Blog Post 7: Russian Peasant and Ancient Egyptian Multiplication Methods

Commonalities between Russian peasant and Ancient Egyptian multiplication

• Both use repeated doubling 
• Both have two columns 
• Both work step-by-step/row-by-row to simplify large calculations 
• Both exclude odd numbers from the left-hand column
• Both methods have a greater number in the right-hand column than in the left-hand column

I found the Russian peasant system a bit less intuitive whereas with the Ancient Egyptian system, by looking at the example I was able to find patterns and figure out how it worked relatively quickly. 

Blog Post 6: Ancient Egyptian Multiplication

Multiplying 30 by 6

1                                                                                                                                    6

2                                                                                                                                    12

4                                                                                                                                    24

8                                                                                                                                    48

16                                                                                                                                  96

Blog Post 5: Babylonian Word Problems

I found it interesting reading about word problems as I struggled with them (applied math) far more than pure math growing up. Although I dreaded them in school, I think word problems help students develop the skills they need to transfer their math knowledge to real-world situations (i.e., making the skills students learn useful in their daily lives). 

During the reading, I liked the section by Ainley on practicality as it answered questions I myself had as a student. I previously maintained the argument that applied math was too contrived to feel useful, though the interviewer's response was something I had never considered; that if they were not, they may be far too difficult (or easy) to be of use. 

I found the discourse on pages 6 and 7 thought-provoking. In my opinion, although abstract problems may appear unuseful, they can be healthy for the brain and can enhance our cognitive abilities. As a psychology student, I rarely (or never) use high-level math, so the way that I see math coming into play in my life is mainly for developing creative problem-solving skills. While I may never need their lessons, I have held onto some math 9-12 workbooks from my schooling to use as brain puzzels. 

Blog Post 4: Babylonian Multiplication Table

 Col 1        Col 2

2                22, 30

6                7, 30

10              4, 30

18              2, 30

25              1, 48

Blog Post 3: Why based 60?

 When thinking about why Babalonian’s would use base 60 instead of base 10, I wondered if it might have to do with time (60 seconds, 60 minutes…). I also thought it would be convenient since it’s an even number which makes it easy to divide. Similarly to what we discussed in class, it could have to do with geometry (360 degrees in a circle). 

Through google, I found my predictions pretty reasonable. I read that babylonians came up with the concept of time being 24 hours, 60 minutes and 60 seconds, so base 60 would make perfect sense. I also read that some ancient groups used base 5 while others used base 12 so 60 became a common factor. Like what I speculated, some attributed base 60 to the fact that it is convenient for fractions.

Blog Post 2: Crest of the Peacock intro math history

 

I found it amazing to read about how despite their isolation, the Mayans made remarkable contributions to numeration and calendar construction. Specifically, the accuracy of Mayan astronomical discoveries and calendar construction without advanced technology is incredible. 

I was also impressed when reading about The House of Wisdom in Baghdad, where early scientific research thrived through a library, observatory, and university. 

Last, I was most surprised by the knowledge transmission of math among diverse cultures. For example, collaboration between Indian and Chinese astronomers was something I had never learned about. Similarly, it was cool to learn about how Spain and Sicily served as points of contact between Arab science and Western Europe.

Blog Post 1: Why Teach the History of Math?

 Pre-Reading Thoughts 

I think math history should be incorporated into teaching as it helps students understand the purposes of math concepts. I also think teaching the history of math in a math class would help engage students who struggle with solving math problems or those who are more interested in humanities. On my first day of Grade 12 Calculus, I remember my teacher asking the class if we thought math was invented or discovered. It sparked an amazing conversation that got the class invested into thinking about math. When thinking back on that discussion, I feel that more discussions like that would’ve kept me more interested in math in school. 

Post-Reading Reflection 

I understood the critiques that there may not be time to integrate teaching the history of math into classes, but I think there are ways teachers can make an effort to incorporate the history of math into the teaching of math skills. Like I mentioned in my pre-reading thoughts, introducing a new concept or starting the year off is a great time to open the discussion about math as it can be done quickly and get students excited for what they’re about to learn. 

I also loved the idea that learning about the history of math could help kids from getting discouraged when struggling with math, as persistence and failure is part of the discovery of math.

As a student that struggled with math in school, I remember constantly asking my teachers “why do we have to do math,” the teachers always responded with something along the lines of, because its in the curriculum, which I didn’t find to be a very good answer. I think by teaching the history of math we can explain to students why we do math in a way that inspires them to think creatively.