Mathematics

Research

31 pages, 6172 KiB

Open AccessArticle

Maker Math: Exploring Mathematics through Digitally Fabricated Tools with K–12 In-Service Teachers

by Jason R. Harron, Yi Jin, Amy Hillen, Lindsey Mason and Lauren Siegel

Mathematics 2022, 10(17), 3069; https://doi.org/10.3390/math10173069 - 25 Aug 2022

Cited by 4 | Viewed by 4284

This paper reports on nine elementary, middle, and high school in-service teachers who participated in a series of workshops aimed at exploring the wonder, joy, and beauty of mathematics through the creation and application of digitally fabricated tools (i.e., laser-cut and 3D printed). [...] Read more.

This paper reports on nine elementary, middle, and high school in-service teachers who participated in a series of workshops aimed at exploring the wonder, joy, and beauty of mathematics through the creation and application of digitally fabricated tools (i.e., laser-cut and 3D printed). Using the Technological Pedagogical and Content Knowledge (TPACK) framework to investigate technological, pedagogical, contextual, and content knowledge, researchers applied qualitative methods to uncover the affordances and constraints of teaching and learning math concepts with digitally fabricated tools and examined how the workshops supported broadening participation in mathematics by focusing on the connections between mathematical inquiry, nature, and the arts. Affordances include opportunities for hands-on learning, visual support at the secondary level, and real-world connections that go beyond the state standards. Barriers include purchasing a laser-cutter, ventilation and noise issues, time constraints, misalignment with school and district priorities, and a lack of administrative support. All participants indicated that they were interested in additional workshops focused on designing their own digitally fabricated mathematics tools that better align with their grade level(s) and standards. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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23 pages, 1010 KiB

Open AccessArticle

How Do Pre-/In-Service Mathematics Teachers Reason for or against the Use of Digital Technology in Teaching?

by Peter Gonscherowski and Benjamin Rott

Mathematics 2022, 10(13), 2345; https://doi.org/10.3390/math10132345 - 4 Jul 2022

Cited by 2 | Viewed by 2841

Abstract

The role and the availability of digital technology in society is growing, which is why educators need to increasingly more often decide which types of digital technology to integrate into their teaching and when to integrate them. Thus, those decision-making skills need to [...] Read more.

The role and the availability of digital technology in society is growing, which is why educators need to increasingly more often decide which types of digital technology to integrate into their teaching and when to integrate them. Thus, those decision-making skills need to be developed and measured especially for pre-service mathematics teachers. Therefore, we conducted an explorative interview study to understand the portfolio of argumentation on whether to use digital technology in different teaching phases and what criteria are used when making those decisions. Our results are based on ten interviews with pre- and in-service mathematics teachers in Germany. The analysis shows that (1) different levels of argumentation can be distinguished and (2) there are indications that teachers need to be aware of digital technology when deciding whether or not to use digital technology in a teaching setting. In addition, (3) besides the teaching-phase perspective and the learner-perspective, we expanded current research by formalizing the educator-perspective in a list of decision criteria. The compiled list of decision criteria was theoretically validated through the literature. In combination with the applied teaching phase framework and taxonomy of digital technology the list could aid in the development of the decision-making skills and potentially could result in a more reflective use of digital technology by pre-service and in-service teachers. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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20 pages, 993 KiB

Open AccessArticle

Developing Prospective Teachers’ Beliefs about Digital Tools and Digital Feedback

by Annabelle Speer and Andreas Eichler

Mathematics 2022, 10(13), 2192; https://doi.org/10.3390/math10132192 - 23 Jun 2022

Cited by 1 | Viewed by 2649

Abstract

In classrooms today, teachers are asked to support their teaching with digital tools. For this purpose, teachers require not only technological knowledge but also corresponding beliefs about the advantages of digital tools. The development of those beliefs should already be embedded in the [...] Read more.

In classrooms today, teachers are asked to support their teaching with digital tools. For this purpose, teachers require not only technological knowledge but also corresponding beliefs about the advantages of digital tools. The development of those beliefs should already be embedded in the university education of teachers. To this end, we developed a university seminar aimed at fostering prospective teachers’ confidence in the utility of digital tools, using the digital tool STACK as an example. The seminar is based on learning mathematics with the digital tool STACK, independently designing digital tasks with said tool, and finally, reflecting on a teaching experiment with school students using STACK. To make the development of prospective teachers’ beliefs visible throughout the seminar, we worked with different qualitative methods. The results of this case study show that there are four developmental phases of prospective teachers’ beliefs which include an initial situation, a purely positive phase, a disillusionment, and a phase of differentiated beliefs. It becomes apparent that it is possible to develop prospective teachers’ beliefs about digital tools in a positive way. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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11 pages, 1003 KiB

Open AccessArticle

Application of ROC Curve Analysis for Predicting Students’ Passing Grade in a Course Based on Prerequisite Grades

by Alibek Orynbassar, Yershat Sapazhanov, Shirali Kadyrov and Irina Lyublinskaya

Mathematics 2022, 10(12), 2084; https://doi.org/10.3390/math10122084 - 16 Jun 2022

Viewed by 2056

Abstract

Determining prerequisite requirements is vital for successful curriculum development and student on-schedule completion of the course of study. This study adapts the Receiver Operating Characteristic (ROC) curve analysis to determine a threshold grade in a prerequisite course necessary for passing the next course [...] Read more.

Determining prerequisite requirements is vital for successful curriculum development and student on-schedule completion of the course of study. This study adapts the Receiver Operating Characteristic (ROC) curve analysis to determine a threshold grade in a prerequisite course necessary for passing the next course in a sequence. This method was tested on a dataset of Calculus 1 and Calculus 2 grades of 164 undergraduate students majoring in mathematics at a private university in Kazakhstan. The results showed that while the currently used practice of setting prerequisite grade requirements is accurately identifying successful completions of Calculus 2, the ROC method is more accurate in identifying possible failures in Calculus 2. The findings also indicate that prior completion of Calculus 1 is positively associated with success in a Calculus 2 course. Thus, this study contributes to the field of mathematics education by providing a new data-driven methodology for determining the optimal threshold grade for mathematics prerequisite courses. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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18 pages, 954 KiB

Open AccessArticle

Factors Affecting the Use of Digital Mathematics Textbooks in Indonesia

by Tommy Tanu Wijaya, Ying Zhou, Tony Houghton, Robert Weinhandl, Zsolt Lavicza and Farrah Dina Yusop

Mathematics 2022, 10(11), 1808; https://doi.org/10.3390/math10111808 - 25 May 2022

Cited by 18 | Viewed by 4226

Abstract

Digital mathematics textbooks differ from traditional printed textbooks in, among other things, their dynamic structural elements, representing a potential that traditional textbooks cannot fulfil. Notably, dynamic structural elements, i.e., multimodal representations of mathematics, could be of particular importance for learning, which is why [...] Read more.

Digital mathematics textbooks differ from traditional printed textbooks in, among other things, their dynamic structural elements, representing a potential that traditional textbooks cannot fulfil. Notably, dynamic structural elements, i.e., multimodal representations of mathematics, could be of particular importance for learning, which is why the scientific interest in digital mathematics textbooks has increased in recent years and many digital textbooks have been developed. However, research related to predicting teacher usage behavior of digital textbooks is still limited. Therefore, this research aims to analyze the predictors that may influence the intentions of mathematics teachers and the actual usage of digital textbooks by applying the Unified Theory of Acceptance and Use of Technology (UTAUT). Data were collected from 277 teachers in West Java Province, Indonesia, and analyzed using structural equation modeling (SEM). The results indicated that Performance Expectancy (PE) is the biggest significant factor, followed by Social Influence (SI), that influences the Behavioral Intention (BI) of mathematics teachers to use digital textbooks in Indonesia. Effort Expectancy (EE) does not affect the intention to use a digital textbook. In turn, BI has the largest and most significant effect on teachers’ actual usage of digital textbooks. This result contributes to the understanding of the predictors that can increase the use of digital textbooks by mathematics teachers. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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21 pages, 6350 KiB

Open AccessArticle

Using Augmented Reality to Enhance Students’ Representational Fluency: The Case of Linear Functions

by Shuhui Li, Yihua Shen, Xinyue Jiao and Su Cai

Mathematics 2022, 10(10), 1718; https://doi.org/10.3390/math10101718 - 17 May 2022

Cited by 11 | Viewed by 3530

Abstract

Using multiple representations is advocated and emphasized in mathematics and science education. However, many students have difficulty connecting multiple representations of linear functions. Augmented Reality (AR) may affect these teaching and learning difficulties by offering dynamically linked representations. Inspired by this, our study [...] Read more.

Using multiple representations is advocated and emphasized in mathematics and science education. However, many students have difficulty connecting multiple representations of linear functions. Augmented Reality (AR) may affect these teaching and learning difficulties by offering dynamically linked representations. Inspired by this, our study aims to develop, implement, and evaluate an AR-based multi-representational learning environment (MRLE) with three representations of linear functions. The data were collected from 82 seventh graders from two high-performing classes in an urban area in China, through a pre-test, a post-questionnaire, and follow-up interviews. The results reveal that students were satisfied with the AR-based MRLE, which assisted in enhancing their understanding of the real-life, symbolic, and graphical representations and connections among them. Regarding students’ interactions with multiple representations, apparent differences in learning sequences and preferences existed among students in terms of their representational learning profile. In sum, learning in the AR-based MRLE is a complex interaction process between the mathematics content, forms of representations, digital features, and students’ representational learning profile. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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36 pages, 3102 KiB

Open AccessArticle

Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment

by Simon Barlovits, Amélia Caldeira, Georgios Fesakis, Simone Jablonski, Despoina Koutsomanoli Filippaki, Claudia Lázaro, Matthias Ludwig, Maria Flavia Mammana, Ana Moura, Deng-Xin Ken Oehler, Tomás Recio, Eugenia Taranto and Stamatia Volika

Mathematics 2022, 10(10), 1628; https://doi.org/10.3390/math10101628 - 10 May 2022

Cited by 6 | Viewed by 4585

Abstract

The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements [...] Read more.

The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements for distance and online learning tools. As one example for online learning in mathematics education, the ASYMPTOTE system is introduced. It will be freely available by May 2022. ASYMPTOTE is aimed at the adaptive and synchronous delivery of online education by taking a mobile learning approach. Its core is the so-called digital classroom, which not only allows students to interact with each other or with the teacher but also enables teachers to monitor their students’ work progress in real time. With respect to the theoretical framework, this article analyses to what extent the ASYMPTOTE system meets the requirements of online learning. Overall, the digital classroom can be seen as a promising tool for teachers to carry out appropriate formative assessment and—partly—to maintain personal and content-related interaction at a distance. Moreover, we highlight the availability of this tool. Due to its mobile learning approach, almost all students will be able to participate in lessons conducted with ASYMPTOTE. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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20 pages, 2831 KiB

Open AccessArticle

Characterizing Tasks for Teaching Mathematics in Dynamic Geometry System and Modelling Environments

by Carolina Guerrero-Ortiz and Matías Camacho-Machín

Mathematics 2022, 10(8), 1239; https://doi.org/10.3390/math10081239 - 9 Apr 2022

Cited by 1 | Viewed by 2701

Abstract

With an empirical study, we explore the process of designing modeling tasks for teaching mathematics in a Dynamic Geometry environment. We address the research questions: What are the characteristics of the tasks that pre-service teachers design to teach mathematics in digital and modeling [...] Read more.

With an empirical study, we explore the process of designing modeling tasks for teaching mathematics in a Dynamic Geometry environment. We address the research questions: What are the characteristics of the tasks that pre-service teachers design to teach mathematics in digital and modeling environments? What are the activities like that these tasks encourage in students? By means of a qualitative methodology, we characterize the tasks designed by secondary pre-service mathematics teachers and identify the activities that these tasks encourage in students. By analyzing the process of designing and planning a class, we can determine how the characteristics of the modeling tasks are modified based on the software used. In this context, the software also acts as a medium that reflects aspects of the models involved, the objectives of the tasks, and the activities intended for the students. The results contribute to the discussion regarding task design, where technology is a means of supporting the exploration, understanding, and study of different phenomena. Full article

(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)

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