Mathematics Learning in Online Spaces
Anthony Matranga
School of Education
Overview
In this poster an emerging proposal for a research study is
presented. In particular, focus is on (1) a conceptual framework
that provides a lens through which the nuances of learning in an
online space will be investigated, and (2) presentation of a webbased software designed to enhance teacher collaboration.
Introduction
Reform-oriented instructional strategies are an important
factor for successful mathematics learning by school students. The
crux of “reform-oriented” instruction is student-centered
problem-based mathematics instruction and pedagogy, which is
substantiated by the National Council of Teachers of Mathematics
(National Council of Teachers of Mathematics, 2000). Given the
availability of technological resources, current professional
development programs, and the implementation of the Common
Core Standards (National Governors Association Center for Best
Practices & Council of Chief State School Officers, 2010) it is not
unreasonable to contend that a majority of U.S teachers are aware
of the widespread endorsement of reform-oriented instruction.
Problem Statement
While recent reports are promising, a finer-grained analysis of
teachers’ pedagogy and instruction as displayed in mathematics
classrooms across the nation suggests that, as whole, mathematics
instruction in U.S schools does not reflect the vision set forth by
policy makers and educational researchers (Stigler & Hiebert,
1999).
Integrating existing theoretical perspectives
In this conceptual framework multiple existing theoretical models are integrated to develop a refined lens through which mathematics learning will be analyzed in an online space. The crux of this
online space is related to individual understandings, collective activity and available technological tools. To account for these three
conceptual model is the belief that the production of mathematics in an
aspects in learning a social constructivist perspective of learning (the emergent
perspective) is integrated with a view that takes cognition as qualitatively different when mediated by technology (humans with-media).
The Emergent perspective
Humans-with-media
Collective of
humans-withThe emergent perspective is a social constructivist
Borba and Villareal (2006) take the relationship between
media
perspective of learning that takes as a point of reference the
individual and technology to be reflexively related and suggest
reflexivity between individual participation and patterns in
that the “unit” of analysis is the computer and human as a single
collective activity (Cobb & Yackel, 1996). The focus of analysis
entity. To capture this relationship they introduce the metaphor,
from this perspective is the emergence of social norms as a
human-with-media, to suggest a single knowledge producing
way to make conjectures about individual mathematics
“unit.” In other words, at a one level one can “zoom in” and
learning. In particular, three types of norms are explicated:
analyze the reflexivity between individual and technology,
Individual
Individual
Social norms: general participation structures that are not
however regardless of where on a continuum of development
human-withhuman-withspecific to mathematics and could be enacted in other
the individual-technology relationship falls, the knowledge
media (1)
media (2)
classrooms (i.e. English or history).
produced is by a single knowledge producing unit—the human Sociomathematical norms: participation structures that
with-media. Moreover, as this knowledge-producing unit
are specific to a mathematical ways of reasoning.
becomes more integrally related, cognition becomes qualitatively
Mathematical practices: participation structures and
different even when the technology is not present.
“shared” ways of reasoning that are specific to particular
In this model, a reflexive relationship is argued to exist between a collective and
mathematical ideas and concepts (i.e. counting on to solve
individuals as they engage with multiple technologies. The reflexivity is symbolized
addition problems).
by the straight arrows above. The curved arrow is meant to symbolize the fluidity
It is the impact of technology on these characterizations of
by which individuals interact with different technological interfaces and tools in
norms that will be under investigation in this study.
an online space to produce different forms of knowledge.
]
Conceptual Framework
Purpose
The purpose of this study is to understand how a
technologically enhanced collaborative model for developing
mathematics
knowledge in online teacher education courses
enhances
teacher collaboration in the development of
mathematics knowledge.
Research questions
1.  How does a technologically enhanced instructional model
foster emergence of normative ways of communication in an
online teacher education course?
2.  To what extent does technologically mediated interaction
support emergence of norms and practices that are embodied
by the particular technology?
References
Borba, M. C., & Villarreal, M. E. (2006). Humans-with-media and the reorganization
of mathematical thinking: Information and communication technologies, modeling,
visualization and experimentation (Vol. 39): Springer Science & Business Media.
Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural
perspectives in the context of developmental research. Educational Psychologist,
31(3-4), 175-190.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap. New York, NY: Free Press.
As part of the EnCoMPASS research project
around improving STEM education through the
cultivation of a virtual community, an enhanced
technological environment is under production.
This web-based tool is designed to support
teacher collaboration around student work,
feedback, and assessment. For the purposes of the
current study, this technological tool will be
integrated into an online master’s course to
enhance the means by which teachers collaborate
around mathematics. In particular, affordances of
the software are specifically designed to engage
teachers with best practices around giving
evidence-based feedback.
** This material is based upon work supported by the National Science
Foundation under Grant Nos. 0717732 and 1222355. Any opinions, findings, and
conclusions or recommendations expressed in this material are those of the
author and do not necessarily reflect the views of the National Science
Foundation.
Enhanced
Technological
Environment
Conjectures
In developing the above conceptual model a few
conjectures have emerged with respect to
teacher engagement with the enhanced
technological environment. In particular, it is
conjectured that students will begin to use
evidenced-based feedback strategies with the
use of other technological tools other than the
EnCoMPASS environment. This conjecture is
supported by the theoretical framework as
Borba & Villareal (2006) suggest that
engagement with technology impacts individual
cognition even when this technology is not
being used.