Karen Hollebrands

High school students’ understandings of geometric transformations in the context of a technological environment

Abstract This study investigated the nature of students’ understandings of geometric transformations, which included translations, reflections, rotations, and dilations, in the context of the technological tool, The Geometer’s Sketchpad . The researcher implemented a seven-week instructional unit on geometric transformations within an Honors Geometry class. Students’ conceptions of transformations as functions were analyzed using the APOS theory and were informed by an analysis of students’ interpretations and uses of representations of geometrical objects using the constructs of drawing and figure . The analysis suggests students’ understandings of key concepts including domain, variables and parameters, and relationships and properties of transformations were critical for supporting the development of deeper understandings of transformations as functions.

IDEA: Identifying Design Principles in Educational Applets.

The Internet is increasingly being used as a medium for educational software in the form of miniature applications (e.g., applets) to explore concepts in a domain. One such effort in mathematics education, the Educational Software Components of Tomorrow (ESCOT) project, created 42 miniature applications each consisting of a context, a set of questions, and one or more interactive applets to help students explore a mathematical concept. They were designed by experts in interface design, educational technology, and classroom teaching. However, some applications were more successful for fostering student problem-solving than others. This article describes the method used to mine a subset (25) of these applets for design principles that describe successful learner-centered design by drawing on such data as videos of students using the software and summaries of written student work. Twenty-one design principles were identified, falling into the categories of motivation, presentation, and support for problem solving. The main purpose of this article is to operationalize a method for post hoc extraction of design principles from an existing library of educational software, although readers may also find the design principles themselves to be useful.

Characterising and Developing Teachers’ Knowledge for Teaching Statistics with Technology

Developing the pedagogical expertise needed to effectively engage students in learning statistics with technology requires teachers to have a depth of knowledge about statistics, technological tools for exploring statistical ideas, and of pedagogical issues related to teaching and learning statistics with technology. In this chapter, a framework for a specialised knowledge that is called technological pedagogical statistical knowledge (TPSK) is presented and examples of how aspects of this type of knowledge may assist a teacher are provided. Implications for training teachers are described.

Factors that influence secondary mathematics teachers' integration of technology in mathematics lessons

Abstract While many studies describe the use of technology in the mathematics classroom, few explore the factors that influence teacher decisions around its use. The participants in this study were 21 early career secondary mathematics teachers who had completed an undergraduate mathematics teacher preparation program in the USA with a strong emphasis on the use of technology to teach mathematics. In this qualitative study, interview data were collected and analyzed with attention toward why teachers choose to use technology to teach mathematics, what tools they chose to use and why, as well as the general factors they consider when selecting particular technology tools. Findings indicate that one of the most important factors when deciding whether to use technology was how well it aligned with the goals of a lesson. The range of technology used spanned mathematical action tools, collaboration tools, assessment tools, and communication tools. When selecting particular tools teachers most heavily considered ease of use for both themselves and their students. These findings suggest that when considering how to infuse technology into teacher education programs we suggest that it is important to focus more broadly on types of tools, ways teachers can position them, and how particular activities align with specific mathematics learning objectives.

An analysis of context-based similarity tasks in textbooks from Brazil and the United States

ABSTRACT Three textbooks from Brazil and three textbooks from the United States were analysed with a focus on similarity and context-based tasks. Students’ opportunities to learn similarity were examined by considering whether students were provided context-based tasks of high cognitive demand and whether those tasks included missing or superfluous information. Although books in the United States included more tasks, the proportion of tasks focused on similarity were about the same. Context-based similarity tasks accounted for 9%–29% of the similarity tasks, and many of these contextual tasks were of low cognitive demand. In addition, the types of contexts that were included in the textbooks were critiqued and examples provided.