Mathematics Teachers Research Articles

The pedagogical insights of mathematics teachers integrating artificial intelligence in rural upper primary schools of Namibia

This paper presents a qualitative intervention study that explores the pedagogical experiences of mathematics teachers integrating Artificial Intelligence (AI) technologies into teaching mathematics in rural upper primary schools in Namibia. The Technological Pedagogical Content Knowledge (TPACK) framework, which intersects teachers’ understanding of technology integration with pedagogical techniques and subject matter knowledge, was adopted for the study. The research involved 13 mathematics teachers selected through purposive sampling. Data collection included two sharing circle discussions, lesson observations, and semi-structured interviews. A thematic analysis approach was employed to interpret the collected data. The findings reveal a diverse range of AI tools used by the selected teachers, such as Geogebra, Khan Academy, Virtual Tutors, and various problem-solving mobile applications, including Photomath, Mathway, and Microsoft Math Solver. These AI resources were noted for enhancing the visualisation of mathematical concepts, providing adaptive learning experiences, and promoting independent, paced learning that supports learners' learning styles. Teachers reported a marked improvement in learners’ comprehension and problem-solving abilities attributable to AI integration. Despite the benefits of AI in education, challenges remain, particularly in rural areas. Key issues include inadequate infrastructure, limited access to devices, and the need for ongoing teacher training in technological pedagogical content knowledge. Additionally, the lack of culturally relevant AI technologies hinders effective AI-supported learning in diverse contexts. Greater investment in localised AI educational tools is needed to achieve equitable and effective learning outcomes.

Developing survey-based measures of mathematics teachers’ pedagogical technology knowledge: a focus on computational thinking and programming tools

ABSTRACT The aim of this research is to develop a survey to explore Norwegian teachers’ perceptions regarding integrating computational thinking (CT) and programming tools into mathematics teaching by using Rasch analysis. For this purpose, three measures are developed: mathematical knowledge for teaching (with technology), instrumental genesis and personal orientations, aligning with the components of Pedagogical Technology Knowledge framework. The empirical data to validate and refine the developed measures includes a relatively large sample of 356 Norwegian primary and secondary school mathematics teachers. Through the three measures, analysis of the survey data revealed insights into teacher perceptions and challenges in tool adoption. These results, first, highlighted the complexity of tool integration and the necessity of unpacking country-specific competencies linking CT and programming to mathematics. Second, the results underlined a need for qualitative research to delve deeper into teacher perceptions and understandings of CT and programming to address challenges and enhance classroom practices.

Context of Contextualized Teaching Situations in the Initial Training of Mathematics Teachers at the Popular University of Cesar

The purpose of this research is to reflect on the role of the context environment of the contextualized situations of teaching school mathematics, which make significant contributions to the initial training of the mathematics teacher at the Universidad Popular del Cesar-Valledupar-Colombia, where the informants were the twelve students enrolled in the subjects of Elective III, Mathematics Didactics, History and Epistemology of Mathematics and Degree Work II, of the VI, VII, VIII and IX semesters respectively, of the Bachelor's Degree in Mathematics program; assigned to the Faculty of Education, of the Universidad Popular del Cesar. The study was situated in the qualitative paradigm, under the epistemological approach of sociocultural constructivism, with the recapitulations of the foundations and orientations of the phenomenological-transcendental methodology. It is concluded that it is feasible to change the mathematics master class for a space where students can interact in the teaching-learning process, with the necessary knowledge to understand the messages of the context of the habitat of the subject who learns; and for this reason, the relationships of the trio: Teacher-School Mathematical Knowledge-Students and these with the context can always be placed in the context of mathematics education.

Gifted Students’ Views on Integrating History of Mathematics in Mathematics Lessons

ABSTRACT This qualitative study aimed to explore the perspectives of gifted students on incorporating the history of mathematics into their lessons. The research involved 51 fifth-grade students, identified as gifted, attending a Science and Art Center in Ankara, Turkey. The study spanned 12 weeks, equivalent to one semester, during which the lesson plans were enhanced and diversified with various instructional activities. Data were gathered through the History of Mathematics Student Questionnaire (HMSQ), worksheets, and students’ reflections on the instructional activities. The HMSQ data were subjected to descriptive analysis techniques such as percentages, frequencies, and arithmetic means. Additionally, responses to short-answer questions were independently reviewed by another mathematics teacher, leading to the formation of distinct categories. Reflections from the students were analyzed through the lenses of “history as a tool” and “history as a goal.” Employing history as a tool increased students’ motivation and curiosity while viewing history as a goal enriched their understanding of mathematics’ evolution and the lives of mathematicians. Moreover, survey findings revealed a significant shift in their perceptions regarding the integration of the History of Mathematics into mathematics lessons.

Perception of the elementary mathematics teachers about assessment for learning: a case study of Sukkur IBA community colleges, Sindh, Pakistan

This study aims to explore the perceptions of elementary mathematics teachers regarding assessment for learning (AfL). The participants of this study included three elementary mathematics teachers, each with over 5 years of teaching experience at Sukkur IBA community colleges and schools in Sindh, Pakistan. These participants were selected using purposive sampling techniques. A qualitative exploratory case study research approach was used, with data collected through semi-structured interviews and observations. To ensure the trustworthiness of the study, the interview guide and observation checklist were reviewed by experts. The data were analyzed using thematic analysis. The findings of this study revealed that teachers had a limited understanding of the concept of assessment for learning. Based on these results, the study recommends several measures: the initiation of an assessment literacy program, an increase in class time, reducing the number of students per class, using moveable chairs to enhance classroom flexibility, and making amendments to the assessment policy.

Heutagogy in Action: Empowering Mathematics Teachers Through Innovative Pedagogical Approaches

As a result, mathematics teachers are prompted to focus on the heutagogical approach. However, challenges arise, like inadequate training and support among mathematics teachers. Thus, this study concentrated on formulating a series of teaching activities aligned with the heutagogical approach, specifically tailored to assist mathematics teachers in enhancing their teaching methods. This study was conducted using the Fuzzy Delphi Method (FDM) involving 15 experts with various fields of expertise such as mathematics education, educational technology, heutagogy, pedagogy and the curriculum as well as primary and secondary school mathematics teachers. The data was collected from October 2023 to November 2023 by using a questionnaire as the primary means of collecting data. Findings were analysed using triangular fuzzy number, threshold value, percentage for expert consensus and defuzzification process to determine the acceptance and ranking for each teaching activity. The results indicate that teachers assign projects that require students to explore real-world applications of mathematical concepts, were ranked first, followed by other activities, while teachers arrange virtual sessions with guest speakers from the mathematics field to provide insights to real-world applications were ranked last. In conclusion, this study offers valuable insights for mathematics teachers interested in enhancing student-centered learning within the framework of Education 4.0.

Navigating the seas of the curriculum: A mathematics teacher’s interactions with curriculum materials

Curriculum materials are not a fixed object; they are an active partner in a teacher’s practice. Teachers and curriculum materials interact in a participatory relationship where both the characteristics of the teacher and the characteristics of the curriculum material affect the instruction. Teachers interpret and tailor these materials to create particular instructional strategies, therefore, teachers can be considered as lesson designers. The study presented in this paper uses longitudinal case study design to investigate the relationship between a mathematics teacher and curriculum materials over a period of nine years. Using the lens of curricular noticing, the study examined what the teacher attends to, interprets and responds to while planning a lesson. Data collection occurred at four distinct time points, encompassing both teacher observations during lesson planning and interviews after lesson planning, as well as the teacher’s lesson plans for the same topic at each time point. The obtained longitudinal data provided comprehensive insights into how the teacher’s curricular noticing changed over time and how it affected the teacher’s practice. The findings show that the teacher attended the national curriculum and textbook at all four time points, indicating the stability of these particular resources; however, the interpretation of the textbook elements and response to this interpretation changed significantly. The teacher’s practice became more student-centered and inquiry-oriented. The implications of the study are also discussed.

Principles to Actions—A Reflective Journey

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

Teaching practice: Contributions to Spanish prospective mathematics teachers

Prospective primary education (PE) teachers of mathematics are trained on university programs which include core subjects in the field of the didactics of mathematics. However, these subjects have no general practical component. Therefore, this research aims to analyze the contribution of practical courses to the development of good practice in mathematics education. For this purpose, an ethnographic study was carried out with the participation of 23 prospective teachers who completed a questionnaire with closed and open-ended questions. The closed responses were analyzed by frequency and percentage, and the open-ended responses were analyzed using the ATLAS.ti software (v. 22) (ATLAS.ti, 2022). The results show that most of the prospective teachers identified principles of good practice in mathematics classes, and most of them found a relationship between their initial training and what they experienced in these classrooms. In the light of the results, contributions are made to improve the initial training of mathematics teachers in PE.

Comparison of the experience of using digital games in mathematics education in Ukraine and Israel

Abstract The study examined the opinion of school students regarding the expediency and possibilities of using digital mathematical games in the process of teaching mathematics, and also carried out a comparative analysis of the results of the research conducted in Ukraine and Israel. The issue of the distribution of digital mathematical games in Ukraine and Israel was studied, and it was found out which digital mathematical games are the most popular in the process of teaching mathematics to students in schools in these countries. It was found that the vast majority of students from these countries played digital mathematical games. In the study of students’ interest in playing digital mathematical games, the questions were whether students played digital mathematical games, whether their mathematics teachers used digital mathematical games in mathematics lessons, whether students would like to use digital mathematical games when learning mathematics at school. Also, most students responded that their teachers used digital math games in math lessons and would like their teachers to continue using them. However, despite a relatively high percentage of students who are interested in using digital math games in math lessons, there are students who consider traditional math lessons to be more appropriate. It was established that there is a statistically significant difference between the results of a survey of schoolchildren in Ukraine and Israel regarding the expediency of using mathematical digital games in teaching mathematics: with a probability of 95% more surveyed schoolchildren in Ukraine (9.6%) are supporters of traditional teaching of mathematics (without the use of digital games), compared to 2.4% of surveyed schoolchildren in Israel. The statistical significance of the differences in the answers of students of the schools of these countries was checked using the ϕ*-Fisher criterion. As a result of the research, it was found that the interest of schoolchildren of both countries in the use of digital mathematical games in the learning process is growing. Almost half of the respondents in these countries expressed the opinion that they would be interested in learning more about digital math games and trying to play them. However, there remain a number of unresolved important issues related to the methodology of this process, including didactic ones.

The case classification and their development for would-be mathematics teachers’ training

Abstract The article looks into the issue of the case classification for the training of Mathematics teachers. The analysis, which was carried out, and the survey of 47 University teachers of methodical disciplines allowed to highlight the classification features of cases in the process of teaching methodical disciplines: the amount of time to complete, the way of presentation, the level of complexity and the breadth of the covered problem. Classifying cases by the amount of time for their implementation contributed to the separation of mini-cases, medium-term cases, and long-term cases. Classification by the method of presentation of cases in the process of studying methodical disciplines ensured their use in printed (handwritten) form, multimedia presentation of cases, and video cases. According to the level of complexity, the cases were divided into reproductive-training, partial-research, and creative-innovative cases. Thematic and integrated cases ensured the breadth of coverage of the problem during the teaching of methodical disciplines. The article presents general requirements for the selection and development of cases in the process of studying methodical disciplines. These requirements are based on the principles of accessibility, scientificity, contextuality, systematicity, methodological expediency, and practical orientation. The classification and specific requirements became the basis for the development of cases that can be used in the process of teaching methodological disciplines of would-be Mathematics teachers.

After initial acquisition, problem-solving leads to better long-term performance than example study, even for complex tasks

BackgroundSuccessful implementation of effective acquisition strategies (e.g., example study, problem-solving) could help improve mathematics performance. However, it is not yet fully understood when each acquisition strategy should be used, despite the practical value of this knowledge for mathematics textbook authors, teachers, and students. AimsBuilding upon two recent perspectives on when example study and problem-solving are beneficial, we proposed that the optimal acquisition strategy could depend on both task complexity and retention interval (i.e., time between the final practice opportunity and the test). We conducted a multi-classroom experiment to test this proposition. Sample166 typically-developing Dutch fifth-grade students participated (Mage = 11.14 years; 42.2% boys). MethodsWe used a 2 (Task Complexity: simple vs. complex) x 2 (Acquisition Strategy: example study vs. problem-solving) x 2 (Retention Interval: 5 min vs. 1 week) between-subjects design with problem-solving performance as dependent variable. ResultsThere was no evidence for the hypothesised three-way interaction effect of task complexity, acquisition strategy, and retention interval. However, there was evidence for the hypothesised two-way interaction effect of acquisition strategy and retention interval, independent of task complexity. More specifically, after 5 min, there was no statistically significant performance difference between students studying worked examples and those solving practice problems, but after 1 week, students solving practice problems outperformed those studying worked examples. ConclusionsOur findings imply that, after initial acquisition, problem-solving leads to better long-term problem-solving performance than example study. This holds true even for a relatively complex task and with limited instruction.

Structural-mathematical thinking and its development in teaching Mathematics

Abstract The paper highlights the content and components of structural-mathematical thinking, substantiates its classification basis and establishes typological characteristics. In the conceptual-categorical section of the present study, structural-mathematical thinking is introduced as a form of theoretical thinking that embodies the specifics of mathematical comprehension of reality. The content as well as structural and functional characteristics of the phenomenon under study represent the content and components of the mathematical structure. Hence, the adherence to the deductive nature of Mathematics was ensured in the study, also emphasizing the phenomenological characteristic of structural-mathematical thinking regarded as the ability to reflect reality in accordance with the content components of the mathematical structure. Taking into account the theoretical advances, using the system approach and the modeling method, a model of developmental-conceptual teaching of Mathematics was elaborated. By considering the theoretical advancements and applying both a systemic approach and modeling method, a model for instructing Mathematics in a developmental-conceptual approach was elaborated, which represents a problem-based approach and develops students’ structural-mathematical thinking. The crux of teaching Mathematics through a developmental and conceptual approach lies in creating a framework that addresses the three-fold challenge of problem-solving ↔ competency-building ↔ problem-solving proficiency. Taking into account the addressed issue, the paper elicits the outcomes of a pilot study how structural-mathematical thinking is manifested by the would-be teachers of Mathematics. Furthermore, the efficacy of the authors’ approach to its enhancement is experimentally validated.

Conceptual images and learning obstacles in exponentiation and logarithms: A hermeneutic phenomenological analysis

The concept of exponentials and logarithms is one of the essential concepts in mathematics as part of transcendent functions. However, students' understanding of these two concepts has yet to be fully mastered, so there are still errors in solving problems related to these two concepts. This study aims to describe the meaning and meaning process and explore the potential learning obstacles of students based on the meaning and experience of students in obtaining the meaning of exponents and logarithms in senior high school. This qualitative study uses a hermeneutic phenomenological approach with student participants and high school mathematics teachers. Data was collected using tests, documentation, and interviews with students and teachers. Data were analyzed qualitatively to identify learning obstacles and the meaning of exponentials and logarithms. The results showed the meaning of exponents and logarithms according to students, namely exponents as power numbers and logarithms as the opposite of power numbers. In addition, the results also show the existence of learning obstacles in students, both ontogenic, epistemological, and didactic. Based on the findings, these learning obstacles can be considered when developing an appropriate didactic design.

Impact of school experiences on the beliefs and instructional practices of future mathematics teachers

This study examines the impact of cumulative experiences and beliefs during the school career on the pedagogical development of future mathematics teachers in Chile. A sample of 252 pedagogy students from 18 higher education institutions participated in the study, completing a questionnaire that focused on instructional paradigms, teaching experiences, and pedagogical practices. The research employed latent class analysis to identify distinct profiles based on the teaching paradigms experienced by the participants. A logistic regression model further corroborated these profiles. The findings indicate a prevalent inclination towards constructivist beliefs and practices among future teachers, which are significantly shaped by their secondary education experiences, often devoid of a constructivist approach. This study emphasizes the critical role of prior educational experiences in shaping professional competencies in teaching mathematics.

AI 디지털교과서 도입과 활용에 관한 중등수학교사의 인식 조사 연구: 학습자 맞춤 교육 실현을 위한 과제

This study explores mathematics teachers' perceptions of the adoption and utilization of AI digital mathematics textbooks and provides implications for both the development of AI digital textbooks and teacher education. A survey was conducted in November 2023 with 130 secondary school mathematics teachers to analyze their perceptions regarding (1) understanding and necessity of AI digital textbooks, (2) key features, (3) application in mathematics instruction, and (4) teacher professional development. The results reveal that while secondary mathematics teachers recognize the necessity of adopting AI digital textbooks, there is a significant gap in their understanding and experience with the core functionalities. There is a strong demand for features such as learning diagnostics and dashboard to support adaptive learning, along with expectations for student-centered adaptive learning and emotional support. However, concerns were also raised about decreased interactivity and challenges in lesson preparation due to changes in the educational environment. Based on these findings, the study suggests the need for enhanced teacher professional development to deepen teachers’ understanding and support practical implementation, as well as functional improvements to AI digital textbooks to ensure their effective and practical adoption in educational settings.

Data Moves as a Focusing Lens for Learning to Teach with CODAP

Innovative dynamic data tools afford opportunities for K-12 students and teachers to explore multivariate data and create linked data representations. These tools also support engagement in data moves, which are transnumerative actions to process, organize, and visualize data. The current study sought to understand how prospective K-12 mathematics teachers (PMTs) use data moves in the Common Online Data Analysis Platform (CODAP) to create and interpret visualizations and statistical measures to make sense of state-level data about education in the United States. Extending the work of Erickson et al. (2019), a framework is presented to characterize data moves and provide examples of actions within CODAP that illustrate each data move. Based on analysis of thirty screencasts created by PMTs, four examples highlight PMTs’ use of data moves to investigate data in CODAP.

Improving Mathematics Education through Teacher Professional Development: A Tanzanian Perspective

This study aimed to explore mathematics teachers’ perceptions of professional development. The study involved two public secondary schools in Ilala Municipality, Dar es Salaam. This was a qualitative study based on case study design. The study involved fourteen (14) participants that were selected purposefully. Two (2) heads of the schools, two (2) Academic Teachers, two (2) heads of mathematics departments, and eight (8) mathematics teachers were equally involved from both schools. Interviews, focus group discussions, surveys, and document analysis methods were used in data collection. Both interviews and focus group discussion were audio-recorded by using a protected smartphone with password to ensure data security. The documents reviewed includes; school policies, school calendars, and mathematics departmental meetings’ minutes. The data collected were analysed thematically to identify and interpret key themes. The data analysis was based on the following steps: transcription, data reduction, presentation, and discussion of findings. Fictitious names were used for names of people and schools to ensure confidentiality and anonymity. The study revealed that teachers perceived professional development as formal programs to improve teachers’ quality that were time-consuming and costly, while informal professional development programs were overlooked by teachers and other educational stakeholders. The study recommends that, in order to improve teachers’ quality as intended in professional development, there is a need to raise awareness for both formal and informal professional development programs among teachers and a learning community as a whole.

Effect of Kinesthetic Learning on Students’ Interest and Achievement in Mathematics

One of the pertinent reasons for poor academic achievement in Mathematics is fundamentally linked to the application of ineffective teaching methods by teachers to impact knowledge to learners. This study adopts a quasi-experimental pre-test post-test research design to examine the efficacy of kinesthetic learning on interest and achievement in Mathematics. Four research questions were raised to guide the study and four hypotheses were formulated and tested at 0.05 level of significance. The sample comprises 101 Junior Secondary School students drawn from two secondary schools in Bekwarra Local Government Area of Cross River State, Nigeria. Two intact classes were randomly selected from each school and assigned to experimental and control group. Data for the study were sourced using a modified Mathematics Interest Inventory (MII) and mathematics achievement test designed by the researchers tagged Students’ Mathematics Achievement Test (SMAT). Data collected were analyzed using mean, standard deviation and Analysis of Covariance (ANCOVA). The findings revealed a high post-test interest cluster mean of 3.10 (above the decision benchmark of 2.50) and also a higher post-test mean achievement score with (Mean = 20.82; Standard Deviation = 3.63) for students in the experimental group compared to the control group. The result also indicated that both male and female students taught mathematics using kinesthetic learning in the experimental group had positive interest and achievement after exposure to the treatment. The test of the hypotheses indicated that there is significant difference in interest and achievement between students taught mathematics using kinesthetic learning and conventional method, whereas there is no significant difference on the interest and achievement of male and female students taught mathematics using kinesthetic learning. The study concluded that kinesthetic learning has a positive effect on interest and achievement in mathematics; and that gender is not a sole determinant of good academic performance or interest in mathematics but teaching method. The study recommended that mathematics teachers should adopt kinesthetic learning or play way method in teaching because of its relevance in improving learners’ interest and achievement.

DEFINING THE ROLE OF EDUCATIONAL PLATFORMS IN MATHEMATICS IN THE EFFECTIVE TRAINING OF FUTURE MATHEMATICS TEACHERS

The present study analyzes the results of a survey of teachers and students designed to identify the preferences and needs of universities in using educational platforms in mathematics to study the subject «Elementary Mathematics». The aim of the study was to determine the preferred characteristics and functionality of mathematics learning platforms that can contribute to effectivelearning and increase interest in mathematics for future mathematics teachers. To achieve this goal, questionnaires were developed, which were distributed among mathematics teachers and first-year students in the specialty «Mathematics» when teaching the subject «Elementary Mathematics» and third and fourth-year students when teaching the subject «Methods of teaching mathematics». The questionnaires included questions about preferences in using educational platforms in mathematics, the level of comfort andperception of educational material when working with technologies, preferred learning formats and expected learning outcomes. The analysis of the obtained results allowed us to identify the key principles that should be taken into account when using educational platforms in mathematics to study the subject «Elementary Mathematics» at the university. Following these principles contributes to the use of educational platforms in mathematics, and as a result, to improving the quality of mathematical education at the university and improving the learning ability of future mathematics teachers.