PRESERVICE MATHEMATICS AND SCIENCE TEACHERS IN AN INTEGRATED TEACHER PREPARATION PROGRAM FOR GRADES 7–12: A 3-YEAR STUDY OF ATTITUDES AND PERCEPTIONS RELATED TO INTEGRATION

The purpose of this article is twofold: (a) to describe a unique teacher licensure program for grades 7–12 that integrates mathematics, science, and technology education and (b) to explore the attitudes and perceptions related to the integration of mathematics, science, and technology education of three cohorts of preservice teachers enrolled in the first 3 years of the program. Eighty-one preservice teachers responded to a semantic differential to measure attitudes and perceptions related to “mathematics, science, and technology education integration.” Principal components and internal consistency reliability analyses were computed to provide validity and reliability evidence. Preservice teachers also responded to one open-ended, free-response written question, “What does the integration of mathematics, science, and technology education mean to you?” Multivariate and univariate analyses of variance with repeated measures and Pearson cross-tabulation chi-square analyses were computed to identify pretest–posttest differences for the value and difficulty scales, identified by the principal components analysis. Analytic inductive methods were used to identify emergent themes in student written responses to the open-ended question. Results indicated no change in preservice teacher attitudes and perceptions related to the value of integration—they clearly valued integration at the onset and completion of the program, often citing student benefits. However, a significant change in preservice teacher attitudes and perceptions related to difficulty was noted. Upon completion of the program, preservice teachers perceived integration to be more difficult and identified barriers and challenges—demonstrating a more realistic, practical, and cautious approach to the integration of mathematics, science, and technology education.     

Students’ geometrical perception on a task-based dynamic geometry platform

This paper describes a task-based dynamic geometry platform that is able to record student responses in a collective fashion to pre-designed dragging tasks. The platform provides a new type of data and opens up a quantitative dimension to interpret students’ geometrical perception in dynamic geometry environments. The platform is capable of generating a collective image map of student geometrical perceptions for a pre-designed dragging task. This map is interpreted as students’ qualitatively different ways of perceiving a geometrical phenomenon under the drag mode, ways which are quantified and categorized in a collective way. The idea of task perceptual landscape is proposed to facilitate discussion on the pedagogical significance of this platform. Specifically, a task case is presented and analysed in which a methodology is developed that provides a way to classify students’ geometrical perceptions with respect to the task. The task perceptual landscape is interpreted as a collective example space of student perception of a task. Furthermore, an idea of personal example space is developed through the findings from a qualitative study for the same task. This brings about discussion on possible pedagogical correlation between the quantitative and qualitative aspects of the platform.     

Learning opportunities from group discussions: warrants become the objects of debate

In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In analyzing a videotaped episode of eight middle school students discussing a statistical problem, we observed that these students frequently challenged the arguments that their colleagues presented. These challenges invited students to be explicit about what mathematical principles, or warrants, they were implicitly using as a basis for their mathematical claims, in some cases recognize the modes of reasoning they were using were invalid and reject these modes of reasoning, and in other cases, attempt to provide deductive support to justify why their modes of reasoning were appropriate. We then describe what social and environmental conditions allowed the discussion analyzed in this paper to occur.

Using video surveillance footage to support validity of self-reported classroom data

The use of video surveillance footage presents a new possibility in educational research as a reliable and valid source of learning and teaching activities in classrooms. However, the unique nature of surveillance footage requires different approaches and poses distinctive challenges in utilizing it in research, yet no methodological guides are currently available in educational research. The purpose of this reflective methodological review is to share our lessons learned from a mixed-methods study that utilized video surveillance footage for triangulating self-reported classroom data. We discuss (1) the importance of triangulation of self-reported data to reduce biases of it, (2) the unique benefits and limitations of using video surveillance data, (3) a methodological framework for video surveillance data analysis, and (4) our process of data analysis with technical, ethical, and other issues in mind when using such data. Software programs to aid video data analysis are briefly introduced as well.