Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
TABLE OF CONTENTS
Volume 6, Number 3 - - Spring 2014
Mathematics Teaching: Listening, Probing, Interpreting and
Responding to Children’s Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-28
Maureen Neumann, University of Vermont
Abstract
The perception of what a teacher says s/he does in the classroom may or may not match
the reality of their actual teaching practice. This case study considers one second-grade teacher’s
instructional methods and pedagogical decisions when teaching number sense and her perception
of what informed her teaching practice. This teacher supported students’ development of
mathematical strategies, valued debriefing time, and students’ sharing mathematical strategies.
Additionally, she listened to students purposely by probing their thinking. Her experience in a
mathematics professional development program helped her be consistent in her beliefs about
mathematics learning, her perception of her teaching, and the observed practice.
Alternate Trajectories: Women Moving Into
Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-50
Allison F. Toney, University of North Carolina - Wilmington
Abstract
While only about one-third of each year’s doctoral graduates in mathematics are women,
about two-thirds of the doctoral graduates in mathematics education are women. This article
reports on the results of a qualitative investigation into the nature of the graduate school-related
experiences of women in collegiate mathematics education doctoral programs (Toney, 2008).
Eight women with advanced mathematics degrees were interviewed. Each woman chose to move
into a collegiate mathematics education program in a mathematics department. The twointerview protocol explored and extended a framework about women doctoral mathematics
students’ experiences suggested by the research of Herzig (2002,2004a, 2004b), Hollenhead,
Younce, and Wenzel (1994), and Stage and Maple (1996). Results support an addition of three
new categories to this framework: Self as scholar, “my teaching,” and future possible self.
Concluding remarks include suggestions for future research and new directions for practice,
graduate program development, and faculty recruitment.
Prospective Teachers’ Procedural and Conceptual
Knowledge of Mean Absolute Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51- 69
Randall E. Groth, Salisbury University
Abstract
The recommendation to study statistical variation has become prevalent in recent
curriculum documents. At the same time, research on teachers’ knowledge of variation is in its
Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
beginning stages. This study investigated prospective teachers’ knowledge in regard to a specific
measure of statistical variation that is new to many curriculum documents: the mean absolute
deviation (MAD). Seventy-six prospective teachers participated in the study. Participants
exhibited various procedural and conceptual characteristics in their thinking about the MAD. The
majority was able to successfully select and carry out a procedure for computing the MAD.
However, some had difficulty dealing with procedures for absolute deviations, and others
confused the procedure for the MAD with the procedure for a different descriptive statistic.
Conceptually, participants offered a variety of interpretations of the MAD, with some
demonstrating deep understanding of the measure and others demonstrating shallower
understanding or misconceptions. Those who demonstrated the strongest conceptual knowledge
of the MAD also exhibited sound procedural understanding, suggesting that the two types of
knowledge are intertwined in the process of fully understanding the measure.