MTMS - A Framework for Analyzing Geometric Pattern Tasks

Friel, S. N., & Markworth, K. A. (2009). A framework for analyzing geometric pattern tasks. Mathematics Teaching in the Middle School, 15(1), 24-33.

A Framework for Analyzing Geometric Pattern Tasks is an article that discusses how teachers can use geometric patterns to promote the understanding of functional relationships by students. The article focuses on figural reasoning during the process of inductive reasoning. The authors state "when students use figural reasoning, they are able to make sense of patterns, ..., by paying attention to visual cues that can be organized and translated to numeric sequences (Friel & Markworth, 2009). The article was organized into three sections. The first section discussed various problem solving processes that support the use of figural reasoning as a way to explore and interpret geometric pattern tasks and generalize function rules. The second section discussed a framework for distinguishing the complexity of geometric pattern tasks. The framework may be used as applied contexts for figural reasoning. The third section provides a summary of various ways for how the long-term and extended use of geometric pattern tasks contribute to an overall development of students' functional thinking.

I thought that this article was good, but could be confusing at times. There were many instances that I found myself having to go back and re-read multiple sections. I liked that it explained and directly stated how the topic discussed in the article relates to the NCTM Principles and Standards for School Mathematics. I really liked that the there were many examples provided in the article. Having those tables and figures helped apply what was being said in the article with real world student work. I thought that this could be helpful to teachers. Sometimes it is difficult to fully understand how something can be applied to in the classroom. Providing the examples helps teachers have a greater understanding on the techniques explained and discussed. Although I found the tables and figures provided in the article to be very beneficial, there were times when it was very confusing and irritating to flip back and forth between the pages to try and see what was being discussed and referenced in the article. I liked that the authors included a brief paragraph explaining that geometric pattern tasks, although a valuable way to promote figural reasoning and develop a rich conceptual understanding of functions, it has its limitations as well. This information provides teachers with a realistic view of the topic. That realistic view allows teachers to be prepared for the limitations they will reach, and allows them the opportunity to be prepared for dealing with those limitations.