## Teaching Philosophy

As an educator, I believe that all students have the potential to understand and appreciate the beauty and utility of mathematics. However, over the years of teaching mathematics, I have learned that many students approach mathematics with a negative disposition, using phrases such as “I’ve never been good at math” or “math is only for smart people.” One of my goals as an educator is to change these perceptions, so that all students believe that they can pursue careers in science, technology, engineering, and mathematics. I do this by fostering relationships with students so that they feel both challenged, yet supported to grow and further develop their mathematical abilities.

I consider myself a social constructivist, that is, I believe that students should construct knowledge through series of social interactions. Rather than simply being a source of information, my role as an educator is to facilitate learning through rich tasks and discussions. In the course Tiles and Tessellations, that I developed and taught for Duke TIP, students discover which regular polygons can be used to tile the plane. This is done through a series of small group tasks and whole class discussions.

When students discover a concept through inquiry, they are much more likely to conceptualize this concept as opposed to learning through direct instruction. That is not to say that a lecture based approach should not be implemented. Rather, a balance of direct instruction and discovery based learning should be implemented to maximize student learning. In fact, when direct instruction must be done, I do my best to still make learning interactive and engaging by asking probing questions and using technology, such as Desmos or Plickers.

How do we determine what students have learned? In addition to homework assignments, quizzes, and exams, I find it beneficial to assess students using projects. For example, in the courses I have taught for the Trilogy School, I always give students an end of the semester writing project. In this project, students choose a mathematics topic which they feel is pertinent to their everyday life and future career. In the past, students have conducted and presented research ranging from the history of mathematics to the mathematics of being a sniper in the United States Army. Although traditional assessments do provide a relatively efficient way to determine what students know, this only provides a snapshot of their understanding in a single moment. By engaging students in open ended projects, such as the ones described above, I am able to gain a deeper understanding of what they know about a given topic.

Additionally, allowing students to make several decisions about their projects gives them a sense of agency. In turn, I find that they are much more motivated to produce meaningful results. In both An Information Age: Math and Technology of Data and From Startups to World Hunger: A Mathematical Perspective, students were afforded the opportunity to choose data sets or problems that were particularly relevant to them. This lead them to choose fascinating problems, such as determine the best place to raise a child and the feasibility of keeping the penny in circulation. These projects often include a presentation component, where students must communicate their results in a clear and coherent manner. Students are then provided written and oral feedback from both myself as well as their peers. By doing this, students develop worthwhile skills relevant to any career or field of study.

Student feedback is an integral part of my development as a teacher. In addition to the required course evaluations students must complete, I find it beneficial to have students complete informal mid-term evaluations. This allows me to make adjustments sooner, rather than waiting until the end of the term. Based on mid-semester student feedback, I increased the number of examples we worked through as a class in my Calculus for Elementary Education courses and provided more scaffolding as they worked through problems. My students took notice and felt more supported and prepared to engage in problem solving.

In addition to student feedback, peer evaluations of my teaching have also served as an essential component of my development as an educator. Since I have first started teaching, my use of precise mathematical language has greatly increased. This improvement in my teaching came as a result of being observed by fellow teachers. Conversely, observing other mathematics teachers has also greatly improved my teaching practices. During my time working on the MAP:TICCS project, which is discussed in my research statement, I have learned a great deal about teaching practices that are actually effective in the classroom. For example, I observed various teachers using a warm up problem to get students to jump right into mathematics as soon as the class began. I have since implemented this strategy and begin each of my classes with a warm up problem.

I consider myself both a lifelong teacher and learner of mathematics. Whenever I teach a new course or topic, I often find myself discovering a new connection or novel way of presenting the topic to students. During my time at NC State University, I have worked to connect the theories of learning discussed in my courses to the practice of actually teaching mathematics. In fact, the focus of my dissertation is to investigate the relationship between knowledge of real analysis and teaching practices so that we can better prepare teachers to teach mathematics. I hope to use the results of my study so that I can apply my knowledge of advanced mathematics, to better teach concepts from elementary algebra and calculus. I believe that the intersection of my research interests and passion for teaching provides me the opportunity to continuously grow as an educator.

I consider myself a social constructivist, that is, I believe that students should construct knowledge through series of social interactions. Rather than simply being a source of information, my role as an educator is to facilitate learning through rich tasks and discussions. In the course Tiles and Tessellations, that I developed and taught for Duke TIP, students discover which regular polygons can be used to tile the plane. This is done through a series of small group tasks and whole class discussions.

When students discover a concept through inquiry, they are much more likely to conceptualize this concept as opposed to learning through direct instruction. That is not to say that a lecture based approach should not be implemented. Rather, a balance of direct instruction and discovery based learning should be implemented to maximize student learning. In fact, when direct instruction must be done, I do my best to still make learning interactive and engaging by asking probing questions and using technology, such as Desmos or Plickers.

How do we determine what students have learned? In addition to homework assignments, quizzes, and exams, I find it beneficial to assess students using projects. For example, in the courses I have taught for the Trilogy School, I always give students an end of the semester writing project. In this project, students choose a mathematics topic which they feel is pertinent to their everyday life and future career. In the past, students have conducted and presented research ranging from the history of mathematics to the mathematics of being a sniper in the United States Army. Although traditional assessments do provide a relatively efficient way to determine what students know, this only provides a snapshot of their understanding in a single moment. By engaging students in open ended projects, such as the ones described above, I am able to gain a deeper understanding of what they know about a given topic.

Additionally, allowing students to make several decisions about their projects gives them a sense of agency. In turn, I find that they are much more motivated to produce meaningful results. In both An Information Age: Math and Technology of Data and From Startups to World Hunger: A Mathematical Perspective, students were afforded the opportunity to choose data sets or problems that were particularly relevant to them. This lead them to choose fascinating problems, such as determine the best place to raise a child and the feasibility of keeping the penny in circulation. These projects often include a presentation component, where students must communicate their results in a clear and coherent manner. Students are then provided written and oral feedback from both myself as well as their peers. By doing this, students develop worthwhile skills relevant to any career or field of study.

Student feedback is an integral part of my development as a teacher. In addition to the required course evaluations students must complete, I find it beneficial to have students complete informal mid-term evaluations. This allows me to make adjustments sooner, rather than waiting until the end of the term. Based on mid-semester student feedback, I increased the number of examples we worked through as a class in my Calculus for Elementary Education courses and provided more scaffolding as they worked through problems. My students took notice and felt more supported and prepared to engage in problem solving.

In addition to student feedback, peer evaluations of my teaching have also served as an essential component of my development as an educator. Since I have first started teaching, my use of precise mathematical language has greatly increased. This improvement in my teaching came as a result of being observed by fellow teachers. Conversely, observing other mathematics teachers has also greatly improved my teaching practices. During my time working on the MAP:TICCS project, which is discussed in my research statement, I have learned a great deal about teaching practices that are actually effective in the classroom. For example, I observed various teachers using a warm up problem to get students to jump right into mathematics as soon as the class began. I have since implemented this strategy and begin each of my classes with a warm up problem.

I consider myself both a lifelong teacher and learner of mathematics. Whenever I teach a new course or topic, I often find myself discovering a new connection or novel way of presenting the topic to students. During my time at NC State University, I have worked to connect the theories of learning discussed in my courses to the practice of actually teaching mathematics. In fact, the focus of my dissertation is to investigate the relationship between knowledge of real analysis and teaching practices so that we can better prepare teachers to teach mathematics. I hope to use the results of my study so that I can apply my knowledge of advanced mathematics, to better teach concepts from elementary algebra and calculus. I believe that the intersection of my research interests and passion for teaching provides me the opportunity to continuously grow as an educator.