Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
TABLE OF CONTENTS
Volume 5, Number 3 - - Spring 2013
Activity Approach to the Formation of the Method of Addition and Subtraction in
Elementary Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 8
L.K. Maksimov, Volgograd State Advanced Training Academy, Volgograd, Russia
L.V. Maksimova, Volgograd State Advanced Training Academy, Volgograd, Russia
Abstract
One of the main tasks in teaching mathematics to elementary students is to form calculating
methods and techniques. The efforts of teachers and methodologists are aimed at solving this
problem. Educational and psychological research is devoted to it. New scientific and
methodological recommendations on improving the methods of oral and written calculations
are now being developed and introduced, and optimal methods of teaching relevant topic in
mathematics are being sought.
Writing about the History of Mathematics as a Means for Growth in
Understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 - 24
Kelli M. Slaten, University of North Carolina, Wilmington
Abstract
The purpose of this qualitative study is to explore students’ self-reported growth of
mathematical understanding resulting from writing about the historical development of a
mathematical concept. Using excerpts from undergraduate students’ written reflections about
their experiences with the task of writing about mathematics, this study describes three
emergent themes concerning how these students explicitly assessed their own learning: selfawareness of initial understanding, learning from the task of writing, and deeper
understanding of mathematics. The results indicate that writing about the historical
development of mathematics encouraged students to acknowledge their existing
mathematical understanding as well as extend or develop new understandings. Furthermore,
writing about mathematics can serve as a viable assessment of individual student learning
and provide insight into what students understand independent of formal assessment based on
procedural skills.
Problem Solving Concretely with the Word Like . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 - 43
Sean Yee, California State University, Fullerton
Abstract
While the average teenager’s conversation may seem inundated with the word like, in the
mathematics classroom, teenagers use it with purpose. Linguists study the word like to
understand and categorize comparative statements. By overlapping linguistics and
Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
mathematics education within the frame of cognitive science, this study found that high
school students do not use the word like arbitrarily. Its use within conceptual-metaphor
analysis (Lakoff & Johnson, 2003; 1980) suggests a specific purpose within mathematical
problem solving. This interdisciplinary study identifies distinctions in high school students’
use of the word like. Specifically, students predominantly used the word like in a concrete
manner to aid in conceptualization. This article offers practical indicators for teachers to
improve students’ ability to solve mathematics problems.
Closing the Math Gap of Native American Students Identified as
Learning Disabled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 - 59
Judith Hankes, University of Wisconsin, Oshkosh
Stacey Skoning, University of Wisconsin, Oshkosh
Gerald Fast, University of Wisconsin, Oshkosh
Loretta Mason-Williams, Binghamton University
This article serves as an overview of activities and selected assessment findings of a threeyear research study titled, Closing the Mathematics Achievement Gap of Native American
Students Identified as Learning Disabled Project (CMAG Project). Methods used were
problem-based, consistent with those of Cognitively Guided Instruction, and culturally
relevant. Teachers who participated in the study taught students in special education and
inclusive education classrooms at grade kindergarten through twelve. Findings of this study
documented significant learning gains of the target students. Three classroom vignettes
provide examples of project classrooms.