Table Mountain Delta: Reflect. Connect. Be inspired!

This special issue comprises articles presented at the Fourteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, held in Cape Town, South Africa in November 2023. Each conference in this series is named a ‘Delta’ conference in recognition of the constant state of change experienced by educators and students alike. The conferences are also named in recognition of where they are held. As such, the 2023 conference is named Table Mountain Delta in acknowledgement of this characteristic Capetonian feature. This is the 10th such Special Issue, affirming the strong link between the Delta community and the International Journal of Mathematics Education in Science and Technology (IJMEST), a journal that provides a forum for researchers and practitioners to disseminate and derive insights from high-quality pedagogical research with tangible applications for the mathematics classroom.

Rooted in the Southern Hemisphere, the Delta conference series owes its inception to the members of the mathematics education communities of South Africa, Australia and New Zealand, and meetings have been held in South Africa, Australia, New Zealand, Argentina and Brazil. Table Mountain Delta is the fourth time South Africa is hosting, the others having been in 2001, 2009 and 2015. While the Southern Hemisphere is well represented in the Delta community, we welcome our Northern Hemisphere colleagues as well, as the articles in this Special Issue attest, indicating the global reach and relevance of the Delta community. In this Issue we have four articles from the North, all from the United States, as well as one from New Zealand, two from Australia and three from South Africa. This diversity of voices and perspectives collectively underscores the intrinsic international character of the Delta community and its shared commitment to advancing the frontiers of mathematics and statistics education.

In this Special Issue, there are five articles that delve into the teaching and learning of specific mathematical topics, or suites of topics. These include single and multivariable integration, linear transformations, first-year statistical literacy and engaging with proofs in topology. Of the remaining five articles, two have applicability beyond the mathematics classroom. These are a study on growth mindset interventions and assessment methods, and a study on the intersection of active learning with equitable and inclusive teaching. The remaining three investigate students’ journeys in tertiary mathematics, each from a different perspective, shedding light on the role of mathematics in shaping academic success, identity formation and the learning process itself.

El Turkey, Kottegoda and Siriwardena report on a study into the design of inquiry-oriented tasks in single variable integral calculus. Employing a methodological lens of design-as-intention, seven themes emerge as key to the design process. Two of the 11 inquiry-oriented tasks in the study are included in an Appendix, as an illustration of the design principles. The researchers observe that their design intentions were found to span the instructional practices of inquiry-oriented instruction, teaching for fostering creativity and teaching for fostering reflections. Also in the area of integral calculus, Khemane, Padayachee and Shaw focus on double integrals, specifically the challenges students encounter when required to change the order of integration. They use the APOS theoretical framework (Dubinsky & Mcdonald, 2001) to construct a preliminary genetic decomposition, which they encourage others to use as a starting point for designing instructional materials. Also employing APOS theory (Arnon et al., 2014; Oktaç et al., 2022), Dogan considers students’ different conceptualisations of the range of a linear transformation. Analysing students’ responses to a transformation task, they categorise responses and identify coordinated topics connected with each category, such as matrix multiplication or linear combinations. Certain coordinated topics were more enabling of mental progression than others. They find an important link between the progression of mental mechanisms of the range concept, and the coordinated topics.

Khan and L’Boy apply a suitably statistics-based methodology to a study on statistical literacy, using the Rasch measurement method (Rasch, 1960) to develop a hierarchical framework of concepts. The three levels of tautological concepts, non-contextual understanding and critical statistical thinking and reasoning are suitable for applying to a first-year university statistics curriculum. The qualitative study by Gallagher and Infante is the last of our ‘topic-contextualised’ articles, highlighting the importance of generic examples in understanding mathematics. They use a framework grounded in the Toulmin argumentation model (Yopp & Ely, 2016) to analyse generic examples generated by a student producing proofs in a topology course and conclude that, while generic examples were key to the student’s development of understanding, they need to be fit for purpose. A generic example which is ideal for one context is unlikely to be straightforwardly transferrable to another context.

Two of the articles in this Special Issue locate their studies in a mathematics classroom context, yet could be broadly applicable elsewhere. Bennett, Uhing, Williams and Kress are interested in the intersection between active learning and equitable and inclusive teaching, drawing on literature that defines and discusses these approaches separately as well as together. Data were gathered from undergraduate mathematics faculty members participating in a year-long equity workshop and who were also familiar with active learning practices. Results show an inclination towards considering equitable and inclusive teaching as a subset of active learning, yet the authors acknowledge that their study generates more questions than answers and call for more research. Campbell employs adapted surveys and interviews to assess mindsets of engineering students studying mathematics. She finds that, of the experiences that promote the development of growth mindsets reported in the literature, several were prominent among the students in her study, while others were completely absent. Campbell uses this as an opportunity to critique mindset assessment methods and the utility of mindset interventions. She closes with a list of implications for practice and calls for more studies of mindsets outside the US and in the post-secondary education sector.

Three articles share a common thread of exploring the intricate relationship between mathematics and identity in the context of education. Khan and Tsui ask how much mathematics performance affects performance in engineering and if it is a barrier for student retention and completion of an engineering course. They use both statistical analysis of student performance, demographics and survey data and thematic analysis of student interviews to investigate the importance of mathematics to overall academic success and persistence in engineering. Locke, Kontorovich and Darragh use positioning theory (Van Langenhove & Harré, 1999) to analyse the changes in the mathematical identity of a Chinese international student over the course of her first year of mathematics at university. Viewing the formation and development of mathematical identity as a dialectical relationship between personal and social identities, they analyse four interactions between the student and her tutor which show how her positioning of herself in collaborative first-year mathematics tutorials changed over the duration of the course. Rewitzky re-envisions the journey of learning mathematics as a series of adaptive cycles in a complex adaptive system. Through this lens, learning emerges between phases of destabilisation and development. Balancing sources of coherence and disruption, two key features for successful learning emerge: interconnectedness and decentralised control, and internal diversity of ideas with shared knowledge.

Within this Special Issue, there is a broad range of theoretical frameworks and methodologies. Certain approaches are established stalwarts that underscore their enduring relevance in mathematics and statistics education. Examples are the Rasch measurement method (Khan and L’Boy) and APOS theory (Dogan, as well as Khemane et al.). Other approaches are innovative and thought-provoking. We include here Rewitzky’s envisioning of the mathematics learning journey as a complex adaptive system, viewing mathematical identity as a dialectic relationship between personal identity and social identity (Locke et al.), and taking a set-theoretic approach to the intersection (or not) between pedagogic approaches such as active learning and equitable and inclusive teaching (Bennett et al.). These diverse perspectives collectively enrich our understanding of the field, offering a wide-ranging view of the ever-evolving landscape of mathematics and statistics education.

A defining feature of the Delta community lies in its diverse composition, including theoretical educational researchers, mathematicians, educators and students. The Delta conferences themselves serve as unifying occasions, set in beautiful parts of the world, where our community convenes physically for six days once every two years. Among these, Table Mountain Delta in the picturesque Waterfront area of Cape Town stands as a noteworthy gathering point. The Delta community is united by a shared passion for enhancing the teaching and learning of undergraduate mathematics and statistics, each offering distinct perspectives to this common goal. It is this steadfast commitment to the scholarly and practical aspects of mathematics and statistics education that infuses the conference with invaluable discourse, combining research and practice to foster educational excellence, and this Special Issue is testimony to this commitment.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.