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Integrating Artificial Intelligence [AI] into mathematics education offers promising advancements and potential pitfalls. Striking a balance between AI-driven developments and preserving core pedagogical principles is critical in the teaching and learning environment. AI has emerged as a transformative force in various fields, including education. In the realm of mathematics education, AI technologies offer a spectrum of potential benefits (including personalize instruction, adaptive assessment, interactive learning environments, and real-time feedback, among others) and challenges (such as lack of creativity and problem-solving skills, inability to explain reasoning, bias in data and algorithms, absence of emotional intelligence and data privacy and security concern etc). This conceptual study used autoethnography as the methodology and qualitative content approach to analyze data. The study discussed historical background of AI and considered ethical issues around AI. It was concluded that the journey to harness the full potential of AI in mathematics education requires careful navigation of the good, the bad, and the ugly aspects inherent in this technological evolution.

The COVID-19 pandemic has had a significant impact on high-stakes testing, including the National Benchmark Tests in South Africa. Current linear testing formats have been criticized for their limitations, leading to a shift towards Computerized Adaptive Testing [CAT]. Assessments with CAT are more precise and take less time. Evaluation of CAT programs requires simulation studies. To assess the feasibility of implementing CAT in NBTs, SimulCAT, a simulation tool, was utilized. The SimulCAT simulation involved creating 10,000 examinees with a normal distribution characterized by a mean of 0 and a standard deviation of 1. A pool of 500 test items was employed, and specific parameters were established for the item selection algorithm, CAT administration rules, item exposure control, and termination criteria. The termination criteria required a standard error of less than 0.35 to ensure accurate abilities estimation. The findings from the simulation study demonstrated that fixed-length tests provided higher testing precision without any systematic error, as indicated by measurement statistics like CBIAS, CMAE, and CRMSE. However, fixed-length tests exhibited a higher item exposure rate, which could be mitigated by selecting items with fewer dependencies on specific item parameters (a-parameters). On the other hand, variable-length tests demonstrated increased redundancy. Based on these results, CAT is recommended as an alternative approach for conducting NBTs due to its capability to accurately measure individual abilities and reduce the testing duration. For high-stakes assessments like the NBTs, fixed-length tests are preferred as they offer superior testing precision while minimizing item exposure rates.

With the emergence of emerging 4IR technologies, AI application tools (chatbots) are becoming more and more popular and widespread in various fields, including education. This study investigates the factors that influence undergraduate students' inclination to utilize AI application tools, specifically chatbots, for educational purposes. We applied an expanded diffusion theory of innovation framework to examine the relationships between relative advantages, compatibility, trialability, trust, perceived usefulness, perceived ease of use, and behavioral intention. Data from 842 undergraduate students were collected through a questionnaire using a 7-point scale, and the findings were analyzed using SmartPLS 4.0.9.2 software with a covariance-based structural equation model. The results confirm the hypotheses regarding the relative advantages, compatibility, trialability, perceived usefulness, and trust of chatbots. Students who perceive the benefits of chatbots express a strong intention to use them for academic purposes. The perception of compatibility between students and chatbots positively influences their adoption intention, and those who have the opportunity to try out chatbots are more likely to use them, indicating the importance of trialability. Surprisingly, the study did not find direct relationships between perceived usefulness, perceived ease of use, and behavioral intention, suggesting the presence of other influencing factors or dynamics in the adoption of chatbots for educational purposes. The findings offer practical insights for students and contribute to the theoretical understanding of the diffusion theory of innovation. Future research can further explore these findings to gain deeper insights into the complexities of chatbot adoption and enhance the adoption of AI tools in educational settings.

This study explored the utilisation of GeoGebra as a modelling tool to develop undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers. This mission was accomplished by implementing GeoGebra-enriched activities, which provided carefully designed representational support to mediate between students’ initially developed conceptual and procedural knowledge gains. The rectangular and polar forms of the complex number were connected and merged using GeoGebra’s computer algebra systems and dynamic geometric systems platforms. Despite the centrality of complex numbers to the undergraduate mathematics curriculum, students tend to experience conceptual and procedural obstacles in mathematics-dependent physics engineering topics such as mechanical vector analysis and electric-circuit theory. The study adopted an exploratory sequential mixed methods design and involved purposively selected first-year engineering mathematics students at a South African university. The constructivist approach and Realistic Mathematical Education underpinned the empirical investigation. Data were collected from students’ scripts. Implementing GeoGebra-enriched activities and providing carefully designed representational support sought to enhance students’ conceptual and procedural knowledge of complex numbers and problem representational competence. The intervention additionally helped students to conceptualise and visualise a complex rectangular number. Implications for technology-enhanced pedagogy are discussed. Contribution: The article provides exploratory insights into the development of undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers using GeoGebra as a dynamic digital tool. Key findings from the study demonstrated that GeoGebra appears to be an effective modelling tool that can be harnessed to demystify the complexity of mathematics students’ conceptual and procedural knowledge of complex numbers.

The COVID-19 pandemic has had a significant impact on high-stakes testing, including the national benchmark tests in South Africa. Current linear testing formats have been criticized for their limitations, leading to a shift towards Computerized Adaptive Testing [CAT]. Assessments with CAT are more precise and take less time. Evaluation of CAT programs requires simulation studies. To assess the feasibility of implementing CAT in NBTs, SimulCAT, a simulation tool, was utilized. The SimulCAT simulation involved creating 10,000 examinees with a normal distribution characterized by a mean of 0 and a standard deviation of 1. A pool of 500 test items was employed, and specific parameters were established for the item selection algorithm, CAT administration rules, item exposure control, and termination criteria. The termination criteria required a standard error of less than 0.35 to ensure accurate abilities estimation. The findings from the simulation study demonstrated that fixed-length tests provided higher testing precision without any systematic error, as indicated by measurement statistics like CBIAS, CMAE, and CRMSE. However, fixed-length tests exhibited a higher item exposure rate, which could be mitigated by selecting items with fewer dependencies on specific item parameters (a-parameters). On the other hand, variable-length tests demonstrated increased redundancy. Based on these results, CAT is recommended as an alternative approach for conducting NBTs due to its capability to accurately measure individual abilities and reduce the testing duration. For high-stakes assessments like the NBTs, fixed-length tests are preferred as they offer superior testing precision while minimizing item exposure rates.

The purpose of this mixed methods study was to investigate the effect of a graphing calculator (GC) intervention on Grade 11 learners’ achievement in quadratic inequality problem solving. The quantitative aspects of the study involved an experimental and control group design in which the experimental group received instruction using the GC activities and the control group was taught without using the GC. The qualitative aspects of the study involved script analysis and task-based interviews. We used three data collection instruments: a quadratic inequality problem solving test used both as a pre- and a post-test administered to both the experimental and the control group learners, a written task analysis protocol and a task-based interview schedule. The results of the dependent samples t-test confirmed a statistically significant improvement in the quadratic inequality problem solving achievement of the experimental group with a Cohen’s d effect size of 1.3. The dependent t-test results for the control group were also a statistically significant improvement but with a smaller Cohen’s d of 1.2. The results of the independent t-test indicated that the experimental group achievement was significantly higher than that of the control group with a Cohen’s d effect size of 0.79. Script analysis of selected learners’ post-test solutions also showed that learners in the experimental group employed more problem-solving strategies (at least three – symbolic, numeric and graphical). Interview results of purposively selected learners also affirmed that experimental group participants perceived the GC intervention to have prepared them more effectively for multiple solution strategies of the quadratic inequality problem tasks. The researchers recommend the integration of GCs in the teaching and learning of mathematics in general and quadratic inequalities in particular. However, more research is needed in the integration of the GC in high-stakes assessment.

This study investigated the scalability of a cognitive multiple-choice test through the Mokken package in the R programming language for statistical computing. A 2019 mathematics West African Examinations Council (WAEC) instrument was used to gather data from randomly drawn K-12 participants (N = 2866; Male = 1232; Female = 1634; Mean age = 16.5 years) in Education District I, Lagos State, Nigeria. The results showed that the monotone homogeneity model (MHM) was consistent with the empirical dataset. However, it was observed that the test could not be scaled unidimensionally due to the low scalability of some items. In addition, the test discriminated well and had low accuracy for item-invariant ordering (IIO). Thus, items seriously violated the IIO property and scalability criteria when the HT coefficient was estimated. Consequently, the test requires modification in order to provide monotonic characteristics. This has implications for public examining bodies when endeavouring to assess the IIO assumption of their items in order to boost the validity of testing.

This study explored the utilisation of GeoGebra as a modelling tool to develop undergraduate engineering mathematics students' conceptual and procedural knowledge of complex numbers. This mission was accomplished by implementing GeoGebra-enriched activities, which provided carefully designed representational support to mediate between students' initially developed conceptual and procedural knowledge gains. The rectangular and polar forms of the complex number were connected and merged using GeoGebra's computer algebra systems and dynamic geometric systems platforms. Despite the centrality of complex numbers to the undergraduate mathematics curriculum, students tend to experience conceptual and procedural obstacles in mathematics-dependent physics engineering topics such as mechanical vector analysis and electric-circuit theory. The study adopted an exploratory sequential mixed methods design and involved purposively selected first-year engineering mathematics students at a South African university. The constructivist approach and Realistic Mathematical Education underpinned the empirical investigation. Data were collected from students' scripts. Implementing GeoGebra-enriched activities and providing carefully designed representational support sought to enhance students' conceptual and procedural knowledge of complex numbers and problem representational competence. The intervention additionally helped students to conceptualise and visualise a complex rectangular number. Implications for technology-enhanced pedagogy are discussed. Contribution: The article provides exploratory insights into the development of undergraduate engineering mathematics students' conceptual and procedural knowledge of complex numbers using GeoGebra as a dynamic digital tool. Key findings from the study demonstrated that GeoGebra appears to be an effective modelling tool that can be harnessed to demystify the complexity of mathematics students' conceptual and procedural knowledge of complex numbers.

The COVID-19 global pandemic widely affected education across the world and engendered unprecedented scenarios that required expeditious responses. In South Africa, the pandemic came on top of pre-existing inequalities in the education system. Using a qualitative research method of exploratory and descriptive nature, this study engaged a social justice framework to explore the teaching and learning of mathematics during the COVID-19 lockdown in a context of historical disadvantage. A sample of twenty-three Grade 12 mathematics teachers at various public secondary schools in Gauteng, South Africa was used in the study. The teachers were selected through purposive sampling. A Google-generated open-ended questionnaire and follow-up telephonic interviews were used to collect data. Data were analysed thematically in five steps. The findings revealed that the WhatsApp platform is a valuable tool that can support the teaching and learning of mathematics beyond the classroom in the contexts of historical disadvantage. The findings also provided insights into how mathematics teachers became learners themselves during emergency remote teaching (ERT) as they had to adapt to digital teaching, find solutions to unfamiliar problems and acquire knowledge from a larger mathematics education community around the globe. The article discusses these findings and teachers’ challenges of transitioning from traditional face-to-face classrooms to ERT and how they were addressed. At the time of publishing the article, most learners in South Africa had started going to school on a rotational basis. Nonetheless, the study reported in this article is of importance as ERT in the context of historical disadvantage has foregrounded issues of inequality in the South African education system that must be dealt with urgently.

This article reports on the qualitative aspects of a study that examined whether introducing a Problem-based Learning (PBL) approach in a one-year foundation programme can create conditions for learners to develop and sustain self-directed learning skills. This interpretive-constructivist case study was located in evaluation research. Data were collected by means of classroom observations and interviews with 35 students and 14 former students. Findings indicated that introducing students to a PBL approach did promote more meaningful learning patterns, typified by processing the subject matter critically and self-regulating learning processes. The sustainability ofthe meaning-directed learning skills was questionable ifstudent beliefs in the approach did not support the activities employed. Introducing PBL into a foundation programme can develop self-directed learning skills in students and set in motion a process of growth towards lifelong learning.

The purpose of this article is to report on an investigation of the perceptions and performance of mathematics teachers in a teacher professional learning (TPL) programme based on realistic mathematics education (RME) principles, which included a topic on transformations, undertaken by the researcher. Forty-seven Senior Phase (Grade 7–9) teachers took part in the mixed-methods study in which they answered a questionnaire with both closed and open-ended items. Fifty teachers took an achievement test at the end of the programme. The TPL programme used the RME approach in the design and delivery of mathematical tasks intended to enhance teachers’ mathematical knowledge for teaching. The sessions were conducted in a manner that modelled one way in which RME principles can be adopted as a teacher professional development strategy. The significance of the study is that continuing TPL is acknowledged to contribute to improvement in teaching and learning to address the concern about unsatisfactory learner achievement in mathematics. The responses suggested that the majority of teachers experienced the sessions positively in relation to all but one of the six RME principles. The teachers reported that they took an active part both as individuals and in small groups and expressed their willingness to adopt the type of activities and materials for their classrooms, which is an essential first step in Guskey’s first level of evaluation of a teacher TPL programme. The teachers’ average performance in an achievement test at the end of the topic was 72% which was indicative of modest learning gains at Guskey’s second level of TPL effectiveness.

South Africa’s performance in international benchmark tests is a major cause for concern amongst educators and policymakers, raising questions about the effectiveness of the curriculum reform efforts of the democratic era. The purpose of the study reported in this article was to investigate the degree of alignment between the TIMSS 2003 Grade 8 Mathematics assessment frameworks and the Revised National Curriculum Statements (RNCS) assessment standards for Grade 8 Mathematics, later revised to become the Curriculum and Assessment Policy Statements (CAPS). Such an investigation could help to partly shed light on why South African learners do not perform well and point out discrepancies that need to be attended to. The methodology of document analysis was adopted for the study, with the RNCS and the TIMSS 2003 Grade 8 Mathematics frameworks forming the principal documents. Porter’s moderately complex index of alignment was adopted for its simplicity. The computed index of 0.751 for the alignment between the RNCS assessment standards and the TIMSS assessment objectives was found to be significantly statistically low, at the alpha level of 0.05, according to Fulmer’s critical values for 20 cells and 90 or 120 standard points. The study suggests that inadequate attention has been paid to the alignment of the South African mathematics curriculum to the successive TIMSS assessment frameworks in terms of the cognitive level descriptions. The study recommends that participation in TIMSS should rigorously and critically inform ongoing curriculum reform efforts.

The role of proof in school geometry has been a subject of intense debate throughout the twentieth century and that debate persists even today. This study aims to identify and analyse deductive geometric proof difficulties encountered by Bachelor of Education (BEd) in-service student teachers and to propose possible ways of remediating them. The authors conducted a content analysis of responses to a circle geometry item in an achievement test taken by 170 students. Although 78% of the students performed well in the deductive proof item, 22% evidenced misunderstandings or misconceptions which varied in complexity. The misconceptions were analysed into four categories and implications for pedagogy proffered to turn the misconceptions into critical teaching and learning opportunities.

Encouragement to integrate information and communication technologies into mathematics education curricula is an increasingly universal phenomenon. As a contribution to the discourse, this article discusses the potential use in the classroom of The Geometer’s Sketchpad® (Key Curriculum Press, Emeryville, CA, United States) mathematics software in modelling the derivative and related concepts in introductory calculus. In an empirical study involving first-year non-mathematics major undergraduate science students, a hypothetical learning trajectory (HLT) was conjectured and implemented for students to experience the visualisation and multiple representations of calculus concepts on the Cartesian plane with a computer graphic interface. The utilisation scheme is interpreted through the lens of the instrumental1 approach proposed by Trouche. The HLT was partly informed by the historical development of the derivative as synthesised from the literature on the history of calculus and partly by the affordances, enablements, constraints and potentialities of Sketchpad itself. The findings of the study suggest that when exposed to the capabilities of this software, learners can experience Geometer’s Sketchpad® as an effective visualisation tool or instrument for the representation and learning of the derivative and related concepts in introductory calculus. However, the effectiveness of this tool is not a given or a foregone conclusion − it is a product of the teacher’s instrumental orchestration, gradual learner mastery of the software syntax and careful resolution of theoretical-computational conflicts that can arise during early use of the instrument.

National Benchmark Test Project (NBTP) was conceived as far back as 2004 by the public higher education leadership in South Africa and formally launched in 2005. NBTP was initiated to provide additional information to higher education in South African institutions in the admission and placement of students, establish the relationship between entry-level proficiencies and school-level exit, and inform the nature of foundation courses and curriculum responsiveness. The NBTP assessed the academic proficiency of candidates in three core domains. This test is criterion-referenced, providing additional information to complement the norm-referenced National Senior Certificate (NSC) results. About 22 studies dealing with various NBT titles are examined in a systematic review from multiple databases. There is no doubt that the end-product of NBTP will be an invaluable addition to the available current tools used for programme placement at higher education institutions (HEIs) in South Africa. In this fourth industrial revolution (4IR) era, we also recommend NBTP to include Digital Literacy (DL) in the existing core domains. [ABSTRACT FROM AUTHOR]