Eric Knuth

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CONTACTING US

Main Office

Curriculum & Instruction
School of Education
UW-Madison
210 Teacher Education Building
225 North Mills Street
MadisonWI  53706

Tel: 608/263.4600
Fax: 608/263.9992

Email: curric@education.wisc.edu
or by contact form
 

Eric Knuth

Profile Photo

Eric Knuth


Curriculum and Instruction (CI)

476C Teacher Education Building  binoculars icon
225 N Mills St
Madison, WI 53706-1707
Office: 608/263-3209

knuth@education.wisc.edu

Curriculum Vitae

Personal Biography

Eric Knuth received his Ph.D. from the University of Colorado in mathematics education. He received a master's degree in mathematics from San Diego State University, and his bachelor's degree in electrical engineering from the University of Illinois. Prior to coming to UW-Madison, he spent several years teaching high school mathematics and physics as well as several years working as an electrical engineer.

His research concerns the meaningful engagement of students in mathematical practices and their development of increasingly more sophisticated ways of engaging in those practices. By mathematical practices, he refers specifically to activities such as justifying and proving mathematical claims and using algebraic representations appropriately, flexibly, and efficiently to model and to solve problems. A primary goal of his research is to develop sufficiently detailed accounts of learning and instruction in classroom contexts to guide the development of instructional practices, curricula, and professional development programs aimed at facilitating students’ learning of mathematics.

Research Projects

- http://algebra.wceruw.org

- http://examples.wceruw.org

- http://idiom.wceruw.org

- http://labweb.education.wisc.edu/knuth/taar

- http://labweb.education.wisc.edu/knuth/mathproject



 

 

Grants and Sponsorships

  • 2014-2018 - Amount: $3,499,995.00, "The Impact Of A Teacher-Led Early Algebra Intervention On Children’s Algebra Readiness For Middle School," Awarded By: Institute of Education Sciences, Sponsor Type: Federal, Eric J. Knuth, Principal; Ana C. Stephens, Co-Principal; Maria Blanton, Principal; Despina Stylianou, Co-Principal.
  • 2012-2015 - Amount: $939,935.00, "The Impact Of Early Algebra On Students’ Algebra-Readiness," Awarded By: National Science Foundation (DRK-12), Eric J. Knuth, Principal; Maria Blanton, Principal; Ana C. Stephens, Co-Principal.
  • 2012-2015 - Amount: $995,997.00, "The Role And Use Of Examples In Learning To Prove," Awarded By: National Science Foundation (DRK-12), Eric J. Knuth, Principal; Amy B. Ellis, Co-Principal; Orit Zaslavsky, Co-Principal.
  • 2008-2013 - Amount: $741,938.00, "Understanding And Cultivating The Connections Between Students' Natural Ways Of Reasoning And Mathematical Ways Of Reasoning," Awarded By: National Science Foundation (REESE), Eric J. Knuth, Principal; Amy B. Ellis, Co-Principal; Charles W. Kalish, Co-Principal.
  • 2009-2013 - Amount: $1,578,658.00, "Developing Algebra-Ready Students For Middle School: Exploring The Impact Of Early Algebra," Awarded By: National Science Foundation (DRK-12), Eric J. Knuth, Principal; Maria Blanton, Principal.
  • 2009-2012 - Amount: $999,789.00, "How Do Instructional Gestures Support Students’ Mathematical Learning?," Awarded By: National Science Foundation, Grant Institution: National Science Foundation Research and Evaluation on Education in Science and Engineering (NSF-REESE), Sponsor Type: Federal, Mitchell J. Nathan, Co-Principal; Martha Wagner Alibali, Principal; Eric J. Knuth.
    Abstract: Mathematics lessons often focus on relations between mathematical ideas. Our previous work suggests that teachers’ communication about such relations is crucial for students’ learning about them. The purpose of the proposed research is to understand how variations in teachers’ communication about relations between mathematical ideas affect students’ learning. In the proposed work, we focus on teachers’ instructional gestures, with a specific focus on gestures that occur in instructional episodes that link related representations of mathematical information, in particular, gestures that serve to ground ideas in the physical environment or in familiar actions, experiences or representations. The research has three specific aims: • Aim 1. To investigate whether students’ learning is facilitated if the teacher grounds both (as compared to one or neither) of the to-be-linked ideas with gestures (Experiments 1 and 2); • Aim 2. To examine whether learning is facilitated if the teacher grounds the links using redundant rather than complementary gestures (Experiments 3 and 4); and • Aim 3. To examine whether gestures offer a “special” way to ground ideas, in the sense that they are more effective at doing so than other, non-gestural methods of grounding (Experiments 5 and 6). We will address each of these aims in two domains: early algebra, with a specific focus on the concepts of slope and intercept as they apply to linear functions; and inferential statistics, with a specific focus on confidence intervals (CIs) and their connections to concepts of variability and distinctions between sample and population means. This work will contribute to our scientific understanding of learning and instruction from an embodied cognition perspective. By experimentally manipulating the ways in which relations between mathematical ideas are conveyed, and exploring the consequences for learning, we will gain a deeper understanding of the cognitive processes involved in acquiring mathematical understanding.
  • 2006-2009 - Amount: $683,753.00, "Does Visual Scaffolding Facilitate Students’ Mathematics Learning? Evidence From Early Algebra," Awarded By: Institute of Education Sciences, Eric J. Knuth, Co-Principal; Martha Alibali, Principal; Mitchell J. Nathan, Co-Principal.
  • 2001-2006 - Amount: $701,649.00, "Understanding And Cultivating The Development Of Students’ Competencies In Justifying And Proving," Awarded By: National Science Foundation (CAREER), Eric J. Knuth, Principal.
  • 2001-2006 - Amount: $5,798,281.00, "Understanding And Cultivating The Transition From Arithmetic To Algebraic Reasoning," Awarded By: IERI (NSF, NICHD, DOE), Eric J. Knuth, Co-Principal; Mitchell J. Nathan, Principal; Martha Alibali, Co-Principal; Sharon J. Derry, Co-Principal; .

Publications

  • Ellis, A.B., Bieda, K., & Knuth, E.J. (2012). Essential understandings project: Reasoning and proving in high school mathematics (Gr. 9-12). Essential understandings project: Reasoning and proving in high school mathematics (Gr. 9-12). Reston, VA: National Council of the Teachers of Mathematics.
    Online Publication/Abstract
  • Knuth, E.J., Kalish, C.W., Ellis, A.B., Williams, C., & Felton, M. (2011). Adolescent reasoning in mathematical and non-mathematical domains: Exploring the paradox. The adolescent brain: Learning, reasoning, and decision making. Washington, DC: American Psychological Association.
  • Cai, J., & Knuth, E.J. (2011). Early algebraization: A global dialogue from multiple perspectives. ZDM/Springer.
    Online Publication/Abstract
  • Boerst, T., Confrey, J., Heck, D., Knuth, E.J., Lambdin, D., White, D., Baltzley, P., & Quander, J. (2010). Strengthening research by designing for coherence and connections to practice. Journal for Research in Mathematics Education. 41(3), 216-235.
  • Knuth, E.J., Choppin, J., & Bieda, K. (2009). Proof in middle school: Moving beyond examples. Mathematics Teaching in Middle School. 15(4), 206-211.
  • Blanton, M., Stylianou, D., & Knuth, E.J. (2009). Teaching and Learning Proof across the grades: A K-16 perspective. New York, New York: Routledge.
    Online Publication/Abstract
  • Knuth, E.J., Stephens, A., McNeil, N., & Alibali, M. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education. 37(4), 297-312.
  • McNeil, N., Grandau, L., Knuth, E.J., Alibali, M., Stephens, A., Hattikudur, S., & Krill, D. (2006). Middle-school students' understanding of the equal sign: The books they read can't help. Cognition & Instruction. 24(3), 367-385.
  • Nathan, M.J., & Knuth, E.J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition & Instruction. 21(2), 175-207.
  • Knuth, E.J. (2002). Secondary school mathematics teachers' conceptions of proof. Journal for Research in Mathematics Education. 33(5), 379-405.
  • Knuth, E.J. (2000). Student understanding of the Cartesian Connection: An exploratory study. Journal for Research in Mathematics Education. 31(4), 500-508.

Awards and Honors

  • Co-chair
    Organization: American Education Research Association Special Interest Group on Research in Mathematics Education
    Date(s): 2011 - 2013
  • Research Committee
    Organization: NCTM
    Date(s): 2008 - 2011
  • Doris Slesinger Award for Excellence in Mentoring finalist
    Organization: UW-Madison Women Faculty Mentoring Program
    Date(s): 2009
  • Doris Slesinger Award for Excellence in Mentoring finalist
    Organization: UW-Madison Women Faculty Mentoring Program
    Date(s): 2006
  • Steering Committee
    Organization: American Education Research Association Special Interest Group on Research in Mathematics Education
    Date(s): 2004 - 2006
  • Early Career Award
    Organization: National Science Foundation
    Date(s): 2001
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