Mathematics Education

The Development of Mathematical Argumentation in an Unmoderated, Asynchronous Multi-User Dynamic Geometry Environment

by Tim Fukawa-Connelly & Jason Silverman
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This paper explores student interactions from the Virtual Math Teams-With-GeoGebra Project, a computer-supported collaborative learning environment that allows individuals to interact, collaborate, and discuss user-created dynamic mathematics objects.  Previous studies of virtual math teams have focused on the coconstruction of a joint problem space and the ways collaborative meaning making can be accomplished in the online environment. Instead, this study explored the development of the students’ argumentation practices. The researchers used Toulman’s (1969) model to analyze and explain the structure of the online interactions and the argumentative practices that become normative among students. In particular, the researchers found that the students made increasingly detailed and mathematical descriptions of the data, developed more abstract warrants, and increasingly acted as if giving reasons was normative in the discussion.

Using a Technology-Supported Approach to Preservice Teachers’ Multirepresentational Fluency: Unifying Mathematical Concepts and Their Representations

by Daniel McGee & Deborah Moore-Russo
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A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers.  For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to pass seamlessly among verbal, geometric, symbolic, and numerical representations of the same mathematical object.  The preservice teachers in this study attended a seminar where they were introduced to the underlying concepts and the pedagogical advantages of multirepresentational fluency.  For select topics, this idea was reinforced with interactive GeoGebra applets that allowed preservice teachers to alter a parameter and simultaneously view how it changes all four associated representations simultaneously.  A qualitative study found that this approach appeared to (a) promote the use of multirepresentational fluency in problem solving approaches used among preservice teachers, (b) change preservice teachers’ perceptions of what it means for a student to understand a concept, and (c) change the nature of evaluations that preservice teachers felt were appropriate for high school students.

Science Education

Peer Communication Through Blogging

by Steven D. Wall & Janice Anderson
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With the emergence of mobile technologies, students’ access to computing devices is omnipresent, as is their ability to collaborate through multiple modalities. This 21st-century affordance has generated a shift in the way preservice teachers are prepared to use, understand. and interact with social media (e.g., blogs) during their academic years.  This paradigmatic shift involves a movement toward a participatory culture using Web 2.0 technologies—dynamic environments that are not limited to the interactions of academic classrooms.  These changes present both new types of challenges and vast opportunities for teacher educators.  Based on repeated observation of minimal interaction amongst members of a peer cohort, a research study was conducted to analyze the interactions of three students who consistently posted comments on each other’s blogs in contrast to the trends found in their cohort.  Analysis of their posts and comments illuminated preservice teacher expectations for science teaching roles and how preservice teachers applied their expectations when commenting on their peers.  These interactions were professional in nature and revealed that previously established interpersonal relationships did not alter the type of interactions that occurred.

Social Studies Education

Struggling to Move Beyond Projection: A Case Study of Instructional Use of an Interactive White Board in Elementary Social Studies

by Caroline C. Sheffield
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Interactive whiteboards (IWBs) are increasingly prevalent in U.S. classrooms. Yet, little is known about how this tool is being used to teach social studies. This case study through classroom observations, interviews, and student focus groups examines how two fifth-grade teachers use t he IWB to teach U.S. history.  The data indicate that when the teachers were observed utilizing an IWB in their social studies instruction, they shifted away from the student-centered instructional practices observed when they did not use the device. Their IWB-centered instruction was teacher centered, utilizing the device predominantly for projection. This trend is likely due to a lack of confidence in how to integrate the IWB technology with social studies pedagogy, as well as a perceived lack of ready-made social studies materials for the IWB. Hammond and Manfra’s (2009) giving-prompting-making model of technology-based social studies pedagogy was used to frame the teachers’ instructional practice.

Supporting In-Service Teachers’ Professional Teaching Knowledge With Educatively Scaffolded Digital Curriculum

by Cory Callahan, John Saye & Thomas Brush
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This article advances a continuing line of inquiry into the potential of digital educative curriculum materials to support teachers’ development of professional teaching knowledge.  Instead of standalone levers of change, the educative curricula in this study were featured resources within a novel professional development approach.  The qualitative, design-based research experiment asked, “Can sustained, collaborative professional development experiences with digital educative curriculum materials help in-service social studies teachers develop professional teaching knowledge?”  Following a 13-month study, none of the six participants fully adopted the promoted wise practice pedagogy, problem-based historical inquiry.  However, findings suggested that sustained, collaborative experiences with digital educative curricula helped teachers in this study begin to articulate and demonstrate tenets of problem-based historical inquiry (e.g., purposeful student-inquiry grounded in recurring societal concerns, structuring classroom events to promote historical thinking).  The authors proposed three features to strengthen future teacher-support efforts: dynamic experiences modeling wise practices, digital curriculum designed for collaboration, and expert mentors to help facilitate learning.


Software’s Smile: A Critical Software Analysis of Educational Technology Certification in New York State

by Tom Liam Lynch
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Technology is increasingly positioned by policy makers as a necessary part of 21st-century schools. However, it is not always clear how well preparation programs in educational technology truly prepare educators for such work. In this study, the author critically analyzed official standards documentation for an educational technology specialist program in order to determine the degree to which preservice educators are being prepared for what is expected of them. The author articulated a framework called critical software studies, which seeks to unpack the way software, which is what comprises modern technologies, demands a kind of scrutiny few acknowledge and consider when preparing future educators. The author concluded that the standards themselves do not take a critical stance with regard to technology, but rather presuppose technology as something neutral and purely functional. Recommendations to improve standards and programs are then made to different stakeholders in teacher education.