Technology Integration into Mathematics Teaching and Learning: Home

There is a significant body of research relating to technology-enhanced mathematics education and the perceived potential of digital tools to enhance the learning experience. The aim of this research is to take a structured look at the types of empirical interventions ongoing in the field, and to attempt to classify and analyse the ways in which digital tools are being employed in such research. A systematic analysis of 139 recent, published studies of technology interventions in mathematics education, selected from in excess of 2000 potential studies, has been undertaken. A system of classification, developed as a part of this research, is used to categorise the digital tools, the pedagogical foundations and goals of the activities, and the levels of technology integration in the studies. Analysis of the results of this classification highlights a disparity between what is being researched in published empirical studies, and approaches that have been recognised as optimizing the potential of technology to enhance mathematics education. Potential reasons for current trends are proposed and explored.

It is important to assess the cumulative effects of technology on student achievement captured in the last 30 years of technologyenhanced mathematics instruction. Synthesizing the thousands of articles and gray literature on this subject is necessary but would require a considerable commitment of academic resources. A second-order metaanalysis or meta-analysis of meta-analyses is an alternative that is reasonable and effective. Thus, a second-order meta-analysis of 19 prior meta-analyses with minimum overlap between primary studies was conducted. The results represent 663 primary studies (approximately 141,733 participants) and 1,263 effect sizes. The random effects' mean effect size of .38 was statistically significantly different from zero. The results provide a historical and contextualized summary of 30 years of meta-analytic research, which supports meta-analytic thinking and better interpretation of future effect sizes. Results indicate that technology function and study quality are major contributors to effect size variation. Specifically, computation enhancement technologies were most effective, while studies that examine combinations of enhancements were least effective. Implications for technology-enhanced mathematics instruction and meta-analytic research are provided.

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We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, but we also discuss several alternate types of projects. We describe a model that incorporates projects at all stages across the undergraduate mathematics curriculum. Finally, we provide samples of projects that we have used in selected courses.

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We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion of the course, while simultaneously teaching programming fundamentals. Building on this foundation, we give significant programming assignments to our upper-division students, requiring them to regularly use and apply their programming skills to investigate the mathematical topics.

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We review literature relevant to using technology in the teaching/learning of mathematics to highlight four roles of effective technology use: (a) promoting cycles of proof; (b) presenting and connecting multiple representations; (c) supporting case-based reasoning; and (d) serving as a tutee. We then discuss how they intersect with good instruction. Finally, we provide specific examples to illustrate how these roles of technology can be used to maintain the focus of a technology course on mathematics.

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.

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Additional note: This is a reprint of an article from 1983 but may be useful in the philosophical discussions of mathematics and computer science.
The roots of computer science are mainly in mathematics. For a variety of reasons computer science has strayed from these roots. Many, perhaps most of the major research problems in computer science, particularly in the software and systems area, badly need a mathematical and the development of new mathematics to be applied to them.

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A key debate in computer science education is whether and how computational thinking (CT) is used within disciplines other than computer science. Broad definitions provide many avenues for developing integrated instruction, as practices within existing activities can simply be reframed in terms of CT. But such general use of the term CT may confuse its meaning and dilute its power as a tool for bringing CS to all. In this paper, we take the viewpoint that mathematical thinking and computational thinking share common practices, such as using repetition to accomplish tasks, but these shared ideas may develop differently in mathematics and computer science. We use document analysis to analyze the K-5 Common Core State Standards for Mathematics for the presence of these common practices and describe the specific ways they develop in mathematics. We compare these elements of mathematical thinking to related elements of CT to identify synergies and differences between CT and mathematical thinking. We argue that these synergies and differences have implications for the development of integrated instruction designed to bring CS to all.

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This study evaluated how calculus students’ attitudes towards usage of technology changes according to their learning environment and thinking types at the undergraduate level. Thus, the study attempted to determine the place and importance of technological support in the process of attaining the aimed and obtained acquisitions by students. Participants of the study consist of forty-three calculus students who are studying in traditional or CAS-supported teaching environments, and have different thinking types. Pre-and post-assessment tools were used in the data gathering process, and the data were evaluated with descriptive statistics. The results of the study showed that students in the traditional group place more importance on procedural skills, while students in the CAS group attach more importance to conceptual skills in terms of instructional objects. It also determined that acquisitions, which students think developed differ according to learning environment and thinking types. The main implications of the study were discussed in terms of the related literature and teaching practice