
Messages from My Office Door

Teaching Winter 2020

MATH 2070 Introduction to Differential Equations
This course covers the topic of differential equations, which are
mathematical statements of equality relating a function (of one
variable, conventionally representing time) to its derivative (or first
and second derivatives). During this course, we will study first order
differential equations and systems of differential equations, with an
eye to qualitative, analytic, and numeric methods of solution and
analysis.We will use ZIll's A First Course in Differential Equations with Modeling Applications, 11ed. and WebAssign in this course.
Meets 50 min daily.

MATH 115001 Graph Theory in the Real World (Hybrid Section)
During this course, we will study the concepts and results of graph theory, how to solve problems related to graphs, and how solving graph theory problems helps us understand real world problems: scheduling, map coloring, postal delivery routes, amicable seating charts, population life cycle analysis, DNA sequencing, and more. This is a hybrid course, meaning that some of the course meetings are facetoface (Tuesday, Thursday, Friday), while in between facetoface meetings, students engage with course content, complete assignments, and communicate with classmates and the instructor through our online course container on the Canvas learning management system. This course satisfies the DU Common Curriculum AIN requirement.

Who I Am as a Teacher

I take a constructivist and sociocultural approach to teaching, that all learning is social and cocreated. Teaching math is part apprenticeship of developing mathematicians, part opening up new mathematical ideas and ways of communicating the knowledge students create. Mathematics at the college level is a field one succeeds in by hard work and acquiring understanding of how experienced mathematical thinkers frame and solve problems. I encourage persistence and sensemaking through active or inquirybased learning activities such as derivatives dominoes, limit puzzles, and openended questions about graphs of functions. I want my students to discuss their reasoning and how ideas connect.
I believe that every student is capable of learning and developing a positive mathematics identity. Who a student is and how she has previously engaged with mathematics and school in general, her own sense of intelligence and intellectual and cultural capital, will shape the social setting in which she learns. My role as a teacher is to facilitate learning in a classroom where restrictive visions of mathematics, mathematicians, and what it means to do mathematics are transformed to create space for every student to own their learning. In practice, this means developing norms of communication, elevating conversations about why concepts work, and allowing students to develop the problems, questions, or plans of learning they embrace. From selfevaluations of exam performance to debriefs of group solutions to a math problem, I provide assignment “wrappers” that encourage students to become aware of the story of who they are as mathematical thinkers and doers, and I celebrate, and encourage them to celebrate, the ways they communicate mathematically with one another. Mathematics learning is seen as a collaborative enterprise that builds collective and valuable knowledge—just as it happens with real mathematicians.
I want to encourage learning in which the student takes the lead as the thinker and information processor, versus having me to be the mathematical storyteller they listen to and emulate. This is why I believe in hybrid or flippedclassroom teaching methods where selfregulation techniques are used to engage students in "tastes" of the day's concepts or skills for low stakes points prior to class, so that class time can be used to confront misconceptions, try out more problems, or engage in metacognitive activities.
I want to improve access to concepts across the diversity of students (of varying cultures, languages, learning abilities and prior experience) and their own paths to learning. I believe a course must be supported with robust instructional materials available for selfpaced experiences with content so as to not privilege fast readers, native speakers, or students who can repeat a process after the first example. I make sample solutions, explorations of key concepts, traditional lecture notes (often the very ones we create during class as well as a “clean” set), video explanations, and online quizzes and homework available to all students via Canvas modules, or through Microsoft OneNote class notebooks.
I am present for and communicate the worth of the students I teach. I want to and do learn as much as possible about each of my students from early on in the term through surveys and inclass introductions. I often ask them to share on the first day “what you bring to class as a learner”, or what math they did last week, as a way to infuse who they are into their mathematics identity. Building on this personal relationship, I can help them grow. In office hours or class, I am their partner in identifying where any obstacles lie to acquiring skills or applying concepts. I tell my students before each exam that their test performance is not a measure of their value or mathematical intelligence; the test is a measure of what happened, not who they are or what they know or learn. I share research behind growth mindset and challenge them to reject a predestined view of who they are in the class. I encourage them to think not only why they are making correct mathematical choices, but what sometimes gets in the way of them making these choices, and what are their own strengths they can use from other courses or interests.

Summer 2019 Teaching

MATH 1953 Calculus III
End of firstyear calculus sequence for science, engineering, and mathematics students, covering parametric and polar coordinates, L'Hospital's Rule, improper integrals, infinite sequences and series, power series, and Taylor series expansions of functions.
This is a selfdesigned online course offered over 8 weeks.
We are using James Stewart's Single Variable Calculus: Early Transcendentals, 8e with WebAssign in this course.

Courses Spring 2019

MATH 2070 Introduction to Differential Equations
Meets 2hr twice a week with instructor for lecture and 1 hour Friday recitation with TA.

MATH 1200 Calculus for Business and Social Sciences
Lecture Format; Course meets two days/week for 2 hours with extended calculus topics (differentiation and integration) and projects/group work included.

Courses Winter 2019

MATH 1200 Calculus for Business and Social Sciences (Lecture Format)
MATH 1150 Graph Theory in the Real World (Hybrid Format)

Courses Fall 2018

MATH 1200 Calculus for Business and Social Sciences (Lecture Format)

FSEM 1111 Mathematics Through Fiction
An exploration of mathematical topics as they arise in mathematical fiction. Topics such as counting, infinity, number theory, sequences, topology, and the geometry of 2, 3, and higher dimensions will be studied. Students will read literature that introduces mathematical ideas, learn about the associated mathematics, and create works of mathematical fiction. The course closed with a Mathematical Fiction Reception celebrating student writing as well as the literature we read.

Courses AY 20172018

MATH 1953 Calculus III: Sequences & Series (Summer; Online)
MATH 1200 Calculus for Business and Social Sciences (3 sections)
MATH 2070 Differential Equations
MATH 1150 Graph Theory in the Real World (Hybrid)
FSEM 111139 Mathematics Through Fiction

Courses AY 20162017

MATH 1951 Calculus I: Differentiation (Summer Session)
MATH 1200 Calculus for Business and Social Sciences (Lecture)
MATH 1150 Graph Theory in The Real World (Hybrid Section)
FSEM 111139 Mathematics Through Fiction

MATH 1200 Calculus for Business and Social Sciences (Hybrid Sections)
This course teaches differential calculus concepts (without trigonometry) with an eye to their realworld applications and interpretations, and is the appropriate AIN calculus class for students majoring in business and the social sciences. Topics include limits, differential calculus of one variable, including exponential and logarithmic functions, and applications of calculus to business and the social sciences. These sections were offered in Combined/Hybrid format which uses online video content prior to class meetings to offer a reduced class size (30 students) and a more active learning environment, meeting facetoface three days/week.

Courses AY 20152016

FSEM 111139 Mathematics Through Fiction
MATH 1951 Calculus (Summer Session)
MATH 1200 Calculus for Business and Social Sciences (Lecture & Hybrid Sections)
MATH 1150 Graph Theory in the Real World (Hybrid Section)
MATH 2070 Introduction to Differential Equations

Courses AY 20142015

MATH 1951: Calculus I
MATH 1952 Calculus II: Integration (Summer Session)
MATH 1200 Calculus for Business and Social Sciences (Lecture & Hybrid Sections)
MATH 2070 Introduction to Differential Equations

Courses Taught 20072014

Many sections of:
FSEM 1111 Mathematics Through Fiction
MATH 1150 Graph Theory in the Real World (Hybrid)
MATH 1150 Graph Theory and the Real World
MATH 1200 Calculus for Business and Social Sciences (lecture & hybrid format)
MATH 1951 Calculus I
MATH 1952 Calculus II
MATH 1953 Calculus III