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Making sense of structure through patterns

Making sense of structure through patterns. Tami S. Martin Illinois State University Roger Day Glencoe McGraw-Hill School Mathematics. Patterns as a tool for reasoning. Generalized arithmetic: From counting to symbols. Algebra as a way to concisely capture structure.

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Making sense of structure through patterns

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  1. Making sense of structure through patterns Tami S. Martin Illinois State University Roger Day Glencoe McGraw-Hill School Mathematics

  2. Patterns as a tool for reasoning • Generalized arithmetic: From counting to symbols. • Algebra as a way to concisely capture structure. • Connecting geometry or physical objects with algebraic representations. • Situations that lead into multiple, connected representations and interpretation of those representations; connections back to context.

  3. Toothpick Patterns

  4. Making Sense of Toothpick Patterns • How many toothpicks are needed for the 4th step? The 10th step? The nth step? • How many 1-by-1 squares are contained in the 4th step? The 10th step? The nth step? • Is the pattern describing the number of toothpicks per step a linear relationship? Quadratic? Something else? How about the number of 1-by-1 squares per step?

  5. Making Sense of Toothpick Patterns • How could these data be organized to help determine the patterns? • How does each representation connect back to the context? • How is slope revealed within your representations? How about intercepts? • In a table showing (step number, number of toothpicks), what is revealed when you calculate the differences between consecutive rows?

  6. MTWI: Stack Attack • Stack Attack: Rules and requirements • Try it in your small group! • Watch these videos: • A Traditional Stack Attack • A Young Stack Attack • A Fast Attack!! • What are some mathematical questions that could be asked about this scenario? • What representations could be used to model the scenario?

  7. Discussion • What are the key elements of reasoning and sense making that you can drawn upon or emphasize with the use of pattern-finding activities in the algebra classroom? • What actions will you take as a teacher to ensure that pattern-finding activities engender student thinking and sense-making?

  8. Discussion • What challenges to teaching and learning emerge when we engage students in pattern-finding activities such as these? • What are two or three actions you can take to begin (or increase!) implementation of pattern-finding activities in the courses you teach?

  9. Contact Info Tami S. Martin: tsmartin@ilstu.edu Roger Day: dayr@pontiac.k12.il.us

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