Douglas McDougall

Collaborative Learning on the Internet

This study examined graduate students perceptions of the educational value of their collaborative learning when using the Internet for course delivery. Students enrolled in a summer class conducted entirely online were interviewed, and their communications analyzed, to determine the salient factors associated with their collaborative experiences. Respondents indicated that although they enjoyed the convenience and opportunity for collaboration, a number of dissatisfiers were apparent with the instructional strategy and the delivery medium. Recommendations are documented in an effort to improve future courses utilizing this methodology.

Integrative Mixed Methods Data Analytic Strategies in Research on School Success in Challenging Circumstances.

There are both conceptual and practical challenges in dealing with data from mixed methods research studies. There is a need for discussion about various integrative strategies for mixed methods data analyses. This article illustrates integrative analytic strategies for a mixed methods study focusing on improving urban schools facing challenging circumstances. The research was conducted using a concurrent mixed methods approach. The qualitative and quantitative strands of data were analyzed independently through thematic analysis of qualitative data and factor analysis of survey data, followed by integrative data analytic procedures. The integrative data analytic approach included strategies such as parallel integration for member checking, data transformation for comparison, data consolidation for emergent themes, and case analysis for fine-grained descriptions of school profiles. The integrative data analysis process featured the iterative nature of mixing data sources at various points and allowed the researchers to pay attention to emergent insights made available through mixed methods research.

The Contribution of Technology to the Implementation of Mathematics Education Reform: Case Studies of Grade 1-3 Teaching

Previous research suggests that access to technology contributes to the implementation of mathematics education reform. This case study of three primary (grade 1–3) teachers investigated how access to computers and math teaching software influenced nine dimensions of reform. Teachers were selected on the basis of their commitment to math reform and their technological literacy. Interviews and observations over five months found that technology had its greatest impact by helping teachers expand the scope of their programs and by promoting positive attitudes toward math. Teachers adapted computer tasks to fit their off-line activities, heightening or depleting the contribution of technology to reform. The computer promoted equity of access to all forms and strands of mathematics but this did not necessarily ensure that all students had access to higher math. None of the teachers realized the potential of the computer to increase student-student construction of mathematical ideas, in part because of hardware problems but more because of their decision to assign students to individual computer tasks.

Starting to Publish Academic Research as a Doctoral Student

This article presents some opinions, views and advice that graduate students might consider in order to assess and improve their success as new scholars. Contrary to the famous motto ‘publish or perish,’ we argue that publishing academic research should be headed by intrinsic motivation for becoming a scholar and not by external pressures of social or professional requirements to produce scholarly work. This paper gives practical recommendations about building and sustaining the initial momentum in publishing. First, we discuss the importance of practicing academic writing as a way to improve scholarship and modalities to practice it. Some important issues about social collaboration, ethics, and policies that should be considered in the process of publication are also presented.

Secondary school teachers’ conceptions and their teaching practices using graphing calculators

This article investigates secondary school teachers’ conceptions of mathematics and their teaching practices in the use of graphing calculators in their mathematics classrooms. Case studies on three teacher participants were developed using quantitative and qualitative data that consisted of self-assessments on beliefs in mathematics, observations, surveys on professional and personal technology use and semi-structured interviews. All three teachers had a similar goal of attempting to use the graphing calculators to eliminate mechanical processing time and enhance their students’ ability to construct their own learning. The major findings of this article relate to: (1) proficiency with the graphing calculator; (2) a common starting point and (3) integration into the curriculum. This article concludes that factors such as teachers’ personal experiences and teaching practices, together with the level of proficiency of the students with the technology, influence how the graphing calculators are used in the mathematics classroom. When graphing calculators are effectively used in the mathematics classroom, they are a powerful tool to assist teachers in providing their students with an environment to help them construct their mathematical knowledge and understanding.

Using Dynamic Geometry Software for Teaching Conditional Probability with Area-Proportional Venn Diagrams

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes’ theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships, describe the quantitative relationship between two sets. The second feature is the slider and animation component of dynamic geometry software enabling students to observe how the change in the base rate of an event influences conditional probability. A hypothetical instructional sequence using a well-known breast cancer example is described.

Geogebra as a Cognitive Tool

In this theoretical chapter, we explore the features of GeoGebra under the perspective of cognitive theories and further discuss its pedagogical implications. As a dynamic and interactive learning environment, GeoGebra is relatively new to many of us and needs to be explored, discussed, and understood under various perspectives. Our goal is to initiate this cognitive discussion and motivate researchers and practitioners to join the ongoing conceptual and practical experimentation.