Pre-service Mathematics Education Research Articles

Mathematical beliefs: What topics appear, and how has this changed over time?

This research uses the Systematic Mapping Study (SMS) method to identify knowledge trends in beliefs about the nature of mathematics, learning, and learning mathematics and identify new development opportunities for further research. The Systematic Mapping Study (SMS) method is the initial stage for selecting primary sources in a literature study. The Scopus database was used for SMS, then 171 articles were found ready for further analysis. The results show that mathematical belief has become a current research trend. The keywords are "beliefs." The new trending keyword is "pre-service teachers." The thematic map shows thirteen clusters, where the motivation, pre-service mathematics teachers, mathematics education, beliefs, and attitudes clusters are the motor themes currently a global challenge. This means there are still great opportunities to research this theme to complete the knowledge puzzle. In closing, 41 articles are primary articles related to this theme. Three of them, namely articles from Stipek et al. (2001), Beswick (2012), and Felbrich et al. (2012), can be seen as primary references.

Students’ Engagement in a Mathematical Investigation through Online Problem-Based Learning

The core components of mathematical activity are involved in mathematical investigation: problem formulation, processing of conditions for which there is no clear solution, formulation and justification of conjectures, and generalization. However, introducing mathematical investigation to students is a challenging activity. A crucial aspect of the student’s learning and understanding of the process is the kind and degree of their engagement in the learning activity. This phenomenological study sought to describe how pre-service teachers engaged in an online problem-based learning (PBL) while doing a mathematical investigation (MI). The researcher explored the cognitive, behavioral, and affective components of the 35 pre-service mathematics education students who had their first-hand experience of MI through online PBL. The students were given two contextualized, ill-structured problems, worked in groups, and proposed solutions to the problem. Data from the teachers’ observation notes, students’ learning logs, and the transcripts of the focus group discussions were gathered. Qualitative data analysis suggests that students were involved in peer-to-peer learning that included task-related conflicts, pattern recognition, self-regulation, critical analysis, participation in the learning activity, attention to the tasks, and interaction with the learning community which led to their enjoyment and motivation in conducting MI. The extent of their engagement during the presentation and analysis of the problem, planning and developing a solution, presenting and assessing solution, and summary and debriefing were further analyzed. The findings revealed that while students were initially puzzled at the start of their investigation, they shared, welcomed new information, analyzed it, and valued different approaches to a challenging mathematical problem as they progress with their inquiry. The results also revealed respondents' perspectives on how to manage online PBL. These findings can help teachers design collaborative online activities.

Exploring Conceptions of ‘Number Sense’ Evident in Pre-service Programmes for Primary School Teachers: A Review of Texts Used Across 11 University Programmes

This paper examines the conceptions of ‘number sense’ as promoted in pre-service primary mathematics education courses at 11 South African Higher Education Institutions through the texts used by academics or prescribed for students. While all the participating institutions agree that the development of primary school learners’ ‘number sense’ is central to their mathematics methodology courses and that there is an overwhelming amount of research and literature on ‘number sense’ nationally and internationally, their conceptualisations of the nature of ‘number sense’ vary. Teacher educators, who develop pre-service teacher education courses, were asked to provide the texts, used to underpin the 11 universities’ mathematics education modules in the Bachelor of Education (Foundation and Intermediate Phases) and Post Graduate Certificate in Education (Foundation and Intermediate Phases) programmes. These texts were analysed drawing on Whitacre et al.’s emphasis on three ‘number sense constructs’ identified as Innate Number Sense, Early Number Sense and Mature Number Sense. The results show that there is no common language of description for ‘number sense’ across the 11 universities. This research implies that there is a need to develop a consistent understanding of ‘number sense’ and how it is developed across institutions.

Research on critical thinking of pre-service mathematics education teachers in Indonesia (2015-2023): A bibliometric review

Critical thinking involves being mentally organized and participating in a judgmental process to solve problems. The purpose of this study is to look at the focus of research related to critical thinking of pre-service teacher teachers of mathematics education, especially in Indonesia from 2015 to 2023. The method used in this study is a descriptive bibliometric analysis method. The Scopus database is used to obtain the necessary data. The results of the research show that publications related to the critical thinking of pre-service teacher teachers of mathematics education in Indonesia have increased from 2018 to 2020. Most of the publications were published in conference papers and some were in Q2 journals. The research focus is divided into 4 sections, namely, 1) mathematics teacher , mathematical problems , algebra , and qualitative research ; 2) critical thinking skills , mathematics education , and learning systems ; 3) problem based learning and STEM; 4) data analysis techniques, information analysis. The material that is the focus of research is algebra. New themes for this field are experimental research, digital platforms, quantitative methods, and group theory. The keywords of critical thinking skills are not directly connected with these new themes

Assessing Pre-service Mathematics Education Teachers Deductive Reasoning via Proof Writing in Basic Geometry: The Power of SOLO Taxonomy

Assessing Pre-service Mathematics Education Teachers Deductive Reasoning via Proof Writing in Basic Geometry: The Power of SOLO Taxonomy

Assessing Pre-service Mathematics Education Teachers Deductive Reasoning via Proof Writing in Basic Geometry: The Power of SOLO Taxonomy

Assessing Pre-service Mathematics Education Teachers Deductive Reasoning via Proof Writing in Basic Geometry: The Power of SOLO Taxonomy

The Exploring of Visual Imagery: In their Relation to the Students’ Mathematical Identity

The learning principles usually not visually. The visual understood as an analytical and facilitate an idea. That is the visual is parallel to other representation. The visual ability is not only a tool, or a strategy, or a type of thinking, but also the chain of reasoning to achieve the formal analytic abilities. In this study, the visual ability examined, as a strategy or way of thinking to solve a problem. The question to be addressed is: How do students come to their mathematics identities based on visual imagery? The research conducted at classes of the preservice mathematics education students namely provides evidence for what is their identity relative to their experiences. The results conducted based on explorative studies for the visual abilities. The performance obtained during the teaching and learning, i.e., visualizing and answering analytically or visually, manipulating and answering analytically or visually or by formulas, and visualizing and the answering visually or analytically or based on the conditions. The performance linked to the visual representation and related to intuition underlies formal abilities. The visual perceptions disturbed by prior knowledge, and the level based on optical illusions, so the teaching and learning make a difference between potential and abilities. The analytical affects visual perception and the belief system, so difficult to construct knowledge. However, the level of thinking is different, i.e., not yet formal or new optical illusion. The visual model related to high-level thinking, which distinguished from the analytical thinking model. In the visual model, thinking activities based on the transformations and understood as the other operations in mathematics. The visual model also shows the analytic thinking and hierarchical. The visual and the analytical thinking integrated to develop a richer understanding of mathematical concepts. Through visual thinking, the mental processing was constructed and interpreted as mental objects and processed analytically. The next, exhibits the analytical, consist of the construction process from the visual, namely the reflective abstractions. The visual abilities not related to the duration of courses in the mathematics education department. The longer increases the analytic but in contrary to the visual. Through the learning of the visual abilities, the difficulties in solving the problems decrease, but resistant to the analytic show a specific performance. Visual learning reveals a hierarchical level of the thinking, so the best performance is the highest learning ability. When learning the visual abilities given, the performance increases.

Rate your course! Student teachers’ perceptions of a primary pre-service mathematics education programme

Although research suggests that many pre-service mathematics education programmes are weak interventions having a negligible effect on student teachers’ knowledge, beliefs and attitudes, there is consensus that programmes that model and engage student teachers in reform teaching and learning approaches have the potential to effect positive change in attitudes and knowledge of mathematics. This paper focuses on the perceptions of 345 student teachers regarding their mathematics education programme. The authors consider that in order to further our understanding of the characteristics of an effective pre-service mathematics education programme, the opinions of participating student teachers are fundamental. Participants reported improved mathematical subject matter knowledge and pedagogical content knowledge in addition to greater confidence and decreased anxiety towards mathematics. Programme features such as small group tutorials and interactive engagement were identified as impacting this positive change.

Enactivism as a Powerful Theoretical Framework for Research and Tool to Reflect on My Own Role as a Supervisor

Enactivism, as an interesting and useful theoretical underpinning is gaining traction in Mathematics Education research. It forms the central theme of this paper whose aim is two-fold: first to describe and engage with how elements of enactivism informed a PhD study, both on a theoretical and analytical level, and second to reflect on the enacted role of the supervisor of this study. Despite the inevitable embodied relationship between the supervisor and the supervised PhD project, it is not often written about. This paper thus attempts to address this. The PhD study in question used constructs of enactivism such as autonomy, sense-making, emergence, embodiment and experience to design a pre-service mathematics education programme and then explored the growth of student teachers’ mathematical identity and disposition in their development of becoming mathematics teachers. The PhD supervision process was framed by the enactivist notion that learning and the construction of meaning and knowledge is co-created by the lecturer, the student and the particular context. The role of the author of this paper in the study was that of supervisor. The relationship between a supervisor and his/her student is often complex and multilevelled. This paper argues that this relationship can best be described as one of embodiment and co-emergence. The paper thus starts with the author’s own enactivist ontological perspective vis-à-vis this relationship and how elements of enactivism permeated his practice with regard to the PhD he supervised. The study found enactivism to be a powerful theoretical vantage point from which to develop research instruments that enabled deep and meaningful reflection on teacher practice in the mathematics classroom––and on supervision.

Using HIV&AIDS statistics in pre-service Mathematics Education to integrate HIV&AIDS education

In South Africa, the HIV&AIDS education policy documents indicate opportunities for integration across disciplines/subjects. There are different interpretations of integration/inclusion and mainstreaming HIV&AIDS education, and numerous levels of integration. Integration ensures that learners experience the disciplines/subjects as being linked and related, and integration is required to support and expand the learners' opportunities to attain skills, acquire knowledge and develop attitudes and values across the curriculum. This study makes use of self-study methodology where I, a teacher educator, aim to improve my practice through including HIV&AIDS statistics in Mathematics Education. This article focuses on how I used HIV&AIDS statistics to facilitate pre-service teacher reflection and introduce them to integration of HIV&AIDS education across the curriculum. After pre-service teachers were provided with HIV statistics, they drew a pie chart which graphically illustrated the situation and reflected on issues relating to HIV&AIDS. Three themes emerged from the analysis of their reflections. The themes relate to the need for further HIV&AIDS education, the changing pastoral role of teachers and the changing context of teaching. This information indicates that the use of statistics is an appropriate means of initiating the integration of HIV&AIDS education into the academic curriculum.

Integrating HIV&AIDS education in pre-service Mathematics Education for social justice

Since 1999, many South African education policy documents have mandated integration of HIV & AIDS education in learning areas/disciplines. Policy document research has shown that although South African politicians and managers have produced volumes of eloquent and compelling legislation regarding provision for HIV & AIDS education, little of this is translated into action. The impact of HIV & AIDS permeates the social, economic and political arenas in South Africa. Integration of HIV & AIDS education across disciplines can serve as a strategy to further the ideals of social justice. This paper focuses on how integration in the teaching and learning of Mathematics Education provides opportunities to take action for social justice. The inquiry explores the following question: How can the myth that there is ‘nothing we can do’ about HIV & AIDS, which is linked to social justice issues, be addressed through integration of HIV & AIDS education in Mathematics pre-service teacher education? Drawing on self-study, the work of a Mathematics teacher educator who worked with pre-service teachers to integrate HIV & AIDS education at a higher education institution is described. By considering integration of HIV & AIDS education in Mathematics Education and taking action it is possible to develop strategies which directly relate to social justice. Keywords: integration; mathematics; pre-service teachers; self-study; social justice

Extended analyses: finding deep structure in standard high school mathematics

This paper describes an approach for pre-service or in-service mathematics education that teaches sophisticated mathematics using only the tools of high school mathematics. The idea is to start with a standard problem from high school mathematics and let the solution to this problem serve as a platform for asking good mathematical questions and searching for deeper mathematical structure beyond the obvious “answer” to the question. Surprisingly, it turns out that high school mathematics is remarkably open to this sort of analysis, and the results are more interesting mathematically than one might initially think.

Pre-Service Teacher Training in Mathematics Using Tablet PC Technology

This study focuses on the use of innovative Tablet PC technology in learning and teaching mathematics. Specifically the effects of incorporating Tablet PC technology in pre-service teachers' mathematics education were analyzed. The significant impact of technology use in mathematics education was assessed by evaluating and comparing students' final project and course grades. Grade performance of two groups of students was compared. One group was the treatment group where students extensively used Tablet PCs to work on mathematical investigations and explorations and to create lesson plans and animated games through PowerPoint presentations. The other group was the control group where students worked on identical mathematics investigations and created lesson plans without utilizing any technology. The outcome shows that the technology enhanced group achieved significantly higher scores than the control group. This outcome indicates a greater improvement in the treatment group's understanding of mathematical content versus that of the control group's.

Geometry content knowledge: Is pre-service training making a difference?

Huge financial investments are made annually in teacher training in order to prepare prospective teachers for a career in teaching. The impact of pre-service training on prospective mathematics teachers' (n=124) content knowledge (using the Van Hiele Theory) is investigated. Results seem to indicate that prospective teachers exit their school career with higher geometric understanding than after three years of mathematics content and methodology training or after four years of methodology training. The deterioration in prospective teachers' geometry content knowledge indicates that pre-service education does not assist in maintaining or improving levels of geometric understanding. Possible contributing factors are identified such as the fragmented nature of pre-service teacher education programme and the absence of a long-term strategy connecting teacher education to teaching practice in a meaningful way. The results have serious implications for pre-service mathematics education programmes and some suggestions on the features of an improved programme are made.

Indexing Distributions of Data: Preservice Teachers' Notions of Representativeness

The purpose of the study was to identify strategies used by preservice elementary teachers to index distributions of data. A secondary purpose of the study was to investigate whether representational form influenced the type of representative values constructed. Two hundred eighty‐three preservice teachers were administered a selection of tasks requiring them to construct representative values for a variety of distributional shapes. Participants were asked to provide justifications for their chosen representative measures. Data were analyzed from two perspectives: nature and adequacy of representative measure. Results indicated that when presented with skewed data sets, over half of the participants constructed poorly representative values. Symmetric data sets were best indexed with 67% of participants constructing highly representative values. Representational form played a significant role in determining representative values. Data presented graphically were more likely to be represented using measures of variability than were those presented nongraphically. Conversely, measures of central tendency were more frequently used to represent nongraphical data. The information arising from this study indicates that many preservice teachers construct poorly representative values to index data sets and utilize identical measures of representativeness regardless of distributional shape. The findings of the study highlight the need for exploratory data activities at the preservice level, call for provision of experiences affording insights into construction of representative values, and thus, have implications for the design of preservice mathematics education curricula.

Peer Assessment of Student Constructed Posters: Assessment Alternatives in Preservice Mathematics Education

In this article I discuss a four-year action research project that involved the development of effective assessment tools for preservice mathematics teachers. The focus of the article is on peer assessment in which students reviewed posters created by their peers. The article discusses the strategies that were used and the implications that arose from the project. I argue that peer assessment is an effective tool for assessment in preservice mathematics teacher education but must not be seen as an alternative to teacher-based assessment due to the variability in marks between and within student cohorts. The value of peer assessment is its potential as a learning tool.

Theory, Practice and Reflection: A pre-service primary mathematics education programme

This paper describes a case study investigating the impact of a primary mathematics method programme on pre-service primary teachers' capacity, and willingness to learn and teach mathematics for relational understanding. The programme, a collaborative endeavour between primary schools and university tutors, enables student teachers to practice in an on-going, integrated and consistent manner what they are learning in theory, and to reflect on their experiences. The findings from test, questionnaire and interview data indicate that the weekly cycle of theory, practice and reflection in which student teachers engage enhances their capacity, and provides an incentive for them to learn and teach mathematics for relational understanding.

Practitioner's Research: A Study in Changing Preservice Teachers’ Conceptions About Mathematics and Mathematics Teaching and Learning

Educators involved in the current reform movement in mathematics education recommend that students be actively involved in constructing their own knowledge and developing powerful mathematical concepts. This study suggests how ideas based on constructivist learning theory can be put into practice in a preservice mathematics education class.

Student teachers' subject matter knowledge within the domain of area measurement

This paper describes a research project whose major aim was to evaluate first-year teacher education students' understanding of subject matter knowledge in the domain of area measurement. In contrast to many previous approaches to evaluating teacher education students' subject matter knowledge, the approach adopted in this study not only focused on the student teachers' substantive knowledge but also on their knowledge about the nature and discourse of mathematics, their knowledge about mathematics in society and their dispositions towards mathematics. To this end, each student was clinically interviewed whilst engaged on a set of eight tasks that were developed for the study. The development of the tasks was a major component of the study and this is described in detail. The results of the tasks are given and the paper concludes with a discussion of the findings. This discussion focuses primarily on the implications that these results have for preservice mathematics education courses.

Difficulties of students with limited english language skills in pre-service mathematics education courses

Student teachers who are recent migrants to Australia from non-English-speaking countries experience difficulties in mathematics method courses and in teaching practice, but there are no published reports of research into their difficulties. This paper reports on a preliminary investigation into how students with limited English skills perceive their problems and how they think courses could be adapted to meet their needs. Information was obtained from a questionnaire, by conversation with individual students, by observation of micro-teaching sessions and teaching practice, and from a student counsellor. The factor which most concerned the repondents to the questionnaire was the difficulty which pupils might have in understanding their speech. The results of the study highlight the present lack of resources to provide intensive training for student teachers in the use of specifically mathematical English. The teacher education course was identified as the only vehicle available to them for improving their English.