Dan Siebert recently published an article title “GPS: Replicating Patterns” in the Mathematics Teacher: Learning and Teaching PK-12 journal. Dan has answered a few questions about this article below:
Who were your co-authors on this article?
Monica G. McLeod
Who would you say is the target audience for this article?
K-12 teachers
What is the big problem you hoped to address with this article?
This article provides 4 problems, one for each of the grade bands K-2, 3-5, 6-8, and 9-12. It addresses how the activity of identifying patterns changes and evolves as students progress in mathematics.
What are some of the key ideas in the article?
One of the big ideas is that students need to learn how to identify which quantities stay constant and which grow linearly. Often this involves creating representations and identifying corresponding parts to see how different parts of a figurative pattern change in a sequence of figures (e.g., number of blocks, number of sides of a shape, number of chairs in an arrangement of chairs around a table, number of tiles that make up the boarder on a hot tub, etc.). Students should learn to break figurative patterns into parts that they can describe using numeric and algebraic notation.
What are some of the main ideas you hoped your audience will take from this article?
One of the important ideas for teachers to understand is how to break up figural patterns into parts that can be described through numeric or algebraic notation, and how to interpret notation as descriptions of figural patterns broken into parts. For many of the figural patterns, there are multiple ways of breaking that pattern into parts, and notation can often communicate which parts the problem solver identified in the pattern and the solution method they used to count the number of items in the figure.
What else would you like to say about this article?
This is an article written for the Growing Problem Solvers (GPS) Department in MTLT.