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Unformatted text preview: M316K Section 1.4- At the simplest level, a representation is a picture-- a picture of your image of a prob- lem- It can take many forms: diagrams, graphs, tables, sketches, equations, words, etc...- One of the key ideas: most problems and most mathematical concepts can be represented in different ways Section 1.5- Standard 7: Reasoning and Proof (Principles and Standards:- Recognize reasoning and proof as fundamental aspects of mathematics- Make and investigate mathematical conjectures- Develop and evaluate mathematical arguments and proofs (formal proofs in high school and children can construct informal proofs)- Select and use various types of reasoning and methods of proof as appropriate- Another maladaptive belief: Making sense of math is reserved only for the smart stu- dents and for the rest, the best advice is just do it.- Mathematical reasoning is often categorized as:- Quantitative: using quantities (numbers)- Qualitative: not using quantities (no numbers)- More specific kinds of mathematical reasoning: numerical, proportional, algebraic, and...
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This note was uploaded on 02/21/2009 for the course M 316K taught by Professor Ermer during the Spring '09 term at University of Texas at Austin.
- Spring '09