# The Philosophy of Teaching, part 3

This summer, Cohort I completed their final summer residency at Harvard. Their final course was a Teaching Projects/Capstone Course intended to give current and aspiring secondary math teachers an opportunity to become engaged in a variety of teaching-related projects. Students completed a series of research and presentation requirements during the course focused on issues such as the impact of various pedagogical approaches, the use of technology in classrooms, assessment techniques, and curriculum design, among other topics. The Capstone Course was led by Dr. Andy Engelward, director of the Math for Teaching graduate program. All students were required to write a teaching statement outlining their experience and philosophy on their profession. This is the first of a series of statements we’d like to share.

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**Ricardo Delgado, San Benito CIS**D

My passion for the subject along with my passion for student’s success are the main reasons for being in the classroom. Building students’ self confidence towards math is my second priority in the classroom. The first would be steady and significant progress from beginning to end. 100% comprehension and application would be ideal but unrealistic. Being able to diminish the negative connotations one enters the math classroom with is an achievement in itself. Learning occurs when the students allow themselves to be wrong, and they realize that trying may not always lead to mastery but does result in improvement. An attitude I like to portray is to always strive to be better. I make the analogy using my newfound interest, running, to address common occurrences or urges of quitting. Since I reach high school students, the majority of them will have completed 13 years of education to obtain their diploma. Any student expressing their desire to quit is compared to running a half marathon and quitting at 11, more than 80% of the way. I also stress the importance of setting goals and working the most efficient to achieve them.

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**Julio Tobias, Edinburg CIS**D

To be the most effective teacher, one must go back and understand the students’ perspective to gain better understanding of your students in general. We must understand that everyone is different and teaching must be adaptive and ready to change for every student. No one student is strictly an auditory learner, given a specific task. For example, when assembling an object together, students do not rely on someone reading the instructions to them and understanding how to build it in one go. They must read the instructions and understand them. They must have a visual representation of what the object should look like and they must have some kinesthetic awareness of where a certain piece of the object is in relations to the whole. This is how students learn, a combination of styles that moves with fluidity. By giving students an environment where they can create dialog within the student body and can collaborate and interact with each other allows them to learn. Math knowledge is not simply being able to spit out quick, random facts that are math related, math knowledge means students can approach a problem, reason through it logically and come up with their own conclusion/conjecture. Even if it is wrong I want to create an environment where they can defend their reasoning or find where someones logic falls apart. An environment where it is understood that math is not “easy” but that it takes hard work and perseverance. As a math teacher I want to make sure that my students are well prepared for what they will see in their lives. Whether it has to do with mathematics or not, I hope they develop a sense of reasoning and problem solving that goes beyond the classroom, that they do not just take things as a matter of fact, but logically reason through what they are told is true and decide for themselves if it actually makes sense.

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**Karina Araiza, PSJA IS**D

I have had the joy and privilege to discover mathematics at least twice in my lifetime, once as a student in middle school and the second time during my graduate studies at Harvard Extension School where there is a wonderful program for teachers. I started a M.S. in mathematics some time back in Texas, but I left the program about half way into it because id did little to appeal to my previous jubilant experience in middle school as a discoverer of the subject or even to connect to my teaching of high school mathematics. Somebody once told me that I am very much like a child, I replied, “Yes, I have noticed.” Reflecting on the meaning of the phrase, I came to the following conclusion, “How great would it be if everyone of us could be like a child when it comes to learning mathematics.”

Children have an innate ability to qualify the world around them as a place worth discovering, and mathematics is perplexing in essence, but ironically, teachers of mathematics find ways to take all that power out of the subject and disconnect all of its concepts to provide the students with a set of steps to follow whenever the key words of a problem point to a specific direction. The underestimation of students in America is a practice that must be eradicated; whenever I question colleagues about their reasoning for not providing students with challenging tasks, their response is always, “How can I expect them to know how to solve such as task if I have not given them any notes on the topic yet?” Sadly, those lines translate into practices in which the child will be trained to algorithmically answer in a certain direction, whenever prompted in a specific way, and that is the exact opposite of the meaning of mathematics.

One must understand the meaning of mathematics in order to teach children about mathematics. Reflecting and searching within ourselves about what it was that ignited our passion for the subject when we made the decision to dedicate our lives to the students and education of mathematics can be a powerful way to make our practice interesting and meaningful.

As a high school mathematics educator for more than a decade, I have come to realize that if we want our students to persevere in the classroom, then it is our responsibility as educators to challenge them by evoking their knowledge and emotion which will in turn direct them through the wonderful journey of intrinsic, self motivated search for understanding and discovery.

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