We share the impact different models have on students' fraction thinking. We have come to understand, through several teaching experiments, how fraction circles, paper folding and number lines support students' learning about key fraction ideas including the role of the unit, partitioning, and fraction order.
Debra Monson, Kathleen Cramer and Sue Ahrendt
Kathleen Cramer, Sue Ahrendt, Debra Monson, Terry Wyberg and Karen Colum
Working with this challenging model helped students in urban classrooms in a large Midwestern city develop robust mathematical understandings.
Kathleen Cramer, Debra Monson, Stephanie Whitney, Seth Leavitt and Terry Wyberg
See how a class of sixth graders used concrete and pictorial models to build meaning for arithmetic operations with fractions.
Kathleen Cramer, Debra Monson, Sue Ahrendt, Karen Colum, Bethann Wiley and Terry Wyberg
Follow children who used grids and decimal +/− charts to taste the richness of Common Core decimal standards.
Kristin Lesseig, Stephanie Casey, Debra Monson, Erin E. Krupa and Maryann Huey
Effective mathematics teaching involves eliciting and interpreting student thinking, and then using students' current understandings as a basis for instruction. Research indicates these skills are not innate but can be acquired through structured experiences. In this article, we describe the development and implementation of an interview module aimed at supporting secondary preservice teachers' ability to elicit and use evidence of student thinking. Analysis of preservice teachers' noticing of student thinking across components of the interview module demonstrated positive benefits of the assignment. We share our design considerations and results, and offer potential adaptations to the module for other mathematics methods instructors interested in using the module to develop secondary preservice teachers' ability to notice student thinking.
Kathleen A. Cramer, Debra S. Monson, Terry Wyberg, Seth Leavitt and Stephanie B. Whitney
Put a twist on the familiar 10 × 10 grid model to build your students' understanding of effective decimal models.
Thomas R. Post, Debra S. Monson, Edwin Andersen and Michael R. Harwell
in the early 1990s, after a long series of disappointing results on national and international mathematics achievement tests—for example, TIMSS (1998) and NAEP (Campbell, Hombo, and Mazzeo 2000)—the National Science Foundation (NSF) funded the development of thirteen complete mathematics programs at the elementary school, middle school, and secondary school levels.
Terry Wyberg, Stephanie R. Whitney, Kathleen A. Cramer, Debra S. Monson and Seth Leavitt
Help students understand an important algorithm by using a piece of paper and a number line.
Thomas R. Post, Amanuel Medhanie, Michael Harwell, Ke Wu Norman, Danielle N. Dupuis, Thomas Muchlinski, Edwin Andersen and Debra Monson
This retrospective study examined the impact of prior mathematics achievement on the relationship between high school mathematics curricula and student postsecondary mathematics performance. The sample (N = 4,144 from 266 high schools) was partitioned into 3 strata by ACT mathematics scores. Students completing 3 or more years of a commercially developed curriculum, the University of Chicago School Mathematics Project curriculum, or National Science Foundation-funded curriculum comprised the sample. Of interest were comparisons of the difficulty level and grade in their initial and subsequent college mathematics courses, and the number of mathematics courses completed over 8 semesters of college work. In general, high school curriculum was not differentially related to the pattern of mathematics grades that students earned over time or to the difficulty levels of the students' mathematics course-taking patterns. There also was no relationship between high school curricula and the number of college mathematics courses completed.