Teaching

Adopting Wenger’s (1998) social theory of learning, I understand learning to be socially constructed. Wenger identified four interrelated components to define learning: 1. Meaning––learning as experience 2. Practice––learning as doing 3. Community––learning as belonging and 4. Identity––learning as becoming. Below, I share brief examples of how these four components are exemplified in my teaching practice.

Learning as Experience

     I facilitate experiences for students to support their learning. One way that I do this is by using the Learning Cycle in my mathematics pedagogy courses. This research-backed cycle has four steps: 1) Introducing open-ended mathematics tasks to preservice teachers 2) Supporting them to prepare and rehearse lessons they will teach 3) Sending them into field placements to enact their lessons and 4) Eliciting reflection on their experiences. Through this process, my students learn to teach through experience.

Learning as Doing

      I engage students in doing mathematics through my problem-solving approach to teaching mathematics. For example, in one of the mathematics content courses that I teach for preservice elementary teachers, I teach students to understand place value by providing them with manipulatives in different bases. When students do mathematics by grouping base-4 tiles, they begin to understand how each place value in base four represents four raised to a different power of zero, one, two, and so on. The way that I engage students in doing mathematics tasks facilitates conceptual understanding first, which then leads to procedural fluency.

Learning as Belonging

     My role as an educator is to invite students in from the theoretical periphery of a community to develop a sense of belonging in the classroom. One way that I do this is through creating mathematical discourse by following NCTM’s five practices: anticipating, monitoring, selecting, sequencing, and connecting. These practices support conceptual understanding and develop a sense of belonging to the classroom community where all voices are valued. In this way, my focus on belonging also aligns with my commitment to inclusive teaching. I foster a classroom environment where all students experience a sense of belonging as a necessary part of their learning.

Learning as Becoming

     Aligned with my research focused on mathematics identity, I emphasize learning as becoming in my classes to support the positive mathematics identity development of my students. For example, in one of my recent studies, I piloted a reflective journaling tool intended to support preservice teachers to reflect on who they are becoming both as mathematics learners and as mathematics teachers. I use this tool when teaching my mathematics pedagogy courses to support my students’ mathematics identity development. I support who my students are becoming both as mathematics learners and mathematics teachers.

Teaching Experience

Instructor of Record, Syracuse University, Syracuse, NY

MAT117 - Foundational Mathematics via Problem Solving I (FL24)

MAT118 - Foundational Mathematics via Problem Solving II (SP25)

EED 323 - Primary Grades (K-3) Mathematics Methods and Curriculum (SP22 & SP23)


Mathematics Teacher, River Bend Middle School, Sterling, VA

Algebra 1 (15-16, 16-17, 17-18)

Algebra II/Trigonometry (18-19, 19-20)

Coding at the Middle School (19-20)

Foundations of Algebra (20-21)

Geometry (15-16, 16-17, 17-18, 18-19, 19-20)

Math 6 (20-21)

Teacher Professional Development & Presentations

Sharpe, C. & Caviness, S. L. (2024, March). Roxboro middle school PD series: Three-act tasks. Roxboro 

Middle School, North Syracuse, NY. 

Sharpe, C. & Caviness, S. L. (2024, January). Roxboro middle school PD series: Building thinking 

classrooms.Roxboro Middle School, North Syracuse, NY. 

Caviness, S. L. (2023, October). Implementing open middle tasks with thinking classrooms strategies. 

Association of Mathematics Teachers of New York State Conference. Syracuse, NY.

Sharpe, C. & Caviness, S. L. (2023, October). Roxboro middle school PD series: Choral counting. 

Roxboro Middle School, North Syracuse, NY. 

Caviness, S. L. (2020, August). Implementing desmos in distance learning. Mathematics Teachers 

Professional Development. Loudoun County Public Schools, VA.

Russell, S., Caviness, S. L., et al. (2019, August). Beginning teacher orientation. Beginning Teacher 

Orientation. Loudoun County Public Schools, VA.

Shaffer, D., Ales, T., Fritz, E., Kenny, J., & Caviness, S. L. (2018, November). Can personalized learning 

and project based learning co-exist? Virginia Association for Supervision and Curriculum Development Conference. Williamsburg, VA.

Ales, T. & Caviness, S. L. (2018, August). Personalized learning and project based learning in the 

geometry classroom. PL-Palooza, Loudoun County, VA.

Caviness, S. L. (2017–2018). Incorporating desmos in the math classroom: Three-part PD series. River 

Bend Middle School Professional Development. Sterling, VA.

Shaffer, D., Caviness, S. L., et al. (2015, October). Communication with parents through social media. 

Association for Middle Level Education Conference. Harrisonburg, VA.

Course Evaluations

Spring 2023. EED 323 - Primary Grades (K-3) Math Methods and Curriculum. Course Feedback.

Spring 2022. EED 323 - Primary Grades (K-3) Math Methods and Curriculum. Course Feedback.