ABSTRACT. Challenge-based learning (CBL) is a student-centred pedagogic approach in which students work in interdisciplinary teams to find solutions to societal challenges. In CBL, the student teams are assisted by and present solutions to a real-world stakeholder. CBL has several dimensions, including flexible learning paths, real-world impact, 21st century skills, flexible teacher roles, stakeholder involvement and flexible assessment.

There are obvious strengths to CBL reported in the literature, yet teachers find designing courses or programmes that employ a comprehensive adherence to CBL very difficult. An alternative is to identify courses or programmes that already exhibit some characteristics of CBL and strengthening those. We recognise that CBL can be present at three different levels, Mild, Moderate and Intense. For example the teacher role could be learning supervisor and/or field expert (mild), a coach as learning guide (moderate), or a co-researcher and co-learner (Intense) [1].

We present an interactive online tool that draws from an evidence-based database to provide practical advice on how to to transition from current ways of teaching towards CBL ways of teaching [2]. The tool is unique and has drawn interest as being particularly effective for helping teachers focus on those areas of their courses most amendable to a CBL approach [3]. To illustrate how to use the tool, we shall use as a demonstration case a Statistics course offered to second-year bachelor students at our institution. We shall provide a link to a beta version of the tool for those who attend the presentation.

[1] Imanbayeva, A. (2022) Challenge-based learning for fostering students' sense of impact. Masters thesis, University of Twente. [2] Imanbayeva, A., de Graaf, R.S., Poortman, C.L. (2023). Challenge-based learning in courses: the implementation continuum (practice). Proceedings of SEFI 2023. [3] Winner: best poster. CBL conference at the Eindhoven University of Technology, 2023.

ABSTRACT. In many countries, international students form a distinct cohort in first-year mathematics courses. For these students, the transition to university mathematics may demand significant adaptation. A research-based understanding of their experiences would enable host universities to provide effective support as they transition from school mathematics in their home countries to a foreign university context. In this study we analyse four episodes in which an international student from China interacted with the tutor during collaborative first-year tutorials at a New Zealand university. The first two episodes occurred near the start of the semester, and the others towards the end. The analysis reveals changes in the student’s positioning of herself over successive episodes as she embraced local classroom norms. We propose that her positioning shift facilitated a process through which the tutor was able to support her mathematics learning more effectively.

IJMEST special issue: https://doi.org/10.1080/0020739X.2023.2259917

ABSTRACT. When embarking on our journey of learning in mathematics, we may envision a linear path of modules for acquiring mathematical knowledge and understanding to reach a predetermined outcome. However, this is a partial representation since the outcome and path are developing and adapting and our learning is continuously emerging. In this paper, our journey of learning in mathematics is re-envisioned as a complex adaptive system with agents, internal diversity, internal redundancy, decentralised control, sources of disruption and sources of coherence. As will be illustrated through the adaptive cycle of a complex adaptive system, learning may emerge between phases of destabilisation and development. For this emergence there needs to be openness to embrace a disruption, reflection to interpret the disruption, connection to respond to the disruption and inspiration to grow and adapt in response to the disruption. There also needs to be a balance between individual and collective learning. Through navigating these cycles along our journey of learning there may be emergence of learning experiences within and beyond mathematics.

IJMEST special issue: https://doi.org/10.1080/0020739X.2023.2257698

ABSTRACT. Many first-year students find the transition from high school to university mathematics a challenging experience. First-year university mathematics students are expected to demonstrate a higher level of mathematical thinking and problem-solving skills than in high school, and many are unfamiliar with the new learning environment.

This presentation highlights preliminary findings from an ongoing study investigating the effectiveness of Mathematical Thinking Workshops in bridging the gap between high school and university mathematical thinking practices, focusing on at-risk students. Two distinct, self-selected cohorts participate in the study: a general group of first-year university mathematics students, which may include those identified as at-risk, and a group specifically identified as at-risk.

The workshops, whose design and implementation are informed by theoretical frameworks such as APOS theory, ZPD, cognitive load theory, and constructivism, are implemented twice a week throughout the academic year.

We qualitatively gathered insights through focus group interviews with students about the workshops. Quantitatively, we built a predictive model using students’ pre-university data (such as high school results and NBTs) to forecast university performance. We then used this model to predict the performance of workshop attendees and the findings indicated that the workshop students performed better than expected with statistical significance.

Preliminary findings are in line with the enhancement of students' understanding of and the ability to apply mathematical concepts, with notable improvements in their confidence and metacognitive skills. Although our quantitative data revealed promising trends, it’s important to note that students’ outcomes are shaped by a multitude of unaccounted-for factors (which does not form part of this research).

As part of the larger research project, data is being analysed in real-time to provide a more comprehensive ongoing evaluation of the workshops' impact. This study highlights the value of pedagogical interventions in supporting at-risk students in their transition to university-level mathematics.

ABSTRACT. The First Year Mathematics Project is one of the research foci of a tertiary mathematics community of practice in South Africa. The project’s main focus is to research the use of interventions to improve the first-year undergraduate mathematics. The first part of the programme involved the study of published literature in this area. The research question guiding the study was: What was the nature of first year undergraduate mathematics interventions at South African universities? We conducted a scoping review of the relevant literature from 2015 to 2022, using several databases, in particular the SABINET African Journals database which covers all South African online publications. We preferred a scoping review, because, unlike a systematic review, it has less stringent criteria for inclusion and exclusion of articles, as well as a broader scope, providing a better option at this exploratory stage of the study. Three researchers assessed 30 pre-selected articles independently and 14 of the articles met the inclusion criteria. These criteria were: 1) the article must involve first year undergraduate mathematics students of science or engineering and 2) the research must be an intervention aimed at improving student performance. We studied the articles without any pre-assumptions to identify the main themes from the review following grounded theory techniques. Each article was analysed based on the following: the research design, research sample, aims of the study, nature of the intervention, and findings. We identified four main themes; the use of tutors and teaching assistants; 2) feedback from academics and students; 3) teaching approaches; 4) the use of technology. We presented these preliminary findings to the community of practice. The community decided to set up subgroups whose task was to conduct further research into each of the themes. Their work in ongoing.

ABSTRACT. The differences between schooling and school mathematics on the one hand, and university and undergraduate mathematics on the other, are well recognised. These differences - epistemic, ontological, social, linguistic, pedagogical - prompt multiple, varied responses to support students in the school-university transition, each tailored to the contextual specificities. Our four-year long collaborative, research-led curriculum change project focuses on first-year core mathematics for science students at the University of Cape Town. Not only is first-year mathematics performance generally poor, but also inequitable by proxies for ‘race’ and language (Shay et al., 2020), signaling the stubborn legacy of social and educational inequality in South Africa. This has considerable implications for a student’s sense of being, belonging, learning, and ultimate progression as a ‘university science student’. Our multi-level project necessarily attends to micro-level classroom pedagogy and learning resources – the focus of this workshop – and also degree programme structures, course models, student advising, and data analytics.

Recognising and acknowledging students’ schooling experiences, our pedagogy creates opportunities for students to learn and use multiple mathematics practices at the intersection of mathematics knowledges and ways of knowing, mathematics learning, and living. These include: metacognition (e.g. sitting with discomfort, risk-taking, posing questions, ‘knowing’ mathematics); literacies (reading, writing, drawing, using manual and electronic technologies); mathematics discourse practices such as proving, defining, and problem-solving; and working individually and collaboratively. This 90-minute workshop will be experiential, with delegates engaging both as students and metacognitively as lecturers with the material offered, and also discussing the experiences. Specific examples of pedagogies of/for mathematics practices will include storytelling as a means to taking ownership of a learning space; establishing norms for collaborative work; mapping learning of content and process on multiple levels; engaging with different mathematical representations as a route to understanding; and a reading and writing exercise for mathematical proof.

ABSTRACT. In this paper we describe the diagnostic testing processes and purposes for three universities in Australia, Ireland, and the United States, including their design and implementation. We outline the rationale for each process and provide results related to student success (and non-success) and discuss future research agendas in this area. We include summary statistics related to how students perform on certain fundamental mathematical topics, how at-risk and/or under-represented students achieve on such tests, and what actions students are recommended to take after their diagnostic test results. We also discuss pandemic-related impact of diagnostic testing and item classification via factor analysis.

ABSTRACT. Before the COVID-19 pandemic the Mathematics Education Support Hub (MESH) at Western Sydney University ran a series of face-to-face refresher workshops for incoming undergraduate students who wanted to improve their mathematics and statistics skills required for university study. With the onset of the pandemic, it became necessary to redesign these workshops as online modules which students could study in their own time. One aspect of the face-to-face delivery that was lost was the ability of MESH tutors to direct students to the parts of each workshop where they needed to focus their studies.

To overcome this deficiency MESH developed a series of diagnostic tools to help students to determine which sections of each module they needed to study. In order to make the diagnosis as efficient as possible these tools were developed as computer adaptive tests, meaning that questions asked depend on responses to previous questions and students are not asked questions on concepts which they can be assumed to have mastered or which it appears that they are not conversant with.

In order to develop the tools we first needed to construct a “knowledge map” of concepts covered in each module with logical linkages between them. The tools were then built using the Numbas testing system’s Diagnostic test algorithm. Since deployment of the tools in February 2023, the diagnostic tool has been attempted over 800 times.

Whilst we feel that this tool is serving its intended purpose, we felt that it was important to validate its efficacy. To do this we have been able to access full details of all attempts and have used item response theory to rank questions using both direct and implied scoring. In this talk we will discuss the development of the diagnostic tool and the results of the analysis to date.

ABSTRACT. The significance of cross-domain mapping in the context of diagnostic assessment lies in its potential to promote the accuracy of interpretation of performance data and any underlying traits, as well as its ability to illuminate curricular associations and gaps. The university readiness in South Africa is assessed by the National Benchmark Testing (NBT) instruments: the Academic and Quantitative Literacy (AQL) and the Mathematics (MAT). The test scores place candidates in four benchmarks (Proficient, Intermediate Upper and Lower, Basic) and provide an indication of the level of support that will be required once a student is placed in a university programme.

One of the important uses of NBT data is the provision of additional diagnostic information. The diagnostic information must be evidence-based, and consider various perspectives, including subject-specific skills, cross-domain skills, and cognitive demands involved in the acquisition of these skills. From the relative importance analyses performed for multiple disciplines and courses, it is evident that the patterns of the predictor variables (NBT subdomains) explaining variance (R-squared) in the course scores are different for students of differing ability groups. This study explores the relationship between Mathematics and Academic Literacy domains, while supporting the argument for within-class ability-grouping for differentiated instruction/support, considering the skills from both domains.

Using the principles of Cognitive Diagnostic Modelling (CDM) as a framework, we have mapped within-domain and cross-domain associations to two test forms (AQL and MAT) that were administered to 1 050 students on the same day. We conducted various statistical analyses in each of the four performance benchmarks to unpack the combination of attributes (skills measured by two domains) and their impact on the interpretation of the candidates’ abilities.

This research adds to the body of literature on students' academic profiles by examining their competence across various domains and skill sets specific to their disciplines.

ABSTRACT. Statistical literacy has a large and important role in the teaching of statistics. Most mathematics and statistics courses are hierarchical, and the earlier material forms the foundation for later material. We construct a hierarchical structure for an introductory statistics course using Rasch analysis of the student scripts for the final examination. This forms the basis of a statistical literacy construct that has wider implications than just an undergraduate course. The world is overwhelmed with data from an exponentially increasing number of sources. Such data is of various types and contexts, ranging from social, commercial, scientific, survey and human. Statistical literacy has therefore assumed a larger and more important role.

IJMEST special issue: https://doi.org/10.1080/0020739X.2023.2261453

ABSTRACT. The journey from the concept of natural numbers to that of real numbers is some kind of evolution with multiple transitions involving subtle conceptual-imagery shifts. It is challenging to get a precise conceptual understanding of real numbers by the end of the school mathematics education. The reason for this challenge is probably that there is simply no complete set of tools accessible to school learners to help them construct a conceptual imagery of real numbers as devices to measure continuous quantities like duration (time), distance, temperature, etc. The understanding of real numbers is the core prerequisites for calculus, which in turn forms part of essential prerequisites for higher mathematics including applications of mathematics to science, engineering and technology. The lack of conceptual understanding and / or the lack of at least intuitive “working understanding” of the reals shown by freshers at tertiary mathematics education explains the sources difficulties students have in Calculus and in the later branches of mathematics. It is however possible to get school graduates to some working understanding of real numbers positioning Calculus within their zone of proximal development. There are aspects of school mathematics, which if given the appropriate emphasis and interpretation(s) some good working understanding of real numbers can be achieved and at the same getting closer to the accessibility of the notion a continuum, essential for understanding of real numbers.

ABSTRACT. Although research on active learning suggests strong connections to equitable and inclusive teaching, few studies have explored the relationship between the two concepts. In this qualitative study, we examined how 13 participants in an equity-focused workshop described the relationship between active learning, and equitable and inclusive teaching. We used set theory as an analytic tool to categorise their descriptions. We found that all participants saw active learning, and equitable and inclusive teaching as related. The two relationships that were most strongly supported by participants’ statements were that active learning, and equitable and inclusive teaching are related yet independent sets, or that equitable and inclusive teaching is a subset of active learning. We discuss implications of these findings and pose questions for further exploration.

IJMEST special issue: https://doi.org/10.1080/0020739X.2023.2255183