Induction
From BluWiki
Contents |
Overview
Induction is less a topic than an approach to a problem or a proof strategy. A good model for it is dominoes. In short, we can say that if a certain base statement is true, and that if a statement is true, then the next is true, then every such statement is true.
An overview of what the topic is all about, including
- important ideas, vocabulary, and definitions
- important theorems
- history of the topic, including mathematicians who played a role in developing the topic
- related unsolved (open) problems
- how this topic applies to specific state and NCTM standards (include state and grade)
Motivating questions and problems
The Hourglass problem neighborhood
Algebraic identities
Sum formulas
DeMoivre's Theorem
Under this heading should be posted questions or problems that motivate this specific topic. They should be short, easily accessible, and intriguing�the kind of question or problem that a teacher can just walk into a classroom, throw out there, and start kids thinking and responding. They should provide a bunch of different ways of approaching a topic from the outside, giving a teacher a choice as to how to kick things off, based upon their and their kids' taste and personality. They should be big questions that are thematic and context building, problems that are memorable and can be referred back to. They should be flashy enough to attract attention and deep enough to allow sustained inquiry.
Finding such motivating questions and problems is hard; won't it be great to share them?
Lesson plans
Under this heading should be posted more specific ways to approach this topic, including:
- ideas for particular kinds of tasks that could be required, like "find 234 in base-5."
- links to more elaborate, already-made or customizable worksheets, with solutions
- grade level these have been used for (remembering that since whether a lesson is appropriate for a class depends students' background and ability, recommendations should be kept as broad as possible and include any grades that this concept has been taught).
- time needed to complete lesson
- sequences of lessons that have been successful
- examples of student output
- places and/or ideas that are stumbling blocks
These can be filed according to the following categories.
Exercises
Posted here should be links to lessons and sheets intended to practice and reinforce concepts, ideas, and vocabulary
Problems
Posted here should be links to lessons and sheets intended to explore the topic in a more abstract and deep way
Extensions
Posted here should be ideas for projects or subtopics
Assessments
Posted here should be quizzes, tests, or other assessment tools
Follow up topics, or Where to next?
Other topics that could be explored during or immediately after this topic. Decribe directions that could be taken and connections that could be made (especially with kids of particular tastes and inclinations) and link to other Wikiteacher pages.
External links
Links to useful outside sites related to this topic.
