S COTT S CHNEIDER : T EACHING S TATEMENT
I have been teaching mathematics ever since my friends began having trouble with algebra in high
school, and while I have honed my technique quite a bit in the intervening years, the tutor in me remains
firmly in place: I still believe that the best context for teaching mathematics is unhurried conversation,
preferably with an involved and trusted acquaintance instead of an anonymous and distant instructor. My
teaching style is the result of attempting to reconcile these beliefs with the demands of the lecture hall.
I have taught sixteen undergraduate courses and one graduate course over the past five years as an
Assistant Professor, and before that ten courses as a graduate student. My duties have included preparing
and delivering lectures, assigning and grading homework, writing and grading quizzes and exams, holding
office hours and review sessions, selecting course textbooks, and assigning final grades. At the University of
Michigan I became familiar with the Inquiry Based Learning style of teaching, which emphasizes studentdriven investigation of material under the guidance of an instructor whose role is to encourage and facilitate
collaborative exploration and the asking of questions rather than to lecture. I participated in a conference
on IBL and taught six courses using the method while at Michigan.
From my experiences I believe that successfully teaching mathematics to university students involves
consistent excellence in at least two contexts. One is the lecture hall, where an instructor must engage in
a uniform manner many students at once, each of them bringing to class his or her own past knowledge,
learning style, and natural ability, to say nothing of mood, personal issues, and dispositions towards the
material and the instructor. The ideal lecturer will be part rigorous mathematician, part cognitive psychologist, and part theatrical entertainer, all at once and in real time: no easy task. I believe the likelihood of
success greatly improves, however, through attention to a second critical context in which teaching takes
place: personal interactions with students. For some students this may mean time spent at the end of class
or in office hours; for others it may simply mean knowing names, strengths and weaknesses, past performance, and an occasional timely remark indicating this knowledge. But I believe it essential for students to
be treated as more than simply one of many, a consumer of this strange product, the math lecture.
Whether in lecture or outside it, the key to building a successful learning environment is getting students
to care, to feel invested. There is no single formula for accomplishing this, and every teacher must rely upon
his or her own personal strengths. My own include a knack for story-telling and an interest in the “human”
side of math – the history, biography, and philosophy behind the theorems and proofs – along with a natural
ability to communicate and connect with students in a way that puts them at ease and replaces anxiety and
anonymity with the sense that each contribution they make in the class is valued. I make an effort to present
material not as abstractions in a vacuum, but as the gradually polished end result of often messy human
activity, not unlike students’ own struggles to learn it. My education students take greater interest in the
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Pythagorean proof that 2 is irrational after hearing the legends of its suppression and the execution of
its discoverer; my logic students remember Russell’s and Skolem’s paradoxes better after I tell them of
Russell’s correspondences with Frege, and that Skolem introduced his proof as an intended critique of the
axioms for set theory; my calculus students typically soften their distaste for epsilon and delta once they can
view their own difficulties in the context of the 200 year journey it took to supply the subject with rigorous
foundations. I attempt to humanize not just the content of a class but also my style of teaching, striving
at all times to be approachable and to establish strong channels of communication with my students and
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Teaching Statement
Scott Schneider
making a point of encouraging them to discuss material with each other or with me after class, or in office
hours where more personal attention is possible. A student at Wesleyan wrote in my teaching evaluation
that he or she had “never heard of a professor having so many office hours.” I feel that one of my strongest
qualities as a teacher is my ability to develop meaningful connections with my students that induce them
to care about the material more than they otherwise would, and allow me to teach in a way that is tailored
to their specific interests and needs.
The wonderful thing about getting students to buy into a class is that then you can really push them and
obtain an incredibly high level of effort and achievement. As a teacher I consider myself to be rather “soft”
when it comes to demeanor and approachability, but “hard” when it comes to content – indeed, as hard
as I can get away with, without losing them and becoming the enemy. When students care about a class
and respect the instructor, their motivation to do well stems from internal forces as much as from external
ones such as grades, and they can achieve remarkable results. In a first course on real analysis, two of my
stronger students pursued side remarks I made in lecture about topology and measure theory to the point
where they were regularly coming into my office for questions and were essentially teaching themselves the
subjects even though it was not part of the syllabus. In a unit on symmetry, my primary education majors
learned about the wallpaper groups through a hands-on activity involving matching pairs of patterns with
isomorphic symmetry groups, even though they knew no abstract group theory.
Of course, no amount of theater or charisma in the classroom or personal attention outside of it can
replace the need for a clear, organized, and professional presentation of the material. It is in my boardwork and organization of lectures that my teaching style connects most directly with my disposition as a
researcher, and with my area of expertise in logic. I once heard a colleague remark that it is the job of every
generation of mathematicians to make the work of the previous generation seem trivial. The remark resonated with me; while proving new theorems produces a high that cannot be replicated, I have found that
my real calling is in organization and exposition, in the custodial work that comes after the initial advances
are made and in which the “right” definitions and proofs are found that illuminate what is really going on
in as simple and elegant a way as possible. This attitude informs my lectures, leading one of my analysis
students to remark in an evaluation that “Scott’s lectures are probably the most organized, logical, and easy
to follow lectures that I have ever seen.” My lectures are consciously designed to be understood twice: in
the present moment, and during future study, possibly weeks later.
I want to conclude briefly with some comments on teaching as it relates to research, and specifically my
experience that there need be no conflict between the two. My teaching is a constant source of inspiration
for my research, and vice versa. Just last spring, a question that came up in the real analysis course I was
teaching led to a paper that I recently published. More generally, my attempts to understand as deeply as
possible any material that I teach invariably lead to new learning experiences for myself and occasionally to
research ideas. Conversely, doing research inspires me to want to pass on an appreciation for mathematics
to my students, and I have found that, especially in the upper-level classes, students are fascinated by
the notion of research and often ask about my own during office hours. I view these two primary duties
as complementary rather than competing, and believe that this attitude is evident to my students, that
it makes a positive impression on them, and that it enhances rather than detracts from their classroom
experience. My favorite comment to see in evaluations, and one that I have seen often, is some variation on
the following from a linear algebra student a couple years ago: “My interest in math has grown significantly
as a result of this course.”
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