Research

18 pages, 1135 KiB

Open AccessArticle

Multiple-Solution Tasks in Pre-Service Teachers Course on Combinatorics

by Ingrid Semanišinová

Mathematics 2021, 9(18), 2286; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182286 - 16 Sep 2021

Cited by 4 | Viewed by 2852

In the paper, we present a study devoted to the utilization of multiple-solution tasks (MSTs) in combinatorics as a part of a pre-service teachers course on didactics of mathematics from the view of the mathematics teachers’ specialized knowledge (MTSK) theoretical framework. The study [...] Read more.

In the paper, we present a study devoted to the utilization of multiple-solution tasks (MSTs) in combinatorics as a part of a pre-service teachers course on didactics of mathematics from the view of the mathematics teachers’ specialized knowledge (MTSK) theoretical framework. The study was carried out over the standard course of a summer semester in 2021. The course was attended by 13 pre-service teachers (PSTs). It was carried out online, due to COVID-19 restrictions. Ten combinatorial multiple-solution tasks were assigned to the PSTs. Analyzing pre-service teachers solutions to these tasks, we sought the description and better understanding of the combinatorial knowledge of the topic from the perspective of MSTK. The results revealed some critical aspects of mathematical knowledge in combinatorics that pre-service teachers education should focus on. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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20 pages, 9627 KiB

Open AccessFeature PaperArticle

Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry

by Mária Kmetová and Zuzana Nagyová Lehocká

Mathematics 2021, 9(18), 2185; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182185 - 07 Sep 2021

Cited by 4 | Viewed by 9672

Abstract

Creating a mental image of our spatial environment is a key process for further abstract geometric thinking. Building a mental representation can be understood as a part of the process of visualisation. From the wide concept of visualisation, in this article, we will [...] Read more.

Creating a mental image of our spatial environment is a key process for further abstract geometric thinking. Building a mental representation can be understood as a part of the process of visualisation. From the wide concept of visualisation, in this article, we will focus on the part where the mental representation of spatial relations, mental objects and mental constructions are created, and their manifestations as a 3D physical object and its plane representations arise. Our main goal is to follow the transition between 2D and 3D representations of physical objects and also to observe how and when such a transition happens in students’ thinking. For that purpose, we also use Tangram, because manipulation with the Tangram pieces in space and filling out planar figures by them indicates the transition between 3D and 2D. Our research, using an action research methodology, was conducted on the students of three 5th grade primary school classes as a part of a larger long-term project. We pointed out a relationship between spatial abilities and the perception of 2D–3D relationships in students’ mind. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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14 pages, 475 KiB

Open AccessArticle

Characterizing Mathematics Learning in Colombian Higher Distance Education

by Elizabeth Martinez-Villarraga, Isabel Lopez-Cobo, David Becerra-Alonso and Francisco Fernández-Navarro

Mathematics 2021, 9(15), 1740; https://0-doi-org.brum.beds.ac.uk/10.3390/math9151740 - 23 Jul 2021

Cited by 1 | Viewed by 1748

Abstract

The aim of this work is to characterize the process of constructing mathematical knowledge by higher education students in a distance learning course. This was done as part of an algebra course within engineering degrees in a Colombian university. The study used a [...] Read more.

The aim of this work is to characterize the process of constructing mathematical knowledge by higher education students in a distance learning course. This was done as part of an algebra course within engineering degrees in a Colombian university. The study used a Transformative Sequential Design in mixed methods research. The analysis also determined the kinds of mathematical knowledge attained by the students and its relationship to the Colombian social and cultural context. The students acquired declarative, procedural, and conditional knowledge, while the learning strategies were often superficial. In a context where power is distant, students take on a passive approach to learning despite being highly respectful towards the educator. Thus, the educational system has the educator at the center. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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23 pages, 665 KiB

Open AccessArticle

From Teacher of Nations to Teacher of Mathematics

by Alena Hošpesová, Jarmila Novotná, Naďa Vondrová, Hana Moraová and Marie Tichá

Mathematics 2021, 9(14), 1583; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141583 - 06 Jul 2021

Cited by 2 | Viewed by 2108

Abstract

The article provides an overview of research focusing on pre- and in-service teacher education, conducted in the Czech Republic by teams of researchers of which the authors were members. It employs the methodology of a qualitative meta-analysis of studies aimed at distinguishing key [...] Read more.

The article provides an overview of research focusing on pre- and in-service teacher education, conducted in the Czech Republic by teams of researchers of which the authors were members. It employs the methodology of a qualitative meta-analysis of studies aimed at distinguishing key areas of research and their main results. Twenty-one studies were analyzed, 11 of which targeted pre-service teachers and 10 in-service teachers. The article briefly describes the historical and cultural context that informs mathematics education in the Czech Republic. It also elaborates on key theoretical concepts shared by the studies analyzed, including teachers’ pedagogical content knowledge, competence and pedagogical reflection. The meta-analysis uncovered a common core of the studies in their focus on the process of professionalization for mathematics teachers in its three dimensions: professional vision, professional knowledge, and professional action. Six core research strands are identified within the group of studies: lesson study as a means of developing teachers’ pedagogical content knowledge; joint reflection; professional vision and its development; culture of problem solving and teacher development; problem posing to support subject-didactic competence and teachers’ competencies for content and language integrated learning and culturally responsive teaching. The article outlines the methodology and main results of the studies in each research strand and discusses their implications. Finally based on the meta-analysis, a discussion of the core concepts of teacher reflection, problem solving and problem posing is developed. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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27 pages, 4244 KiB

Open AccessArticle

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

by Mária Slavíčková

Mathematics 2021, 9(12), 1319; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121319 - 08 Jun 2021

Cited by 5 | Viewed by 2297

Abstract

This paper presents a long-term study of Preservice Mathematics Teachers (PMTs) at the Faculty of mathematics, physics and informatics, Comenius University in Bratislava (FMFI UK), focusing on the implementation of digital technologies (DT) into the teaching of theoretical and practical (or applied) subjects. [...] Read more.

This paper presents a long-term study of Preservice Mathematics Teachers (PMTs) at the Faculty of mathematics, physics and informatics, Comenius University in Bratislava (FMFI UK), focusing on the implementation of digital technologies (DT) into the teaching of theoretical and practical (or applied) subjects. We conducted parallel research into two aspects, one on Calculus lessons as a theoretical subject, another on the Financial Mathematics module as an applied subject. The implementation of DT and the way this was measured varied from year to year and also in the method of implementation into the aforementioned subjects. The methods of implementation and the results are briefly described, and a comparison of these two subjects in the PMTs’ preparation is also discussed. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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26 pages, 462 KiB

Open AccessArticle

Recent Nordic Research in Mathematics Education Illustrated by Examples from NORMA17

by Barbro Grevholm

Mathematics 2021, 9(8), 803; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080803 - 07 Apr 2021

Viewed by 2257

Abstract

A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of [...] Read more.

A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers, teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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24 pages, 1070 KiB

Open AccessArticle

Ethical Reasoning in Mathematics: New Directions for Didactics in U.S. Mathematics Education

by Jordan Register, Michelle Stephan and David Pugalee

Mathematics 2021, 9(8), 799; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080799 - 07 Apr 2021

Cited by 6 | Viewed by 3392

Abstract

In this article we analyze the current state of the didactics of mathematics in the U.S. as it relates to research on equity. The sociopolitical turn in U.S. mathematics education resulted in a push for critical mathematics pedagogies (CMPs) in which predominantly marginalized [...] Read more.

In this article we analyze the current state of the didactics of mathematics in the U.S. as it relates to research on equity. The sociopolitical turn in U.S. mathematics education resulted in a push for critical mathematics pedagogies (CMPs) in which predominantly marginalized populations of students explore social injustices through mathematics. We argue that mathematics education for equity must access broader populations of students and develop students’ ethical reasoning skills to build an ethical and equitable future. To address didactical limitations in U.S. mathematics education, we introduce the Ethical Reasoning in Mathematics Framework (ERiM) as a tool to analyze high school students’ ethical reasoning in real-world mathematics tasks. Using data from the initial phase of a Design Research project with students of privilege, we show how the ERiM Framework can be used to design lessons that elicit students’ critical math consciousness (CMC). We end the article with design implications and recommendations for future research on the didactics of equitable mathematics. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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19 pages, 3259 KiB

Open AccessFeature PaperArticle

Revisiting the French Didactic Tradition through Technological Lenses

by Michèle Artigue and Luc Trouche

Mathematics 2021, 9(6), 629; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060629 - 16 Mar 2021

Cited by 9 | Viewed by 2877

Abstract

There is, in France, a long-term tradition of research in the didactics of mathematics. In this paper, we revisit this tradition using, as a specific lens, the research carried out on the educational use of digital tools and resources for teaching and learning [...] Read more.

There is, in France, a long-term tradition of research in the didactics of mathematics. In this paper, we revisit this tradition using, as a specific lens, the research carried out on the educational use of digital tools and resources for teaching and learning mathematics. We first briefly introduce this tradition and the three main theories at the base of it: the theory of didactical situations, the theory of conceptual fields, and the anthropological theory of the didactic. Then, considering three different technological lenses, i.e., dynamic geometry environments, computer algebra systems, and digital resources, we show how these theories and the long-term connection established in this tradition with the fields of cognitive ergonomics and computer sciences have influenced technological research and its outcomes. We also show that, conversely, didactic technological research has led to original and influential theoretical constructions, such as the instrumental approach and the documentational approach to didactics, and that it has contributed in a substantial way to the opening of this didactic tradition to other didactic cultures and other communities, beyond the didactic one. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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19 pages, 282 KiB

Open AccessArticle

Instructional Moves that Increase Chances of Engaging All Students in Learning Mathematics

by Janette Bobis, James Russo, Ann Downton, Maggie Feng, Sharyn Livy, Melody McCormick and Peter Sullivan

Mathematics 2021, 9(6), 582; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060582 - 10 Mar 2021

Cited by 7 | Viewed by 6204

Abstract

Despite the construct of challenge being recognized as an essential element of mathematics instruction, concerns have been raised about whether such approaches benefit students with diverse academic needs. In this article, we focus on the beliefs and instructional practices of teachers teaching students [...] Read more.

Despite the construct of challenge being recognized as an essential element of mathematics instruction, concerns have been raised about whether such approaches benefit students with diverse academic needs. In this article, we focus on the beliefs and instructional practices of teachers teaching students in the first three years of school (5 to 8 years of age). These teachers participated in professional learning focused on challenging mathematical tasks differentiated through their open-ended design and the use of enabling and extending prompts. The instructional practices are explained using the Theory of Didactical Situations. Questionnaire data from pre-intervention (n = 148) and post-intervention (n = 100) groups of teachers indicated that teachers in the post-intervention group held more negative beliefs than those in the pre-intervention group about the capability of instructional approaches involving a priori grouping of students by performance levels. Interviews with ten teachers from the post-intervention group revealed and characterized the ways teachers employed open-ended tasks with enabling and extending prompts to engage all learners. Findings reveal that teachers knowing their students as individual learners accompanied by knowledge of a range of teaching practices to differentiate instruction are central to engaging all learners. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

17 pages, 526 KiB

Open AccessArticle

The Verbal Component of Mathematical Problem Solving in Bilingual Contexts by Early Elementary Schoolers

by Pilar Ester, Isabel Morales, Álvaro Moraleda and Vicente Bermejo

Mathematics 2021, 9(5), 564; https://0-doi-org.brum.beds.ac.uk/10.3390/math9050564 - 06 Mar 2021

Cited by 5 | Viewed by 3020

Abstract

The main aim of the present study is to analyze the differences that may exist when students address the resolution of verbal problems in their mother tongue and in the language of instruction when these are different. We understand that knowing the type [...] Read more.

The main aim of the present study is to analyze the differences that may exist when students address the resolution of verbal problems in their mother tongue and in the language of instruction when these are different. We understand that knowing the type of verbal problems and their semantic structure can be helpful for students’ contextual and mathematical understanding and will allow teachers to improve instruction during the first years of elementary education in bilingual schools specialized in the area of second language acquisition as well as in CLIL (Content and Language Integrated Learning). This study shows how children, as they are acquiring a greater command of the second language, show similar effectiveness to those students who work on mathematics in their mother tongue. This transversal study was conducted on 169 bilinguals studying in international schools. The sample was made up of 80 1st grade students (39 girls, mean age of 7.1 years and 41 boys, mean age of 7.3 years); and 89 2nd grade students (38 girls, mean age 8.2 years, and 51 boys, mean age 8.2 years). The exploratory analyses let us show how 1st grade students demonstrate lower effectiveness in solving problems when they do it in a second language, compared to 2nd grade students whose effectiveness is higher in carrying them out. It is also relevant that in first graders, the largest number of errors are found in the simplest tasks as students’ effectiveness is less when they are taught in a second language, since it takes them longer to create effective resolution models. This fact will allow us to reconsider appropriate strategies and interventions when teaching mathematics in bilingual contexts. Full article

(This article belongs to the Special Issue Highlights of Research in the Didactics of Mathematics: The Insider’s Perspective)

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