ERIC EJ1093088: Linking Models: Reasoning from Patterns pdf

ERIC EJ1093088: Linking Models: Reasoning from Patterns

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Patterns are commonly used in middle years mathematics classrooms to teach students about functions and modelling with tables, graphs, and equations. Grade 6 students are expected to, “continue and create sequences involving whole numbers, fractions and decimals,” and “describe the rule used to create the sequence.” (Australian Curriculum, Assessment and Reporting Authority (ACARA), 2012). Modelling functions, such as pattern problems, and making links between models in analysing patterns of change is an essential part of middle years mathematics (Lloyd, Herbel- Eisenmann & Star, 2011). Matt Switzer’s students’ approach to pattern problems often entailed extending the pattern and collecting data, which they organised in a table. They used the table to graph their data and used common differences, guess and check, or other strategies to find an equation to model the problem. While this procedure “worked” for many students, others struggled with generating an equation from the data in their table.

Many students who were able to generate an equation struggled to explain what the individual parts of the equation meant, how they were related to the original problem, what the variables represented, or the relationships between the table and equation. To address these issues, Switzer had his students generate tables in such a way that the variant and invariant quantities were evident and related to the posed task. In doing so, the process of generating an equation to model the situation became clearer and more meaningful for the students as they made connections between the numerical and geometric relationships. In this article, Switzer provides a typical geometric growth pattern encountered in middle years mathematics to illustrate this method

• Creator/s: ERIC
• Date: 2013
• Year: 2013
• Book Topics/Themes: ERIC Archive, Equations (Mathematics), Tables (Data), Mathematics Instruction, Grade 6, Middle School Students, Secondary School Mathematics, Mathematical Concepts, Concept Formation, Geometry, Switzer, J. Matt

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