This paper represents a revolutionary advancement in our knowledge of postgraduate education which is of increasing significance to national knowledge systems. South African universities produce 26 doctoral graduates for every one million citizens. This means that the low doctoral graduates’ throughput is a huge challenge in South Africa and needs to be addressed. The paper investigated the challenges experienced by postgraduate students (Honors) at an institution of higher education in Limpopo province of South Africa. The group studied consisted of postgraduate students (Honors) from the Department of Mathematics Science and Technology Education, Faculty of Education. Using a qualitative approach, open-ended questionnaire and interview data were collected from eight participants. Data were analyzed thematically and the results revealed that students find it difficult to walk the landmine-infested postgraduate education road without means to shield themselves from the subsequent explosion. The study recommends aspects that improve postgraduate programs’ performance in the Department of Mathematics Science and Technology Education.

Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.

The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding  . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.

Learners bring prior knowledge to their learning environments. This prior knowledge is said to have an effect on how they encode and later retrieve new information learned. This research aimed at exploring ‘A’ level mathematics learners’ understanding of the determinant concept of 3×3 matrices. A problem-solving approach was used to determine learners' conceptions and errors made in calculating the determinant. To identify the conceptions; a paper and pencil test, learner interviews, and learner questionnaires were used. Ten learners participated in the research and purposive sampling was used to select learners who are doing the syllabus 6042/2 Zimbabwe School Examination Council (ZIMSEC). Data was analyzed qualitatively through an analysis of each learners' problem-solving performance where common themes were identified amongst the learners’ work. Results from the themes showed that Advanced level learners faced some challenges in calculating the determinant of 3×3 matrices. Learners were having challenges with the place signs used in 3×3 matrices, especially when using the method of cofactors. The findings reveal that learners had low levels of engagement with the concepts and the abstract nature of the concepts was the major source of these challenges. The study recommends that; teachers should engage learners for lifelong learning and apply some mathematical definitions in real-world problems. Teachers should address the issues raised in this research during the teaching and learning process. In addition, teachers should engage learners more through seminars where learners get to mingle with others from other schools.

Algebraic reasoning involves representation, generalization, formalization of patterns and order in all aspects of mathematics. Hence, the focus of algebraic reasoning is on patterns, functions, and the ability to analyze situations with the help of symbols. The purpose of this study was to develop a test instrument to measure students' algebraic reasoning abilities based on cognitive systems in Marzano's taxonomy. The cognitive system in Marzano's taxonomy consists of four levels, including retrieval, comprehension, analysis, and knowledge utilization. According to the stage of cognitive development, students are at the level of knowledge utilization. At this level, students can make decisions, solve problems, generates and test hypotheses, as well as carry out investigations that are in line with indicators of algebraic reasoning abilities. The stages in developing the test instrument were based on three phases: preliminary investigation phase, prototyping phase, and assessment phase. The study obtains a set of valid and reliable algebraic reasoning test instruments for students based on the cognitive system in Marzano's taxonomy. Through the development of an algebraic reasoning test instrument based on Marzano's taxonomy, students can build' thinking habits so that active learning exercises occurs.

Mathematics teaching efficacy is an important construct as confidence in one’s ability to teach influences teaching practices. This paper explores pre-service primary teachers’ mathematics teaching efficacy on entry to initial teacher education and the extent that pre-tertiary mathematics experiences and resultant beliefs affected their mathematics teaching efficacy. A mixed-methods approach combined the Mathematics Teaching Efficacy Beliefs Instrument (N=420) and qualitative interviews (N=30). The findings suggest medium personal mathematics teaching efficacy among participants with limited conceptions of what mathematics teaching involves. While uncertain regarding their immediate teaching ability, participants reported confidence regarding their potential. Mathematics teaching outcome expectancy was high; however, an undercurrent of conviction exists that external factors, most notably learners’ natural mathematical ability, are critical to student learning.

During online learning, students were having difficulties in understanding the concept of the application of integrals to find an area. The provided materials in PowerPoint and learning sources such as books are still insufficient to understand the concept. The students’ feedback showed that a learning video is required to help the students understand the concept of the application of integrals. This research aims to develop a learning video concerning the concept comprehension of integrals’ application and determine its validity and practicality. This research utilized the analysis, design, development, implementation, evaluation (ADDIE) development model, where the subjects of this research were the students of mathematics education at the Ahmad Dahlan University. The data collection was conducted by using questionnaires and interviews. The obtained data was then analyzed for its validity and practicality. The media validity test result shows valid criteria with the assessment of the material expert of 4.629 (very good) and valid criteria with the material validity test of 4.735 (very good). The responses of the students to the learning video show 3.50 with the criteria of Very Good. Based on such results, this concept comprehension learning video is feasible to use.

Mathematical connection ability is very important to be mastered by prospective mathematics teacher students as competency to teach in secondary schools. However, the facts show that there are still many students who have weak mathematical connection abilities. This qualitative descriptive study aimed to explore how the process, and product of the mathematical connection made by prospective mathematics teacher students when solving the integral calculus problems based on their prior knowledge. The research subjects were 58 students who were prospective high school mathematics teachers at the University of Jember, Indonesia. Data were collected using documentation, questionnaire, test, and interview methods. After the test results of all subjects were analyzed, six students were interviewed. To find the match between the results of the written test and the results of the interview, a triangulation method was carried out. Data analysis used descriptive qualitative analysis with steps of data categorization, data presentation, interpretation, and making conclusions. The results show that the research subjects have connected and used mathematical ideas in the form of procedures, facts, concepts/principles, and representations in solving integral calculus problems. Students with high prior knowledge abilities can make better mathematical connections than students with moderate and low prior abilities. From these results, it is recommended that lecturers need to improve students' prior knowledge and train the students more intensely to solve integral calculus problems so all students can develop their mathematical connection abilities into very strong categories.

A mathematics instructor with limited knowledge of content and pedagogy has little room for improvement or novelty in the classroom or the ability to arouse students' interest in learning mathematics. This case study was conducted in a foundation center of one of the public universities in Malaysia. The target of current research was to investigate the influence of lesson study (LS) on lecturers’ pedagogical content and content knowledge. The LS group comprises of seven lecturers of the mathematics group and the researcher. The group collaboratively prepared a research lesson on the subject of even and odd functions. Data gathered through interviews and observations on the lecturers’ activities in discussion meetings. Data from observations and interviews were analyzed descriptively and through thematic analysis method respectively. The results of this study show lecturers improved their knowledge in content and pedagogy considerably about even and odd functions. They enhanced their teaching knowledge through collaborative work and sharing of experiences. It seems the findings of this research not only help lecturers to have better performance in teaching the even and odd functions but also encourage them to experience the LS approach in teaching other mathematical concepts.

The prediction potential of the model "emotional intelligence and self-reliance" to students' mathematical performance was investigated in this study. This research was conducted in the third and fourth quarters of the academic year 2021-2022. The quantitative research design, specifically comparative and regression analysis, was used in this study. The comparative design was utilized to assess the differences in emotional intelligence and self-reliance between male and female students, and the regression analysis was performed to see if the model "emotional intelligence and self-reliance" can predict students' mathematical performance. In terms of emotional intelligence and self-reliance, the findings show no significant difference between male and female students. Furthermore, the student's emotional intelligence and self-reliance were strong predictors of mathematics performance. It implies that emotional intelligence and self-reliance are essential factors in better math learning. The study suggested that teachers may improve their students' emotional intelligence and self-reliance by integrating social and emotional learning programs into their classes.

Learning in STEM subjects is to a high degree based upon understanding logic, especially in subjects like mathematics. It has always been challenging to preserve the benefits of on-campus teaching and learning while digitalizing the teaching of mathematics. In this article an approach to design for a suitable online pre-calculus course is discussed, that aims to address the challenges. The main focus will be on student active learning in synchronous online environments, technical teaching methods in lectures, and pre-planning of the course. The final exam in the course was held as a closed-book proctored exam on-campus with pen and paper, providing data on comparisons of the final exam scores with the exam from the previous year, in which the entire course was held on-campus. The results indicate a positive effect from the presented design. Also, student surveys indicated high student satisfaction.

Numerical literacy refers to the knowledge and ability to use various numbers and basic mathematical symbols to solve problems, while math self-concept means the assessment of students’ skills, abilities, enjoyment, and interest in the subject. However, children with special needs and normal students in inclusive Elementary Schools are yet to sufficiently acquire learning that accommodates literacy and maths self-concept. This causes a need for the implementation of a children-friendly learning process. Therefore, this study aimed to identify the factors influencing the numeracy level and math self-concept, and also explore the obstacles in implementing children-friendly learning in order to facilitate students’ abilities. A qualitative method was applied because of in-depth data exploration regarding children with special needs, while the utilized instruments include tests, questionnaires, and interviews. Both the data collected and the analysis are qualitative, which are obtained through excavation, identification, and description. Consequently, this paper was able to (a) describe the factors influencing the numeracy level and math self-concept in inclusive elementary schools; (b) explore the barriers to implementing children-friendly learning; and (c) identify the relationship between students’ numeracy and math self-concept.

Research into knowledge which mathematics teachers require to teach abounds. There is also mounting interest among mathematics teacher education researchers to characterize mathematics teacher educator knowledge (MTEK). However, there is a generic dearth of studies focusing on conceptions of mathematics teacher educators (MTE) regarding MTEK. This article is a product of a qualitative case study underscoring teacher educator conceptions in that regard and the investigation involved two MTE who were practicing in a university. The research site was conveniently chosen, and participants were intentionally selected to respond to interview questions which elicited espoused views. Narrative analysis was used through exploration and subsequent interpretation of transcripts which aligned with questions posed. Analyses suggested a complexity to exhaustively categorize the MTEK necessary for MTE to train mathematics teachers. Notwithstanding, MTE believed that MTEK should include understanding of research in mathematics teacher education and teaching, mathematics teacher knowledge, and MTE professional development. Additionally, the findings suggested that MTE acquire mathematics teacher educator knowledge through postgraduate studies, on the job practice, mentorship, and participation in professional development activities. Research in other contexts is recommended to identify mathematics teacher educators’ understandings of MTEK and how that knowledge should be acquired.

Preservice elementary teachers have had a variety of experiences in their math classes which influence their willingness to engage in math as well as their confidence in doing so. This study examined the responses of two sets of preservice elementary teachers, in 2017 and in 2022, to questions about their "best" and "worst" experiences in math classes. Previous research has seldom asked preservice elementary teachers to examine what they do as students to create a better math experience and research is only now beginning on how COVID-19 may have affected student behavior. Inductive analysis revealed that the emotional intelligence of teachers greatly affected preservice elementary teachers' willingness to meaningfully engage in math. For example, a recurring theme in the data was a strong sense of not wanting to appear dumb, which prevented the students from asking questions or seeking help when needed. This study demonstrates that the classroom environment plays a significant role in preservice elementary teachers' success in math, confidence and comfort level with the subject, and, undoubtedly, how they will eventually teach math to their future students.

During the Covid-19 pandemic, this study investigated the role of metacognitive awareness as a mediator in the correlation between attitude and mathematical reasoning among undergraduates who are first year university students. These studies distribute mathematical reasoning assessments, metacognitive awareness questionnaires, and attitude surveys as research data. One hundred eighty-four undergraduate students from one public institution in Malaysia's Klang Valley area participated in the research. The impact of metacognitive awareness on attitude and mathematical reasoning was studied using Version 25 of the Statistical Packages for the Social Sciences. The findings indicated that undergraduate mathematics and science education students excelled in non-mathematics and science education students in mathematical reasoning capacity. According to the findings, undergraduate mathematics and science education students had good metacognitive understanding and used more approaches in mathematical reasoning assessment. Further study implies that more research should be conducted to assess different demographics, such as institute training teachers' metacognitive awareness and attitude towards mathematical reasoning.

Bring your own device (BYOD) policy implementation in schools worldwide has allowed students to learn subjects, including mathematics, using personal mobile devices (PMDs). PMD use has enhanced students’ mathematics enjoyment by bridging the gap between theoretical mathematics concepts and their practical applications, which makes mathematics more meaningful and leads to improved results. Nonetheless, students in Namibian basic education are not authorised to learn with PMDs in school. While students’ PMD use in school remains a topic of debate, there remains a need to investigate its impact on students’ mathematics learning and teachers’ perceptions of BYOD in mathematics classrooms. This study evaluated the perceptions and intentions of 209 Namibian mathematics teachers from the Omusati and Khomas regions regarding students’ mathematics learning using PMDs in schools. Data were collected through an online survey. A structural equation model revealed teachers’ positive intentions towards students’ use of PMDs through BYOD in learning mathematics in school. Perceived usefulness (PU), perceived ease of use (PEoU), and price value (PV) factors directly affected the teachers’ behavioural intentions (BI) towards students learning mathematics through BYOD. PEoU significantly affected teachers’ PU, and PV significantly affected teachers’ PEoU and PU. PU significantly mediated the relationship between PEoU and teachers’ intentions. PV significantly indirectly affected teachers’ intentions through PU. PEoU non-significantly mediated the PV and intention relationship. Practical implications are discussed, and recommendations are offered for the Namibian Ministry of Education, Arts and Culture and teacher training institutions.

Teachers and teaching styles are two important factors influencing students’ academic performance. In this action research study, we investigated the differential effectiveness of two teaching methods, conventional learning (CL) and peer-cooperative learning (PCL), on students’ academic performance in fractions. A sample of 120 tenth grade mathematics students from Ibadan North Local Government Area of Oyo State in Nigeria was used for the study. The students were selected from three different secondary schools and grouped into two groups: the experimental (PCL) group and the control (CL) group, each having 60 students. A sample of 5 multiple-choice objective and 5 theory test questions titled Fraction Performance Test (FPT) was used to measure their academic performance after the treatment, and the assessment test scores were recorded. Descriptive statistics of the mean were used to answer the research question, while the two-way ANOVA technique was adopted for testing the research hypothesis at an alpha of 0.05. Summarily, the F (3, 116) statistic (= 8.55, p < .001) indicates significant differences in the effectiveness of the teaching methods. The mean scores also reveal that peer-cooperative learning was more effective than the conventional teaching approach. While the former proved to be a more efficacious treatment for female students, the latter was more suitable for male students. We recommend that different approaches be attempted by teachers, and the most effective in overcoming students’ resistance to learning and improving their academic performance be adopted.

Each student has a different amount of time to fully understand information, students with high academic ability (UA) need less time than students with low academic ability (LA). Teachers should apply learning models that can facilitate their study time according to their individual needs. The aim of this research is to assess which learning model is most optimal in reducing the gap in understanding mathematical concepts between UA and LA students. Apart from that, this research also evaluates the effectiveness of implementing the flipped class (FC) model in increasing students' understanding of mathematical concepts, compared to the problem-based learning (PBL) model and conventional learning models. The research method used was the N-Gain Test and ANCOVA. The research results show that the FC model is the most optimal in reducing the gap in understanding mathematical concepts between LA and UA students. In addition, both FC and PBL models have proven effective in increasing students' understanding of mathematical concepts when compared to conventional models. Future research could consider combining the FC model with PBL or other learning models to see whether combining these models can improve students' understanding of mathematical concepts more significantly.

The study investigated the impact of YouTube video assisted instructions (YVAI) on pre-service teachers’(PSTs) attitudes and academic performance in chemistry classroom. A quasi-experimental design was adopted for the study. One hundred and twenty (120) Pre-Service Teachers (PSTs) pursuing primary education programme constituted the participants of the study. Sixty (60) PSTs each were non-randomly assigned to the Experimental Group (EG) and Control Group (CG). Data on PSTs’ attitude and performance were collected with PSTAS and GCPT respectively. The SPSS software version 20 was used to analyse the data to generate descriptive and inferential statistics. A non-parametric analysis was used in the inferential statistics. The attitude means rank (MR=78.62) of EG (U = 713.000, Z=-6.924, p <.001) was statistically higher than CG (MR=42.38) (U = 713.000, Z=-6.924, p <.001) after treatment. The EG after treatment recorded a mean rank (80.86) statistically higher than CG (40.14), U = 578.500, Z = -6.441, p <.001 after treatment. YVAI was proven as an effective instructional strategy that enhances learners’ altitudinal changes and performance. The study recommended the use of YouTube technological-driven instructions to support classroom instructions.

Learning to teach mathematics has become crucial since its application in real life cannot go unmentioned. The desire of mathematics education researchers to make mathematics concepts easier for pre-service teachers to easily understand has attracted attention. This has become indispensable since after college, pre-service teachers are deployed from K-12 to assist learners in understanding mathematics concepts. The study aimed to ascertain how improvement in the learning of mathematics concepts using the Problem-based learning (PBL) approach could be understood and/or explained among pre-service teachers. This was viewed in two folds: how improvement in learning outcomes using the PBL approach could be explained; and how pre-service teachers’ disposition about the PBL could be explained/understood. Exploratory case study design involving qualitative and quantitative data was concurrently gathered and used. This involved the use of data collection instruments such as focus group discussion, pre-post-test scores, PBL observation protocol, and PBL disposition questionnaire. The study showed that the PBL method improved the learning of mathematics concepts among pre-service teachers. Pre-service teachers also showed a positive disposition (interest, belief, and attitude) toward the PBL intervention. The authors advocated for the conduct of a longitudinal study to understand the direction of change over time.