Philosophy of Education

I believe all students have the potential to think critically and mathematically. However, each student manifests this ability at a different level and pace. Thus, it is the role of the teacher to facilitate learning by providing each student with the opportunity to grasp mathematical concepts. Too often teachers assume that only those who have demonstrated a high level of achievement in the classroom will be able to experience higher-order problem solving situations. Often, problems that require critical thinking are simplified to mere procedures and rules. Instead, I contend that it is precisely the struggle and challenge of these situations that can enhance all students’ understanding in some way. As an educator, it is my responsibility to provide the resources (information, experiences, problem solving strategies, etc.) to enable each student to improve his or her reasoning skills.

However, it is often difficult to reach students individually and even more difficult to change the deep-set attitudes towards mathematics, especially among those who struggle. I propose that creating a caring, problem-solving based community is the best way to combat negative attitudes towards mathematics and to help individuals make gains in their critical thinking ability. If I encourage students to be working together as mathematicians in a community, then they can learn from and communicate with each other. In this setup, every student has some insight to bring and each will struggle and learn from problems at their own level. My role in this environment is that of a guide, presenting tools and strategies for the class to discover and reason through mathematics. The more students see that there are different ways of thinking about the same situation, the more they will be able to access resources when they encounter a problem on their own. For instance, in a 7th grade classroom, we used two color counters to introduce integer operations. For the exit exercises, some students still needed the idea of chips while others had established generalizations. Through guided discovery, they took away a level of understanding that best suited them. The students who needed visuals still were not forced to resort to generalized procedures that they did not yet understand. They were able to correctly perform the calculations in a way that made sense to them.

I also must guide the establishment of a strong community by encouraging mathematical communication, critical commentary and sensitivity.

I believe all students have the potential to think critically and mathematically. However, each student manifests this ability at a different level and pace. Thus, it is the role of the teacher to facilitate learning by providing each student with the opportunity to grasp mathematical concepts. Too often teachers assume that only those who have demonstrated a high level of achievement in the classroom will be able to experience higher-order problem solving situations. Often, problems that require critical thinking are simplified to mere procedures and rules. Instead, I contend that it is precisely the struggle and challenge of these situations that can enhance all students’ understanding in some way. As an educator, it is my responsibility to provide the resources (information, experiences, problem solving strategies, etc.) to enable each student to improve his or her reasoning skills.

However, it is often difficult to reach students individually and even more difficult to change the deep-set attitudes towards mathematics, especially among those who struggle. I propose that creating a caring, problem-solving based community is the best way to combat negative attitudes towards mathematics and to help individuals make gains in their critical thinking ability. If I encourage students to be working together as mathematicians in a community, then they can learn from and communicate with each other. In this setup, every student has some insight to bring and each will struggle and learn from problems at their own level. My role in this environment is that of a guide, presenting tools and strategies for the class to discover and reason through mathematics. The more students see that there are different ways of thinking about the same situation, the more they will be able to access resources when they encounter a problem on their own. For instance, in a 7th grade classroom, we used two color counters to introduce integer operations. For the exit exercises, some students still needed the idea of chips while others had established generalizations. Through guided discovery, they took away a level of understanding that best suited them. The students who needed visuals still were not forced to resort to generalized procedures that they did not yet understand. They were able to correctly perform the calculations in a way that made sense to them.

I also must guide the establishment of a strong community by encouraging mathematical communication, critical commentary and sensitivity.

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