Statement of Teaching Experience and Philosophy Adam Giambrone

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1 Statement of Teaching Experience and Philosophy Adam Giambrone As someone who cares deeply about teaching, I still find magic in those moments when a classroom comes alive with the energy of students working together to discover mathematical concepts and results. With these types of experiences, students are given the power to truly understand mathematics and to see that mathematics is created by everyday people, not just geniuses. Everyone regardless of academic, cultural, ethnic, or social background has the capacity to learn and grow mathematically. Everyone deserves a seat at the table. To get my classes to be open to learning opportunities, I try to bring to my courses a sense that we are all on the same side. Saying let s think about this conveys a di erent message than saying you must learn this. To help my students build a sense of community and establish the norm of collaboration, I use the first day of class to have students introduce themselves to the entire class and to work in groups on a mathematical task. Throughout the semester, I bring student names into our discussions with the hope that students will no longer see the instructor as the only source of knowledge. I also try to build rapport with my students by sharing my goals and rationale with them; this is done in written form on syllabi and assessments, verbally during class meetings, and electronically through regular correspondence and class webpage announcements. These practices not only provide a level of transparency to my students, but also help me to continually align the various components of my course with the learning outcomes I want my students to achieve. By maintaining a steady dialogue between my students and me, I aim to make the entire arc of the semester feel like a continuous conversation rather than a series of short weekly interactions. As an educator, I believe that students can and should be held to a high standard and challenged academically, with the caveat that this will only work if encouragement and guidance are provided along the way. Consequently, one of my main responsibilities is to teach in a way that helps students rise to meet these standards, grow from the experience, and leave the course with a sense of accomplishment and pride. For me, this means getting students to actively engage with mathematics both inside and outside of the classroom. My teaching practices have evolved over time to become centered around various forms of inquiry based learning (IBL). My transition to IBL is based on the benefits I feel it provides to students, which agrees with a steadily growing body of research into the e ectiveness of IBL and, more generally, active learning pedagogies ([4], [6]). According to the Academy of Inquiry Based Learning, the twin pillars of IBL are (1) student engagement in rich mathematical tasks, and (2) regular opportunities for student-to-student and student-to-instructor collaboration ([1]). With this in mind, a typical class meeting usually involves my (a) framing in-class activities and/or providing guided notes to help students explore, discuss, and engage with the material, (b) having students think about the tasks themselves and then work in small groups on these tasks, (c) bringing the class back together for students to report out on their findings, and (d) giving mini-lectures as needed. As a result of attending an IBL Workshop during the summer of 2017, I will also be incorporating student presentations of regular homework problems into my upper-level courses, the first of which will be a Fall 2017 topics course in knot theory. By using IBL teaching methods, I hope to give students the time and opportunity to take charge of their learning in the classroom, to make their own personal connection with the material, and to have the chance to collaborate with and learn from others. While students work on a given task, Teaching Experience and Philosophy, Adam Giambrone, 1

2 I walk around the classroom to see how students are doing, to ask questions and provide a little guidance if students seem to need it, and to make myself accessible for students to ask questions. In a written reflection about how people learn, a student in Honors Calculus II wrote the following. Rather than having to chug through an endless wave of similar problems, I appreciate that we take the time to truly explore mathematical concepts as well as practice them. It allows us students to not only get the rote practice that we need to succeed, but it also allows us to experiment with and discuss the true inner mechanisms of calculus. I ve never had a math class like this before, and it has been a refreshing experience. Never have I left a math class thinking Wow, that was actually interesting until this class because I am allowed to discover the ideas of calculus myself rather than having to memorize how to do some problem without any understanding of what it means. Outside of the classroom, I have increasingly made use of take-home exam portions and group assignments/projects. Using take-home exam portions allows me to convey to my students that doing mathematics takes time and that using resources like the textbook and technology appropriately is more like what mathematicians do when they work on mathematics. By being given more time to think outside of class in a low-pressure environment, students can be asked to engage in authentic mathematical behavior like sense-making, conjecturing, discovering, proving (or justifying), and validating. Using group assignments/projects allows me to show students that doing mathematics can be and often is a collaborative experience. Additionally, I often allow students to drop their lowest grade on certain assessments such as written homework assignments, quizzes, and exams. In addition to relieving student pressure, this practice also allows students the opportunity to learn what is expected of them and to focus more on growth (the journey) and less on complete perfection (the destination). This can be especially valuable in lower level courses where reducing math anxiety and changing student attitudes and beliefs about mathematics are at least as important as, if not more important than, the content. For example, every in-class exam and quiz in my liberal arts mathematics classes begins by reminding students that this exam/quiz is meant to check for understanding not judge you as a person. Starting in the spring of 2014, I have been working on expanding the types of assessments I use in my courses to include, whenever possible, reading/writing assignments in which students summarize and reflect on readings about topics such as intelligence mindsets, learning theory, and e ective thinking strategies. As an example, the readings for a Fall 2017 liberal arts mathematics course currently consist of (1) the article Mindsets and Equitable Education by Carol Dweck ([5]), which contrasts a fixed mindset the belief that one s intelligence is static with a growth mindset the belief that one s intelligence can increase with hard work and healthy struggle; (2) the first chapter of the book Make It Stick by Brown, Roediger, and McDaniel ([2]), which discusses the theory and misconceptions surrounding how people learn and retain information; and (3) three chapters of the book The 5 Elements of E ective Thinking by Burger and Starbird ([3]), which discuss how understanding simple things deeply, initially failing to succeed, asking questions, following the flow of ideas, and being willing to change are all valuable strategies for e ective thinking. By having students reflect on how the readings relate to their lives both inside and outside of the classroom, I hope that students will see the course in a new and broader context. These reading/writing assignments also create a new avenue for students to share their past experiences, their current struggles, their plans for the future, and their feelings about the course. After reading about the importance of failure in the process of learning, a student in Elementary Discrete Mathematics wrote the following. Teaching Experience and Philosophy, Adam Giambrone, 2

3 This chapter applies to me as a student in this class because I find that if I have an issue with a concept, I still will be able to learn from the mistakes and go forward. Particularly with the teaching style that you employ, it is very clear that you don t think that failure defines a person, which is a nice change of pace it s one of the reasons why I haven t been too stressed about if I don t understand something. I know that I won t be judged as a person in this class. I have also recently been focusing on improving my students written communication of mathematics. Specifically, in both liberal arts mathematics and honors calculus courses, I have had students separate the write-up of their assignment into two stages: a scratch work/rough draft stage and a final draft stage. During the scratch work/rough draft stage, students are free to try things, to make mistakes, to use these mistakes to build a strategy, and to eventually find a solution. During the final draft stage, students use their scratch work/rough draft to write up a clear solution, using numbers, pictures, symbols, and/or words to write to an audience of a hypothetical classmate rather than the instructor. By going through a scratch work/rough draft stage and a final draft stage, students are able to separate the challenging task of finding a solution from the challenging task of clearly and e ectively communicating their solution to an appropriate audience. Additionally, I have also used writing as a way for groups of students to explore new mathematical topics and applications. In Honors Calculus II and Honors Multivariable Calculus, I have used group projects as a way for small groups of students to explore how calculus applies to their academic areas of interest. The projects culminated in the production of both a written report and a poster that was presented during a class poster session. My hope is that group assignments like these will help students learn how to work collaboratively, how to use (and credit) outside resources to increase their knowledge, and how to communicate their findings in written and oral form. These are the skills that students will need in the future, regardless of their particular career path. As I communicate to my students, learning mathematics is about resilience and growth, not immediate perfection. The same can be said for learning to teach mathematics. My current teaching is a product of what I have been able to learn from my past teaching, from my involvement in professional development activities, and from what I have been able to learn from research in undergraduate mathematics education and from the scholarship of teaching and learning. While at Michigan State University as a graduate student, I was fortunate enough to have had many teaching experiences as instructor of record. I taught four semesters of Calculus I, three semesters of Survey of Calculus I, and one semester each of College Algebra, Finite Mathematics and Elements of College Algebra, and Survey of Calculus II. Also during my graduate career, I completed a Certification in College Teaching program that involved working on a teaching project with a teaching mentor from mathematics education, reading from the mathematics education literature in a course on teaching college mathematics, and attending seminars and workshops related to various aspects of teaching. To continue to have teaching-related discussions with my peers, I helped create a Student Teaching Seminar for graduate students in the mathematics and mathematics education departments. After receiving my Ph.D., I taught as a Visiting Assistant Professor at Alma College during the academic year. During this time, I taught three sections of Pre-Calculus and one section each of Liberal Arts Mathematics, Discrete Mathematics, and Math Foundations of Computer Science (a second course in discrete mathematics). I also attended monthly faculty teaching lunches and helped the department explore options for replacing a lower-level algebra course with a quantitative reasoning course. Teaching Experience and Philosophy, Adam Giambrone, 3

4 Currently, I am in my third year as a Visiting Assistant Professor at the University of Connecticut. During my first two years, I taught Elementary Discrete Mathematics (a liberal arts mathematics course), Honors Calculus II, Honors Multivariable Calculus, Applied Linear Algebra, Geometry, History of Mathematics, and Mathematics Writing Seminar. In the fall of 2017, I will be teaching Honors Calculus I, Mathematics Writing Seminar, and a topics course in knot theory. Throughout my time at the University of Connecticut, I have also served as the course coordinator for Elementary Discrete Mathematics. Before beginning my time at the University of Connecticut, I was fortunate to have been accepted into the 2015 cohort of the MAA Project NExT (New Experiences in Teaching) fellowship program, which has provided me with fantastic learning experiences and a place in a national community of mathematics educators. To help build a teaching-focused community in the mathematics department at the University of Connecticut, I helped restart and am a co-organizer for the Mathematics Education Seminar, whose goals are to share research in mathematics education and build connections between the mathematics and education departments. I am also co-organizing a newly-formed Teaching Seminar in the mathematics department, whose goals are to share current teaching projects, discuss teaching practices, and promote reflective and scholarly teaching. By attending a number of lunchtime seminars and teaching talks, I have been able to form a relationship with the Center for Excellence in Teaching and Learning (CETL) at the University of Connecticut. In particular, I have worked with CETL sta to form a university-wide learning community to explore specifications-based grading, helping to organize and run teaching talks, reading groups, and a day-long workshop on the topic. With an understanding of the potential of this grading system to motivate students, to give students more choice and control over their own learning, and to provide students with grades that better reflect their achievement of learning outcomes, I hope to be able to implement specifications-based grading in a future course. Additionally, I have also begun to add the scholarship of teaching and learning and research with undergraduates (which I see as part of both research and teaching) to my program of scholarship. Please see my Statement of Research and Scholarship Interests and Goals for more information. I am excited by the opportunity to work with students in a variety of courses and academic settings. For example, I value the opportunity to teach general education courses (such as liberal arts mathematics courses) because I really enjoy working to show students a side of mathematics they may not have seen, working to change student attitudes and beliefs about mathematics, working to reduce student math anxiety, and working to give students an authentic experience of what it is like to do mathematics. I also hope to be an instructor for courses that introduce the notion of proof, as these types of courses can help students make the sometimes challenging transition to advanced mathematics. Moreover, I am currently teaching (and I would love to continue teaching on occasion) a topics course in knot theory. The textbooks The Knot Book by Colin Adams and An Interactive Introduction to Knot Theory by Allison Henrich and Inga Johnson are both fantastic because they are accessible and because they contain exercises that allow students to think like mathematicians. The beauty of such a topics course is that the theory can be developed and explored by the students from the ground up. Also, the course can be used as an advertisement for things like a future independent study or a future undergraduate research project. Finally, since knot theory has been applied to other scientific fields, I would be extremely interested in creating and team-teaching a course on knot theory and its applications to biology, chemistry, and physics. This course would be a fantastic way to highlight the utility of mathematics in the STEM disciplines and could lead to interdisciplinary pedagogy and/or student research projects. Teaching Experience and Philosophy, Adam Giambrone, 4

5 For me, the excitement and challenge of teaching is in the fact that it involves many moving parts: the balance of careful planning and organization with adaptability and responsiveness to student needs, the creation of a welcoming and energetic classroom environment, the alignment of assessment and teaching practices with goals, and the promotion of active student engagement in authentic mathematical thinking and behavior. With a focus on my continual growth and professional development, I hope to model the love of life-long learning that we all aim to inspire in our students. References [1] Academy of Inquiry Based Learning. [2] Brown, P. C., Roediger, H. L., & McDaniel, M. A. (2014). Make it stick. Harvard University Press. [3] Burger, E. B., & Starbird, M. (2012). The 5 elements of e ective thinking. Princeton University Press. [4] Conference Board of the Mathematical Sciences (2016, July). Active Learning in Postsecondary Mathematics. Retrieved from pdf. [5] Dweck, Carol S. (2010). Mindsets and Equitable Education, Principal Leadership, 10(5), [6] Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), Teaching Experience and Philosophy, Adam Giambrone, 5