Assessing Understanding through Reasoning Books

Assessing Understanding through Reasoning Books
Mathematics Teaching in Middle School.

Summary

This article starts in on a very theoretical note. As teachers do we sometimes avoid the difficult questions? Do we choose to opt for the easy answers? Are we doing a disservice to our students? Asking difficult questions gets overlooked because it’s an investment. Asking difficult questions requires time, effort, a deep understanding of the material and adequate exploration and communication.

This article focuses o the use of mathematical reasoning books as a tool which will help students develop vocabulary, reasoning and proof skills, communication skills and a forum in which to explore and answer the “difficult questions.” The introduction on page 408 can be used with students; it illustrates the purpose of the assignment and the format that is to be used. I also think that figure four and five on page 412 can be used to help students with the assignment. Figure 4 is a feedback checklist that students can use to evaluate if their answers and responses are through enough. Figure 5 is a self reflection rubric that will help the teacher and students reflect on the process.

The article is really a series of prompts and student responses. The authors then analyze the student’s responses for understanding. There are student samples at each level of achievement. Some students fell upon the belief that there was not enough information to reach a conclusion, which is typical of students who are struggling when it comes to transferring the information into a new context. Some students had the right idea but lacked the justification to support their answer. Other answers were very sophisticated and showed a true understanding of the question, answer and the terminology.

In conclusion, the mathematical reasoning book is a very useful tool that, when used properly and taught correctly, can be used to assess students reasoning and proof skill at the middle school level.


Application

I liked this article. Seeing the types of errors and understanding why the student made an error is an important step. Furthermore, I was surprised by the degree of difficulty of some of the problems and how well some students preformed with their math reasoning books. However, I am suspicious of the article as a whole because it is clearly a plug for the NCTM Reasoning and Sense Making book. While I liked the questions that were provided as an example I don’t know that I need a text book to teach me this strategy. It seems to me that this article did a fair job explaining the math reasoning book, which is really a glorified learning log. Personally, I have been using this technique in my classroom without an actual notebook. The students have been preparing for their ISAT exams and my novice teacher has been using the opportunity to review the mathematics extended response, which requires the students to defend their problem solving strategies in paragraph form. My teacher uses a t-chart to teach this concept. The students write the problem at the top and use the right column for the math- diagrams, equations, etc and explain what and why they did what they did in the left column. I like this approach. I feel that with the t-chart approach as prior knowledge that it would be fairly easy to teach the students to keep a mathematic reasoning book or leaning log.

Roberts, S. & Tayeh, C. (2010). Assessing understanding through reasoning books. Mathematics Teaching in Middle School. 15(7) 406.