Research Statement & Teaching Philosophy
Teaching Statement
I am fortunate for my early career experiences in teaching—I worked at small institutions that focused directly on the student-teacher relationship. This involvement has become the foundation of my teaching style as I have moved into higher education and academia overall. In fact, this search for individualizing each student is a big reason that I have taken on a resident hall as the lead director this school year. In the classroom, though, math activities, hands-on projects, relationships, a positive culture, and discussion dialogues are all key ingredients to a successful mathematics course, and my philosophy hinges on the belief that dedication to easing students more comfortably into mathematics while giving them ownership of the experience is essential to success in the classroom and beyond. Mathematics can be a difficult subject—yet when students witness vulnerable processes for everyone in the classroom (i.e. struggling through hard work, wrong answers, and mistakes), often they realize immediate perfection is not the goal and that the end result of understanding is more significant.
My classroom structure typically varies from course to course. That is, a pedagogy course for middle school STEM teachers will not be taught in the same way a math history course would. For example, in a Math for Teachers course, beyond content we also cover methods through activities that the pre-service teachers could use in their future classrooms. In a statistics course we shot basketballs to build best-fit line projections and normal distribution curves. In a math history course the students chose a modern and historic mathematician to write papers, from which test questions were generated. In these ways, students learn collaboratively and exist in a less isolated classroom, conducive to understanding in a variety of settings.
However, a generalized classroom format would include some type of warm-up problem to get students back focused on the material we have been covering, paired with some lecture. However, lecture cannot be the primary form of learning; projects, group work, classwork practice, and discussions all come into my courses at some point. Because students display a wide scope of learning methods, I adjust accordingly and attempt to provide many of these options with the hope some connections are made, particularly those students that are shy and scared about asking for assistance. For this reason, I also am quick to respond to student emails and am available to students beyond the limitations of office hours. For example, I was walking to the bookstore/cafeteria area for an on-campus lunch, and a student saw me and said they were struggling with derivatives. I asked if he had a few extra minutes, so we sat down at a nearby table and began going through the notes and example problems right there on the spot. I genuinely do not mind interactions like this in the slightest, because it is absolutely rewarding when there are signs of improvement and, often more importantly, confidence. I promote a comfortable, open classroom, peppered with lighthearted jokes and pointed questions with the expectation that the class moves forward together based on their responses. I continue to advise many students in a variety of capacities, including courses, homework, clubs, and recommendations. I look forward to continuing all of the methods mentioned above with students so that mathematics education improves through each new group of future university students.
Research Statement
My research experience has reflected both my graduate degrees and background in mathematics education. Broadly, my focus has aimed toward assessing teaching and learning strategies for a wide variety of mathematical content. First, as primary investigator, the purpose of one research study was to select, observe, and analyze three specific factors that could influence the transitional experience of former third grade Montessori students entering a more traditional, fourth grade atmosphere—within a mathematics context. Using observational tools and qualitative coding techniques, the three factors of pacing, classroom roles, and change in learning materials were scrutinized, with effects on students’ problem solving abilities covered through a series of Cognitively Guided Instruction (CGI) open-response problems. Another student-centered research study I was part of focused on assessing the impact of prompted writing reflections on students’ motivation and focus in a college Calculus 1 course. The writing assignment was given mid-semester in one section but not in the other, while pre- and post-surveys compared student opinions on the interest, utility value, and performance expectations in Calculus 1. Our goal was to determine if the writing assignment provided statistically significant improvements for students concerning those items. My next project, also as principal investigator, was instead focused on teacher preparation, specifically through designing a geometry- and statistics-focused professional development session for middle school teachers. In the study, the control group was taught using standard, direct instruction methods, while the experimental group worked with hands-on materials. Both groups covered the same concepts within the program, and pre- and post-surveys, discussion, and written problems are currently being analyzed to compare the results of the two groups regarding content knowledge and confidence. Topics included, but were not limited to, application of ratios, differentiating between surface area and volume, probability misconceptions, and statistical representations.
Looking ahead, I have a few interesting projects approaching, currently in the early stages of development. For example, I am analyzing data in fall and spring semesters among course start times, including unit test scores (limits, derivatives, application, and integrals), to statistically compare the groups and determine to what extent course time and semester truly affects student performance in an introductory calculus course. Further, I have secured classroom technology funding for both a classroom set of iPad Minis and Nintendo Switch Labo sets. The iPads will be used with pre-service elementary teachers regarding STEM and geometry subjects. The Labo kit is one of the newest potential educational tools accessible, with very little data available since its release earlier last year. Beyond determining its usefulness as a STEM tool, the purpose is to potentially improve young student self-efficacy and excitement for future STEM careers—particularly in females and minorities in the elementary and middle school grades who need to fill a continuously growing number of job vacancies in STEM fields. Additionally, I have a university-hosted field trip from a nearby public school planned as a joint research project, with hands-on activities to solidify historically weak content scores regarding proportions and ratios in high school students, particularly minorities. Similarly, I am working with others in my department to secure funding for a localized educational summer program for students to learn more about the higher fields of mathematics that generally are not explored until post-secondary courses, while also providing teaching and research experience to undergraduates.
From some of these brief descriptions, my goals and interests form a general theme of finding progress in improving student mathematical interest and understanding. The new-age problem solver is different than in the past, and thrives on interconnected topics among the disciplines. My objective is to create active thinkers in the classroom, rather than passive learners. In order to achieve this goal, my research interests collectively inform myself and others on improved practices and current classroom misconceptions that exist in the field. Clearly, more classroom preparation is necessary to build a course that goes beyond the typical whiteboard lecture. However, another step is the inclusion of undergraduates on the research front. Personally, I was not included on research ventures until graduate school, and I always felt a need to “catch up” as a result. I want my undergraduate students to gain plenty of traction and experience in their major/field. Since I have been a faculty member, many undergraduate students have been part of my projects, whether in preparation, survey analysis, data recording, data cleanup, charts and graphs, writing, and organization. Often, students come up with fresh ideas that give new perspectives on old ideas—this is one of the greatest values of their input. I continue to include students post-graduation in professional developments that I host on campus, and research projects that extend into community classrooms.
My research goals have slowly evolved over my career to this point, yet are still united under one important theme: legitimate mathematical understanding. I am currently leading a quantitative analysis of predictive variables in Calculus I performance (examples of such variables include time of day, major, ethnicity, semester, etc.) over five years of student data. Additionally, I am deeply engaged in a national qualitative study regarding school district policy and procedures for adopting digital mathematics curriculum. Both of these projects involve many faculty members from outside of my university. Along with the research studies mentioned earlier, these projects have continued to reinforce the focus on mathematical understanding for all ages.