During the beginning of the semester, I remember reading the article Becoming Environmentally Aware by Rob Allen and Kathryn B. Chval. In the article, a teacher received a class of fifth grade students who saw themselves as "less smart" than the other math class. Because the teacher recognized this negative mindset, he decided to establish mathematical goals to increase student morale. Students were able to arrange how the classroom would look, feel, and sound. For the "sound" portion, Mr. Allen "asked [students] to think about the differences between effective and ineffective classroom learning environments." Through this, the students created a list "that explained what the students wanted to experience from one another" (Allen and Chval, p.30-31).

I found this article to be very refreshing, and wished I had a similar opportunity during grade school. There were moments where I feared being called on because I was embarrassed that I might have the wrong answer. The teacher in this article approached the uncomfortable feelings of a mathematical setting. All students should feel equally valued, even if their mathematical understanding is different. Despite this, students can assist one another in problem solving skills and introduce new ways to solve problems to one another through mathematical conversation.

I will have this conversation with my students and establish goals before proceeding with the semester. I want to create a list of effective and ineffective classroom environments so that my students can have a say in their learning and find a common ground. This is especially important in a mathematics classroom because many students have this stigma that math is exact and certain strategies are expected. Creating goals will drive my students to work with less fear of judgement and will allow them to align their thought processes with those of their peers.

In order to help them better understand the task at hand, Katherine and I implemented a new task during the warm up activity, Top-It. If the boys told us how they got their answer, they earned an additional point. On that same day, the boys were way more successful during the equation string activity. They were able to produce multiple ways to get to the same answer, which was very exciting. This gave us the chance to revoice their answers and further emphasize the goal of this activity.

In the future, I plan on coming up with new ways to revise my lessons so that my students can be more successful. In order to do this, I will consult my coworkers for advice on what works best for them. During our debrief session, Hope brought about the Top-it idea. This was immensely helpful as the boys were able to reason how they got their answers.

I plan to break concepts down into a simpler form and gradually increase the difficulty in order to help students understand the concept more holistically, as I had done in this lesson. This may require differentiated instruction so that all students can challenge themselves in ways that best suit their understanding. I also plan on using manipulatives, as I had done when using skittles. This allows students to manipulate numbers and see equations as groups. In the future, I will replace “equals” with “same as” during this lesson to further clarify what the question is asking them to do.

The combination of encouragement and use of manipulatives helped Carter understand the why behind his incorrect answer. This made him more successful in equations posted soon after. In the future, I will emphasize the importance of revising our thinking. I will also use some of these mistakes to conduct a Troubleshoot and Revise discussion. This will allow all of my students to play different roles in understanding the problem at hand; they can revise their thinking, or help other students come to a more accurate conclusion.