The topic of how to incorporate word problems is a hard one for me. I have personally always enjoyed word problems and I was able to see the beauty and the imagination in them. Perhaps I've also enjoyed them because I was good at them and I was able to show off my skills. But I realize that not everyone shares my sentiments and I do recognize that word problems are often not related to the real world in any way. Acknowledging this, I would love for my students to see the imagination and perhaps partake in creating their own crazy word problem in my future classroom. Depending on the demographic of my classroom, and students opinions, word problems might even be optional in my classroom so that the students who enjoy them can do them and the students who don't, can skip them and focus on something else in the unit that resonated with their learning.
Additionally, I was impressed by the anecdote that Dr. Gerofsky toldin class about her colleague(?) who brought the students outside their classroom to collect data points and then had them work on a relevant word problem. Doing this would change students' impression of word problems and they would probably be more inclined to give it a chance.
The article 'Surveying in Egypt' talks about the two ways in which surveys took place in Ancient Egypt. We talked during our class about some of the ways Ancient Egyptians measured their fields to report losses and taxes, which was confirmed in the article. It was surprising to me that the methods ancient Egyptian employed to measure distances were so sophisticated that these methods are still used in today's time. I had not comprehended before taking this course how mathematically advanced some civilizations were.
While reading this article, I wondered how did ancient Egyptians keep track of the cubit system to measure in a wide population? Surely, different people must have had different lengths of their forearms and fingers. Secondly, the article mentions that less is understood about how ancient Egyptians understood angles and which tools they used to measure angles and yet, one of the ways they created a right angle was with the help of two equilateral triangles. So, I wonder how they managed to get this far without the tools needed. Perhaps they did have the tools and we haven't been able to uncover them yet.
I really enjoyed this week's reading as it explores the topic of word problems, something that, in my experience, I have never struggled with and most of my students have. I noticed this pretty early on in my tutoring career that students find word problems difficult because they have trouble representing the scenario using math. I like to think about it as translating from one language (often English) to another (Math). To help my students overcome this barrier, I explored storytelling - I would not show them the written word problem, but rather make up characters and stories to present the scenario. Sometimes it helped, but often students got frustrated because the story was not realistic.
This reading, in a way, comforted me in the sense that I was not doing wrong as the tutor. I explored creative avenues to make word problems slightly easier for my kids and it is just that word problems historically have not been realistic. It is a funny thing to comprehend but it makes sense because word problems are imaginative. You make up scenarios that help you visualize, for example, a boy buying a 100 cantaloupes. For the Babylonians, they had no means to measure a grain pile 18-24 (referring to word problem mentioned on page 6) but they were willing to imagine. Perhaps word problems need not be realistic today, but we can hope for them to be so in the future.
Before our discussions in class about Babylonian math and the sexagesimal system, I had not really put much thought into how I perceive time. Of course, when I was younger and just beginning to learn to read the clock, I thought it would be convenient if a quarter of the hour was 25 minutes instead of 15 minutes. When I asked my teacher as why it was different, they told me this was how time was "set up" long long ago and I accepted it as a little blip along the way. I am only now realizing the significance of 60.
I found it really interesting that every eight years a minute has 61 seconds in order for the atomic time to stay consistent with the astronomical sign. There is also an inconsistency between the two articles as the MacTutor one mentions that no civilization came up with base 12 for their counting system but the other article mentions that Egyptians used the duodecimal system as it was easier to count up to 12 on the fingers joints of each hand.
I was, however, surprised to find out that I didn't know anything at all about the contributions of Spain towards the advancement of mathematics. There wasn't much about Spain in this chapter but I hope to learn more about it in this course. Another surprising fact that I encountered in this reading was the Mayans were able to make such advancements in astronomy with no glass or optical devices at all. To get a perfect estimate of synodic period Venus without such equipment is beyond impressive.
This is in response to the in class activity on Babylonian math done on Monday, September 8. My classmates brought up some really interesting reasons as to why the Babylonians chose the sexagesimal system to count. One of my reasons that I can think of related to what was already brought up in class is that they counted on one hand - a fist representing "zero" and the five fingers representing the numbers 1-5. Another reason I can think of is that it has something to do with the position of the sun throughout the day. I'm not sure exactly what - but I suppose I will find out after researching. Today, we see 60 being used in a lot of concepts - an hour has 60 minutes, a minute has 60 seconds, 60, 120, 180 and 360 degrees are some of the special angles in trigonometry.
Upon researching why Babylonians used base 60, I realize that I had been overthinking about an obvious thing. 60 is a composite numbers that has factors that are themselves composite. It is divisible by 2, 3 and 5, thus making it easy to work with fractions. This is such a sophisticated way to do math!
This is not to say that as an educator I did not have questions on how I can incorporate history of math into my own teaching. I realized that a high school classroom is far different for a college lecture room and teachers do not usually have as much resources. The objections posed in the article on why history of mathematics should be incorporated seemed very valid until I read further along and realized that teaching history can be accomplished as easily as making posters, watching a youtube video or simply having a discussion in class. Section 7.4 of the article especially struck me because some of the examples shown in this article are in my teaching practice but I never stopped and realized that I was teaching history. I believe these practices are central to gaining a deeper (relational) understanding of mathematics.
This article has solidified my belief that teaching history of mathematics is very essential. It helps students understand the "why" of math, which satisfies their curiosity and encourages them to keep going.
