Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
TABLE OF CONTENTS
Volume 4, Number 3 - - Spring 2012
Assessing Proofs Via Oral Interviews. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 14
Hortensia Soto-Johnson, University of Northern Colorado
Evan Fuller, Montclair State University
Abstract
In this qualitative study, we explored how oral interviews can inform instructors about
students’ understanding of abstract algebra and their ability to construct a proof in this setting.
Our findings indicate that some student had a good understanding of the ideas needed for a
subgroup proof, but could not write a coherent proof. On the other hand, these same students
provided fairly sound verbal proofs. We discuss the implications of these results for teaching
and future research.
Students’ Quality of Mathematical Discussion and Their
Self-Determination in Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 - 31
Karl W. Kosko, University of Michigan
Jesse L. M. Wilkins, Virginia Tech
Abstract
Mathematical discussion allows for students to reflect upon math concepts and understand
such concepts at a deeper level. This process of reflection requires a certain amount of
internalization on the part of the student. This internalization is facilitated by meeting the
needs of autonomy, competence, and relatedness as advocated by Self-Determination Theory.
The current study provides evidence of a relationship between fulfillment of these
psychological needs and the quality of mathematical discussion students report they engage
in. Correlational analyses and structural equation modeling of data from 176 high school
Geometry students were conducted to examine this relationship. Results support the claims of
a connection between fulfillment of students’ autonomy, competence, and relatedness and
their reported engagement in mathematical discussion.
Five Considerations in Task Design – The Case of Improving Grades . . . . . . . . . . . . . . 32 - 49
Tabach Mihcal, Tel Aviv University
Alex Friedlander, The Weizmann Institute of Science
Abstract
The central role that tasks play in student learning has become clearer in the last decade. As a
result of calls for a structured design process, task design has become one of the main fields of
investigation in mathematics education. Here, we propose five design considerations
(deciding on the mathematical content, choosing the context, deciding on the level of
structural openness, choosing representations, and arranging a task sequence without an
activity). We show how these considerations influenced the design of an activity, and compare
students’ actual work while solving this particular activity and the designers’ considerations.
Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
Write is Right: Using Graphic Organizers to Improve Student
Mathematical Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 - 60
Alan Zollman, Northern Illinois University
Abstract
Teachers have used graphic organizers successfully in teaching the writing process. This paper
describes graphic organizers and their potential mathematics benefits for both students and
teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and
discusses results using the four-corners-and-a-diamond graphic organizer with 186 inner-city,
minority middle school students.