May 442 Blog

Here is a link to our powerpoint :  https://docs.google.com/presentation/d/1infhLZ4Ow7wofXp-yRHw7PSjB_5yOkyrOllgYZgh5pY/edit#slide=id.g9a6108e0dc_10_32 In this project we looked at the fractals in art pieces and Indigenous designs,  and then developed a way to teach fractals using diagrams. I was in charge of the hypothetical class plan. I found the picture and labelled it. I didn't want to make it too hard for the first part of the class so I used a simple version of fractals. I asked them to measure the length and calculate the ratios.  I believe the first diagram is easy to manage/ understand. Then I led a class discussion to link the observations to the concepts. After that I led the lesson to a more complicated version of fractal tree. To make sure they understand the latter one, I asked them to draw a fractal tree themselves.  In this project I learned about how to incorporate art pieces into the math classroom. We could use graphics to teach certain concepts, ...

  4 3 8 9 5 1 2 7 6     To add to 15: 1+6+8 3+5+7 2+4+9 2+6+7 2+5+8   First fill in 2,5,8 as the diagonal Then fill in 6 and 7 at the bottom. since 7+8 exceeds the limit, use 6 for the column with 8 Using the two numbers present, fill in the rest. It works.       8   5   2 7 6

 Research online the significance of the Eye of Horus and unit fractions in ancient Egypt. What was most interesting to you in your findings? The Egyptian Unit fractions are based on the Eye of Horus. Horus was the ancient Egyptian sky god who was usually depicted as a falcon, most likely a lanner or peregrine falcon.[7] His right eye was associated with the sun god, Ra. It was believed by the Greeks and Romans that an evil heart could get to the eye. The thought to be powerful effects of eyes and optics created the myth that the energy-producing power of the eye had the ability to cast evil spells with just a glance. Because the ancients believed the evil eye could be counteracted with a 'good eye', myths about Horus arose.[9]  The eye of Horus was often used to symbolise sacrifice, healing, restoration, and protection.  I think the most interesting thing here is that the eye has so many connotations and it is something almost sacred in Egyptian culture. The an...

Adam gave Sam 45 dollars to buy groceries. He requires that the number of apples should be three times the number of bananas. The number of bananas should be double the number of oranges. suppose apples cost 2 dollars and bananas cost 1 dollar, and oranges cost 1 dollar, how many of each fruit should he buy? modern solution:  let the number of oranges be x.  x +2x+6x*2=45 15x=45 x=3 false position method: let x be 2  2+4+6*2*2=30 we need 45, which is 45/30=1+1/2 as big, so x must be 2 times 1+1/2 , which is 2+1=3 check: if x=3, x +2x+6x*2=45

 I think it is important to acknowledge non-European sources of mathematics because it promotes respect for other cultures. When only European sources of math are acknowledged, students tend to develop an understanding that only Europe is the origin of all creations in math/science. They would have unnecessary ego for their own ethnicity. When we acknowledge other cultures’ mathematical discoveries, we tend to have some level of humility, especially when some of the theorems claimed to be European are actually from China. For instance, “The method of the double-false-was first described in Jiu Zhang suanshu,indicating the method was known in China around 50 AD. Subsequently, the method was transferred to Muslim mathematicians at some point and then on to Europeans sometime during the Middle Ages. It then was brought back to China by the Jesuit missionaries, who claimed the method as their own.”   Also, “accounts and facts of Greek work during this time tilt more on the s...

  These ideas do rely on our familiarity with contemporary algebra because for Babylonians they don’t have a distinct separation of pure and applied mathematics. Their word problems are both practical and theoretical : “many look like real-world problems at first; but as soons as......the complete artificiality of the problems is revealed...has been disconnected from immediate practice” The Babylonian mathematics was based on problems that seemed practical but were actually “’pure’ in substance” They are used to train students in the use of ‘methods at hand’, which are essentially generalization or abstraction of the real world. Mathematicians use abstract methods and concepts to solve real world problems. There is certainly a stronger connection between the practical world and mathematics concepts in the Babylonian era than today. Nowadays there is a distinction between pure and applied mathematics and problems are not all based on real life situations. A part of math is based on ...

  1)     My pre-reading ideas was that math history is an important aspect of mathematics education because it shows where the theorems / concepts came from and gives us a better understanding of the process of mathematics exploration. It could be incorporated in to my math teaching by showing the students how a theorem was discovered (the experiments/ steps mathematicians took to figure out the theorem). We could also show them ancient ways to solve the problems which differs from modern methods. In this way they could realize that math is not only just the formulas they see in class but a result of logical thinking process and repeated experiments by mathematicians.  2)     one thing I agree is that history may be tortuous and confusing rather than enlightening. students may not enjoy learning the history of mathematics even though it might be beneficial. however, it is still crucial to integrate math history into the curriculum. Another thi...

  One thing that struck me was how the Pythagorean theorem took such a long time to complete. I never thought that such a theorem would be so hard to get. It leads me to think about how we are privileged to have so many theorems at our disposal when dealing with problems. We only need to learn the theorems and never thought of how hard mathematicians might have tried to figure that out.                                                Another one is how math is a universal language of the world which can be spread across countries. Arabs helped spread the Indian numerals and their associated algorithms to Europe as well as the trigonometry. India and China also exchanged knowledge about the concepts of mathematics, such as kuttaka and qiuyishu. It is obv...