Covariation And Correspondence In Middle Schools

This article is about a mathematical classroom experiment given to fifth graders by Nicole Panorkou and Alan P. Maloney. The experiment they perform in the article helps create a successful foundation for what the students need to know about numerical functions when they get into middle school and high school. The experiments demonstrated test the children’s knowledge through activities, contextual problems and discussions that determine how well they can express relationships in terms of covariation and correspondence. Through the experiment, the children show tremendous growth by going from simply being able to describe patterns and sequences at the beginning of the experiment to being able to show greater understanding through actually distinguishing specific relationships between numerical patterns using the ideas of

“Students’ transition from describing patterns and rules for individual numerical sequences to recognizing, describing, and generating relationships between two sequences.” This was most meaningful because it demonstrates the success of the experiment. The children go from knowing how to initially recognize something to gaining a deeper understanding that allows them to comfortably manipulate patterns in terms of covariation and correspondence. Before this article, I was not sure what the terms, “covariation” or “correspondence” clearly meant. Covariation is simply the variation, or differences between two variables. In this case, the variables are patterns and sequences. Correspondence is simply the connection, or similarity between variables. Again, correspondence, in this article, refers to the similarities between the numerical functions discussed. Not only did I learn about a very successful experiment performed on fifth grade students, I also learned, in more depth, how these terms correlate to mathematics and relationships between patterns and