Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
TABLE OF CONTENTS
Volume 7, Number 1 - - Fall 2014
Redefining the Whole: Common Errors in Elementary Preservice Teachers’
Self-Authored Word Problems for Fraction Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . 1-22
Juli K. Dixon, University of Central Florida
Janet B. Andreasen, University of Central Florida
Cheryl L. Avila, University of Central Florida
Zyad Bawatneh, University of Central Florida
Deana L. Deichert, Montgomery County Community College
Tashana D. Howse, Daytona State College
Mercedes Sotillo Turner, University of Central Florida
Abstract
A goal of this study was to examine elementary preservice teachers’ (PSTs) ability to
contextualize and decontextualize fraction subtraction by asking them to write word
problems to represent fraction subtraction expressions and to choose prewritten word
problems to support given fraction subtraction expressions. Three themes emerged from the
data: (1) subtraction problems were represented by an incorrect redefinition of the whole; (b)
the type of unit chosen for the whole (e.g. cups, gallons, pounds vs. pizzas, pies) influenced
the success of PSTs in representing Separate (Result Unknown) context problems for
subtraction; and (c) the structure of the problem influences PSTs’ performance in writing
subtraction word problems.
Responsive Decision Making from the Inside Out: Teaching
Base Ten to Young Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-53
Susan B. Empson, The University of Texas at Austin
Abstract
Decision making during instruction that is responsive to children’s mathematical thinking is
examined reflexively by the researcher in the context of teaching second graders. Focus is on
exploring how the research base on learning informs teaching decisions that are oriented to
building on children’s sound conceptions. The development of four children’s understanding
of base ten over a ten-week period is tracked.
“The work of teaching orients teachers to constantly consider their next move”
(Jacobs, Lamb, Philipp, & Schapelle, 2011, p. 98)
Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
Second-Graders’ Mathematical Practices for Solving
Fraction Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54-81
Patricia S. Moyer-Packenham, Utah State University
Johnna J. Bolyard, West Virgiia University
Stephen I. Tucker, Utah State University
Abstract
Recently, over 40 states in the United States adopted the Common Core State Standards for
Mathematics (CCSSM) which include standards for content and eight standards for
mathematical practices. The purpose of this study was to better understand the nature of
young children’s mathematical practices through an exploratory examination of the practices
of a group of second-grade students engaged in several mathematical tasks focused on
rational number concepts. Twenty-five second-grade students completed three fraction tasks
in structured clinical interviews. The interviews and student work were analyzed using an
interpretational analysis to examine the data for constructs, themes, and patterns that were
useful in explaining children’s mathematical practices. The results reveal that children used a
variety of mathematical practices during the interviews to respond to the mathematical
problems presented. Children’s mathematical practices were both a product that they used to
solve the mathematical situations, and a process that was developing during the interactions
of the interview. The findings lead to new insights about how mathematical practices develop
and what promotes their development.