Course Final Reflection - Blog Response #18

It has certainly been a wonderful semester and getting to know great people. The structure and nature of the course was collaborative and refreshing, which was completely different when comparing it to my math undergraduate classes that I took alongside this course. There was a lot about math history that I didn't know of before this taking this class like base 60 number systems and the exact origins of Pythagoras theorem. I also knew very little about the contributions that ancient civilizations like Babylonians and Egyptians made to current mathematics. Some of the in-class activities involving solving ancient math word problems are definitely one of my favourite memories. Even seeing the glimpse of the origins of modern mathematics through Euclid's Elements was extremely interesting to me!

Overall, listening to my peers' discussions and presentations were the most valuable to me. Everyone is so passionate and intelligent about their ideas which makes learning from each other extremely enjoyable. The structure of this course further supports and fosters environments like this, which I'm sure that Susan will continue to maintain! 

I look forward to continue learning about more math history, story-telling, and art as I take more courses, participate in classrooms, and engage with the community. I hope to implement in my own class someday and pass all these fun ideas to my future students.

Until next time,

JJ Kim

Assignment 3 Reflection - Blog Response #18

Cellular automata was a fun topic to research about. The first time I learned about it was during a computer science undergraduate course about a year or two ago. When I realized that the project could be presented as a digital piece of media, I immediately thought that this topic would be suitable. Other than John Conway's Game of Life, there was very little that I knew of related to its history. It's quite interesting to find out that the origins started with a theoretical concept of populating other planets with self-replicating machines. 

While I figured that this topic would have interesting historical backgrounds due its modernity and implications, I was worried about how we could implement it to showcase to the class. My knowledge of coding is not very extensive, after all, I study mainly math and not computer science! Regardless, we decided to stick with the idea and figure out things along the way. Thankfully, I knew about the existence of Pygame which allowed the creation of the art piece to be possible in the first place. Another challenge came about when it came to implementing the rules for some of the cellular automata. Initially, the "Reaction" one would become static and lose its mesmerizing patterns after a few generations, but a solution to this problem was to add some slight randomness to continuously shake up the state of the cells. Since Pygame isn't a very robust software, our board sizes were finite and relatively small. I dealt with this issue by allowing the cells to wrap around the edges, which is possible thanks to our favourite modulo operator! I still have questions regarding on how I can create cellular automata with even more complex rules and patterns, or how it would like like in higher dimensions.

Our presentation slides looked amazing, especially due to Carson's contributions and his drawing expertise! We didn't realize how fast 20 minutes could go by during the presentation so we should have been more mindful.  There was a lot of historical details despite it being popularized in about the last 50 years. If we managed our time better, maybe it would have been nice to go over a bit more in detail on how some of the algorithms ran; I'm not entirely sure but maybe some people were curious about how the code runs. Overall, I was very happy with our presentation and glad that the project turned out the way it did. The mathematics involving cellular automata is very interesting and it is capable of producing some amazing artistic pieces!

Assignment 3 - Blog Response #17

Carson and I worked on the history of Cellular Automata. It originates from the field of computer science, which is a branch of mathematics that has garnered a lot of popularity in the last 50 years! Our presentation will feature 4 pieces of digital art. 

The first one is Stephen Wolfram's "Rule 30". This is a 1-dimensional cellular automata with elementary rules that are encoded by binary representation. We wanted to start with this to introduce the basics of what cellular automata looks like. It utilizes Python packages "numpy" and "matplotlib" to allow us to store the rule as an array with 1's and 0's as elements and subsequently plot to show the outcomes of the iterations. Here, the vertical axis represents time and any horizontal cross-section of the image represents the state of all the cells in the array at a specific point in the pattern's evolution. The rules are simple but it produces a complex and chaotic pattern! 

The next three examples utilize pygames, which is an open-source cross-platform library for the development of multimedia applications like video games using Python. It makes programming 2-D cellular automata intuitive thanks to the implementation of certain convenient functions. 

The second one is the classic "Game of Life" by John Horton Conway. We wanted to show it off as it represents a pivotal moment in cellular automaton history, representing the moment when the concept flew into mainstream and wasn't just exclusive to academia. This inspired many others to create their own rules and creative designs. The specifics of how Game of Life works will be expanded on during the presentation. We will showcase it with colours and various patterns like glider, gosper  glider gun, block, and switch engine. 

The third one is called "Reaction". This type of cellular automata is inspired by research done in chemistry, particularly the Belousov-Zhabotinsky reaction. Due to its spiraling and oscillating patterns, it is commonly studied through a mathematical lens through models and simulations. We hope to show it off in a cellular automaton context!

The last one is called "Brian's Brain". This is a particular rule set discovered by Brian Silverman. We thought it would be a great addition to our collage as it produces beautiful patterns. We wanted to capture history, mathematics, art, and philosophy through this creation. There is background music as well, so hopefully it's enjoyable to experience!

Here is the link to the slides:

https://docs.google.com/presentation/d/1e4g0f9ziMtitHs39ReJUr_33CCBnJ21u1PiqiHKduo8/edit?usp=sharing

Here are some snippets of our artwork. To fully visualize the animation, a suitable source code editor like VS Code is convenient for running the .py files.

Here are the associated .py files:

https://drive.google.com/drive/folders/14WwBmJ-hpqTB0CyzKBXLSdpdYtixIvWh?usp=sharing

Assignment 3 Draft - Blog Response #16

 I will be partnered with Carson, and we will be working with the history of cellular automata. The format of our artistic piece will be electronic/digital art through the use of code (most likely Python).

Draft reference list:

Berto, F., & Tagliabue, J. (2017). Cellular Automata (E. N. Zalta, Ed.). Stanford Encyclopedia of Philosophy; Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/entries/cellular-automata/ 

Poundstone, W. (2024, October 24). John von Neumann. Encyclopedia Britannica. https://www.britannica.com/biography/John-von-Neumann

Sarkar, P. (2000, March 1). A brief history of cellular automata. ACM Computing Surveys, 32(1), 80–107. https://doi.org/10.1145/349194.349202

Schiff, J. L. (2008). Cellular Automata: A discrete view of the world. Wiley-Interscience. https://doi.org/10.1002/9781118032381 

Wolfram, S. (2002). A new kind of science (pp.876-878). Wolfram Media. 

Assignment 2: Math History Reflection - Blog Response 15

My presentation was focused on the history of limits to infinity. It was really interesting to research on how it all started, especially before a time of mathematics where Arabic numerals and algebraic notation were absent. The majority of my presentation was focused on the findings of Archimedes and the area of a circle via infinitesimals. It incorporated a clever use of a proof by contradiction method, which somewhat surprised me as I thought that would have been more of a modern notion. Due to time constraints, it was impossible to cover the entire history of limits with every detail. It stretches over a millennia and the most interesting part is that the order of development started with integrals, then derivative, and finally limits. This is the opposite order of what is being taught in schools! 

One of the main things I want to take away from this and show students is that infinity is not mere value that we plug in the limits notation. It seems like due to the extensive amount of analytic work that students have to in a calculus class, they get desensitized to the concept of the idea and ignore the beauty and complications that come with it. Infinity was deemed as beast by mathematicians, and even the very best failed to wrestle with such concepts. Perhaps by presenting these historical moments, students will be able to relate and realize why it's okay to find calculus confusing. We have prime examples of moments of epic collaboration and battles between pairs of mathematicians like Kepler and Galileo, and Leibniz and Newton. And we can't forget that none of their work wouldn't occur without the work of Ancient Babylonians, Greek, Egyptian, and Indian mathematicians that pioneered the early foundations. 

Dancing Euclidean Proofs - Blog Response #14

 Although I consider math as art, I never considered the medium of conveying it through dance and human body movements. I was surprised and enlightened to see that there is a cultural pursuit in mathematics that utilizes both body and mind. One of the statements posed in the article is that the body's natural symmetries can be used to make simple geometric shapes like circles and triangles. I find this interesting because its such an obvious and unobvious fact at the same time. Perhaps the beauty we were looking for in mathematics was always right in front of our very eyes, or body I should say. 

I appreciate the amount of visible effort that was put into the choreographs of the dances. When watching the video, the performances were very fluid and smooth in transitions, which makes excellent clarity of the proofs that they were depicting. As the article describes, the process of going through various iterations of dance moves, concern in maintaining mathematical integrity, and the deliberate choice of the environmental location and sounds. All these considerations brought harmony in the arts and math, making the final product visually and auditorily pleasing, without reducing the technical contents of Euclid's proofs. 

Incorporating such activities in a high school classroom will definitely spark interest in students. Physical activity is almost never seen in a math classroom, so this could be an excellent alternative for students. Availability of classroom or outdoor space may pose as a constraint, as well as funding for specialized camera equipment like drones if top view shots are desired. 

Was Pythagoras Chinese? - Blog Response #13

 I definitely do think that acknowledging non-European sources of mathematics makes an impact to students' learning. Often times, students and even myself take for granted on the origins of mathematics that we get taught in the classroom. There is so much opportunity to create discourse in a classroom and promote diversity amongst students, especially in a math classroom where it's rare to see such actions take place. Leaving out important details of history and only focusing on European contributions can distort a student's view of mathematics. When we talk about the origins of how math came to be, and not just the techniques on solving problems, it provides a more immersing learning experience and gives students with diverse backgrounds a chance to have moments of realizations and possibility relate their own cultures. 

When I see naming's of mathematical concepts, the immediate question that I always have is why are some theorems named after mathematicians, while others are named by functionality, like the Fundamental Theorem of Calculus. While I do understand that recognizing the individual who discovered the theorem is done out of respect, we often have inconsistencies like we have seen with Pascal's Triangle and Pythagoras Theorem. Sure, we can take it with a grain of salt and accept it as it is, but it still feels wrong to eliminate a story that represents decades if not centuries worth of collaborative work across the globe. Perhaps we should try to aim theorems to be named by descriptors or we as teachers should clarify names of theorems whenever necessary. 

Euclid and Beauty - Blog Response #12

Euclid's Elements has proven itself to be one of the greatest mathematical textbooks to have ever exist. I believe that one of the  the reasons why Euclid and his book have been so important and popular for centuries is that it is able to uncover ground without circular reasoning. I speculate that there must have been frustration amongst mathematicians before Euclid when it came to logically proving ideas, despite how blatantly and intuitive it seems. For example, if one were to look at a diagram of a square, how do you know that it is indeed a square? I think that it's the general concept of not taking things for granted, and making sure we always pay attention to our surroundings is what we have valued throughout these years. Also, if I remember correctly, Euclid's fifth postulate raised many eyebrows until hyperbolic geometry was studied. This is a great example to always question the obvious!

There is elegance in the way we prove that things that occur in the world.  Is there beauty in defining the given truth? I believe so. It's quite fascinating how we can fix a couple axioms, and then construct complex theorems out of them. Euclid's work was mainly based on the 2-D plane yet it served as a basis for relatively and related ideas like determining the shape and dimension of the universe. The beauty comes from how we can set some simple, intuitive facts (axioms) and develop them into sophisticated and crazy ideas through logical reasoning and proofs. 

The Dishes puzzle - Blog Response #11

 Here is my approach in solving the dishes puzzle without the use of algebra. 

First I will interpret the information and relationships that are given to us.

• Every 2 guests shared 1 dish of rice
• Every 3 guests shared 1 dish of broth
• Every 4 guests shared 1 dish of meat
• There are 65 dishes used in total

Okay, then to make my calculations easier, I see that 12 is the common multiple of 2, 3, and 4. Then I can say that for every 12 guests there are:

• 6 dishes of rice
• 4 dishes of broth
• 3 dishes of meat

Then for 12 guests, there are 6 + 4 + 3 = 13 dishes. 

Then I interpreted the question like this: If a group of 12 guests enters the restaurant and requests 13 dishes, how many groups are required to reach a request of 65 dishes?

After some quick guess and checking, I see that 13 $\times$ 5 = 65, so 5 groups of 12 is 60 guests in total! 

I think that it makes a difference to our students to offer problems that come from diverse cultures. Especially when students see examples that relate to their own backgrounds, they may feel a personal connection to the material. Maybe it makes them more interested in the problem, or it maybe it's just the simple thought of seeing their culture being recognized in the classroom that makes them happy! To me, it's always the little things that matter and if incorporating storytelling in the classroom brings the students joy, I see no reason why we shouldn't do it! 

For similar reasons as above, including fun and informational images can contribute to a lot. I can imagine a student looking at that image of the banquet and going "Mmm..., that makes me hungry." Even if its a small difference, it still has a lot of power to bring colour in a classroom. 

Assignment #1 Reflection - Blog response #10

My group and I tackled problem 1.2.4 from 5000 Years of Geometry. 

Here is the link to our presentation: 

https://docs.google.com/presentation/d/1FsASoA7QqRUaOuKEkFRpz4ao2k-pwjKoL-1nAPdiKfA/edit?usp=sharing

When I first looked at the problem, it seemed rather simple. When observing the provided formulas of calculating the diagonals of 3 by 4 rectangle, it seemed to just work magically. That's when the deceptiveness of the simplicity shocked me. How did the Babylonians manage to calculate the diagonal of a rectangle from its sides without resorting to the Pythagorean rule? When we showcased the modern solution, its quite obvious that we use our handy $a^2 + b^2 = c^2$. The challenge came when we hand to decipher how the Babylonians approached this problem. 

After researching the clay tablet in question, I realized that the Babylonians, given their limitations of modern math tools, figured out ingenious methods of calculating diagonals and had a wide list of rectangle sides written in terms of linear combinations to produce the correct diagonal length. I still have some unanswered questions of regarding their discovery of their methodologies, but it astonishes me nonetheless. 

When we were doing our computations to show our work, we used the calculation of expanding binomials was prevalent. As an extension, I wanted to showcase how we can intuitively teach students on how we expand binomials through pattern recognition and imagery. Although we as teacher candidates have explored deep into math concepts and are aware of how handy Pascal's Triangle is when it comes to expanding binomials, students in high school often times do not get to learn these concepts. If you observe the BC curriculum and the list of topics that are taught, combinatorics and probability no longer exist. I noticed that senior students in math classes only know how to expand binomials through FOIL. 

I believe that combinatorics and probability have excellent content when it comes to developing thinking strategies to solve puzzles and play games, which is listed as a BC curricular competency. My aim with this extension is to remind us that we can teach students solve seemingly painful computational problems through creativity and restore teachings of certain content that has been lost in the past few years. 

The market scale puzzle - Blog Response #9

Since we are given a two-pan balance, given some weights, we have 3 actions to utilize:

1. Place a weight on one side
2. Place a weight on the opposite side with the herbs
3. Not use a weight at all

This gives us a systematical way to give value to our weight such that:

1. We can multiply by 1 to the weight's value to represent placing a weight on one side
2. We can multiply by -1 to the weight's value to represent placing a weight on the opposite side
3. We can multiply by 0 to the weight's value to represent not using a weight at all

This implies we use a base-3 system, given our three choices of 1, 0, and -1. 

Let $W$ be the weight of the herbs. We also choose the four weights to be $1g$, $3g$, $9g$, and $27g$. Note that these are the powers of 3. 

Then we can express $W$ as a combination of these weights such that,

$$ W = (a_1 \times 1) + (a_2 \times 3) + (a_3 \times 9) + (a_4 \times 27) $$ where each $a_i \in \{-1,0,1\}$.

and indeed the sum of all the weights $ 1 + 3 + 9 + 27 = 40$ as required. 

For example, if we want to measure out $W = 25g$ of herbs, 

$$ 25 = (1 \times 1) + (-1 \times 3) + (0 \times 9) + (1 \times 27) $$

Since we place the $1g$ and $27g$ weights on one side, and then place the $3g$ weight on the opposite side with the $25g$ of herbs. to balance the two scales. We do not require the $9g$ weight. 

Another example, if we want to measure out $W = 15g$ of herbs,

$$ 15 = (0 \times 1) + (-1 \times 3) + (-1 \times 9) + (1 \times 27) $$

Since we place the $27g$ weight on one side, and then place the $3g$ and $9g$ weight on the opposite side with the $15g$ of herbs to balance the two scales. We do not require the $1g$ weight.

Now if we are given a one-pan scale, we can apply a similar approach. This time we only have 2 actions:

1. Place a weight on the scale
2. Not use a weight at all

Again, we will represent each action by either multiplying the weight's value by 1 or 0. We choose the five weights to be $1g$, $2g$, $4g$, $8g$, and $16g$, which are the powers of 2. 

Similarly, we represent $W$ this time as, 

$$ W = (a_1 \times 1) + (a_2 \times 2) + (a_3 \times 4) + (a_4 \times 8) + (a_4 \times 16) $$ where each $a_i \in \{0,1\}$.

and the sum of the weights is $1 + 2 + 4 + 8 + 16 = 31$. 

For example, if we want to measure out $W = 11g$,

$$ 11 = (1 \times 1) + (1 \times 2) + (0 \times 4) + (1 \times 8) + (0 \times 16) $$

and we can follow a similar procedure for any $W$ from 1 to 31. 

When it comes to topics related to number theory, we notice that the concepts of representing numbers in different bases and balancing weights can be thought of in modular terms.

We can ask students to determine which weights are needed to weigh items and have a remainder of $1\mod 3$. Then we can have students group weights into congruence classes to understand how different combinations yield the same result in modular arithmetic. We can also change the maximum weight and number of pans. For the stories involved in these problems, we could have students research how different civilizations historically measured things and explore the development of measurement. 

Thoughts on word problems - Blog Response #8

It's quite interesting how word problems, something that has existed for millenniums, are still being questioned of its effectiveness and refined by educators even to this day. When it comes to writing word problems, I would want it well written. But what doe it mean to be well written? I believe that the problem should be clear to understand so that a student's success is dependent on their understanding of the subject, and not be impeded by language. However, as educators, as we focus on making sure that the questions we present for students to solve are unambiguous, includes all the required facts, and mathematically profound, it's easy to forget to add the flavouring that make math interesting. At least that was something I realized. Even if the problem presents itself as a plausible real-life scenario, is it truly and genuinely relatable to the students reading them? 

I want to be able to design problems that aren't just translations of math problems and create scenarios where students develop an algorithm in their head that they follow to solve such word problems. Perhaps, word problems can adopt a different medium that doesn't just involving reading a paragraph with specific criteria and writing down the solution that suits it. I would suggest to creating word problems that are open-ended where students have an opportunity to present their ways of thinking and create conversations in the classroom.

Ancient Egyptian surveying - Article Response #7

After reading the article on Egyptian surveying, I was quite astonished by how peculiar their measurement system was. Although there's not doubt that the Egyptians were masters of architecture, I still can't wrap my head around the fact how they achieved such remarkable levels of measurements and alignments given their limited tools at the time. But now I have come to realize how important surveying was for Egyptians in order to construct monumental structures, such as pyramids and temples, as well as for agricultural purposes, like measuring and restoring land after the annual flooding of the Nile. 

A question I have is regarding the creation of the unit, cubit. Why did the Egyptians decide to choose on a measurement that is not fixed in length? I acknowledge that the cubit is quite flexible, but I wonder what made it so convenient to dividing it into 7 palms or 28 fingers? In addition judging the terms "royal" cubit and "short" cubit, it seems to indicate that certain types of measurements are associated with pharaohs and power. Or was it tied more towards religious or cosmic beliefs, as speculated by the article as well? 

Babylonian word problems - Response #6

The context of what a world problem should be has always been an interesting topic to discuss about. Two opposing arguments that commonly comes up is whether a word problem should test one's practical or theoretical abilities. Indeed, when we solve word problems appear to have real world applications, we may deem it as practical. However, just because we replace numbers and symbols with sentences and phrases, does that make it actually practical? I think that applications that are contrived are quite meaningless. It is the ones that have real implications that prove to be beneficial. We need to make sure that word problems are true applications and not simply translations of mathematical formula. The difficulty arises when we try to represent the physical word using limited ideas. Questions that are ill made often have unnecessary jargon. 

Most of us here have most likely dealt with mathematics in an abstract and theoretical setting. Some people often hate dealing with proofs, while others thrive in an application-free environment. Both are great but I do think the former tends to not suit well for most individuals. We also see all the time, students become lost and experience math anxiety which leads to them jamming numbers with random operators. But realistically, what kind of application would ever satisfy a student? Should we provide the Babylonian ways about legal practices in dividing land heritance to beneficiaries? This was one of the first motivators of applications in history! Or do they need to know how to compute compounded interest rates and understand its growth? I don't think that the value of a word problem is always measured by how relatable it is. It is also important to hold high standards for both literacy and numeracy, while also effectively bridging the gap between them. 

Babylonian-style base 60 multiplication table for 45 - Blog Response #5

Here are some pairings of numbers that multiply to 45 that utilize base 60 fractions:

$$2 \times 22,30 = 45$$ since $2 \times 22.5 = 45$ so we can represent $0.5$ as $\frac{30}{60}$.

$$4 \times 11,25$$ since $4 \times 11.25 =45$ so we can represent $0.25$ as $\frac{15}{60}$.  

$$6 \times 7,30 = 45$$ since $6 \times 7.5 = 45$ so we can represent $0.5$ as $\frac{30}{60}$.

$$8 \times 5,37,30 = 45$$ since $8 \times 5.625 = 45$ so we can represent $0.62$ as $\frac{37}{60}$ and $0.005$ as $\frac{5}{60^2}$.

$$12 \times 3,45$$ since $12 \times 3.75 =45$ so we can represent $0.75$ as $\frac{45}{60}$.

  

History of time calculations, base 60 and base 12 - Blog Response #4

The two articles show how historical practices in measuring time and developing numerical systems are intertwined. The division of time into days, hours, and minutes has connections to the natural world and has evolved over time. It is an accumulation of astronomical observations, cultural practices, and historical developments. It is quite interesting how numbers like these may appear as simple or natural divisions, but they represent a story of refinement. Although the Babylonians used a base-60 sexagesimal system, it still influences how we measure time today. In fact, their historical number system reflects an extremely sophisticated understanding of mathematics and has left a lasting legacy on how we approach calculations and measurements. The remnants of their civilization can still be seen when it comes to angles, circles and spheres, and of course, time! 

There seems to be different reasonings between the two articles when it comes to why a base-60 system was chosen. The first article simply suggests that it is because 60 is a convenient number to express multiple fractions. It also learns towards historical context and practical aspects of time keeping in a more general sense. The second article goes in more depth and provides various theories. It focuses more on the technical aspects of numerical systems and their mathematical implications. 

Why Base 60? - Blog Response #3

    When I compare the numbers 60 and 10, I see that 60 has more factors 10. It has many factors that include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, while 10 only has 1, 2, 5, 10. This means that 60 is a lot more flexible and effective when it comes to dividing it by smaller numbers. I also think that certain fractions like halves, thirds, quarters, fifths, and sixths can be easily represented with a system based off 60.  The most useful application of 60 that I use in my daily life is, of course, time! It is indeed an important number to help us convert between seconds, minutes and hours. I also enjoy listening to music set at 60 BPM because it tends to be relaxing and emotionally powerful. 

    After doing research, it does indeed seem that the Babylonians valued 60 for its highly composite nature. Without needing to resort complex fractions, they were able to effectively carry out trade, measurements, and astronomical calculations. To add onto the point regarding astronomy, the Babylonians divided the sky into 360 degrees, a multiple of 60, to track celestial movement and accurately create calendars.

The Crest of the Peacock introduction - Blog Response #2

     It is quite surprising to read about the adverse affects of colonization when it comes to overwriting history in a mathematical context. It is disheartening to hear that European ideologies dominated in the 19th century, resulting in the devaluation of colonized peoples contributions. We see the same occurrence even further back in history as the Eurocentric model credits Ancient Greece for the origins of math and not Egypt nor Mesopotamia. I like how the book goes into more depth and shows us gradual improvements of figures that holistically represent the trajectory of mathematical development. Although the later figures depict confusing arrows that point in various directions and even having multiple of them converge to a singular spot, it emphasizes how math and culture is intertwined through diverse eras of countries and civilizations. Math is a collaborative process and we should aim to recognize all those who have contributed. 

    I also find it interesting that there are sources and possible factual evidence that describe Pythagoras travelling around the world to places like India. It makes me wonder if there are documented cases of any other notable scholars at time decided set off on foot or sail to explore the world in search of knowledge. Something that also came to my knowledge in recent years is that math concepts like place-holder values, solving quadratic equations, and the infamous Pythagoras theorem have all made their appearance in various regions. I wouldn't have ever guessed that the word "algebra" is of Arabic origin if I never took the time to inquire about it. I hope that our society continues to attribute mathematical findings to their appropriate contributors and accept it in all its diverse forms!

Why teach math history? - Blog Response #1

    

    My initial opinions on how math history should be incorporated into teaching is to give students a tour of how historical and ancient mathematics were tackled by past mathematicians. Ever since the modernization and formalization of math, students will be inevitably introduced to rigorous theorems and definitions. There are many math concepts that I struggled to grasp but something that shocked and gave me a sense of validation is when I learned that these concepts were giving headaches to the very mathematicians that developed them. This is why I think implementing history is a great way to help students gain an intuitive understanding of hard concepts by putting them through the lens of a period where information was not widely available. In addition, I was always inclined to believe that learning math is more individual focused during my time in school. But in fact, history says quite the opposite. Collaboration is the catalyst that drove generations of mathematicians from all over the world to work together and uncover the mysteries of our world.

    After reading the article, I appreciate the fact that they touched on the concepts of dialectical learning. Indeed, history is like the naïve and confused kid in their first year of high school figuring out where their classes are and who their friends are. While mathematics is now the successful and mature adult who’s got their life figured out. The contrast between developmental and polished stages of work provides completeness and an appropriate beginning and end to a wonderful story. I also like how the article points out math as a cultural endeavor. To gain practical skills and maximize utility are not the only reasons to learn math. In fact, to say to oneself, “I want to study math because it seems cool,” is a simple yet excellent reason to learn math as well. Students are often stripped of their creativity once they get lost in memorizing definitions to score well in exams. In fact, there is sublimity in mathematics, and we often times forget that art is inherently embedded in math.

    The article has further strengthened my belief that teaching historical math is important to students. I wasn’t aware that articles that included integration methods and models like this existed since I was rarely exposed to it as a high school student. Just recently, a professor of mine brought up the Navier-Stokes equation during a lecture and said that whoever can solve it first will be granted one million dollars! We need to pose more thought-provoking to students and provide the necessary motivation that they deserve. Thanks to the article, I hope to challenge myself in the future and incorporate these ideas in my classroom.

JJ Kim EDCP 442 2024_09_04

Hello, this is JJ Kim's EDCP 442 blog!