A Storied Approach to Mathematics

Eighth grade mathematics teacher Amy Barnhill Smith adapted a narrative approach to problem solving while encouraging her students to engage in metacognitive strategies.

Amy’s Working proposal:

Question: How can I get students to write about solving math problems and meta-cognition?

Research: Websites — Using Writing in Mathematics , NCTM “Tony’s Walk Task”

Data Sources: Student Survey, Teacher Journal, Video

Method: Following our math lesson on rate of change (and showing line graphs of date of change) I will introduce meta-cognition. Explain to students that they already do this like when they got dressed this morning. They also do this in LA by answering discussion boards on Edmodo and in Daybooks.

The assignment will be for them to write a narrative for “Tony’s Walk.”  They will then go back to each change in Tony’s walk and explain why they decided to do each task as the graph changed.

Based on the students’ responses we will get an idea of their meta-cognition towards the understanding of line graphs as displays of rate of change.

Possible Findings: Hopefully the students will be able to accurately identify when and why Tony’s walking rate is interrupted on his way to Grandma’s.

Amy’s Mini-Inquiry Findings:

Rate of change was a difficult concept for my students to comprehend. They were able to perform the routine method of solving an equation but didn’t really understand what they were doing. When I first introduced rate of change in the form of a graph some students immediately “got it” while others struggled. We first had a mini-lesson on how to read a graph’s rate of change using Attachment 1. The students used a handout right after that lesson to write a min-story about a given graph. They were given 15 minutes to write this mini-story in class. At the end of the time period I collected the worksheets and anonymously read each story to the class. While reading each story we traced as a class the rate of change line on a graph presented at the front of the classroom. I helped to point out misconceptions in the students’ stories that were not accurately represented by the graph. By the end of the period, students seemed to have a good understanding of the graphs. Most students knew that when the line stayed steady (horizontal) the rate was not changing but staying the same. They also seemed to understand that if the line was along the x-axis, the subject was not moving and how to tell when speed was increasing or decreasing.

At the beginning of the next class I presented “Tony’s Walk” in the form of a handout for each student. I explained to the class what the assignment was. We reviewed the previous day’s lesson and I explained that this was a continuation from that. I also added in that I wanted the students to write a “meta cognition” of their story about Tony. We talked about what meta cognition was and how to think about their thinking. Students worked independently on this assignment and I assisted them when needed. Several students had trouble getting started and others had a difficult time writing about what they were thinking. After getting them working, their thoughts seems to move right along.

I was excited to read the student responses. Overall about 60% of students in my classes showed true comprehension of understanding of rate of change from a graph. Allowing the students the opportunity to write a story about the graph to demonstrate this rate of change enhanced their understanding. Attached you will find some of the better stories that came out of this research. One student, “Kevon”, developed a real understanding of the rate of change and wrote a detailed, accurate story of Tony’s walk. This student typically performs below grade level in class so this assignment definitely tapped into his interests of writing and got him involved in the lesson.

In the next unit students will learn how to find the slope of a line on a graph which is essentially the rate of change of the line. Having true comprehension through this assignment will hopefully aid future understanding for the students. This assignment has also led me to research more on the impacts of writing in the math classroom. I am now working on an Action Research Project that aims to determine what impact writing about math concepts and problems has on student understanding.

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