September 2013 – August 2017



In this research project we study responsive teaching and its development in the context of a professional development design experiment focused on rational numbers in grades 3–5. Responsive teaching refers to instructional decisions by teachers who elicit and build on children’s ever-changing ideas and actions. Recent policy documents highlight the enormous potential of this type of teaching, but realizing this potential poses a serious challenge because there is a gap between the field’s capacity to produce research-based knowledge of children’s mathematical thinking and to provide resources to support teachers to take up and effectively use this knowledge.

This study addresses this gap by answering three questions, using mixed-methods:

  1. What characterizes responsive teaching in the domain of rational numbers? The exploration of responsive teaching focuses on teachers’ knowledge of children’s mathematical thinking and three instructional practices that have proven critical in the project directors’ earlier work with primary-grade teachers: noticing children’s mathematical thinking, enacting moves to support children’s thinking, and enacting moves to extend children’s thinking.
  2. How can professional development support the development of responsive teaching?
  3. How is responsive teaching related to student learning gains?

The professional development is designed to empower teachers to make instructional decisions guided by the project directors’ research-based framework of children’s thinking about rational numbers. Instruction guided by this framework — based on children’s informal ideas of partitioning quantities and their understanding of the fundamental properties of operations and equality — enhances teachers’ capacity to support the development of children’s rational number understandings and to foster connections across number, operations, and algebraic thinking.


Partners / Collaborators

This project is funded by the National Science Foundation (DRL—1316653), and it is a collaborative research effort among The University of Texas at Austin, University of North Carolina at Greensboro, and SRI International. An additional partner is Teachers Development Group, a nonprofit organization specializing in providing professional development in mathematics nationwide.



  • Victoria R. Jacobs, Ph.D. (University of North Carolina—Greensboro)
  • Co-PI





Jacobs, V. and Empson, S. B. (in press). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM (The International Mathematics Education Journal).



Jessup, N., Hewitt, A., Jacobs, V. R., & Empson, S. B. (2015, November).  Understanding teachers’ perspectives on children’s strategies for equal sharing problems.  Presentation at the 2015 annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, MI.

Empson, S. B. & Jacobs, V. (2015, June).  They’ve gotten the right answer!  Now what? Keynote address at the 8th Cognitively Guided Instruction (CGI) National Conference, Lawndale, CA.

Krause, G., Pynes, D., & Empson S., (2015, June).  “Notating Fractional Relationships”. Presentation at the 8th Cognitively Guided Instruction (CGI) National Conference, Lawndale, CA.

Hewitt, A., Jessup, N., & Jacobs, V. R. (2015, June).  Exploring children’s sharing for equal sharing fraction problems.  Presentation at the 8th Cognitively Guided Instruction (CGI) National Conference, Lawndale, CA.

Jacobs, V. R. (2015, May).  Research on mathematics teaching.  Presentation at the UCSD/SDSU Mathematics and Science Education Seminar Series 2015, San Diego, CA.

Jacobs, V. R., Empson, S. B., Krause, G., & Pynes, D. (2015, April).  Responsive teaching with fractions.  Presentation for the research conference of the 2015 annual meeting of the National Council of Teachers of Mathematics, Boston, MA.

Jacobs, V. R., Lamb, L. C., Philipp, R. A., & Empson, S. B.  (2015, February). The complexity of noticing children’s mathematical thinking. Presentation for the 2015 annual meeting of the American Association of Colleges for Teacher Education, Atlanta, GA.

Webel, C., Deleeuw, W. W., Empson, S. B., Jacobs, V. R., Land, T., Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R.  (2015, February). Defining and developing teaching practices related to responding to students’ mathematical thinking.  Symposium at the 2015 annual meeting of the Association of Mathematics Teacher Educators, Orlando, FL.

Empson, S.B. & Jacobs, V.R. (2014, November). Responsive teaching in elementary mathematics: The case of fractions. Presentation for the annual regional meeting of the National Council of Teachers of Mathematics, Houston, TX.

Jessup, N., Jacobs, V. R., & Hewitt, A. (2014, October). Fractions through equal sharing.  Presention for the annual meeting of the North Carolina Council of Teachers of Mathematics, Greensboro, NC.

Empson, S. B. (2014, June). Thinking about children’s thinking about fractions. Featured session at the 20th annual meeting of the Texas Regional Collaboratives, Austin, TX.