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Integrating history of mathematics in the classroom: an analytic survey

  Before reading this paper my thoughts were that mathematics history can easily be added in education in the classroom but it should be mostly a short thing like a story of a mathematician or a fun fact. I had a worry that it might divert the student's attention from the main path even though it will make the math education more interesting, like elaborating the start of negative numbers, observing how people used to solve problems in old times or understanding the discovery of pythagoras theorem. I did not think that  math history could entirely change the methods of teaching math. One thing that surprised me was the differentiation between ‘developed mathematics’ and ‘mathematics in progress’.It is explained in the article that mathematics is the science of trials and errors developed through centuries rather than the logical finished thing explained in books. I felt connected here with my own experience as a teacher and I learned that mistakes are a part of normal learnin...
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Response to Blog post due Wed Sept 23: Did Mesopotamian scribes have algebra? (And how can we recognize 'rhetorical' and 'syncopated' algebra?)

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  General principles before algebra Any mathematical statement does not necessarily need symbols to be considered general. It can be stated through words, diagrams , tables, or examples. Ancient Babylonians used to practice mathematics like this in their culture. Is mathematics all about generalization and abstraction Mathematics is not only generalization and abstraction. Mathematical activity also includes: Solving real life problems . Studying patterns. Measuring and comparing quantities. Making predictions.  Making diagrams. Making procedures. Communicating. Studying why a method works. Abstract ideas to focus on real results , mathematics often develops through movement between the concrete and the abstract. Therefore, mathematics is both particular and general, as well as both practical and abstract. General ideas without algebra Number theory A general number-theory principle could be stated verbally: When an even number is added to another even number, it will give...
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Response to articles for Monday September 21

  Main Idea It is explained in these two articles that the methods we use to measure time have come to us by many different civilizations. Egyptians have thought to construct the 24-hour day, and Sumerians and Babylonians invented the base-60 which shows an hour has 60 minutes and a minute has 60 seconds. How the systems developed The first article elaborates how Egyptians divided daylight and night into 12 parts using sundials and by observing stars. As a result a 24-hour day was produced. But summer hours were longer than winter hours. After that Greek astronomers invented 24 equal-length, 12 hours of daylight and 12 hours of darkness. Equal hours did not become common for ordinary people until mechanical clocks were invented in Europe after many centuries. The Babylonians inherited base 60 number system from the Sumerians and used it positionally, similar to decimal numbers today. The articles suggest several possible explanations for the use of 60: Sixty can be divided evenly b...
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