Areas of Interest
Teaching and learning of rational numbers for children in grades 4-8, fraction learning in 4th & 5th graders, teacher preparation and development
I have been working in the area of teacher preparation for over 20 years. I have taught mathematics methods courses for pre-service elementary education majors and similar courses for in-service teachers at the graduate level. I teach graduate courses and advise doctoral students in mathematics education. I started my career as a Title I mathematics teacher in a K-6 setting and have taught mathematics to students at the middle-school level, as well as adults in the General College at the University of Minnesota.
As a member of the Rational Number Project (RNP) team, my early research interests focused on the teaching and learning of rational numbers and proportionality for children in grades 4-8. RNP publications addressing fraction and proportionality learning can be accessed at www.cehd.umn.edu/rationalnumberproject.
The National Science Foundation has funded my most recent research ($550,000). The goals of this project are (a) to better understand why middle-school students have difficulty working with fractions and decimals in a meaningful way, (b) to construct an instructional module to overcome these difficulties, and (c) to create an online workshop for teachers to support their use of this instructional module. The curriculum module will be a companion to the Rational Number Project (RNP) fraction lessons created with previous NSF support, and will meet the 6-8 National Standards for fractions and decimals as stated in the NCTM (2000)Principles and Standards for School Mathematics. This research/curriculum development project has been done in partnership with the Minneapolis Public Schools.
- MTHE 3101 and MTHE 3102: Mathematics and Pedagogy for Elementary Teachers Courses I and II
Cramer, K., Monson, D., Ahrendt, S., Wiley, B., Colum, K, & Wyberg, T. (in press). Five indicators of decimal sense. Teaching Children Mathematics.
Cramer, K., & Henry, A. (2013). Using manipulative models to build number sense for addition of fractions. In F.Fennell & W. Speer (Eds.), Defining mathematics education: Presidential yearbook selections, 1926-2012 (pp. 365-371). Reston, VA: NCTM. (Reprnted from Making sense of fractions, ratio and proportions: NCTM 2002 yearbook, pp. 41 – 48, by B. Litwiller, Ed., 2002, Reston, VA: NCTM)
Stohlmann, M., Cramer, K., Moore, T., & Maiorca, C. (2014). Changing preservice elementary teachers’ beliefs about mathematical knowledge. Mathematics Teacher Education and Development.
Wyberg, T., Whitney, S. Cramer, K., Monson, D., & Leavitt, S. (2011). Unfolding fraction multiplication. Mathematics Teaching in the Middle Grades, 17 (5), 288 – 294.
Cramer, K., Wyberg, T. & Leavitt, S. (2008). The role of representations in fraction addition and subtraction. Mathematics Teaching in the Middle School, 13 (8), 490-496.
Cramer, K., & Wyberg, T. (2007). When getting the right answers is not always enough. In M. Strutchens & W. G. Martin (Ed.s). The learning of mathematics 2007 National Council of Teachers of Mathematics Yearbook (pp. 205 â€“ 220). Reston, VA: NCTM.
Rachlin, S., Cramer, K., Finseth, C., Foreman, L., Geary, D., Leavitt, S., & Smith, M. (2006). Navigating through number in grades 6-8. Reston, Va.: National Council of Teachers of Mathematics.
Cramer,K., Post, T., & delMas, R. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the Rational Number Project curriculum. Journal for Research in Mathematics Education, 33 (2), 111-144.
Cramer, K. (2003). Using a translation model for curriculum development and classroom instruction. In R. Lesh & H. Doerr (Eds.), Beyond Constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp.449 - 464 ). Mahwah, N.J.: Lawrence Erlbaum Associates.
February 2015 AMTE: School and University Collaboration: Working Together to
Enhance Children’s Understanding of Fractions (2012-2014)
April 2015 NCTM Annual Meeting: Making sense of the number line model for fractions
April 2015 NCTM Annual Meeting: Decimals: Models and language that build