Letters from Future Students

 

Hi Mr. Braun,

 

I just wanted to send you a quick shoutout and say thanks. While math wasn’t always easy for me, you were able to help me get through. My mom was so happy that I was able to make it through high school, even though I never continued with math in academia.

The reason I’m reaching out is because I just finished an exam for my plumbing apprenticeship. It wasn’t the math that you are probably used to, but studying for it ended up being really easy. I remember what you said about pattern recognition and was able to build upon that to ace the exam. None of my friends in the program know anything about math, but I was able to help them out.

Thanks for never giving up on me!

 

Hi Mr. Braun,

I just wanted you to know the repercussions of your words. I remember how much you I spired me to follow skills and further my math knowledge. Well guess what? I graduated and got a job in a highly math related field and it is terrible. My life is terrible. You never told me math used in the real world is so soul sucking. Sure it’s fun in the abstract ways of beauty, but what good is that when I have to pay the bills?! And guess what? My job is being automated next week because it’s all algorithm based anyways. Going into a field which emphasizes social skills would have been a better investment, but because you showed me the “beauty of math” I got bewitched and am now here.

Thanks for ruining my life.

**UPDATE**

I worry that my excitement about math may inadvertently deify the subject to some students. My enthusiasm for math is one of my strongest assets, and I feel that I will make math more attainable to many students who would have otherwise been scared of the subject. However, I worry that my excitement could bring a level of fanaticism that is not compatible with our current society. In my experience in the corporate field, I found that math used in the real world really was soul sucking. I obviously don't want to tell this to students because I want them to be engaged, but I don't want to lie to them.

Math is an art, but when art and a capitalistic society merge the art can become tainted. My experience with engineering was exactly this. I will try to guide students down proper paths that allow them to play with the art of math more earnestly. 

The dishes Problem

 My first step was to reword the problem and understand what was happening. When the chef says “every 2 used a dish of rice” it means that each guest had half a dish of rice. Another way of looking at this is that, of the total number of guests, half of them had a dish of rice, one third had a dish of broth, and one quarter had a dish of meat.

Let’s represent the total number of guests by twelve groups of one twelfth. This is because we can easily figure out halves, thirds, and quarters of twelve. Half the guests had a rice dish, that is 6 twelfths. A third had a broth dish, that is four twelfths. A quarter had a meat dish, that is three twelfths.

Rice

Rice

Rice

Rice

Rice

Rice

Broth

Broth

Broth

Broth

Meat

Meat

Meat

 

You can see that we have an extra twelfth of dishes. Because there are 65 dishes served, there is an extra twelfth. The problem becomes “What number, when increasing that number by one twelfth of itself, becomes 65.” Traditionally, algebra would be used at this point. However, a culture could guess and check until they arrived at the correct number of 60 guests.


While presenting itself as a problem of Chinese origin, the Chinese culture does not exist in the problem outside of the choices of food. However, the existence of the problem as a piece of history, going so far as to provide the original historical text, is very important. It shows that the traditional western view of mathematics is incomplete by giving a concrete example of maths existing outside that realm.

The fact that this is presented as a story does make the problem more enjoyable to solve, almost as if we are being transported back to an ancient Chinese restaurant. It is still nonsensical, one would simply count the number of tables and average table size before counting dishes. But if one can understand the problem as a fun test of our math abilities with a flair of the dramatic, it becomes much more enjoyable. 

Evan's Reflection on Lockhart

The points Lockhart makes about math and culture in this article were amazing. The analogies to the musician and artist’s dreams were beautiful. I agree that the art of math has been lost due to a societal fascination with utility. This obsession can also be seen in the lack of funding awarded to arts programs. Mathematics is an art who functionality is more widespread, but that does not mean that math and its function are inseparable. I loved Lockhart’s point that marching bands may make armies more efficient, but music exists outside this concept. I also appreciated Lockhart’s elegant definition of math as the art of manipulating simple, imaginary things and seeing how they react.



I was enamoured by Lockhart until he began his critique of “the curriculum,” after which I began to disagree with him more and more. The idea that math does not build upon itself is non-sensical. Even if one were to buy into Lockheart’s idea that students should learn their own math, some concepts will still require students to know the solution to other simpler problems. One cannot imagine the abstract nature of multiplication as groups before understanding the abstract nature of incremental increases. There is no correct way to structure the math curriculum, but I would argue that some structure is necessary. I would use a metaphor of driving from BC to Halifax; sure there are many different roads and paths that you can take, but to contrive of a path that jumps from BC to Ontario to Alberta to NWT to Nova Scotia is nonsensical.



This article relates heavily to Skemp’s idea of instrumental vs relational mathematics. However, Lockhart takes a very radical approach that I do not necessarily agree with. Lockheart seems to argue that not only is instrumental mathematics bad, but teaching it is a moral failing that would make Euclid and Pythagoras roll in their graves. I prefer Skemp’s position of neutrality on this issue, recognizing that there are benefits to both types of instruction.



Moving forward in my teaching career, I will strive to coax the beauty of math out of the hollow shell Lockhart describes as "The Curriculum." I understand that I will not be able to change the curriculum myself, but I believe that by knowing the beauty is there, my excitement and appreciation will be contagious enough to invigorate my students. Hopefully they will learn that math is not the scary beast of boredom, but the beauty of our universe.