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. |

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|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. |

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|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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