Integrating the history of mathematics into our math classes is not dispensable because the fusion of math and its history can demonstrate how the mathematical idea was invented and what we can learn from those mathematicians’ problem-solving techniques. Although history might be boring to some students, I believe that incorporating math history into our daily teaching in an appropriate manner can stimulate students’ motivation. For instance, before introducing the Pythagorean theorem to our students, we can present the vast chronicle of the theorem and arouse students’ curiosity by asking them who is credited with the invention of the theorem. “No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down . . . [and turn] the hot invention into icy beauty,” the quote taken from Freudenthal makes me reflect on our current didactic method. I begin to un...
The sexagesimal system invented by the Babylonian brings us a very different perspective on our current place value system. At first glance, it is a bit inconvenient and challenging for us to use 60 and its powers for representing numbers or doing calculations. Some people like me might prefer solving sexagesimal problems by firstly converting them into base 10 numbers before doing calculations. However, we cannot deny the fact that the number 60 is to some extent more attractive and useful as the base for a number notational system. For instance, 60 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, whereas 10 is only divisible by 1, 2, 5 and 10. Most importantly, the prime number 3 is one of the divisors of 60 whilst all the multiples of 10 can not be divided by 3. Having a variety of divisors made calculation more convenient in the past, especially for merchants who attempted to divide up a huge amount of goods [1]. It is interesting that the sexagesimal system still exis...
I am glad that I could collaborate with Aakriti and Nancy to exhibit our work in front of our classmates and demonstrate Ahmes' Loaves problem both in modern and ancient approaches. For me, as a teacher candidate in the subject of mathematics, the assignment is a process of experiencing the wisdom of ancient mathematicians who was able to solve "pure" mathematical problems without relying on algebra, thus broadening my horizon. By researching into the terminology of false position or regula falsi , we started our journey of exploring how ancient Egyptians solve an arithmetic problem. Ahmes' Loaves Problem [1] It did not take too much time for us to solve the problem by using modern algebraic solution. We let d be the common difference of the arithmetical progression and expressed each term in terms of d . By establishing an equation based on the second condition given by the question, we quickly obtained the common difference which is equal to 55/6. However, it was...
Great!
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