Educ 475 – Lesson #1
|Educ 475 – Lesson #1 |
|Place Value |
|Lesson Summary – Part #1 |
|The numeration system we use is a base-10 system that is constructed on the Hindu-Arabic symbol system. However, it is usually |
|referred to as a decimal (deci – ten) system. Why base-10? We have 10 fingers – or digits. If we had 12 fingers we would be using a|
|base-12 system, which may seem like it would be complicated, but it wouldn’t be – and all of mathematics would still work out. |
| |
|There is a problem, however, with our numeration system. Kids learn how to count fist through chanting the numbers and then through|
|symbol recognition. They spot/learn the pattern on the hundreds chart that enables them to count, and often write the numbers, up |
|to 100 before they enter kindergarten. As a result, all the wonderful properties of our numeration system are missed – or taken for|
|granted. If they can be awakened to these properties then understanding of larger number representation will be more easily |
|facilitated. But, how do you awaken awareness in something that you are already so familiar with? How do you make the implicit |
|explicit? There are two possibilities: you either sneak up on it or you see it through someone else’s eyes. |
| |
|Sneaking up on a topic is the approach I used in class. It is a pedagogical trick whereby you focus the students’ attention on some|
|situation that is so new, and often so unusual, that the activities they do around it become new as well. In this way the student |
|is able to experience familiar things as if they were new. In class I used a base-6 system to focus your attention on the |
|properties of ten-ness, position, and zero that are inherent in the base-10 system. In the end, when the connection is made to the |
|base-10 system a greater understanding is achieved. |
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|The other way to achieve this is by seeing it through others eyes. In this case this could involve the study of ancient numeration |
|system that may not have had these properties. For instance: the Babylonians used a base-60 system, Mayans base-20, Romans were |
|base-10 but with a pinch of base-5, the Chinese almost had a base-10 system but they weren’t positional, the Egyptians were also |
|not positional. References for each system are abundant. |
|Readings |
|chapter 11 |
|Problem Solving Log |
|Addition Magic: You pick three three-digit number, I pick two three-digit numbers, and then instantly (magically) write down the |
|sum. Solve this problem (how does it work) and explain how it works. |
|Reflective Journal |
|What is mathematics? Why do we teach mathematics? What does it mean to learn mathematics? What does it mean to teach mathematics? |
|Did Peter teach today? How did you feel when you solved the Addition Magic problem? |
|Respond to today’s reading. |
|Things to Do |
|You need to form your groups for the Group Problem Solving assignment. |
|You need to decide which problem you are going to do – Repeat 4 or Pentominoe Problem. |
|Watch |
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