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1.2 ConceptsBecause many elementary and middle school tasks rely on inductive reasoning, teachers need to be aware that students might develop an incorrect expectation that patterns always generalize in ways that would be expected on the basis of the regularities found in the first few terms. NCTM Standards 2000, page 265The first four terms of the following number pattern were introduced by two teachers in separate classes: 1 2 4 8. Teacher A asked, “What is the next number in this pattern?” Teacher B asked, “What are some possibilities for the next number in this pattern?” Which teacher’s question is preferable and more illustrative of the preceding statement from the Standards? Explain your reasoning using the given sequence as an example. 1.2 Concepts Initially, students may describe the regularity in patterns verbally rather than with mathematical symbols (English and Warren 1998). NCTM Standards 2000, page 38Write examples of number sequences that can be described verbally, as opposed to using algebraic symbols, for the following cases: a pattern with a core that repeats; a pattern with a core that grows; a pattern that is a geometric sequence; a pattern that is an arithmetic sequence. 1.2 Teaching The recognition, comparison, and analysis of patterns are important components of a student’s intellectual development. NCTM Standards 2000, page 91It has been said that mathematics is the study of patterns. How would you explain this point of view to parents of the children in your classroom? Provide examples to support your position. |