Lesson Summary Part #1

Educ 475 – Lesson #1

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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.
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