks, but also for the beauty of his work. The first thing that jumped out to me was just how easy it was to communicate Euclid’s proofs into dance form. The simplicity of Euclid’s proofs makes it so easy to understand and therefore easy to communicate. There are not many other mathematicians that come to mind when thinking about interpretive dance, which I think really speaks to the artistry behind his work. Secondly, I was really taken by the way these shapes symbolized connections between two people. Despite the size of people’s arms not being the same, the dancers didn’t let that stop them from using their limbs to create connections in this dance. When I see lines of a triangle, I have always thought of them as just that, lines, now I will be able to see the symbolic connection of two people. Lastly, this article and video opened my eyes to the math and patterns that surround us in nature. This can be in the form of trees, shells and waves, all things that I have never thought of as being math related but truly, they are. Altogether, this article and video has made me think of math more as a living, breathing thing and less like numbers on a board. 

Euclid Alone Has Looked on Beauty Bare

 Admittedly, I have never been very good at understanding or writing poems. As far back as middle school, poems have never made a ton of sense to me. This poem was no different, it wasn't until I did further research that I began to understand this poem. Euclid was a Greek mathematician, often referred to as the "founder of geometry". His elements are often thought of as one of the most influential works in the history of mathematics, often being used as the main textbook for teaching math, especially geometry. 

My interpretation of these poems is that Euclid has seen beauty in shapes that no one else at that point was able to see. His geometric proofs have given beauty and grace to shapes that were once thought of as just "shapes". In "The Euclidean Domain", David Kramer questions this notion, asking "Has no one else seen hide or hair?". This is basically Kramer saying "we have all seen shapes, how is Euclid the only one that sees this beauty?". Kramer may have a point, during the current day and age I'm sure a lot of people see the beauty and complexities of geometry. Is this only because of the discoveries and proofs of Euclid though? I guess we will never know, but I think even Kramer would acknowledge how important Euclid's proof are still to this day.