Teaching Philosophy
Kirsten Hogenson
During my time as a graduate teaching assistant at Iowa State University, I’ve had the opportunity to take
on a variety of both teaching and administrative jobs. As an instructor, I’ve taught classes ranging from
Math 10: High School Algebra through Math 166: Calculus II. On the administrative end, I served one
year as the Lead Teaching Assistant, two semesters as the departmental liaison for both the MyLabsPlus
online homework system and the ALEKS placement exam, and one semester helping to start up a new
Special Math Instruction help room. Of the jobs I’ve held, the three positions that have most influenced
my teaching philosophy are being Lead Teaching Assistant, teaching Math 143: Preparation for Calculus,
and teaching Math 10: High School Algebra.
Lead Teaching Assistant
As the Lead Teaching Assistant, I assigned teaching and grading jobs to all graduate teaching assistants
(TAs) in the math department for both the fall and the spring semesters. I also served on the Math
Graduate Student Organization council, where I helped organize mentorship and professional development
activities for my fellow graduate students. During the fall semester, I was charged with training and
mentoring the math department’s incoming class of graduate teaching assistants. This involved organizing
a welcome meeting and teaching program for the new TAs and performing midterm teaching observations
to give them feedback on their instruction. The Lead Teaching Assistant job is an enormous responsibility
that required an extensive time commitment and tremendous organizational and social skills. Not only
did it provide me with a useful administrative experience, but acting as a mentor to new TAs allowed
me the chance to reflect upon my own teaching skills as I helped them develop theirs.
Precalculus
In Fall 2013, I helped launch a new precalculus course, Math 143X: Preparation for Calculus. This 4credit course employs Pathways to Precalculus teaching materials, which were developed by Dr. Marilyn
Carlson and other researchers at Arizona State University and are based on 15 years of National Science
Foundation-funded research into precalculus education. For the first two years it was offered, Math 143
was listed with an X designation to indicate that it was ‘experimental’ as we collected data on the rate
at which precalculus and Calculus I students either earn a grade of D or F, or drop out of the course
(DFX rates). Beginning in Fall 2016, Math 143 has been approved for inclusion in the Iowa State course
catalog, and will be offered without the X designation, due in part to the improvements in the DFX rates
for precalculus and Calculus I.
Initially, Math 143 at Iowa State was structured as a large lecture with recitations, which utilized a
classroom response system (‘clickers’) and inquiry-based learning techniques. Students would attend the
full lecture section twice a week to discuss clicker questions, and they would meet with me twice a week
in a 32-student recitation section to explore new concepts by completing group projects. For example,
when learning about angle measure, group members worked together to construct angles measuring 1
1
radian using only a compass, string, and straight edge. This gave them a hands-on environment to learn
about the relationship between the radius length of a circle and the arc length cut off by a 1 radian
angle. As they worked, I walked around the classroom, asking probing questions about what they were
doing and encouraging discussions amongst group members. Before the lesson occurred, the other Math
143 instructors and I would try to anticipate where students would struggle and how we could help to
correct their misconceptions. This involved looking carefully at our own understanding of the subject, so
that we could present multiple ways to think about any given concept. Then, before adjourning class, I
gauged the effectiveness of the lesson by asking individual students to present tricky problems from the
day’s lesson on the board and report their various discoveries. Math 143 was my first experience with
an inquiry-based style of teaching, and the understanding that students displayed when they presented
problems to their peers had a big impact on the way that I interact with students both in and out of the
classroom.
Teaching My Own Course
In Summer 2015, I adapted the existing Math 143 curriculum to a small class setting and had the
opportunity to apply many of the lessons I learned while teaching recitations. For instance, I learned the
value of discussing the most important lesson topics both before and after students work in their groups.
The most frequent frustration I heard from students who were unsatisfied with the lecture-recitation
format was that they felt abandoned by the instructors and were overwhelmed by the idea of discovering
mathematics on their own. By motivating the lesson at the beginning of class, I helped students feel
more confident that they could competently complete the assignment. In fact, in my course evaluations,
one student wrote:
“I like that when there’s a particularly tricky concept or definition involved in the day’s project,
Kirsten starts with explaining that to the entire class before letting us loose to work on the project on
our own.”
Once the lesson was introduced, the real learning could start. The group work that occurred in my
precalculus course could be really challenging for students, but in my experience, students will understand
a concept much better if they wrestle with it than if I just tell them about it. After participating in the
class for a while, many students realized this themselves. In the words of the student quoted above,
“The group collaboration is nice. It can be frustrating if no one is grasping the concept, but that’s
when we ask for help from Kirsten... If at least one person in the group understands the concept, we’ll
struggle through it amongst ourselves; we may not be as effective as instructors, but when successful,
in-group explanations help everyone solidify their understanding.”
At the end of class, I again called upon students to present selected problems to the class while I took a
seat in the back of the room. This gave students the chance to share the insights discussed within their
groups, and it helped emphasize the concepts that they needed to take away from the day’s lesson. It
had the added bonus of holding every student accountable for the new material, so they were encouraged
to actively participate within their groups. Student opinions about problem presentations were mixed,
but most of them agreed that the presentations helped everyone learn. In my course evaluations, one
student made the following comment:
“Although [the presentations] are helpful, I get really nervous when it’s my turn.”
The nervousness expressed by this student is understandable, but it highlights part of what is so beneficial
about these presentations: students are nervous when it comes to talking about math, so it’s something
they really need to practice! The act of doing so may be scary, but in the end it makes them stronger
both as students and as communicators.
2
High School Algebra
In Fall 2014, I was the sole instructor for a section of Math 10: High School Algebra. This is a 4 hour per
week, no-credit, remedial algebra course for students who do not satisfy the algebra requirement for their
major or who do poorly on the ALEKS placement exam. Math 10 splits up into Track A and Track B,
which cover approximately the first and second years of high school algebra, respectively. I taught Track
B. One of the noteworthy traits of Math 10 students is that they tend to lack confidence when it comes
to mathematics. Some are convinced they will always be bad at math; others have been out of school for
many years and are struggling to relearn concepts they never truly grasped. Because of this, I learned
the importance of getting to know my students personally. On day one, I asked students to share what
skills they excel at and what I could do to help them learn more effectively. Throughout the semester,
I tried to emphasize that they’ve already mastered those non-math skills through hard work, and that
same work ethic can help them to be successful in math. I worked with many students one-on-one, both
in a help room setting and during my office hours. For those students, Math 10 helped build their self
confidence and gave them the necessary skills to learn college level mathematics. I’m very proud to have
been a part of their success stories, and I hope to help many more reluctant students realize that they
are capable of learning and enjoying mathematics.
I’ve had numerous valuable experiences being a teaching assistant at Iowa State University, and I’ve
learned much about how to be an effective instructor. First and foremost, I learned that there is always
more for me to learn. Because of this, I am always open to trying new teaching techniques that might
help me to reach students, improve their understanding, and instill in them a love and appreciation for
mathematics. Second, I’ve seen the positive effects that result when I reach out to students. If I can
encourage a student to come to my office hours for the first time, I’ve found they will be much more likely
to come back and talk to me when they are having trouble later on. I want all of my students to succeed,
and I try to make it clear to them that I really do care about their education and I’m here to help them
when they need me. Finally, I’ve realized how imperative it is for students to understand the ‘why’ of
mathematics, rather than just the ‘how’. To this end, I am always making an effort to get students to
talk about mathematics. As they spend more time discussing problems with their peers and explaining
their work to me, they are more likely to have ‘Aha!’ moments where their understanding clicks and they
get excited about math. These are the moments that make my job worthwhile, and I strive to share that
excitement about mathematics with all of my students.
3