How would I teach word problem?

Our class recently had a thought-provoking discussion about word problems in math. The general consensus was that we’ve all become so adept at solving them that, over time, they’ve lost their meaning in a real-world context. Instead, word problems now feel like an exercise in identifying keywords and units that can easily be plugged into formulas. While we’ve become proficient at this, the process feels mechanical—less about understanding the problem and more about finding the right numbers to fit a predetermined solution.

However, when I was a child, I had a very different experience with word problems. Growing up in my home country, the math curriculum placed a greater emphasis on storytelling and narrative within word problems compared to the curriculum here in British Columbia. I remember that those word problems often felt like a refreshing break from the gruelling algebraic exercises. While algebra could be tedious and repetitive, word problems brought in a sense of creativity and engagement. 

One of the most rewarding moments came when I got my tests back and saw that I had earned full marks on the word problems. It felt like a validation of my abilities, especially because I was often one of the few students who not only understood the questions but could also work through all the steps to arrive at the correct solution. That sense of mastery was incredibly motivating.

Reflecting on both our class discussion and my personal experiences, I believe that to make word problems more conducive to learning, they need to be more engaging and challenging. Teachers should experiment with how word problems are framed—how the information is presented and how the questions are worded. The goal should be to spark curiosity in young learners, encouraging them to think critically and creatively rather than simply applying formulas. By integrating more context, narrative, and even humour, we can turn word problems into opportunities for exploration. Because after all, children are naturally inquisitive and constantly seeking new information.

Response to Surveying in Ancient Egypt

One thing that truly surprised me in the reading was the significant role religion played in ancient Egypt’s measurement systems. Their measurements, proportions, and even the angles of their building structures carried deep religious and spiritual implications. Temples, pyramids, and other sacred sites were designed to honour their gods and reflect their beliefs. This concept reminds me of the Chinese practice of Feng Shui, which also emphasizes the influence of spatial arrangements on energy and fortune. According to Feng Shui principles, the placement and orientation of objects or structures, such as homes or furniture, can directly affect a person’s well-being, luck, and prosperity. For instance, Feng Shui experts often recommend ensuring that a backdoor is not directly aligned with the front door. This is believed to prevent wealth or good fortune, represented by energy entering through the front door, from flowing straight out through the back door. In this way, people can retain the positive energy within the home. It’s fascinating how these two seemingly distinct cultures shared the same belief about spatial orientations. 

I have two questions: First, who was responsible for educating the surveyors about the various types of measurements? Second, building on that, how did the ancient Egyptians teach the measurement concept? Was there a formal system in place for instruction, or was it passed down through verbal or informal methods?

Multiplication Table of 45 in Base 60

 

Response to Word Problems as Genre in Mathematics Education

When I was working as a barista at a local cheesecake café in high school, one of my responsibilities was ordering various types of cheesecake from the main distributor. I estimated how much of each flavor would be sold based on past sales records and placed the order a week in advance. The calculation seemed simple: a variable, x (representing the projected daily sales for a particular flavor), multiplied by 7 to get the weekly supply. However, managing cheesecake orders became one of the greatest challenges of my short-lived barista career. I struggled to account for all the factors that could influence x. For example, there were times when it seemed like everyone in the city suddenly lost interest in hazelnut, and I’d be left with chocolate hazelnut cheesecakes sitting untouched in the fridge. Other times, I'd get a call from a customer requesting 20 blueberry cheesecakes for a catering event, only to realize I didn’t have enough stock. Missing out on such a large sale was frustrating (especially because it could’ve earned me a promotion to manager!).

Reflecting on this experience reminds me of how different real-life situations are from textbook math. In school, math was my strongest subject, and I excelled at it. Yet, when faced with real-world decisions, my judgment wasn’t always spot on. All the neat tricks I learned in math class—like calculating probabilities—felt almost useless in these unpredictable, practical scenarios. As Robson pointed out, applying textbook knowledge to real life isn’t always straightforward. Sometimes, I wonder: in a world full of endless possibilities and unexpected outcomes, how can my math education truly help me succeed both professionally and practically?

Response to two articles on measuring time

The first article discusses the compounding effect of the 12-hour time intervals and Balylonian’s base 60 system on the division of time the way it is today, while the second article expands on why the sexagesimal concept came into place. The article drew my attention to the proposed theories of the origin base 60, and how a lot of them seemed to be self-contradicting. It was an interesting point because it made me go back to article no1. A question formed in my head-- is it really necessary to go to lengths to find out the “real story” behind this counting system? Could it be possible that base 60 happened to be the most applicable in studying astronomy and geometry (as seen in the first article), and for that reason it has persisted all throughout history. In other words, base 60 has more added significance than the real value it possesses. 

I visualize the passage of time as making a pizza. First, you have pizza dough. It is round and malleable, and one is free to choose any shape and thickness, depending how large they want the pizza to be. Next thing comes to stretching out the dough with the choice of shape. Like how the day and night are divided into equal intervals, we can slice the pizza into 12 or 24 pieces, representing the hours. Pizza toppings (black olives, pineapples, sausage crumbs…) come on top of each slice. They are comparable to minutes because they constitute each slice (each hour). Interestingly, the first article introduced me to different variations of time division, and how the standard way of measuring time took its form after a long evolution. I couldn’t help but wonder how weeks came into place. Perhaps this would be my own inquiry on the side! 

Why base 60?

 My thought was that the Babylonians associated 60 with a special meaning, like how people often say 7 is their lucky number. Having 60 as their base, it is possible that people wished for good fortune. My other theory is about some historical events that resulted in this number system. A modern example would probably be “a baker’s dozen”.

After my research online, I found out that  60 is unique in a way that it is the smallest number divisible by all numbers from 1-6. It is easily divided into portions without fractions.The second reason is because 60 is an overarching theme in time. Every 60 seconds is a minute, and every 60 minutes is an hour. Also, 60 is a multiple of 12,  so it is somehow related to the duodecimal system, base 12.The way the people at the time counted by hand. Here is a video that demonstrates this.

https://www.facebook.com/jain108academy/videos/origins-of-base-60-finger-counting-method/760257301495219/

Response to Crest of the Peacock

The first thing that surprised me was how Eurocentrism in mathematical history is constantly being perpetuated even to this date. This reminds me of my middle school math teacher complaining that the world-recognized origin of the Pythagorean theorem was largely western, which was contrary to his belief that the theory started from China. According to ancient Chinese literature, it was called gou-gu theory discovered by a teacher Chen Zi and his student Rong Fang. They were not known historically, unfortunately. In the book, Joseph describes the marginalization of non-European contributions in mathematical history. This could possibly be the cause of the lost documentations, or lack of credits given to math pioneers.

Another thing that surprised me was the exclusion of non-European math contributions through the education system. I found that this is still the case in the modern day school curriculums. In high school, I briefly learned Pascal's triangle. However, multiple mathematicians in the past have made significant contributions to the topic, such as the Chinese mathematician Yang hui. However, we didn’t learn the diverse historical background of the math concept, and we simply accepted the idea that it only has one original root. 

Response to article : Why teach math history?

When I was in grade seven, I distinctly remember my math teacher telling the story of Rene Decartes and his invention of the coordinates system. The story absolutely pulled me into another realm of math -- one that is full of interesting stories and myths. Looking back now, it felt like a starstruck moment, and it motivated me to get on a quest that is equally as significant someday. As a future educator, I believe that learning math history opens up one’s eyes, and I have always been searching for ways to feed my students’ curiosity by teaching them about the topics. 

During my days working as a math tutor at a local learning center, my biggest challenge was to teach kindergarten and lower grade students about numbers. I could definitely relate to their reluctance and fear, so I sought to keep my students’ attention by teaching basic number operations in “ancient” ways, such as using animal stickers and lollipops to help them understand addition, subtraction, etc. I also talked about the origins of math, which they always found mysterious and fascinating. By leading these activities, I boost my students’ interest in learning. I noticed that they no longer dreaded doing homework because I’d made it more enjoyable. 

After reading the article, I was impressed by the number of ways that teachers can incorporate math history into their teaching, as contrary to my belief that learning math history takes only one form (story-telling).  Ranging from worksheets to historical packages, all the creative ways can spark students’ curiosity and encourage them to even continue the learning process by themselves. As mentioned in the article, students from Denmark had their own opportunities to lead learning activities, and use their research results as a platform to educate others. 

Additionally, I agree with the point made in the article that math is not a standalone subject to be studied on its own. It is a multi-disciplinary area inclusive sociology, humanities, politics, and many others. Learning math from an evolutionary and broader scope often inspires one with new perspectives. 

After reading the article, I changed my ideas about my own identity as a future math teacher. Having mostly studied math in my undergrad, I look forward to learning about math history from the course, and also learning from students of other teaching cohorts--literature, art, humanities, etc. Their knowledge in these subject areas continue to inspire me everyday.