Curriculum and Instruction
Ph.D., Curriculum and Instruction with an emphasis in Mathematics Education, University of Connecticut, 2004
Sixth-Year Degree, Educational Administration, University of Connecticut, 2001
M.S., Elementary Education, Syracuse University, 1996
B.S., Mathematics, University of Florida, 1994
Areas of Expertise:
Mathematical Discourse: Writing
Mathematical Discourse: Talk
Many people think of mathematics as something that you “do” by following a teacher’s step-by-step guidance about how to solve problems. My work in discourse counters this perspective and instead is aimed at supporting teachers for them to empower students to grapple with the mathematics and engage with the discipline in ways similar to how mathematicians go about their work. Rather than asking myself whether or not I think students can learn any given math concept, I guide my work by identifying ways how I can get students to think about and ultimately understand them through oral and written discourse.
Students frequently write in math class, yet elementary teachers have had limited guidance about what and why they should have their students write. Thus students may “write about math” rather than “write mathematically.” I currently am focused on developing and researching ideas about written discourse that aims to use writing to leverage the learning of mathematics. I directed a project funded by the National Science Foundation that brought together the Elementary Mathematical Writing Task Force, a group of university- and district-based educators with collective expertise in mathematics education, writing education, mathematics, English language learners, special education, gifted education, assessment, and curriculum. You can access the white paper outlining their recommendations about the types of and purposes for mathematical writing in the elementary grades here.
Curriculum resources also are major tools that can support the implementation of oral and written discourse. Prior to my current appointment, I worked extensively to develop and research the efficacy of advanced mathematics curriculum for elementary students. I served as Co-Principal Investigator for Project M^2: Mentoring Young Mathematicians for 6 years, a National Science Foundation research grant that developed challenging geometry and measurement units for kindergarten through Grade 2 students. As part of this work, I conceptualized the Student Mathematician Discourse Model that supported students’ mathematical communication that results in writing. Prior to that, I worked on Project M^3: Mentoring Mathematical Minds, a series developed for mathematically promising students in Grades 3 through 5 from which Project M^2 was conceived.
2015-2018, Co-Principal Investigator, A Study of Elements of teacher Preparation Programs That Interact with Candidates’ Characteristics to Support Novice Elementary Teachers to Enact Ambitious Mathematics Instruction, National Science Foundation
2011-2013, Principal Investigator, Professional Noticing of Mathematical Discourse-Related Practices by a Preservice and Inservice Teacher: A Case Study of a Coordinated Reform-Based University-Clinic Experience Model, Teachers for a New Era
2008-2009, Principal Investigator, Project Empower: A Pilot Study Investigating Students’ Learning of Basic Multiplication Facts and Strategies, Center for Research in Mathematics Education
2006-2007, Co-Principal Investigator, Preservice Teachers’ Confidence of Evidence-Based Decisions, Teachers for a New Era
Casa, T. M., MacSwan, J. R., LaMonica, K. E., Colonnese, M. W., & Firmender, J. M. (2019). An analysis of the amount and characteristics of writing prompts in grade 3 mathematics student books. School Science and Mathematics, 119,176-189.
Casa, T. M., Firmender, J. M., Gavin, M. K., & Carroll, S. R. (2017). Kindergarteners’ achievement on geometry and measurement units that incorporate a gifted education approach. Gifted Child Quarterly, 61(1), 52-72.
Firmender, J. M., Casa, T. M., & Colonnese, M. W. (2017). Write on: Reasoning through mathematical writing. Teaching Children Mathematics, 24(2), 84-92. [2017 Focus Issue addressing Learning Mathematics Through Reasoning and Problem Solving]
Firmender, J. M., Dilley, A., Amspaugh, C. A., Field, K., Lemay, S., & Casa, T. M. (2017). Beyond doing mathematics: Engaging talented students in mathematically creative writing. Gifted Child Today, 40(4), 205-211.
Powell, S. R., Hebert, M. A., Cohen, J. A., Casa, T M., & Firmender, J. M. (2017). A synthesis of mathematics writing: Assessments, interventions, and surveys. Journal of Writing Research, 8(3), 493-526.
Bostiga, S., Cantin, M., Fontana, C., & Casa, T. M. (2016). Math debate journals: Moving in the write direction. Teaching Children Mathematics, 22(9), 546-554.
Casa, T. M., Firmender, J. M., Cahill, J., Cardetti, F., Choppin, J. M., Cohen, J., … Zawodniak, R. (2016). Types of and purposes for elementary mathematical writing: Task force recommendations. Retrieved from http://mathwriting.education.uconn.edu.
Casa, T. M. (December 2015/January 2016). It’s the right time to start writing! Teaching Children Mathematics, 22(5), 269-271.
Cohen, J., Casa, T. M., Miller, H. C., & Firmender, J. (2015). Characteristics of second graders’ mathematical writing. School Science and Mathematics, 115(7), 344-355.
Casa, T. M. (2014). Supporting writing with the student mathematician discourse framework. In K. Karp (Ed.), Annual perspectives in mathematics education 2014: Using research to improve instruction (pp. 107-117). Reston, VA: National Council of Teachers of Mathematics.
Casa, T. M. (2013). Capturing thinking on the talk frame. Teaching Children Mathematics, 19(8), 516-523.
Gavin, M. K., Casa, T. M., Adelson, J. L., & Firmender, J. (2013). The impact of advanced geometry and measurement units on the achievement of grade 2 students. Journal for Research in Mathematics Education, (44)3, 478-509.
Gavin, M. K., Casa, T. M., Firmender, J., & Carroll, S. R. (2013). The impact of advanced geometry and measurement curriculum units on the mathematics achievement of first-grade students. Gifted Child Quarterly, 57(2), 71-84.
Williams, M. M., & Casa, T. M. (December 2011/January 2012). Connecting class talk with individual student writing. Teaching Children Mathematics, 18(5), 314-321.
Casa, T. M., & Gavin, M. K. (2009). Advancing student understanding of quadrilaterals through the use of mathematical vocabulary. T. Craine, & R. Rubenstein (Eds.). Understanding Geometry for a Changing World, National Council of Teachers of Mathematics 71st Yearbook (2009).
Gavin, M. K., Casa, T. M., Carroll, S. R., & Adelson, J. L. (2009). The impact of advanced curriculum on the achievement of mathematically promising elementary students. Gifted Child Quarterly, 53(3), 188-202.
National Association for Gifted Children (NAGC) Curriculum Studies Award, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2017
“Connecting Class Talk with Individual Student Writing” noted by Teaching Children Mathematics’ Editorial Board’s as their favorite contribution of the yearly volume
2009 Gifted Child Quarterly Paper of the Year Award for “The Impact of Advanced Curriculum on the Achievement of Mathematically Promising Elementary Students”
|Phone||860 486 9078|
|Mailing Address||Unit 3033|
|Office Location||Gentry 413C|