Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
TABLE OF CONTENTS
Volume 6, Number 1 - - Fall 2013
Preservice Teachers’ Understanding of Variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-17
Sue Brown, University of Houston – Clear Lake
Judy Bergman, University of Houston – Clear Lake
Abstract
This study examines the research on middle school students’ understanding of variables and
explores preservice elementary and middle school teachers’ knowledge of variables.
According to research studies, middle school students have limited understanding of
variables. Many studies have examined the performance of middle school students and
offered suggestions on how to improve instruction in middle school. This study considers
preservice elementary and middle school teachers’ knowledge of variables. A total of 73
preservice teachers, all candidates for Early Childhood – 6 certification, were given the same
variable assessments completed by middle school students. Many of the misconceptions
displayed by middle school students were also present in the results from preservice
elementary and middle school teachers. This suggests that another means of improving
middle school students’ performance in algebra is by strengthening the preservice elementary
and middle school teachers’ understanding of variables.
Middle School Children’s Mathematical Reasoning
And Proving Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18-40
Yating Liu, Old Dominion University
Azita Manouchehri, The Ohio State University
Abstract
In this work we explored proof schemes used by 41 middle school students when confronted
with four mathematical propositions that demanded verification of accuracy of statements.
The students’ perception of mathematically complete vs. convincing arguments in different
mathematics branches was also elicited. Lastly, we considered whether the students
recognized and identified advantages associated with using justification models different
from their own in order to offer a theoretical account for how individuals’ proof scheme
choice might be impacted by such an exposure.
Effects of Minute Contextual Experience on Realistic
Assessment of Proportional Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4168
Gabriel Matney, Bowling Green State University
Jack L. Jackson II, University of Arkansas
Jonathan Bostic, Bowling Green State University
Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
Abstract
This mixed methods study describes the effects of a minute contextual experience on
students’ ability to solve a realistic assessment problem involving scale drawings and
proportional reasoning. Minute contextual experience (MCE) is defined to be a brief
encounter with a context in which aspects of the context are explored openly. The study
looked closely at what happened during an instructional unit examining proportional
reasoning. Students completed a pretest and posttest involving items characterizing a novel
context, and data were analyzed to determine the effects of the MCE. Students were
interviewed to gather their perspectives on the problem and their own solutions. Pretest
results indicated that instruction in which student demonstrated growth in understanding had
little effect on students’ ability to solve a novel problem in which they had difficulty
associating their everyday mundane knowledge with the realistic context. The students
demonstrated a significant increase in ability to solve the novel problem after a MCE.
Furthermore, student explicated that the MCE aided their ability to visualize the context, and
this helped them apply instructional learning to solve the problem. A discussion of the
complexities involving the assumptions of students’ familiarity with contexts and their
abilities to draw upon their mundane everyday experiences to solve proportional reasoning
problems is shared.