Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
TABLE OF CONTENTS
Volume 7, Number 2 - - Winter 2014-15
Teachers Promoting Student Mathematical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . 1- 20
Mary Mueller, Seton Hall University
Dina Yankelewitz, Mercy College
Carolyn Maher, Rutgers University
Abstract
During an informal, after-school, math program, a group of middle school students worked
collaboratively on open-ended problems. The students co-constructed arguments, provided
justifications for their solutions, and engaged in mathematical reasoning. This paper describes
the specific teacher moves that promoted this phenomenon. The findings of this study indicate
that through carefully planned interventions, the teachers created a mathematical community
with norms that included listening, sharing, explaining ideas, creating, questioning, revising
justifications and using multiple forms of reasoning. These established norms resulted in the
detection of student autonomy.
With a Little Help from My Friends:
Scaffolding Techniques
in Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-
32
Michelle L. Frederick, Kent State University
Scott Courtney, Kent State University
Joanne C. Caniglia, Kent State University
Abstract
The purpose of this study was to explore middle grade mathematics students’ uses of
scaffolding and its effectiveness in helping students solve non-routine problems. Students
were given two different types of scaffolds to support their learning of sixth grade
geometry concepts. First, students solved a math task by using a four square graphic
organizer that included the identification of critical components, strategy selection,
computation and analyses of answers. The second type of scaffolding occurred with
different grouping formats, alternating work led by the teacher, working alone. Measures
included extended response daily tasks, teacher-created unit test, state standardized
assessments, and surveys gauging student’s satisfaction with types of scaffolding.
Classroom use of a variety of scaffolds led to an increase in the number of correct
responses and more detailed explanations. No significant differences occurred on the
teacher-made tests, yet significant increases were found on students’ state standardized
tests. Students indicated that scaffolding by groups was helpful in initiating solution
pathways.
Investigations in Mathematics Learning
Official Journal of The Research Council on Mathematics Learning
Sustaining Social and Sociomathematical Norms with
Prospective Elementary Teachers in a Mathematics
Content Course . . . . . . . 33 64
George J. Roy, University of South Carolina
Jennifer M. Tobias, Illinois State University
Farshid Safi, College of New Jersey
Juli K. Nixon, University of Central Florida
Abstract
As students contribute to social and sociomathematical norms, they will often reorganize
their own understandings. As such, the purpose of this article is to describe the ways in
which prospective elementary teachers contributed to the norms that were established and
re-established throughout an entire semester in an undergraduate mathematics content
course. Findings illustrate that norms must be renegotiated between an instructor and
prospective teachers when the mathematics content changes.
Keywords: Whole Number concepts; Fractions concepts; Classroom Norms; Prospective
Teachers