Mathematics Teacher Education Programs Research Articles

Unpacking pre-service teachers’ conceptualization of logarithmic differentiation through the APOS theory

Logarithmic differentiation is an effective method that aids the process of finding the derivatives of complex exponential functions. However, there has been a scarcity of studies, particularly in the South African context, that have provided evidence on pre-service mathematics teachers’ understanding of the concept of logarithmic differentiation. This study explored pre-service teachers’ conceptualization of logarithmic differentiation through action-process-object-schema (APOS) theory. We employed a qualitative case study design involving 90 first-year pre-service teachers enrolled in a mathematics teacher education program at a university in South Africa’s Eastern Cape Province. Overall, the analysis showed that 63.9% of the participants demonstrated a substantial understanding of logarithmic differentiation processes, including 46.1% who had reached the schema stage. Nonetheless, common misconceptions and errors persisted, particularly among those who operated at action and beginning process stages. Errors and misconceptions such as the misapplication of differentiation rules, calculation errors in combining derivatives, and conceptual misunderstanding were evident. These findings highlight the need for mathematics teacher preparation programs to emphasize both conceptual and procedural understanding of differentiation. Achieving this goal may involve targeted instruction on relevant foundational concepts, continuous professional development, and integration of active learning strategies, such as the activities, classroom discussions, and exercises (ACE) teaching cycles to address common misconceptions.

The Process of Teaching and Learning from the Views of Prospective Mathematics Teachers: The Case of Algebraic Inequalities

This study explores the views of prospective mathematics teachers on the process of teaching and learning about algebraic inequalities. Phenomenology, one of the qualitative research methods, was used in the study. The participants of the study consisted of 6 prospective middle school mathematics teachers studying in the last year of the Elementary Mathematics Teacher Education Program of a university in the Central Anatolia Region of Türkiye in the spring semester of the 2021-2022 academic year. Data were collected through semi-structured interviews. The obtained data were analyzed using content analysis, one of the qualitative analysis methods. As a result of the analysis of the interviews with the prospective middle school mathematics teachers, three main themes were obtained. Teaching inequalities, the difficulties that students may experience in inequalities, and the methods that can be used to overcome difficulties were the main categories that emerged. Direct quotations from the prospective teachers’ views were also included in the presentation of the findings. As a result of the study, it is recommended that more practice should be included in teacher education programs to improve prospective mathematics teachers' knowledge and experience of meaningful learning and overcoming difficulties.

Changes in Mathematics Teacher Training in Colombia

An analysis of the evolution of mathematics teacher training plans in Colombia is presented, taking the University of Tolima as a case study. The purpose is to analyse and describe the curricular changes in undergraduate mathematics teacher training at the University of Tolima. It is a descriptive, qualitative, ex-post-facto case study, based on the content analysis of curricular changes. Seven curricula approved between 1970 and 2020 were analysed. Interdisciplinary training experiences significant variations in the free choice of subjects and research topics across different study plans. There is evidence that the number of mathematics subjects has gradually decreased and in their place didactics and pedagogical practices have increased. The study contributes to a deeper understanding of the evolution and current state of the mathematics teacher education program at the University of Tolima, offering valuable insights for future curriculum development and educational policy-making.

Publisher Correction: Professionalisation for inclusive mathematics–teacher education programs and changes in pre-service teachers’ beliefs and self-efficacy

Publisher Correction: Professionalisation for inclusive mathematics–teacher education programs and changes in pre-service teachers’ beliefs and self-efficacy

Professionalisation for inclusive mathematics—teacher education programs and changes in pre-service teachers’ beliefs and self-efficacy

Traditionally, in many countries there exist different teacher education programs for special education and for regular or inclusive education, not at all with similar underlying paradigms for teaching and learning or similar definitions and understanding of the term inclusion. In this context, one central question is how to define inclusive mathematics education, how to address the manifold aspects, and how to reduce discrimination and marginalization. On the one hand, teacher education programs might focus on diverse groups and specific students, like students with special needs and integrate important questions of special education. On the other hand, teacher education programs might take explicitly a broader perspective, considering the mathematical learning of all students and not taking a specific focus. In this contribution we present research results of the project ProViel (‘professionalisation for diversity’) to discuss how a teacher education program can be designed to address both with the underlying paradigm of making mathematics accessible for all students, and what role pre-service teachers’ beliefs as well as their self-efficacy might play. The project aimed at subject-specific concept development and research concerning teacher education for inclusive mathematics on the primary level, considering different points in time within the whole education program. Quantitative data of pre-service teachers’ beliefs and self-efficacy have been analysed, while they participated in different university courses and a practical phase at school. Key findings of this study are, that pre-service teachers’ beliefs about student achievement and their self-efficacy for inclusive mathematics teaching changed during the teacher education program.

The effects of functional moves in teacher questioning on students’ contextualization of mathematical word problem solving

AbstractPosing purposeful questions is one of the most effective teaching practices (NCTM in Principles to actions: Ensuring mathematics success for all. National Council of Teachers of Mathematics, 2014). Although the types and functions of teacher questioning have been abundantly studied, research on the role of teacher questioning in students’ contextualization process as they solve word problems is rather scarce. This study was conducted to investigate the function of six elementary preservice teachers’ questioning, its impact on students’ contextualization, as well as the successes and difficulties of enacting questioning. The collected data were analyzed using thematic analysis. The findings indicated that the implementation of task clarification (TC) moves effectively enhanced contextualization only when students possessed a relatively strong sense of agency while solving word problems. Furthermore, when students’ attentional focus was not appropriately redirected by the functional moves, including procedural understanding (PU), making connections (MC), the rationale behind a strategy (RA), and an alternative strategy (AS), their understanding of the contextual features and construction of mathematical relationships in word problem solving could not be refined. Implications for field experience design and future research on the quality of teacher questioning in mathematics teacher education programs are discussed.

Mapping teachers’ perspectives on culturally responsive pedagogy in mathematics: from academic achievement to insights and opportunities

ABSTRACT Following the seminal work of Gloria Ladson-Billings, research on culturally responsive pedagogy (CRP) has, in recent years, expanded significantly. Ladson-Billings proposes three elements of CRP: academic achievement, cultural competence, and sociopolitical consciousness. Nevertheless, in mathematics education research on CRP, the sociopolitical consciousness element is often under-explored or even absent. This paper began as an investigation of how Ladson-Billings’ three elements could be used to examine prospective and practicing teachers’ (PPTs') perspectives on CRP, prior to their participation in a professional development course on CRP in the mathematics classroom. Thirty-one participants from three separate offerings of the course responded in writing to a set of open questions about CRP (in general and in mathematics). Thematic data analysis pointed to the complexities of categorising the data based primarily on Ladson-Billings’ three elements. In addition, our analysis indicated five components underpinning participants’ responses: challenges; opportunities; fears; resistance; insights. We conclude with a revised conceptualisation of CRP for mathematics teacher education programmes aimed at supporting PPTs’ development of their CRP-related knowledge, skills, and dispositions.

Toward proficiency: Developing a multiplication mathematical content knowledge test for pre-service mathematics teachers in Indonesia and Türkiye

This study aimed to develop a specific Mathematical Content Knowledge (MCK) test focused on multiplication for pre-service mathematics teachers in Indonesia and Türkiye. No assessment tool exists to measure MCK related to multiplication among pre-service mathematics teachers. We used convenience sampling to obtain data from third- and fourth-year pre-service teachers in Indonesian and Turkish mathematics teacher education programs. The test items were administered to 423 Indonesian pre-service mathematics teachers and 413 Turkish pre-service mathematics teachers, and their responses were analyzed using factor analysis. The MCK test was found to be reliable, with 18 items that were grouped into four components: procedural knowledge of multiplication (C1), understanding of multiple representations (C2), conceptual knowledge of multiplication (C3), and anticipating students' thinking (C4). The study results suggest that a valid MCK test helps evaluate multiplication in these four components. Additionally, the study findings indicate that Indonesian pre-service teachers score higher in the C1 and C4 categories, while Turkish pre-service teachers score higher in the C2 and C3 categories.

Changes in students’ mental constructions of function transformations through the APOS framework

This study aims to examine the changes in students’ mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in mathematics teacher education program. The data consisted of video records of the designed teaching sessions, students’ worksheets and the researcher’s field notes. The results indicated that ACE teaching cycle was effective in developing students’ mental constructions of function transformation through sequential activities. Even though all the students initially did not reveal evidence for sufficient theoretical or practical knowledge on function transformation, which was evidence of their action level, through the process, it became evident that all the students provided evidence regarding at least their process level of function transformations. Some of the students also showed evidence related to their object levels of function transformations.

Middle Grades Math with Ice Cream Sundaes: Connecting Math to the Real World

This qualitative case study presents findings related to the experiences of one preservice teacher as they attempted to create student-centered math experiences in their middle school mathematics classroom. The participant was enrolled in a graduate secondary mathematics teacher education program and was student teaching at a middle school. In this research study, I asked, “How does one preservice middle grades mathematics teacher understand ways to connect math to the real world?” The data collected included interviews, classroom artifacts, and researcher memos. The data were analyzed using thematic analysis. The findings suggested that, although the preservice teacher wanted to infuse real world experiences in their lessons, they were unsure of ways to do so; they struggled to infuse a real world context in math at the middle school level. This study draws attention to the importance of ensuring that middle grades mathematics educators receive instruction on ways to help their students make connections to the real world and thus create student-centered mathematics classrooms.

Popular conceptions of democracy in a mathematics teacher-education programme

While the meaning of democracy remains multi-faceted centuries after the concept was first conceived of and subsequently formulated, democratic principles have spread to the extent of bringing about democratisation in all fields of education. Thus, with this study we sought to examine the popular conception of democracy in mathematics-education programmes at South African universities. A qualitative research approach and a case study research design were used in this study. Six mathematics teacher educators and 75 second- to fourth-year mathematics education student teachers from 3 different universities constitute the sample for the study. The findings from the study revealed that participants had a contested notion of democracy, since the majority understood it as involving deliberative participation, a shared decision-making process, as well as freedom of expression. Based on the findings of the study, it was concluded that participants were aware of what democracy should look like and were willing to live according to democratic tenets. This understanding was, however, greatly influenced by their experiences and way of life in a democratic South Africa.

Preparing prospective secondary teachers to teach mathematical reasoning and proof: the case of the role of examples in proving

Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research project developed a capstone course Mathematical Reasoning and Proving for Secondary Teachers and systematically studied its effect on PSTs’ content and pedagogical knowledge specific to proof. This paper focuses on one course module—Quantification and the Role of Examples in Proving, a topic which poses persistent difficulties to students and teachers alike. The analysis suggests that after the course, PSTs’ content and pedagogical knowledge of the role of examples in proving increased. We provide evidence from multiple data sources: pre-and post-questionnaires, PSTs’ responses to the in-class activities, their lesson plans, reflections on lesson enactment, and self-report. We discuss design principles that supported PSTs’ learning and their applicability beyond the study context.

Study of the Effects of a Mathematics Teacher Education Program: What Went Wrong?

Abstract If we want to understand what works in studies of teacher education programs, we also need to understand what does not work. In this article, we discuss why a study evaluating the effects of an education program on implementation practices yielded unexpected results. Interviews with a sample of teacher graduates from the program revealed that the program did have effects on implementation practices that were not evident in the original study. These effects are in the form of increased student participation, teamwork and the conception of error as opportunity. The instrument and procedures of the original study did not allow these effects to be seen. The impact sheet to this article can be accessed at 10.6084/m9.figshare.22339567.

Preservice Teachers’ Noticing Skills in Relation to Student Misconceptions in Algebra

<p style="text-align:justify">Many students have misconceptions about mathematics, so preservice teachers should be developing the skills to notice mathematical misconceptions. This qualitative study analyzed preservice teachers' skills in noticing student misconceptions about algebra, according to three aspects of noticing found in the literature: attending, interpreting and responding. Participants in this study were seven preservice teachers from one university in the capital of Aceh province, Indonesia, who were in their eighth semester and had participated in teaching practicums. Data was collected through questionnaires and interviews, which were analyzed descriptively. The results revealed the preservice teachers had varying levels of skill for the three aspects of noticing. Overall, the seven preservice teachers' noticing skills were fair, but many needed further development of their skills in interpreting and responding in particular. This university’s mathematics teacher education program should design appropriate assessment for preservice teachers’ noticing skills, as well as design and implement learning activities targeted at the varying needs of individual preservice teachers regarding noticing student misconceptions, in order to improve their overall teaching skills.</p>

A Quantitative Assessment of High School Math Teacher's Technological Pedagogical and Content Knowledge

The applicability of digital technologies is increasing boundlessly and so are the opportunities of the end-users, with ample opportunities to embed these technologies in the teaching and learning process. Nonetheless, classroom adoption of technologies, particularly in mathematics remains on the lower end of innovation in teaching and learning. To remedy this deficit, education policy makers can take advantage of the existing Technological Pedagogical and Content Knowledge (TPACK) framework. After multiple analyses of Iranian Teachers' self -assessed TPACK, this study places them within the TPACK spectrum, and provides evidence-based policy recommendations. We provide avenues to enhance the effectiveness of mathematics teacher education programs in Iran. We accomplish this by surveying 399 teachers; we then quantify their self-reported assessment of their TPACK; we then determine how their self-reported assessment related to each construct, and their mediating roles, of technological pedagogical knowledge (TPK), technological content knowledge (TCK) and pedagogical content knowledge (PCK). We achieve this by means of structural equation modeling. Our results suggest the existence of high correlations among TPACK components. Additionally, PCK, TPK and TCK had mediating roles in the relationship between three main constructs TK, CK and PK.

Experiences of preservice mathematics teachers during their education in times of pandemic.

Due to the COVID-19 pandemic, educational institutions at all levels closed their doors and began to operate remotely. In this paper, we analyze the educational experiences of preservice mathematics teachers (PMTs) enrolled in mathematics teacher education programs from three South American universities, as the pandemic was unfolding. An exploratory study was conducted, based on an inductive and thematic qualitative text analysis of narratives written by 24 PMTs. Based on the study, we report on the following aspects: (1) experiences of PMTs in the passage to remote education (RE) mode (considering characteristics of remote classes-interactions, the rhythm of the class, teaching work-time management, home-classroom fusion, and physical and psychological discomfort), and (2) opportunities and limitation experienced by PMTs in relation to the use of technologies. The results of the study suggest the need to rethink teacher education programs regarding the integration of technologies in mathematics classes, the opportunities offered by hybrid education, and teacher education for distance teaching.

한국과 미국 예비 초등교사는 자연수 덧셈과 뺄셈 연산에 대한 학생의 수학적 전략과 오류를 어떻게 분석하는가?

This study explores and compares Korean and U.S. elementary preservice teachers’ analytic approaches of students’ addition and subtraction computational strategies. Twenty-six Korean and twenty U.S. elementary preservice teachers participated in the study. Participants were asked to analyze mathematical approaches and errors from students’ addition and subtraction operations. Preservice teachers’ written documents were analyzed by applying open coding and inductive coding based on the grounded theory. As a result, the pattern of error analysis and interpretation of students’ addition computations were similar for both Korean and U.S. preservice teachers whereas there were some differences in the analysis of students’ subtraction computations. Both Korean and U.S. preservice teachers had difficulties identifying students’ strategies and errors for a complicated and unconventional computational approach. Results also indicated that preservice teachers’ noticing and interpretation of students’ strategies and errors were influenced by their K-12 mathematics curriculum and teacher education program. This study suggests implications and future directions for teacher education, more contextualized teacher preparation programs and balanced connection to the K-12 curriculum.

In-service mathematics teachers’ preparedness, knowledge, skills, and self-efficacy beliefs of using technology in lesson delivery

This research examined the competencies (preparedness, skills, knowledge and self-efficacy beliefs) of High School teachers in teaching mathematics with technology. The study employed the explanatory sequential mixed-methods design where a questionnaire, observation guide and semi-structured interview guide were used to collect data. A stratified sampling technique was used to select 202 mathematics teachers for the study. Descriptive statistics and multiple regression were employed to analyse the quantitative data. Thematic analysis was used for the qualitative data. The findings indicated that mathematics teachers possessed high technology knowledge and self-efficacy, but they had relatively low preparedness and ICT skills in using technology in their lessons. In addition, ICT skills and teacher preparedness emerged as the best predictors for technology usage in mathematics lesson delivery. This implies that mathematics teacher education programmes should consider making ICT a core component of their curriculum to prepare prospective teachers to teach mathematics with technology.

The Development of Islamic Context Learning Materials to Facilitate the Conceptual Understanding of Mathematics

This research was conducted to develop and produce Islamic context-based mathematic learning material. The presentation of Islamic context for pre-service mathematics teachers was intended to facilitate conceptual understanding. This learning material contains rank and root, ratio and scale, and material for flat shapes and spatial shapes. The material is included in the Mathematics Materials Study course for Junior Secondary Education in the Mathematics Teacher Education program. The method in this study uses design research with the type of development study with a qualitative approach. The research phases include the preliminary research phase, the development or prototyping phase, and the assessment phase. The data were collected by filling out a learning material scoring scale by Education and Language expert and an Islamic Study expert. The quality criteria for learning material have valid results if the experts score it with excellent and valid categories. Thus, they do not need significant revision. Based on the research results, the quality of Islamic context-based mathematics learning material is classified into valid criteria at a percentage of 84% according to Mathematics Education experts and a percentage of 83.3% according to Education and Language experts and classified as an excellent category at a percentage of 94% according to Islamic Study expert. Based on these results, the product of Islamic contextual mathematics teaching materials is suitable for use in mathematics lectures.

A study on pre-service mathematics teachers’ criteria of proof evaluation

Proof is foundational to mathematics, and constructing proofs and establishing their validity are both important mathematical studies. Determining the validity of a proof is a part of the process of proof evaluation. Proof evaluation contributes to students’ ability to construct and revise their own proofs. The purpose of this study was to determine the criteria pre-service mathematics teachers take into account in evaluating a proof. The study was carried out with 50 first-year university students enrolled in an elementary mathematics teacher education program. The data were collected through activities relating to proving. The results of this study revealed that, when evaluating a proof, the participants regarded use of appropriate definitions, axioms, or theorems in the steps of the proof as the most important criterion with reference to justification, while in terms of mathematical language; they regarded appropriate use of symbolic language as the most important criterion. However, they tended to ignore situations where non-symbolic language was used. To address this issue, it is recommended that mathematics-learning environments include the use of non-symbolic language, as well as symbolic representations, in the definition of mathematical concepts.