Sarah D. Castle

Assistant Professor

Mathematical & Statistical Sciences Department

Curriculum and Instruction Department

University of Idaho

See my work Headshot of Sarah Castle outside with trees behind her. She wears a blue blazer with a teal two tone dress. She has blonde hair and is smiling.

About

Sarah Castle is an assistant professor of mathematics education within the Mathematical and Statistical Sciences Department and is affiliated with the Curriculum and Instruction Department within the College of Education, Health and Human Sciences. She earned her doctorate in mathematics education at Michigan State University in 2023 and her master’s from MSU in mathematics in 2022. Her work is twofold. First, it centers on using computation to uncover manifestations of inequity within undergraduate STEM contexts and working to advance critical investigations of structural systemic inequities. Secondly, she uses computation as an environment for students to engage in mathematical creativity and provide new opportunities for previously marginalized students while also investigating the affordances and constraints of using computing as a mathematical pedagogy. Her most recent project focuses on introducing computational modeling students to linear algebra through a series of modules in Jupyter Notebooks and the relation with mathematical creativity. In her free time, she enjoys hiking, swimming, playing with her cats, and crafting.

A photo of Sarah's 2 cats laying down on an ottoman with a christmas tree behind them. The cat on the left is a striped tabby and is wearing a red plad collar with a bow and a fish nametag. The cat on the right is a tortiseshell with lots of orange and brown fur and is wearing a green bandana with baby yoda jumping out of a christmas box.
A photo of a snowy day with lots of pine trees in the foreground covered with fluffy snow and  blue skies with some clouds. Behind all the trees are rolling holls in various blue tones and lots of snow.

Publications

Castle, S. D., (Accepted, In Press). Embracing Mathematical Conjecture Through Coding and Computational Thinking, Submitted to 54th ACM Technical Symposium on Computer Science Education.

Levin, M., Smith III, J. P., Karunakaran, S. S., Hwang, J., Castle, S. D., Küchle, V., Elmore, B., Lu, Y., Abreu, S. (Accepted, In Press) Re-conceptualizing the Construct of Mathematical Autonomy: From Individual Trait to Quality of Action in Context. To appear in Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education Omaha, NE

Castle, S. D. (2023). Exploring How Computation Can Foster Mathematical Creativity in Linear Algebra Modules. In Cook, S., Katz, B., & Moore-Russo, D. (Eds.). In Proceedings of the 25th Annual Conference on Research in Undergraduate Mathematics Education (pp. 582-590) Omaha, NE

Castle, S. D. (2023). Leveraging Computational Science Students' Coding Strengths for Mathematics Learning. In Proceedings of the 54th ACM Technical Symposium on Computer Science Education V. 1 (pp. 263-269).

Castle, S. D. (2022). If Creativity Return Computing: Exploring the Impact of Computing on Students’ Mathematical Creativity in Linear Algebra . In Proceedings of the 2022 ACM Conference on International Computing Education Research-Volume 2 (pp. 24-25).

Pearson, M. I., Castle, S. D. , Matz, R. L., Koester, B. P., & Byrd, W. C. (2022). Integrating Critical Approaches into Quantitative STEM Equity Work . CBE—Life Sciences Education, 21(1)

Hwang, J., Castle, S. D. , & Karunakaran, S. S. (2022). One is the Loneliest Number: Groupwork within Linguistically Diverse Classrooms . PRIMUS, 1-13.

Castle, S. D. , Smith III, J. P., Levin, M., Hwang, J., Karunakaran, S. S., Küchle, V., & Elmore, R. (2022). Shifts in External Authority and Resources for Sense-making in the Transition to Proof-Intensive Mathematics: The Case of Amelia. In Karunakaran, S. S., & Higgins, A. (Eds.). Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education. (pp.100-107) Boston, MA

Castle, S. D., Byrd, W. C., Koester, B. P., Boenem, E., Caporale, N., Cwik, S., Denaro, K., Denaro, D., Fiorini, S., Matz, R., Mead, C., Whitcomb, K., Singh, C., Levesque-Bristol, C., & McKay, T. (2021) Equity in the STEM Landscape: A Multi-Institutional Approach to Mapping Systemic Advantages Within STEM Courses , 2021 American Education Research Association Annual Meeting Proceedings.

Castle, S. D. (2021). Connecting Computation: Mediating Mathematical Knowledge Through Computational Modules, In Karunakaran, S. S., & Higgins, A. (Eds.). 2021 Research in Undergraduate Mathematics Education Reports. (pp.30-38)

Levin, M., Smith III, J. P., Karunakaran, S. S., Küchle, V., Castle, S. D. , Hwang, J., Elmore, B., Bae, Y. (2020). Math and Moral Reasoning in the Age of the Internet: Undergraduate Students’ Perspectives on the Line Between Acceptable Use of Resources and Cheating , In Karunakaran, S. S., Reed, Z. & Higgins, A. (Eds.). Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education. (pp.366-373) Boston, MA

Smith III, J. P., Küchle, V., Castle, S. D. , Karunakaran, S. S., Bae, Y., Hwang, J., Levin, M., Elmore, B. (2020). Dimensions of Variation in Group Work within the “Same” Multi-Section Undergraduate Course . In Karunakaran, S. S., Reed, Z. & Higgins, A. (Eds.). In Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education. (pp.606-613) Boston, MA

Levin, M., Smith, J. P., Karunakaran, S., Küchle, V. A., & Castle, S. D. (2020). Conceptualizing STEM Majors’ Developing Agency and Autonomy in Undergraduate Mathematics . In Gresalfi, M. and Horn, I. S. (Eds.), The Interdisciplinarity of the Learning Sciences, 14th International Conference of the Learning Sciences (ICLS) 2020, Volume 2 (pp. 887-888). Nashville, Tennessee: International Society of the Learning Sciences.

Sankaran, K., French, A., Gady, S. , Wisniewski, T., & Woodkey, M. (2014). Evaluation of Electric Propulsion Systems for Asteroid and Comet Sample-Return Missions . In 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference (p. 3720). https://doi.org/10.2514/6.2014-3720.

Presentations

Refereed Conference Presentations

*Denotes presenter

Castle, S. D.* (2023, April 27-29) Constructing Creativity: Exploring the effects of computing enacted through coding on students’ mathematical understanding, mathematical creativity, and relationship to mathematics [Poster Presentation]. Symposium on Coding, Computational Modelling, & Equity in Mathematics Education: St. Catharines, Ontario, CA

Castle, S. D.* (2023, March 15-18). Leveraging Computational Science Students' Coding Strengths for Mathematics Learning [Paper Presentation]. 54th ACM Technical Symposium on Computer Science Education: Toronto, Ontario, CA

Castle, S. D.* (2023, February 23-25) Exploring How Computation Can Foster Mathematical Creativity in Linear Algebra Modules [Paper Presentation]. 25th Annual Conference on Research in Undergraduate Mathematics Education: Omaha, NE

Hwang, J.*, Castle, S. D.* , Karunakaran, S. S.* (2023, January 4-7) Two students’ groupwork experiences in a linguistically diverse classroom [Abstract Presentation], 2023 Joint Mathematics Meetings: Boston, MA.

Castle, S. D.* (2022, August 7-10). If Creativity Return Computing: Exploring the Impact of Computing on Students’ Mathematical Creativity in Linear Algebra [Abstract Presentation]. 2022 ACM Conference on International Computing Education Research, Lugano, Switzerland.

Sweeder, R.*, Castle, S. D. , Koester, B. P., Byrd, W. C.; Pearson, M.; Boenem, E., Caporale, N., Cwik, S., Denaro, K., Fiorini, S., Levesque-Bristol, C.; Matz, R., Mead, C., Brownell, S., Molinaro, M., Singh, C., McKay, T. (2022, March 20-24) Exposing inequity: A multi-institutional analysis of systematic advantages in introductory STEM courses [Abstract Presentation]. ACS (American Chemical Society) Spring 2022 National Meeting, San Diego, CA.

Castle, S. D.* Smith III, J. P., Levin, M., Hwang, J., Karunakaran, S. S., Küchle, V., & Elmore, R. (2022, February 24-26). Shifts in External Authority and Resources for Sense-making in the Transition to Proof-Intensive Mathematics: The Case of Amelia [Paper Presentation]. 24th Annual Conference on Research in Undergraduate Mathematics Education, Boston, MA

Castle, S. D.* , Byrd, W. C., Koester, B. P., Boenem, E., Caporale, N., Cwik, S., Denaro, K., Denaro, D., Fiorini, S., Matz, R., Mead, C., Whitcomb, K., Singh, C., Levesque-Bristol, C., & McKay, T. (2021, April 8-12) Equity in the STEM Landscape: A Multi-Institutional Approach to Mapping Systemic Advantages Within STEM Courses [Paper Presentation], 2021 American Education Research Association Annual Meeting

Levin, M.*, Smith III, J. P., Karunakaran, S. S., Küchle, V., Castle, S. D., (2021). Conceptualizing Agency and Autonomy in Tertiary Mathematics [Abstract Presentation], In 14th International Congress on Mathematical Education Conference Proceedings.

Caporale, N.*, Castle, S. D.*, Denaro, K. (2020, November) Developing Multi-institutional Collaborations in Student Analytics [Poster Presentation], AAC&U Transforming STEM Higher Education, Virtual.

Levin, M., Smith III, J. P., Karunakaran, S. S., Küchle, V., Castle, S. D.* , Hwang, J., Elmore, B., Bae, Y. (2020). Math and Moral Reasoning in the Age of the Internet: Undergraduate Students’ Perspectives on the Line Between Acceptable Use of Resources and Cheating [Paper Presentation], 23rd Annual Conference on Research in Undergraduate Mathematics Education, Boston, MA.

Smith III, J. P.*, Küchle, V., Castle, S. D. , Karunakaran, S. S., Bae, Y., Hwang, J., Levin, M., Elmore, B. (2020). Dimensions of Variation in Group Work within the “Same” Multi-Section Undergraduate Course [Paper Presentation]. 23rd Annual Conference on Research in Undergraduate Mathematics Education, Boston, MA.

Levin, M.*, Smith III, J. P., Karunakaran, S. S., Küchle, V. A., & Castle, S. D. (2020, June 19-23). Conceptualizing STEM Majors’ Developing Agency and Autonomy in Undergraduate Mathematics [Paper Presentation], 14th International Conference of the Learning Sciences (ICLS).

Gady, S.* (2019, February 28 - March 2). Integrating Integration: Deepening Mathematical Understanding Through Computation [Abstract Presentation], 22nd Annual Conference on Research in Undergraduate Mathematics Education, Oklahoma City, OK.

Gady, S.*, Kubota, S., & Johnson, I. (2015, November 16-20). Comparison of a 3-D GPU-Assisted Maxwell Code for Synthetic Diagnostics on ITER [Poster Presentation], 57th Annual Meeting of the APS Division of Plasma Physics, Savannah, GA.

Sankaran, K.*, French, A., Gady, S., Wisniewski, T., & Woodkey, M. (2014, July 28-30). Evaluation of Electric Propulsion Systems for Asteroid and Comet Sample-Return Missions [Paper Presentation]. 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH.

French, A.*, Gady, S.*, & Sehgal, A.* (2014, May 1-3). Evaluation of Electric Propulsion Systems for Asteroid Sample-Return Missions [Poster Presentation], Annual Meeting of the Northwest Section of the APS, Seattle, WA.

Other Presentations

Castle, S. D.* (2023, May 12-13) Constructing Creativity: Exploring the effects of computing enacted through coding on students’ mathematical understanding, mathematical creativity, and relationship to mathematics [Poster Presentation]. Symposium – Culturally Relevant Integration of CS and Mathematics: Kennesaw, GA

Castle, S. D.* (2022, June) Exploring the Impact of Computing on Students’ Mathematical Creativity, University of Oslo Physics Education Research Summer Institute, Oslo, Norway

Castle, S. D.* (2021, November) Systemic Advantages Within Introductory STEM Courses, University of Pittsburgh dB-SERC Colloquium, Pittsburgh, PA.

Matz, R.*, Fiorini, S.*, Caporale, N.*, Castle, S. D.*, Fisher, C.* (2021, May) Analytics to support student success in STEM: Stories from the Sloan Equity and Inclusion in STEM Introductory Courses (SEISMIC) Measurement Working Group [Panel Presentation], Indiana University Learning Analytics Summit, Bloomington, IN.

Gady, S.* (2014, September). Modeling Astronaut Central Nervous System Cerebral Fluid Response to Microgravity and Its Effects on Astronaut Vision, Spokane Mathematics Colloquium, Spokane, WA.

Teaching

At the undergraduate level, I have teaching experience as (1) an instructor of record with full responsibility for teaching the class, grading, writing assessments and assignments, developing interactive computational exercises, etc. (2) private and volunteer tutor (middle school to post-secondary), and (3) teaching assistant for the instructor of record where I graded materials, lead recitations, and held office hours.

Courses Taught at University of Idaho

  • Secondary Mathematics Methods (EDCI 434): Specific methods, research, curricula, and media in teaching Secondary Mathematics Methods.
  • Secondary Mathematics Methods Practicum (EDCI 454): Implementation of secondary mathematics methods, research, curricula and technology in secondary classrooms. Course includes 30 hours in grade 6-12 classrooms and 15 hours of associated scheduled activities.
  • Proof and Viable Argumentation (MTHE 410): Develops viable argumentation as it can be found in grades 5-10 as a means of learning content, deepening understanding, and determining what is true and what is false mathematically. Topics include the language of argumentation, argument types, reasoning types, the distinction between proofs and viable arguments. Emphasizes how different argument types can contribute to student learning and increasing student discourse.
  • Geometry, Measurement, and Trigonometry (EDCI 411): Examines topics in measurement, geometry, and trigonometry and the way that grade 5-10 students develop an understanding of these ideas


  • Courses Taught at Michigan State University

  • Elementary Mathematics for Teachers I (MTH 201): Mathematics needed for teaching grades PreK - 6. Place value, algorithms for whole numbers, decimals, and fractions with an emphasis on children’s mathematical thinking.
  • Calculus I (MTH 132): Limits, continuous functions, derivatives and their applications. Integrals and the fundamental theorem of calculus.
  • Survey of Calculus II (MTH 126): Application of partial derivatives, integrals, optimization of functions of several variables and differential equations.


  • Related Teaching Experiences

  • Instructor for the Mead School District Summer STEM Academy: Developed week-long, hands-on STEM modules and curriculum for 5th-7th grade students and was lead instructor on a high-altitude balloon launch for testing of near space phenomena and co-instructor and developer for coding and gaming module
  • S.I. Instructor for Whitworth University's Engineering and Physics Department: Led weekly supplemental instructions session to reinforce physics concepts by developing assignments and resources and held weekly office hours to assist students with homework, and ran review sessions prior to tests
  • Grader and Teaching Assistant for Whitworth University's Mathematics and Computer Science Department: Teaching assistant for Calculus II, Calculus for Social Sciences, Discrete Mathematics, and Mathematical Statistics I and II
  • Projects

    I am a part of some amazing teams who do some truely phenomenal things! Follow the links below to learn more about each of the research teams.

    SEIMSIC Logo of 8 small filled in circles equally spaced on a black circle outline with a spiked frequency line in the center

    SEISMIC Project

    MSU logo of green outline of spartan head

    Transition to Proof Project

    CMSE Logo of a venn diagram with 3 circles that are red, blue, and green and the overlap is white.

    Computational Education Research Lab

    Sarah D. Castle's CV

    Contact Me

    Email:
    scastle@uidaho.edu

    University of Idaho Mailing Address:
    875 Perimeter Drive
    MS 1103
    Moscow, ID 83844-1103