Teach Me How to Factor!

As a fourth-year teacher I have tried many ways to make my classroom more student centered. One of the most successful strategies I’ve tried in my classroom is reciprocal teaching, which involves me teaching a group of students a topic and having them teach it back to their peers. The results were something I had never expected.

My research team is focused on finding ways to encourage effective mathematical discourse between students and I thought I may try reciprocal teaching because it forces students to rely on one another to get to a point of understanding.

Here’s how my lesson worked:

I decided to create four pre-determined groups based on ability levels. My strongest students taught the most challenging factoring method of the lesson which was Difference of Two Squares while my struggling math students taught the diamond puzzle or factoring when a=1. The two other groups taught GCF factoring and the Illegal Move or factoring when a is greater than 1. I taught each group their method separately at my TSGI station in the room while the other groups completed a quarter 2 review assignment. Once all groups met with me and learned their factoring method, I gave all four groups time to devise a plan to teach the class. I didn’t give additional instructions other than they were all required to have a role in the presentation and had to demonstrate the example I gave them. As the groups presented, the other students were to write down the information presented in their factoring foldable. Students were told to ask questions if they needed clarification from the group presenting.

Group 1: 3 boys    

Topic: Factoring when a=1

The first group that presented had an extremely disorganized presentation that was the result of poor communication and preparation. However, they did model the strategies that I taught them in their small group. The group ended up having to reteach the class because of confusion and I even overheard a student say, “I’ll wait for Ms. Bowden to teach it to us.” I knew that at this time I needed to clarify who the teacher was. I explained to the class that I am not the teacher at this moment and that they need to address their concerns with the group that is presenting. At first the students seemed frustrated that I couldn’t be used as a resource, but this experience proved to be something very valuable. The students were now forced to rely on each other and ask QUESTIONS! This was my whole goal for this lesson and I was happy to see that it worked. I was so surprised at the willingness of students to ask each other questions for both clarification and for pure curiosity.

Group 2: 2 girls, 1 boy  

Topic: GCF factoring

This group struggled to explain their thoughts and because of this, students tried reaching out to me again. So now I’m thinking, “Oh, great! Here we are back at square one!” But with some encouragement and reassurance for the group presenting, they were able to carry out their problem. I really noticed that when the teaching wasn’t strong the students felt the need to rely on each other more. This was a useful experience because they realized they can achieve anything as a team.

Group 3: 3 girls   

Topic: Factoring when a>1 (SFDS/Illegal Move)

I was able to determine quickly that this group paid great attention and was able to pick up on errors from previous groups. Their presentation was very neat and detailed, and they also explained their steps more deeply. I think this was because they felt the frustration of feeling confused and didn’t want the same to happen for their classmates. This was the first time students didn’t feel the need to reach out to me!

Group 4: 3 girls  

Topic: Difference of Two Squares

Group 4 was not only my strongest group but also my most quiet and soft-spoken group which I was excited to see play out! Before they started their example, they explained why and when this method of factoring is used. Get ready for a proud teacher moment: This group even created their OWN practice problems for students to try and they all walked around the room to check answers and answer questions. After they walked around for a bit, they asked a student to come up and demonstrate their work to the class. At this point I was crying with happiness. Some major takeaways I had from this group’s presentation was that no student relied on me, they constantly were asking the class if they had any clarifying questions, and most importantly, when the class was forced to rely on each other, they knew that they needed to ask whatever was going to get them to understand the topic.


Overall, I was so pleased with the productive struggle that occurred during this lesson. The students learned that they can achieve anything as a team through asking questions. I want to take this quote from the wonderful Mickey Davis regarding this lesson: “This is how students come to feel that they have a place at the table of mathematicians.” My research team is in the process of determining what encourages students to ask productive questions that encourage mathematical discourse and this experience has given me a glimpse into the possibilities of effective questioning.

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