Raymond EDCP 442

 After learning the long history of word problem, it is my opinion that I will continue the practice of word problem in my own classroom. Word problems have a few strengths in the class room. First, word problems allows learners to begin conceptualize the operations (algebra, arithmetic) into problem solving. Having students to think about applying what they have learned into a context based scenario allows them to gain intuition on when and where a certain skill can be used. Second, world problems are silly. I understand there are criticisms on they are not 'applicable' or 'realistic'. My approach in the classroom would be having students to design their own word problems (with a few examples), once they have entry level proficiency in the topic. This process allows them to engineer context where the topic / technique would make sense. Furthermore, I would use these word problems to formatively assess their understanding. I understand there are a few intrinsic issues w...

 Using the example provided in Susan's blog post, I have attempted the dividing 57 by 6. By outlining the multiple (up to 8) and fraction (down to 1/2) of 6, I am able to pick and choose the appropriate combination for 57. The result of the division is = 1 + 9 + 1/2.

 The Surveying in Ancient Egypt article outlines surprisingly sophisticated methods to measure distance, angle and area. As a modern math teacher, I take the tools and the metric system for granted. The mural which we discussed in class was indeed a depiction of a bureaucrat measuring the area of a flooded field. The measurement can then be used to redistribute land. The measurement of royal cubit, or 7 palms, or 28 fingers and short cubit, or 6 palms, or 24 fingers were used to measure distance. Mentioned in the article, both units were used. Based on the division, I wonder if short cubit was used more due to its divisibility from the prime factor of 2 and 3 while the royal cubit has only prime factor of 2 and 7. Another question arose from reading was the definition of cubit, the length from the elbow to the tip of the middle finger. This must have been the definition for a Pharaoh or a royalty, and it's clear that Egyptians had understanding of precise mathematics. My speculatio...

 The chapter about Babylonian word problem from the book A Man Left Albuquerque Heading East  (written by our lovely Susan) showed a fascinating history about this genre of math problems. In contrast with the recent math curriculum, they share the trait of the problems being somewhat absurd and unrealistic. In both eras, the word problems seems to be a tool for student's instrumental understanding. Questions related a multiple-storey tall stack of grain pile or value difference and multiples in father/son age are for apprentices/students to solve just because they can. My guess on the unrealistic nature of these questions are two pronged. Authors of the questions realized any real-world application requires tangible context. However, society advances and context changes, it's futile to change the question every time society moves forward. Hence, a choice of surreal context has been made for Babylonian and 21st century Math students alike. The other point is that the emphasis w...

Based on the discussion of our lecture, I first started with 3 pairs of factors for 45 which are whole numbers only. Then I went deeper with fractions with finite decimal places for division, I chose 2, 4, 6, 8 as the Column I value, subsequently I worked out the subsequent decimal placed in the sexagesimal form. I have then validated my result in excel through product sum to ensure they multiply back to 45.

In my mind, an hour is always a circle (same as a regular clock) and time is measured in 15 minutes or a quarter of a circle. After reading the Lombardi's article, I was surprised that an hour was not a empirically constant unit of time measurement. It made logical sense that people treated day and night as separate entities where each had 12 hours. It's suggested that Hipparchus introduced 24-hour day around 147 B.C., so people over a millennium had to work out the seasonally varying length of an hour. Another surprising snippet was the usage of clepsydra mentioned in Lombardi's article. This is a fascinating way where fluid dynamics is used as a substitute as sun light or lack of during night. Lombardi stated in his article that the base 60 was first invented by Sumerian, which then passed down to Babylonian, which then passed down to Greek. However, the reason of 60 was unknown. In O'Connor and Roberston's article, they had a different hypothesis about the reason...

The Crest of the Peacock by George Gheverghese John explores non-European history of mathematics. Below are some of my findings in chapter 1. As someone who studied math in the modern age for what it currently is, I was very enlightened by the span of time and geographical coverage of the non-Eurocentric mathematic systems. We take for granted the base 10 and scientific measurements used in everyday life and never thought about the history of them. Asian continent had mathematical development through sharing knowledge by trade. Figure 1.4 illustrates the intricate knowledge transfer happening over 6500 years and across number of regions. Again, as someone who can search anything using my cellphone, the spread and cultivation of mathematical knowledge back in ancient Asia was a feat to be inspired with. I was also fascinated by how the place value principle has been discovered independently four times in math history. Babylonian used it to denote base 60 values, Chinese used It in rod c...

Prior to further researching, 1) I think the reason for a base 60 is that the value itself is divisible by the common prime number of 2, 3, 5. The values of 2 and 3 are commonly used in low value counting, 5 being the value which can be counted through a single hand or foot. For the same reason, 60 allows more natural division than 10 (which is 2 and 5 only). 2) In system of time, 12 and 60 are heavily used. Hour is counted in the multiple of 12, while Minute and Second are counted in the multiple of 60. There are 12 Chinese Zodiac or regular Zodiac signs, moreover, the seasons in Chinese calendars are separated into 24 solar terms. There are also other cultures which use multiple of 12 to track cycles. After researching online, 1) I learned that the groups which became Sumerian had 2 systems, base 5 and base 12. The product of the two system was a base 60 system. Similar to my speculation, the most prevalent use of a base 5, base 12 and base 60 system is counting time. The research wa...

This is my pre-reading thoughts on the idea of incorporating mathematics history into classes: During my K-12 mathematics study, there are often little to no mention of its history. The only tidbit of that was from the names of the theorems. For example, when learning Pythagorean Theorem, I was curious who he is and how he came up with this. This allowed me to explore further information about the discoveries he made through his life as a mathematician. Although it piqued my interest, I did this mostly outside of the classroom and on my own. One of the constraints of incorporating history background is the extra time and attention needed. The current curriculum is already quite compact and adding more seems to be unrealistic. For my future teachings, I believe I can incorporate short historical stories given it can be relatable to the problem. This method provides context to the real-world problems humans faced, as well as the thought process on how a mathematician solves it. When read...