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The Pre-K-2 class consisted of five students. The students were given the task of assembling groups of buttons higher, lower, or equal to ten in various configurations. Critical mathematics is used in an activity designed to show the importance of sharing available resources to achieve common goals (Ernest, Sriraman, & Ernest, 2016; Gutiérrez, 2013). The class consisted of three girls and two boys. They have been studying early number and operations topics for the past week with 45-minute lessons. The previous results were positive, and all of the students have shown an interest in the subject. The pseudonyms for students described in this reflection are James, Donna, and Lilly.
Dialogue of the Students
James was the first student to note that the number ten can be assembled in different combinations of buttons. “It can be two and eight or five and five!” he said during the exercise. Other students quickly realized that this is a possibility and assembled these two different groups of buttons. It was very satisfying to see the students grasp the material so quickly and find different ways of combining buttons.
Donna then proceeded to assemble three and then four stacks of buttons. She said “You can do make them like this too!” and looked proud of the fact that she was the first to provide this answer. When the critical mathematics section began, I took all the buttons away from the students and gave out an unequal amount of buttons to the students totaling ten buttons. Then, the students were provided with a task “assemble ten buttons.” They had to realize that the task is impossible to accomplish on their own and cooperation is required. However, this option was not mentioned to them. It seems that Lilly was the first to realize that they would need to combine their button stacks.
She exclaimed “but they are my buttons!” and covered them with her hands. At the moment, she had the biggest stack and perhaps did not want to share it with the class. Other students placed their buttons together in a row, with only Lilly’s buttons being absent. James said “please share the buttons,” he was not upset by her actions but wanted to complete the task. After a few minutes, she calmed down and calmly added her buttons to the combined row. When asked about the lesson, Donna said that she learned how to “do things with others.”
As previously noted, the students were very engaged in the tasks. I was surprised by the level of their mathematical thinking when they were presented only with the most basic information about the task. I was especially impressed by Donna’s realization that a number can be achieved through many combinations. She understood it effortlessly and immediately provided multiple examples. To maintain the cognitive demand of the task, the resources available to the students were often changed, with the types and number of buttons varying between the phases of the lesson.
A simple version of critical mathematics was used to engage the students in the concept of sharing and how some situations require a combined approach from all the parties involved. This was a relatively simple task, but it allowed the students to understand the importance of sharing. I found this lesson to be important for children because people often find it hard to give their possessions away for the needs of others. However, when a person understands the importance of the goal, such as charity, this becomes an easier process.
The students were very attending and engaged with the material. Some have become initially distracted with the different buttons that I presented, but their interest quickly shifted back to the topic of the lesson. All of the button combinations were achieved solely by the efforts of students which show their ability to think mathematically. After the initial exclamation by James about the different combinations, all of the students produced a combination of their own.
Perhaps the main issue that occurred during the lesson was Lilly’s reaction to the critical mathematics task. I believe that by giving her more buttons than others, she began feeling too attached to them, even if she realized that sharing them was required to complete the task. In future implementations of this lesson, I should make sure not to let one student have too many buttons. Another realization that I received during the lesson was that the students were possibly capable of receiving more complex instructions at this level.
In the future, I could combine the tasks of multiple lessons, and the students should still be able to complete them. However, I would need to examine additional research before implementing elements of other lessons, as the retention of the information gained from tasks may drop with their increased difficulty.
The overall lesson was designed for pre-K-2 students with an element of critical mathematics. The students were engaged with the material of the lesson and had understood the assignment well. Their solutions were creative and accurate. A small issue occurred during the critical mathematics but was soon resolved by the students.
Ernest, P., Sriraman, B., & Ernest, N. (2016). Critical mathematics education: Theory, praxis and reality. Charlotte, NC: Information Age Publishing.
Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37.