Peer-Editing Justifications

Focusing Edits through a Double Traveling Salesman

One of the many ideas that inspired me during the GMWP’s Teacher Workshop presentations was Holli Reckin’s peer editing techniques. Holli shared multiple methods for peer editing, but the one that stood out most was the multiple reads edit (or colored markers edit). This type of editing asks students to read through a piece of writing multiple times, each time focusing on a specific element of writing. This struck me as an excellent way for students to analyze the different aspects of a justification or a proof. Before I go any further, huge thank you to Holli for looking into this topic and making my job easier!

This multiple reads editing process benefits student’s writing in many aspects. By asking the editor to focus on less things at once, they have the opportunity to think deeply about each aspect of writing. The writer has a chance to see which elements of they struggle with most. Both the editor and writer also develop their understanding of the various aspects of writing, or in my case justifications. Holli also suggested using different colors for each edit to make each aspect stand out even more.

Holli’s Teacher Workshop focused on peer editing in her Spanish classes. Students would read their peer’s paper multiple times, each time focusing on a different aspect of writing. Holli outlined two edits and the focuses for each.

• 1st Edit — Content & Organization
• 2nd Edit — Mechanics & Grammar

For the purpose of editing mathematical proofs and justifications, I changed these focuses slightly.

• 1st Edit — Content/Facts & Logic
• 2nd Edit — Reasoning & Notation

I started using this form of editing very early in the proof writing process for my Geometry classes. Students had just learned how to write flowcharts for triangle similarity (students put their facts in bubbles with arrows leading to a conclusion bubble and reason). At this point, they should be focusing on the facts used (side ratios and angles based on similarity condition SSS, SAS, or AA), basic notation, and overall reasoning of their flowchart. I decided to do the multiple edits early in the process in hopes that it would increase their understanding of the flowchart pieces and notation.

I also did the two edits using a Traveling Salesman. I randomly selected a “salesman” from each group to travel to the next group for the first edit. Then they rotated again for the second edit. During each edit, the traveling student “sold”, or explained, their justification to the new team. The new team discussed any edits that needed to be made and the traveling student made corrections to their work. After both edits were completed, the salesman went back to their group to discuss the corrections they made.

I was extremely impressed with how well this process went, especially given students had just learned how to write their justifications using a flowchart. The Traveling Salesman held students accountable, since they knew any member of the group could be randomly chosen to present their flowchart to a new group. Both times I announced a Traveling Salesman was coming, student participation on that problem skyrocketed. If only I could do this with every problem!

I was most impressed with the conversations I overheard during these edits. Students were finding incomplete flowcharts, such as when a group was using Side-Angle-Side to prove similarity but only gave one pair of sides. They were checking the corresponding side ratios and the similarity statements in the conclusions. The groups doing the editing also realized some errors in their own flowcharts while editing the salesman’s flowchart. I overheard discussions about notation as well. There were some notation errors missed on the first day, which was the feedback I need to discuss notation again with students. On the second day, I noticed students did a better job of catching each other notation errors, and needed me less in general.

When it came time for assessing these similarity flowcharts on a formative test, my students did better than last year. There are many factors that could have affected this outcome, especially given that this was my second year teaching the material, but I think the multiple edits played a large role. I had more students write their flowcharts in the correct form (with fact bubbles and a conclusion bubble), and I had less students not attempt the problem. I also noticed that students’ notation was significantly better than notation was last year at this time. I’m glad that the multiple edits technique makes this a priority so students don’t get confused by it later in the year when the justifications are more challenging.

I haven’t tested students summatively on their flowcharts yet, but so far students seem to be much more confident with them. I am excited to try these the multiple edits again with triangle congruence justifications and two-column proofs. Once again, huge thank you to Holli for the idea! I would definitely recommend multiple read edits to other teachers trying to strengthen students’ writing and justifications.