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Establish Mathematics Goals to Focus Learning

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Establish Mathematics Goals to Focus Learning

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https://learn.westminster.edu/d2l/le/content/25865/viewContent/237262/View

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.

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Implement Tasks That Promote Reasoning and Problem Solving

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Implement Tasks That Promote Reasoning and Problem Solving

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During the 5th week of Math Buddies, Katherine and I had asked Carter and Westin (Hawk was absent) to justify their thinking during the number string activity. We would present an equation from our number string on the screen and ask boys to explain how they got their answers before actually giving the answer. Immediately, the boys gave us the sum of the equation and then gave us new ways to get to the same answer (like we had done in prior lessons). After our 30 minute session, Katherine and I brainstormed how to better assist our students so that they could be more successful during week 6.

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.

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Artifact 2 for Implement Tasks That Promote Reasoning and Problem Solving

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Artifact 2 for Implement Tasks That Promote Reasoning and Problem Solving

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Build Procedural Fluency From Conceptual Understanding

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Build Procedural Fluency From Conceptual Understanding

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There was a wonderful opportunity at Union Elementary School where I was able to teach my students the purpose of an Equals Sign. Although they had been working with problems that used this sign all the time, breaking down equations into a simpler form actually helped them better understand how to balance equations. As I had mentioned under "Self Evaluation," one of my students saw an equals sign as an indicator to add all of the numbers and immediately produce an answer. He had thought that the answer to the equation 4+3=2+__ was 9. At the end of the lesson, he raised his hand to answer the hardest number sentence on the worksheet: 15 + 3 = 11 + __. At first, his answer was “4+3,” which was a huge breakthrough. I told him this was a good way to think about it, and then asked him what 4+3 equaled. He then paused for a little. Although this may be a pause that teachers would "move on to somebody else for help," I gave him all of the time he needed. He then responded, saying 7. This was extremely rewarding. Now that he has all of the correct parts, he was able to explain his thinking. I used this moment to talk to the class and explain how valuable it was to revise our thinking. I also reiterated that an Equals Sign means that both sides of the equation are the same.

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.

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Support Productive Struggle in Learning Mathematics

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Support Productive Struggle in Learning Mathematics

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During week 5 of Math Buddies, I was able to support productive mathematical struggles alongside Katherine. It was clear from at least week 2 that our boys responded in very different ways. Carter used the chat function, Westin gravitated towards using a whiteboard, and Hawk would typically unmute himself. Hawk was usually the quickest to answer, and he was almost always right. Sometimes, Westin and Carter would quickly agree with Hawk's responses rather than produce answers of their own. This is why it was so hard for them to justify their thinking. There were, however, moments where Katherine and I took those wrong answers and used visuals (10 base blocks and annotation tools) to help the boys correct their mistakes. In the artifact below, Katherine and I discussed how we assisted Carter when he did not get an answer right. Initially, Carter shut down and seemed discouraged. Katherine and I immediately reinforced that all mathematicians must revise their thinking and that struggles were a part of the process.

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.

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Artifact 2 for Support Productive Struggle in Learning Mathematics

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Artifact 2 for Support Productive Struggle in Learning Mathematics