Focus on Learning Problems in Mathematics, vol. 26, issue 1 (2004) pp. 24-42 ST - Repeating pattern or number pattern: T
What is a pattern Quote from Steen (1988). Mathematical theories explain the relations among patterns: functions and maps, operators and morphisms bind on type of patterns to another to yield lasing mathematical structures. Applications of mathematics use these patterns to explain and predict natural phenomena that fit the patterns. Patterns suggest other patterns, often yielding patterns of patterns. (p612) \ Even the very description of what it means to do mathematics can be devied in the context of patterns. Notes that while mathematic roots are in patterns ther is no place for patterns in the formal representation of mathematics. The contemporary view is that mathematics is axiomatic in nature. - linear deductive form. suggests that the use of pattern often unlocks that truth an d both presents it to the student and convicnes them of it. Suggest that the pedagogy of teaching patterns is a concern. Due care must be taken to preserve the distinction between the types of patterns. This article examines how the lack of explicit attention tot he distinction between repeating patterns and number patterns leads to difficulties for students engaged in problem solving activties that involve investigation of patterns. Definition of pattern - Skemp suggest that in defining a conpcet may in fact limit the meaning of a concept. Philosophical discussion of whether we should in fact define a pattern A repeating pattern is defined as a pattern in which there is a discernible unit of repeat. - a cyclical structure that can be generated by the repeated application of a smaller portion of the pattern. Underlying principles There is an equality between every element in the pattern and one of the first n elements there is an eqaulity between every element in teh pattern and the element n positions prior to it. The length of the unit of repeats creates an isomorphism between repeating patterns.
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