Nadine

  A man who had 12 horses and 3 children wrote in his will to leave 1/2 of his horses to Pat, 1/3 to Chris, and 1/12 to Sam. However, just after he died, one of his horses died too. How will the children divide the 11 remaining horses in order to follow the instructions of the will? This problem gave me a lot of trouble until I realized using unit fractions that 1/2, 1/3, and 1/12 only adds up to (6+4+1)/12 = 11/12! It would actually be harder to allocate the horses to each child if the 12th didn't die since there would be an extra horse! Unit fractions clearly have the added benefit of visualization :) Therefore, Pat receives 6 horses, Chris receives 4, and Sam receives 1. The remaining horse has died. 

 I tried 99/8. See below:

 I have a lot of trouble understanding the ways in which they solved problems when they didn't use algebra. I imagine one way in which they could solve geometrical problems is with symmetry and basic counting, but otherwise struggle really hard to understand their math at all. The way that we were taught math clearly impacts our ability to see problems in different ways. When reading the text about Babylonian algebra, it seems like my brain skips over the method that they used, and solves it in a simpler and faster way before I can even finish reading their method! Isn't that funny! And to be able to actually state or communicate a mathematical principle at that time without algebra ? Forget about it! I wish I could answer this question better, but I can't quite wrap my mind around it. Given my complete loss for words and ideas, I am so impressed that they were able to accomplish solving pre-algebraic quadratics through estimates and approximations. This does bring me back ...

Throughout my reading of the text, I found myself trying to answer the question found on the first page. Why have word problems persisted through time and culture despite not being purposefully preserved? I loved this question in class and wanted to pick up answer from this reading. With the use of word problems concerning unrealistic 8-story high piles of grain, it's easy to think that these were simply to get a good laugh out of people or they were just for fun or for a challenge (pure) which would be easy and enjoyable to preserve. However, I found myself thinking: does a word problem have to be practical for it to have teachable concepts? Perhaps the teachability is why these were preserved throughout time. These word problems could simply be for  beginners with no application to the real world or perhaps just be using easier numbers than in real life that prepare students for the soon to come real world problems. I assume the latter to be the case. After all, we find thes...

Col I          Col II 1                    45 2                    22,30 3                    15 4                    11,15 5                    9 6                    7,30 10                  4,30 12                  3,45 20                  2,15 25                  1,48 27                  1,40 30                  1,30 36      ...

I was so drawn to the first paragraph of this text, especially after reading " Integrating history of mathematics in the classroom: an analytic survey" last week, because it offered some beautifully written points that could be used to argue why Math History is the key to mastering the Math curriculum. The very first line says "an interest in history marks us for life", and it's true isn't it? Don't you still remember one particularly scandalous or riveting story from history class? "From the first time we become aware of the past, it can fire our imagination and excite our curiosity" which is exactly what so many students need in a math class.  Near the beginning of this text, they mention that a concise and meaningful definition of math is virtually impossible because of it's many origins which inspired me to think of how diverse math is ! I find it fascinating that so many groups of people who had never had contact all came up with syste...

My first guess as to why 60 might be convenient was because there are 360 degrees (6x60 and similar to 60^2) and about 6 radians in a circle. However, 60^2 is 3600, not 360 and there are not exactly 6 radians in a circle. I started to think about what is naturally around us such as the self, nature, and systems we have in place. We have 10 fingers and 10 toes, unless maybe back then they only had 6 fingers and toes! Nothing about our physiology seemed to spark an answer. In nature I think primarily about the rotation around the sun (360 degrees), the shape of other planets (circles, 6 radians, 360 degrees), and systems like time (such as days of the year, seconds per minute, minutes per hour, 12 months in a year, 30 (6x5) days in a month).  We still use 60s in time like mentioned above and in length measurements (12 inches in a foot) which both make up a large part of how we think. We revolve our lives around the sexagesimal time system.  In my research I found that ...

I liked the idea from our first class that Math History could personify math, making it relatable and appealing to students. Having known people that would've be much more attracted to math class had there been more references to actual real-life people, I believed immediately that Math history should have its place in the math curriculum.  However, upon reading the text, I found it immediately surprising that I agreed with so many of the objections to teaching Math History. There is so little time to include it within math classes seeing as so many students struggle with math in the first place. Additionally, as someone who loved the actual calculations portion of math, Math History might have taken away from what I loved most about math. This made me question if there could be multiple class options available to students where they could choose to take a course with or without the inclusion of Math History. As I continued reading, I found more and more wonders that would come wit...