The best way to learn is to teach. – Frank Oppenheimer
I have a combined ten years of experience teaching and mentoring students in mathematics and mathematics education courses from secondary school to graduate level. In my practice of teaching, I foster participation in learning through discussion, argumentation, and problem solving—you learn mathematics by doing mathematics. I innovate by implementing research-based practices including sequencing learning goals and instruction with multiple technology-based representations—meaningful understanding of mathematics is connected.
Statement of Teaching Practice
Teaching mathematics is a craft and art form.
My practice of teaching mathematics weaves together innovative thinking that is informed by research and theory on student learning, and effective design of curriculum and instruction. My goal as a teacher is to provide opportunities that challenge yet support students as they grow in their own quests, and to negotiate productive norms within the classroom community.
I never teach my pupils. I only attempt to provide the conditions in which they can learn.
Engagement Through Discussion and Problem Solving
I hold high expectations of my students and build my classes around student engagement, with a requirement for active participation and discussion. My role in the classroom is to both facilitate students’ knowledge acquisition and construction, and to lead the direction of the course as an expert participant, modeling the processes of learning mathematics through argumentation and logic.
For example, in a geometry course for preservice teachers I positioned the students as problem solvers and arguers. They learned to become confident in their mathematical reasoning because mathematical authority was not positioned solely in the textbook or the instructor, but rather on their own clear argumentation and logic. During a heated discussion on classification and definition, the students reached an impasse. When I prompted, “What are we going to do?” one student raised a fist and declared, “We’re gonna’ fight!” After laughter ensued, students led a debate to resolve their issue. This example shows how I push students to explain their thinking, respond to the thinking of others, and engage in mathematical argumentation.
I seek balance in discussion-focused classes by incorporating student-led problem solving in individual, small group, and whole-class settings. The effectiveness of these instructional techniques rests on students’ motivation to engage during class, and their willingness to learn in an environment where multiple perspectives are encouraged and valued. Effective communication is paramount to learning mathematics and mathematics education research, and beyond.
My undergraduate students have reflected, “I’ve never had to talk and write in a math classes before.” My graduate students have welcomed discussion-oriented classes. I support multiple formats of instruction, and encourage students to experiment with their own styles of teaching by leading class sessions themselves.
Linking Research and Practice
My research and teaching are linked both in how I support student learning and how I assess and characterize student learning. I support student learning of mathematics by sequencing learning objectives and multiple representations in ways that have been shown to be effective in empirical research.
For example, in teaching equation solving it is important to understand the equal sign as an equivalence relation. One approach is to first support students’ understanding of equivalent and non-equivalent expressions from multiple representations, and to link this understanding to the meaning of the equal sign as a relationship between expressions.
In learning symbolic algebra, I encourage students to be strategic about the use of technology.The following example shows how reconciling is an effective practice for leveraging technology as a learning tool, not as a crutch.
One algebra student incorrectly applied the distributive property with paper-and-pencil. When he reflected on the outcome of using a computer algebra system, he realized “I needed to multiply it [the coefficient] all the way through [instead of the first term only].” (Source: Fonger (2014). Mathematics Teacher
Finally, in assessing learning, the meaning a student holds of a representation is connected to their conceptions. It is important to probe the meaning of students’ use of representations as both a formative tool to guide instruction and as summative measures of meaningful understandings.
For example, A=aL2 may represent a correspondence rule between length (L) and area (A) of a growing square, or a statement of covariation as length and area change together. (Source: Fonger, Ellis, Dogan. (2016). Students’ conceptions supporting their symbolization and meaning of function rules. Accepted for publication in Proceedings of the North America Chapter of Psychology of Mathematics Education.)
As an educator and lifelong learner, I understand the importance of motivating students to take ownership of learning, and the power of research-based curriculum, instruction, and assessment. I excel when teaching in novel contexts because I approach teaching as an opportunity to experiment with research-based curriculum and instruction—cycles of design, implementation, and analysis builds theory.
TEACHING & MENTORING
Undergraduate Level Mathematics & Mathematics Education
Syracuse University, Mathematics Department
- Precalculus (MAT 194: Fall 2017, Fall 2018, Spring 2019)
Western Michigan University, Mathematics Department
At Western Michigan University I taught for 3 years (total of 8 semesters) at the undergraduate level to mathematics majors and minors, and elementary and secondary preservice teachers. I specialized in the design and teaching of an upper level content course on computing technology for secondary mathematics education across algebra, functions, geometry, and foundations of calculus. I was the primary instructor of record for these courses:
- Computing Technology in Secondary School Mathematics (Math 3510: Fall 2009, Fall 2010, Fall 2012, Spring 2013)
- Geometry for Elementary and Middle School Teachers (Math 1510: Spring 2010, Fall 2012, Spring 2013)
- Excursions in Mathematics (Math 1140: Summer 2011, Summer 2013)
- Number Concepts for Elementary and Middle School Teachers (Math 1500: Spring 2011)
Graduate Level Mathematics Education
Syracuse University, Teaching and Leadership Department, School of Education
- Methods and Curriculum in Teaching Mathematics (SED 413/613: Fall 2017, Fall 2018)
- Linking Research and Practice in (Mathematics) Education (EDU 700: Spring 2018)
University of Wisconsin-Madison, Wisconsin Center for Education Research, Department of Curriculum and Instruction
I have two years of experience mentoring graduate level research in mathematics education. I also co-taught a graduate level special topics course on radical constructivist theory of learning mathematics with Dr. Amy Ellis:
- Seminar in Research on Mathematics Education (C&I 942 Fall 2015)
Secondary School Mathematics
I have two years of part-time teaching experience in secondary schools. This includes both public and private high schools:
- Geometry I & Geometry II (Summer 2006) Kalamazoo Public Schools
- Algebra I (Shared teaching/Internship) (Fall 2007- Spring 2008) Kalamazoo Christian High School
- Honors Geometry (Shared teaching/Internship) (Fall 2007- Spring 2008) Kalamazoo Christian High School
PROFESSIONAL DEVELOPMENT FOR TEACHERS
I have two years of experience in designing and leading professional development for inservice teachers and teacher educators. I have taught in both online and face-to-face workshop settings including:
- MOOC-Ed Series Course on Fractions. July 2014. http://www.mooc-ed.org
- MOOC-Ed Series Course on Mathematics Learning Trajectories, Equipartitioning as a Foundation for Rational Number Reasoning in K-5. October 7 – November 26, 2013. http://www.mooc-ed.org
- Deep Understanding of Geometry, Michigan Mathematics Rural Area Project workshop for elementary teachers. Gaylord, MI, June 26 – 28, 2013.
Learning to write and writing to learn go hand in hand. In this PPT I draw parallels between writing across the curriculum principles in specific course assignments I’ve given to link research and practice in mathematics education. PDF of presentation given at Writing Across the Curriculum Faculty Fellowship Spotlight February 2020