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Research on Teaching and Learning Mathematics in Early Years and...
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Research on Teaching and Learning Mathematics in Early Years and Teacher Training

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 April 2022) | Viewed by 39360

Special Issue Editors

Prof. Dr. Elena Castro Rodríguez

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Guest Editor
Departamento de Didáctica de la Matemática, University of Granada, Granada, Spain
Interests: early childhood education; primary education; mathematics education; teacher training
Prof. Dr. Ana Belén Montoro Medina

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Guest Editor
Departamento de Didáctica de la Matemática, University of Granada, Granada, Spain
Interests: early childhood education; primary education; mathematics education; teacher training

Special Issue Information

Dear Colleagues,

Research on mathematics education highlights the importance of providing students with solid and in-depth mathematics knowledge in the early years of school for later school and life success. “In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures” (NCTM, 2000, p. 5). A high-quality mathematics education is of paramount importance at these stages, since it is the foundation for more advanced skills. Making this education a reality for all students, especially for children aged from three to twelve years old, is both an essential goal and a significant challenge. Achieving this goal requires raising expectations for students’ learning, developing effective methods to support the students’ mathematics learning, and providing teachers with the quality training they need.

Based on these ideas, we encourage researchers from around the world to share studies for the present Issue of the journal Mathematics entitled “Research on Teaching and Learning Mathematics in Early Years and Teacher Training”. The topic proposed in this Special Issue involves research with students aged three to twelve years old as well as teacher training at these stages.

Prof. Dr. Elena Castro Rodríguez
Prof. Dr. Ana Belén Montoro Medina
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Early Childhood Education
  • Primary Education
  • Mathematics Education
  • Teacher training

Published Papers (11 papers)

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Research

14 pages, 1472 KiB  
Article
A Study of the Complexity of Problems Posed by Talented Students in Mathematics
by Johan Espinoza, José Luis Lupiáñez and Isidoro Segovia
Mathematics 2022, 10(11), 1841; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111841 - 27 May 2022
Viewed by 1401
Abstract
Problem posing and mathematical talent are topics of interest to the community of researchers in Mathematics Education, but few studies reveal talented students’ abilities to solve problem-posing tasks. The data were collected using a problem invention instrument composed of four questionnaires that include [...] Read more.
Problem posing and mathematical talent are topics of interest to the community of researchers in Mathematics Education, but few studies reveal talented students’ abilities to solve problem-posing tasks. The data were collected using a problem invention instrument composed of four questionnaires that include free, semi-structured tasks and problem invention structures. The sample consisted of 23 students considered as mathematically talented and 22 students from a standard public school. The results show that the problems posed by the talent group are more complex than those invented by the standard group. The former are longer and show greater diversity of ideas while also requiring more steps to be solved, presenting a higher level of complexity according to the PISA framework, and requiring significant cognitive effort. In conclusion, the problem invention instrument used and the variables defined enabled us to analyze the complexity of the problems posed by the group of talented students. The statistical analysis performed reinforces the differences found in the complexity of the productions by the two groups studied. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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13 pages, 3266 KiB  
Article
Meanings Expressed by Primary Schoolchildren When Solving a Partitioning Task
by Elena Castro-Rodríguez, Marisel Ferreira, Ana B. Montoro and Juan F. Ruiz-Hidalgo
Mathematics 2022, 10(8), 1339; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081339 - 18 Apr 2022
Cited by 1 | Viewed by 1292
Abstract
This study entailed an in-depth exploration of the meanings identified by a group of 105 fourth year primary schoolchildren when solving a task involving partitioning. The research was based on a semantic triangle consisting of a conceptual structure, representation systems, and sense. The [...] Read more.
This study entailed an in-depth exploration of the meanings identified by a group of 105 fourth year primary schoolchildren when solving a task involving partitioning. The research was based on a semantic triangle consisting of a conceptual structure, representation systems, and sense. The content of children’s answers was analysed qualitatively. One of the most prominent findings was that purposes or usages were recognised based on multiple strategies, new categories of which, not envisaged in earlier research, were defined. Most of the students deployed graphic, verbal, and numerical representation and established relationships among them. Concepts such as the part-whole relationship and fractioning appeared in their description of conceptual structure, although errors were detected in terms of inequities and confusion between numerator and denominator. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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17 pages, 13466 KiB  
Article
Knowledge of Fractions of Learners in Slovakia
by Valéria Švecová, Marta Balgová and Gabriela Pavlovičová
Mathematics 2022, 10(6), 901; https://0-doi-org.brum.beds.ac.uk/10.3390/math10060901 - 11 Mar 2022
Cited by 1 | Viewed by 4436
Abstract
In this research, we set two main goals: to provide empirical data that point to the knowledge of fractions among fifth-grade primary school pupils on a national scale; and to determine the level of knowledge about fractions among university students, including future primary [...] Read more.
In this research, we set two main goals: to provide empirical data that point to the knowledge of fractions among fifth-grade primary school pupils on a national scale; and to determine the level of knowledge about fractions among university students, including future primary school teachers. We used two tests—the national-wide test T5 for the fifth-graders (a research sample of approximately 45,000 pupils), and the modified fraction test based on Sfard’s theory of reification, for the university students (162 students). At the end of the study, we focused on a content analysis of the university students’ solutions. We identified persistent difficulties with concepts of fractions not only by fifth graders but also by future primary school teachers. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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15 pages, 3472 KiB  
Article
Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems
by María del Mar López-Martín, Carmen Gloria Aguayo-Arriagada and María del Mar García López
Mathematics 2022, 10(3), 423; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030423 - 28 Jan 2022
Cited by 2 | Viewed by 2021
Abstract
The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning [...] Read more.
The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning process. The present research aims to assess the mathematical content knowledge of 194 prospective teachers about fraction word problems faced by students at the Primary Education stage, based on the Mathematics Teachers′ Specialized Knowledge (MTSK) model. By means of the preservice teachers’ written answers, we explored their knowledge and identified the associated error to fraction word problems (one-step and multistep) in which the fraction has a meaning as an operator. Preservice teachers showed some difficulties when working with this content, difficulties that were intensified when they solved multistep problems. The most common error founded in both types of problems is related to the meaning of fraction as operator. The results show a weak prior mathematical content knowledge and as a consequence, it is necessary to establish preventive actions in the training degrees since an insufficient mathematical content knowledge prevents them having a proper didactic knowledge. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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19 pages, 2283 KiB  
Article
What Challenges Does the 21st Century Impose on the Knowledge of Primary School Teachers Who Teach Mathematics? An Analysis from a Latin American Perspective
by Claudia Vásquez, Juan Luis Piñeiro and Israel García-Alonso
Mathematics 2022, 10(3), 391; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030391 - 27 Jan 2022
Cited by 6 | Viewed by 4757
Abstract
Curricula are usually pointed out as one of the factors that delimit teacher’s knowledge. In this context, this study analyzes the requirements for teacher’s knowledge that can be found in the curricular guidelines of Mathematics Education in the three Latin American countries belonging [...] Read more.
Curricula are usually pointed out as one of the factors that delimit teacher’s knowledge. In this context, this study analyzes the requirements for teacher’s knowledge that can be found in the curricular guidelines of Mathematics Education in the three Latin American countries belonging to the OECD to educate in sustainability. For this, a content analysis has been carried out that examines the meaning given to the teaching and learning of mathematics that would allow the development of key sustainability competences. The results show a teaching-learning process of mathematics that is not very aligned with education for sustainable development, with a low presence of key competences for sustainability. These results represent a roadmap, both for teacher training institutions and for providing a new educational approach that allows Mathematical Education to contribute to educating in sustainability in Primary Education. This new approach should promote students’ understanding of the different problems (social, economic, and environmental) that we are faced with, as well as the measures that must be adopted to transform and act towards a more sustainable world. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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18 pages, 2118 KiB  
Article
Introducing Tables to Second-Grade Elementary Students in an Algebraic Thinking Context
by María D. Torres, Bárbara M. Brizuela, María C. Cañadas and Antonio Moreno
Mathematics 2022, 10(1), 56; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010056 - 24 Dec 2021
Cited by 2 | Viewed by 3474
Abstract
In this study, we adopted a functional perspective on algebra. Our focus was on tables and how they were first used by second-grade elementary school students (7- and 8-year-olds) when working with functions. This qualitative, exploratory, and descriptive study consisted of five classroom [...] Read more.
In this study, we adopted a functional perspective on algebra. Our focus was on tables and how they were first used by second-grade elementary school students (7- and 8-year-olds) when working with functions. This qualitative, exploratory, and descriptive study consisted of five classroom sessions and two semi-structured interviews, one group and one individual, two weeks apart, focused on tasks involving different functions and uses of tables, with and without labels for headings. In this study, we ask the following research questions: How do children organise values in tables with or without (a priori) labels for headings? What are the regularities (structures) identified by students? Our data revealed that students were able to organise the values of variables by listing them in columns and labelling the headings (i.e., identifying the variables involved). The ways in which children organised the data in tables enabled us to identify the structures they identified as regularities between the variables involved in the functions. More structures were correctly identified in the second interview compared to the first. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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15 pages, 549 KiB  
Article
Early Mathematics Learning and Teaching in Chinese Preschools: A Content Analysis of Teaching Reference Books for Preschool Teachers
by Jin Sun, Han Qin, Kerry Lee, Alfredo Bautista and Qiaoping Zhang
Mathematics 2022, 10(1), 10; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010010 - 21 Dec 2021
Cited by 3 | Viewed by 3263
Abstract
Since the 1980s, Chinese children have consistently been found to perform well in mathematics in cross-national studies of academic achievement. This study is one of the first to systematically examine Chinese children’s early mathematics learning experiences through a content analysis of eight sets [...] Read more.
Since the 1980s, Chinese children have consistently been found to perform well in mathematics in cross-national studies of academic achievement. This study is one of the first to systematically examine Chinese children’s early mathematics learning experiences through a content analysis of eight sets of preschool teacher’s teaching reference books that are commonly used in China. A total of 2038 mathematics activities were selected from these classic teaching reference books and analyzed in terms of (i) suggested teaching approaches, (ii) the mathematical concepts covered, and (iii) their integration of a problem-solving component. The results showed that early mathematics teaching in Chinese preschools emphasize the mastery of key mathematical concepts and skills, while less attention is paid to the application of these key concepts in real-life and non-routine problem-solving settings. Collective teaching was found to be the major teaching mode for early mathematics activities in Chinese preschools, with teachers playing a leading role in the collective teaching activities described in the reference books. However, the teacher’s role is not described in detail in the learning corner activities, and few activities were found to integrate a problem-solving component. The implications of these findings for early mathematics education and the need for a more comprehensive review of mathematics education from the pre-primary to secondary stages are discussed. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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14 pages, 2049 KiB  
Article
Geometric Thinking of Future Teachers for Primary Education—An Exploratory Study in Slovakia
by Gabriela Pavlovičová and Veronika Bočková
Mathematics 2021, 9(23), 2992; https://0-doi-org.brum.beds.ac.uk/10.3390/math9232992 - 23 Nov 2021
Cited by 1 | Viewed by 6644
Abstract
Various studies show that the level of knowledge achieved by pupils is influenced by the level of knowledge of their teachers. In this article, we focus on geometric thinking and the solutions for geometric tasks through a study of future teachers of primary [...] Read more.
Various studies show that the level of knowledge achieved by pupils is influenced by the level of knowledge of their teachers. In this article, we focus on geometric thinking and the solutions for geometric tasks through a study of future teachers of primary education. The research sample consisted of 59 master’s students from the Teacher Training for Primary Education (TTPE) program. To determine the level of geometric thinking of TTPE students, the van Hiele geometric test was used. Two geometric multi-item tasks were proposed and the students’ solutions to these tasks were quantitatively and qualitatively evaluated. The main goal was to analyze students’ misconceptions while solving tasks and to compare and reveal the connections between their solutions and their achieved level of geometric thinking. A statistical implicative analysis was used for a deeper analysis, namely the statistical software C.H.I.C. The research findings show that more than 40% of TTPE students in the research sample did not reach the required level of geometric thinking. The achieved level of the geometric thinking of students is also influenced by the type of high school education. We observed problems with understanding the concept of the triangle and square in TTPE students. The connections between the solutions of two geometric tasks and the achieved level of geometric thinking were also revealed. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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17 pages, 1097 KiB  
Article
The Initial Algebraic Knowledge of Preservice Teachers
by Alberto Zapatera and Eduardo Quevedo
Mathematics 2021, 9(17), 2117; https://0-doi-org.brum.beds.ac.uk/10.3390/math9172117 - 01 Sep 2021
Cited by 3 | Viewed by 2064
Abstract
Early algebra proposes to incorporate algebra in primary school from the first years of schooling. The success of this incorporation depends, to a large extent, on the training of teachers, so the objective of this article is to study whether the degree of [...] Read more.
Early algebra proposes to incorporate algebra in primary school from the first years of schooling. The success of this incorporation depends, to a large extent, on the training of teachers, so the objective of this article is to study whether the degree of algebraic knowledge of student teachers at the beginning of their training. To conduct this, 106 preservice teachers were given a questionnaire. This survey is based on two daily life situations. They had to propose tasks to develop algebraic reasoning in primary school students. Most of the participants designed tasks in which they assigned specific values to the indeterminate ones and solved them arithmetically. In this way, they transformed open situations and numerous opportunities to promote algebraic thinking in students through the generalization and representation of relationships and functions into closed single-solution problems that do not promote algebraic thinking. We can see from the results that the participants’ algebraic knowledge is insufficient. Therefore, it is necessary to include in their training process the programs and experiences that will allow them to design tasks in order to detect and promote algebraic thinking in their future students. Sequences of tasks are presented to develop both situations by generalizing and representing relationships and functions, which can serve as a starting point for future training programs and experiences. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
18 pages, 3133 KiB  
Article
Using Wolfram Alpha with Elementary Teacher Candidates: From More Than One Correct Answer to More Than One Correct Solution
by Sergei Abramovich
Mathematics 2021, 9(17), 2112; https://0-doi-org.brum.beds.ac.uk/10.3390/math9172112 - 01 Sep 2021
Cited by 3 | Viewed by 4781
Abstract
The paper is a reflection on the author’s work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the [...] Read more.
The paper is a reflection on the author’s work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the diversity of mathematical ideas behind a contextual question asked by a second-grade pupil allowing for multiple solution strategies to be used in addressing the question. The second issue deals with the use of Wolfram Alpha in aiding different mathematical features of this demonstration. The paper is congruous with mathematics teaching standards used across six continents and illustrated by reflective comments of the author’s students regarding their mathematics teacher education experiences. Teaching ideas shared in the paper may be of interest to instructors who want to explore elementary mathematics in depth with teacher candidates. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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20 pages, 1843 KiB  
Article
Building Preservice Teachers’ Diagnostic Competence: An Exploratory Study in the Domain of Fractions
by Ji-Eun Lee, Byungeun Pak and Woong Lim
Mathematics 2021, 9(16), 1870; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161870 - 06 Aug 2021
Cited by 2 | Viewed by 2229
Abstract
In this study, we explored elementary preservice teachers’ (PSTs’) competence to make diagnostic inferences about students’ levels of understanding of fractions and their approaches to developing appropriate tiered assessment items. Although recent studies have investigated beginning teachers’ diagnostic competency, teachers’ ability to design [...] Read more.
In this study, we explored elementary preservice teachers’ (PSTs’) competence to make diagnostic inferences about students’ levels of understanding of fractions and their approaches to developing appropriate tiered assessment items. Although recent studies have investigated beginning teachers’ diagnostic competency, teachers’ ability to design and evaluate diagnostic assessment items has remained largely underexplored. Fifty-seven PSTs, who enrolled in a mathematics methods course at a midwestern university in the U.S., participated in developing and attempting to differentiate diagnostic assessment items considering individual students’ varied levels of understanding. An inductive content analysis approach was used in identifying general patterns of PSTs’ approaches and strategies in designing and revising tiered assessment items. Our findings revealed the following: (a) the PSTs were well versed in students’ cognitive difficulties; (b) when modifying the core questions to be more or less difficult, the PSTs predominantly used strategies related to procedural fluency of the questions; and (c) some strategies PSTs used to modify questions did not necessarily yield the intended level of difficulty. Further, we discussed the challenges and opportunities teacher education programs face in teaching PSTs how to effectively design tiered assessment items. Full article
(This article belongs to the Special Issue Research on Teaching and Learning Mathematics in Early Years and Teacher Training)
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