Tools In Mathematics Education Research Articles

Using different digital tools in designing and solving mathematical modelling problems

AbstractWhile existing studies acknowledge the importance of using technology in the mathematical modelling process, questions about how to integrate digital tools into mathematical modelling are not still answered. This study aims to examine pre-service mathematics teachers’ designing and solving mathematical modelling problems by using different digital tools through the collaboration of two different courses in their education program. The GeoGebra-supported modelling cycle was adopted as the conceptual framework of the study. The case study was used to design the research. The participants of the study were three volunteer pre-service secondary mathematics teachers, who were able to use and integrate digital tools in mathematics education. The pre-service teachers were asked to design a mathematical modelling problem by integrating different digital tools as the final assignment in both courses. The designed mathematical modelling problem, the video records of pre-service teachers’ explanations including the designing and solving process, and the video records of the focus group interview were the data of the study. The results showed that the pre-service teachers were able to design and solve an effective and comprehensive mathematical modelling problem using technology by combining their skills that they had learnt through different courses. In particular, they were able to use different digital tools in both designing and solving a mathematical modelling problem. Their solution also led to the extension of the adopted framework by adding new technological actions into the modelling stages.

Enhancing mathematical education with spatial visualization tools

IntroductionThis article highlights the innovative approach of incorporating spatial visualization tools in mathematics education, specifically focusing on the exploration of virtual environments and 3D printing. By integrating these advanced technologies, educators can enhance the learning experience and facilitate a deeper understanding of mathematical concepts. This research delves into the potential benefits and practical applications of these tools, shedding light on their effectiveness in fostering spatial reasoning skills and promoting active student engagement. The study aims to uncover new avenues for leveraging technology in the mathematics classroom and re-imagining the teaching and learning process.MethodsTo assess the progress in spatial visualization ability, the Revised Purdue Spatial Visualization Test (Revised PSVT: R) was administered as both a pre-test and a post-test to a sample of 255 students divided into control and experimental groups.ResultsThe findings indicate that the control group exhibited no significant development (p = 0.163) and had a minimal effect size of change (g = 0.035), whereas the experimental group demonstrated a substantial improvement in spatial visualization ability (p < 0.05) with a noteworthy medium effect size of change (g = 0.325). Furthermore, an analysis of variance was conducted to compare the mean normalized change in spatial visualization ability between the control and experimental groups. The results, with 95% confidence, establish that the normalized spatial visualization change is significantly higher in the experimental group. Specifically, the experimental group witnessed a 25% increase in spatial visualization skills, while the control group only experienced a 5% increase.DiscussionOur study demonstrates the significance and effectiveness of integrating spatial visualization tools in mathematics education to enhance students’ spatial reasoning skills and mathematics understanding.

Mathematics Concepts in Making Kites as a Tool in Ethno-STEM Based Learning

Kite is a traditional game with many mathematical concepts, making them applicable in ethno-STEM (science, technology, engineering, and mathematics)-based learning. Therefore, this research explores the mathematical concepts inherent in kite flying related to ethnomathematics and STEM education. This research employs a qualitative exploratory approach. Data are collected through three methods: documentation, observation, and interviews. After collecting data, a descriptive analysis is conducted, including data reduction, presentation, and verification. Based on the data analysis, the mathematical concepts in kite-making include geometry, measurement, area and perimeter calculations, ratios and scales, patterns and symmetry, and arithmetic. Kite-making can be applied in ethno-STEM-based mathematics learning as it aligns with the current curriculum and adheres to STEM learning principles. Therefore, kite-making can serve as a tool for mathematics education, making learning more meaningful, enjoyable, interactive, and contextual. This research exploration suggests that numerous mathematical concepts can be further examined in ethno-STEM-based learning. Additionally, this research highlights the connection between mathematics and the socio-cultural context.

The use of visualization tools in teaching mathematics in college of education: A systematic review

The integration of visualization tools in mathematics education has gained substantial attention within higher education, particularly in college education settings. This systematic review aims to comprehensively analyze the existing body of literature on using visualization tools in teaching mathematics at the college of education level. By examining 22 published papers, this review synthesizes findings to explore the effectiveness of visualization tools, their impact on students' learning outcomes, and the potential challenges associated with their implementation. The systematic review employs a rigorous methodology, including comprehensive search strategies, article selection criteria, and quality assessment procedures. This review categorizes visualization tools through meticulous analysis into various types, such as digital simulations, interactive software, and physical manipulatives. It evaluates their contributions to enhancing students' understanding of mathematical concepts and problem-solving skills. Key findings from the reviewed literature shed light on the positive effects of visualization tools in promoting active engagement, conceptual understanding, and motivation among college of education students. Additionally, the review uncovers potential challenges, including technological barriers, instructional strategies, and varying learning preferences, that educators and curriculum designers need to consider when integrating visualization tools into the mathematics classroom.

Analysis of Research Trends on General Mathematics at Universities : Focusing on Papers Published in Korean Journals Over the Past 10 Years

In this study, in order to provide a developmental discussion on general mathematics in universities and the direction for follow-up research, research trends were examined for papers published in Korean domestic academic journals over the past 10 years. The results of the research are as follows: First, among studies related to mathematics education and general education, research on general mathematics in universities is severely lacking. Considering that nearly all universities offer courses related to general mathematics, professors and researchers responsible for general mathematics should dedicate more attention to research on general college mathematics. Second, concerning the subjects and content areas of mathematics, research on general mathematics shows a bias towards basic general mathematics for science and engineering students. Therefore, there is a need for research on basic general mathematics for students in the humanities and social sciences, as well as research on pure general mathematics applicable to all students. Third, there is a lack of research on evaluation and educational technology in the field of general mathematics. Evaluation plays a crucial role in education, and it is important to conduct research on the evaluation of general mathematics and the utilization of educational technology, especially considering the increasing emphasis on the use of various technological tools in mathematics education. Fourth, in terms of research methods, the majority of studies focus on quantitative research. Therefore, it is necessary to employ diverse research methods that are suitable for the teaching and learning environment of general mathematics. Fifth, concerning the research topic on teaching and learning, while there have been numerous studies targeting science and engineering students, there is a need for a variety of studies on teaching and learning that encompass all students, including those in the humanities and social sciences, as well as the professors themselves.

Development of TPACK with Web 2.0 tools: Design-based study

This mixed-method study, which aimed to examine the development of teacher candidates, was organized as a design-based study. During the 14-week instructional sequence, pre-service teachers were given training based on the designed hypothetical learning trajectory. The data collected through the lesson plans before and after the training and interviews were organized and analyzed by using the rubric prepared within the scope of Web 2.0 tools by the researchers. Moreover, the pre-training and post-training scores obtained using this performance rubric were analyzed with the related sample t-test. In addition, learning packages and interviews were analyzed using content analysis technique. The findings showed that there was an improvement in the technological pedagogical content knowledge of the pre-service mathematics teachers with the training provided for the use of Web 2.0 tools in mathematics education. In the study, an alternative educational content that can be used in lessons related to instructional technologies in undergraduate programs that train mathematics teachers has been prepared.

High School Students’ and Their Teacher’s Experiences with Visual Proofs

Proof is one of the main components of both mathematics and mathematics education. However, students and teachers at every level have difficulties in proof and proof teaching. Presenting alternative proof methods to students will not only provide a rich learning environment but also allow the students to have different perspectives by providing alternative ways they can apply for constructing a proof. The visual proofs are one of the alternative proof methods. The visual proofs are seen as valuable tools for mathematics education; it is planned to investigate the views of high school students and their teacher about visual proof. Case study method is used in the study. Participants of the study consisted of four high school students who were nineth-graders and their teacher. The teacher said that after the visual proof activities, the students started to wonder where the formulas came from, in other words, they started questioning, their interest levels increased, and the formulas were kept in their minds more. The high school students stated that they found the visual proof activities enjoyable, and they were happy when they understood the visual proofs and unhappy when they could not understand them.

Timeline tool for analyzing the relationship between students-teachers-artifacts interactions and meaning-making

Meaning-making in teaching-learning mathematical processes is a relevant issue analysed through different philosophical and educational frames. In particular, the use of digital tools in mathematics education affects the meaning-making processes. This paper discusses meaning-making from a phenomenological standpoint, in which interpretative activities are relevant. This approach requires a careful analysis of the semiotic resources’ evolution, including those related to the used digital tools. The paper aims to introduce an analytical tool, the Timeline. This tool is an elaboration on previous analysis tools, like the interaction flowchart and the semiotic bundle. Such a tool allows the analysis of relationship among interactions, semiotic resources, and meaning-making. In this paper, the Timeline is used to analyze two episodes from two different learning experiments where GeoGebra and augmented reality are used. High school students from Italy and Israel participated in this study. Video recording has been used to document the entire learning experiments. The analysis provides evidence that the Timeline enables investigating the relationship between students-teacher-artifacts interactions and meaning-making. Moreover, results may give teachers ideas for using digital tools to foster students’ meaning-making.

Didactic possibilities of ICT tools in mathematical education of the future mathematics teacher

Problem formulation. Problem formulation. At the present stage of the educational system development, information and communication technologies (ICT) play one of the most important roles in the didactic system of the future teacher of mathematics. In the process of preparing a future mathematics teacher it is necessary from the very beginning to prepare students for future professional activities at the same time with professional competencies in terms of educational informatization. One of the effective ways of informatization of mathematics education can be the using of the Internet during the process of teaching mathematical disciplines. Because of the fact that every student cannot imagine his life without the Internet, it is possible to move from passive presentation of material to active through the tools of the Internet, which will significantly increase the interest in learning the discipline and improve learning outcomes. The aim of the article is to analyze the issues of didactic possibilities of ICT tools in mathematical education of future mathematics teachers. Materials and methods. The following methods were used to conduct this research: analysis of psychological and pedagogical and methodological literature, systematization and generalization of different views on determining the main ideas, types and methods of construction, as well as the use of Wiki technology in training future mathematics teachers. Results. Based on the analysis of the didactic possibilities of ICT tools in mathematics education of future mathematics teachers, it was determined that among the large number of Internet resources, the Web 2.0 service deserves special attention. This service is a block of social services (blogs and microblogs (Twitter, Blog, Live Jornal), social networks and social presentation systems (viber, Telegram, Instagram, Facebook), wiki projects (Wikipedia, Wikiversity, Wikibooks, Wiktionary) and management systems content (Moodle, Jomla, etc.); social media repositories (YouTube, etc.)), which allow students not only to receive but also to create information, information resources. For example, a blog in mathematics education can be used as a platform for information exchange, consultation, research and more. An equally interesting resource is the Wiki service, the use of which achieves the greatest effect in the independent work of students in the process of creating educational and research projects. Using Web 2.0 tools it is possible to create small training modules on a specific problem, illustrated with visualized examples with animation. The set of such modules can be a distance learning course that students can access at any time. The author also considers the directions and some possible types of use of Internet services in the training of mathematics teachers. Conclusions. An analysis of the didactic possibilities of ICT in mathematical education of future mathematics teachers showed that among all possible Internet services, Wiki has all main features and capabilities of Web 2.0 technology, and therefore is well suited for organizing an educational network of future maths teachers. Thus, the active use of various Internet services in the process of preparing future mathematics teachers turns the usual learning process into a joint creative activity in which all participants actively cooperate in the process of learning and acquiring new knowledge, which significantly increases the efficiency of education.

Developing a Personalised Learning Model Based on Interactive Novels to Improve the Quality of Mathematics Education

The lack of sufficiently developed methodological basis before graduation adversely affects the mathematical competency of future experts that are required by the modern economy. The study aims to investigate the features of the development of a personalized model of teaching mathematics by means of interactive novels to improve the quality of educational results. The main methods of research were the generalization of pedagogical experience and science literature, modelling, observation, analysis of results in AXMA Story Research methods. The chosen methods made it possible to justify the necessity of using interactive novels to personalize teaching mathematics and to confirm the qualitative improvements in the pedagogical system. Fisher’s criterion was used to evaluate the results. 121 schoolchildren from Russian and Uzbek schools participated in the experiment. Individual educational routes supporting the studying of mathematical theory, problem solving in the interactive space AXMA Story Maker were developed. The peculiarities to be considered when designing a personalized model of mathematics learning by means of interactive novelties were formulated. These are the correlation between the didactic goal and the result of educational and research work in a nonlinear environment, the selection of the plot for a visual novel, the elaboration of the text component and the personalized learning track, etc. According to ANCOVA test results, the post-score of the experimental group is statistically higher than the control group. The results of the article can be used to develop ideas for personalising of learning in the digital school, as well as justification for the need for inclusion of digital interactive tools in mathematics education at all levels of education and training.

Considering Teachers’ Beliefs, Motivation, and Emotions Regarding Teaching Mathematics With Digital Tools: The Effect of an In-Service Teacher Training

Mathematics teachers’ motivational and emotional orientations regarding digital tools in mathematics classrooms are key aspects influencingwhetherandhowtechnology is used to teach mathematics—making the support of those characteristics one central goal for teacher education. In this article we investigated if and how a workshop-based in-service teacher training can foster teachers’ perceived value of digital media in mathematics education, their self-efficacy, and their anxiety towards teaching mathematics with digital tools. In an intervention study withN= 83 in-service teachers with varying teaching experience, we used cluster analysis based on their experience, value, self-efficacy, and anxietybeforethe intervention to determine three different teacher orientations regarding teaching mathematics with digital tools. Paired samplet-tests with pretest and posttest data revealed that for two of three clusters these beliefs, motivation, and emotions changed in a positive way during the intervention while for the third no change was found. Our study sheds light on the role of motivational and emotional orientations for the implementation of digital tools in mathematics education: it shows that these orientations can be utilized to cluster teachers on this topic and illustrates that these orientations can be successfully fostered—while individual differences may exist in the effect and success of interventions.

Tools and taxonomies: a response to Hoyles

ABSTRACTIn this response paper to Hoyles’ contribution “Transforming the mathematical practices of learners and teachers through digital technology” focuses on three points. First, more knowledge is needed on why teaching and learning practices should transform, into what will they transform, and by what or by whom will they be transformed. Second, a suggestion is made for a more specific taxonomy on the didactical functionality of digital tools in mathematics education. Third, a plea is made for a future research agenda that addresses the ways in which activities with digital tools mediate the learning of mathematics in a fruitful way. This includes the interpretation and grading of online student work through intelligent mathematical software, and the notion of embodiment, as to do justice to the bodily experiences in which mathematical experiences are rooted.

Usefulness of specialized information and communication tools in mathematics education of visually impaired students - the results of teachers' opinion survey

Usefulness of specialized information and communication tools in mathematics education of visually impaired students - the results of teachers' opinion survey

On line and other Game-Based Learning for Mathematics

The last decade, researchers and educators have shown particular interest for the use of educational video games in mathematics education, in an effort to provide educational character to entertainment. In this paper we represent some of the most representative studies which evaluate the effects of video games on mathematics achievement as well as the improvement of memory, attention and cognitive skills. As indicated by the studies, video games may constitute useful tools in mathematics education as they support children’s comprehension on fundamental concepts, but also motivate them to see positively the course of mathematics.

Didáctica de las matemáticas y tecnologías de la información y la comunicación

La incursión de las nuevas herramientas peda­gógicas en el contexto educativo en matemáticas; genera una transformación socio-cultural concer­niente a la praxis pedagógica y didáctica actual. La investigación que derivó en el presente artículo pretende resaltar y fundamentar los procesos de incidencia de las TIC sobre la resolución de pro­blemas en el marco de la didáctica de las mate­máticas. Desde esta perspectiva; se realizó una revisión bibliográfica de fuentes especializadas a partir de una metodología descriptiva basada en la sistematización y clasificación de textos para dar un sustento crítico-argumentativo. Se identificaron unos núcleos de trabajo: Historia y didáctica de las matemáticas; resolución de problemas y tecnolo­gías de la información y la comunicación. El mar­co cuestionador se enfocó hacia el acercamiento a una reestructuración curricular en las matemá­ticas; retomando la vinculación del pensamiento matemático y una didaxis hacia la comprensión mediada por las tecnologías y el software espe­cializado; como recurso implícito en la conceptua­lización de la disciplina matemática en el contexto.

Webbing and orchestration. Two interrelated views on digital tools in mathematics education

The integration of digital tools in mathematics education is considered both promising and problematic. To deal with this issue, notions of webbing and instrumental orchestration are developed. However, the two seemed to be disconnected, and having different cultural and theoretical roots. In this article, we investigate the distinct and joint journeys of these two theoretical perspectives. Taking some key moments in recent history as points of departure, we conclude that the two perspectives share an importance attributed to digital tools, and that initial differences, such as different views on the role of digital tools and the role of the teacher, have become more nuances. The two approaches share future challenges to the organization of teachers’ collaborative work and their use of digital resources.

Mind Mapping as Efficient Tools in Mathematics Education

There are many possibilities how to improve mathematical education and enable students to participate in the process of the cognition of new knowledge. In this paper we present mind mapping as one of graphical representation of mathematical networks which may become another efficient tool for improving mathematical achievement. A pedagogical experiment, whose results are stated in this article, was realised during the academic year 2013/2014 when Mathematics 1 was taught on the Faculty of Civil Engineering, University of Zilina. It consisted in the inclusion of mind maps in mathematics teaching, observation of their influence on the teaching process efficiency.

Animating an equation: a guide to using FLASH in mathematics education

Macromedia's FLASH development system can be a great tool for mathematics education. This article presents detailed Flash tutorials that were developed and taught by the author to a group of mathematics professors in a summer course in 2005. The objective was to educate the teachers in the techniques of animating equations and mathematical concepts in Flash. The course was followed by a 2-year study to assess the acceptance of the technology by the teachers and to gauge its effectiveness in improving the quality of mathematics education. The results of that 2-year study are also reported here.

Combination of traditional and computer based tools in mathematics education

In this paper I analyzed the advantages of the combined use of traditional and computer-based demonstration, which are connected to the solution of a difficult space-geometry problem. The distinguished feature of the paper lies in the combined use of 3-dimensional animations, interactive worksheet and traditional models. The interactive worksheet contains 3-dimensional animations created in DGS. The traditional worksheet harmonizes the traditional edge-model and the interactive worksheet.

Computer algebra systems and dynamic geometry systems in math teaching

In the last twenty years of the 20 century the quick renewal of informational-communicational technology resulted in fundamental new opportunities and in many didactical tasks, which have to be solved in education. This is our particular challenge in math education. The computer algebra systems (CAS) and the dynamical geometry systems (DGS) are probably the most useful elements of the newly created tools. Nowadays the necessity of CAS and DGS usage in math education is accepted in the professional public opinion as well. We know that application of these new tools produces shifting of accents and in some places it rearranges the contents of teaching materials. The elaboration of didactics of CAS has just begun and we have to solve lots of problems, which are frequently recreated. We would like to contribute to this task with this study selection. These papers are based on those lectures which were presented at the International Symposium, Anniversary of Pollack Mihaly Engineering Faculty, May 31-June 1, 2002, Pecs, Hungary. Three of these papers deal with dynamical geometry systems, seven of them discuss computer algebra systems. Some words about our papers: Bertha, Tunde examines the effects of combination of traditional and computer based tools in mathematics education. Schumann, Heinz speaks about computer aided solution of 3D-problems in analytic geometry. Laszlo, Istvan introduces the Euklides dynamic geometric construction program. Fuchs, Karl Jozef reports his research about computer algebra systems in math education Karsai, Janos and his co-workers report their experiences from visualization and art in the mathematics classroom. Klincsik, Mihaly writes about teaching function approximation techniques using MAPLE and INTERNET. Lindner, Wolfgang writes about CAS supported multiple representations in elementary linear algebra. Perjesi Hamori, Ildiko speaks about application of CAS for teaching of integral-transforming theorems. Maroti, Gyorgy reviews his automata constructions in Maple. Sarvari, Csaba reports his works in field of network based math teaching, using CAS.