ABSTRACT. People love to see patterns. People love to tell stories. Most people that is. Statisticians have a different way of looking at the world. In this talk I will introduce three guiding principles so that you too can become a kill-joy.

• GIGO. Statistics tries to generalise from data to answer questions about a population of interest. With your “stats hat” on the first questions you should ask are: Where did the data come from? Did it select itself? Is some of the data missing?
• First rule out the boring explanation. As a statistician a big part of your job is to ask the kill-joy question “But couldn’t that just be due to chance?”
• Correlation doesn’t imply causation. Of course we all know this, but why is it so hard to know when things cause other things? Is that glass of wine with dinner good for us or not?

ABSTRACT. We present the preliminary results from a project investigating a large statistics class designed for and taught using a flipped classroom model, with pre-recorded videos. The study, undertaken in 2021 during the Covid-19 pandemic, utilized student surveys in conjunction with metadata on their engagement with electronic resources. This preliminary investigation focuses on the quantitative aspects of the metadata, final grades, and modes of learning. We aimed to identify which particular resources or activities were most beneficial to student learning, as measured by final grade. We found no differences between different modes of teaching (online/in-person; U=4284.5, P=0.79) or between those who completed a survey and those who did not (U=3383.5, P=0.27). All predictors were positively correlated to the final grade (correlations from 0.211 to 0.763) and each other (correlations between 0.199 and 0.986). Overall, all engagement with the subject, whether passive or active, assessed or not assessed, contributed positively to their learning.

ABSTRACT. Developing statistical literacy skills is an important outcome of mathematics curricula in helping learners meet the demands of the 21st century and teachers need to be well prepared to achieve these objectives with their learners. The purpose of this study was to explore primary pre-service teachers’(PSTs) knowledge of the mean and median as measures of central tendency. There were 1647 written responses generated by 183 PSTs written responses to nine items which were analysed using content analysis based on the Mathematical Knowledge for Teaching framework. The results showed that 95% of the participants were able to carry out simple computations of the mean and median. Furthermore, more than 90% of the group were able to identify errors or underlying misconceptions in learners’ responses. However, the PSTs did not find it as easy to provide feedback to learners about how the learners could correct or recognize the errors related to the mean or the median. Seventy percent of the PST’s gave feedback about the error in the mean while 41% did the same when presented with errors about the median. It is clear that pre-service teachers require more opportunities to think about feedback that can be given to learners when they make mistakes. In terms of the higher level cognitive demands related to the SCK subdomain for the mean, 61% were able to solve the problem requiring them to unpack the calculation of the mean. Effective teaching requires useful feedback to learners on how their misconceptions can be addressed and PSTs need support in developing these skills. Solving problems at a high level of cognitive demand are also important experiences for PSTs to help them develop statistical literacy skills, so teacher preparation programmes must ensure that primary school PSTs are able to solve such problems.

ABSTRACT. Universities in Australia collect a considerable about of demographic data about their students. In this paper, such data is analysed in the context of university mathematics and statistics subjects and students' final marks for these subjects. The aim is to determine what, if anything, can be concluded from such data, especially in the context of informing decisions on targeted resourcing or additional support with the goal of improving students' marks.

Over 5000 records from ten subjects with high failure rates were analysed.

It was found that most of the demographic information collected by our university is of minimal use for predicting students' final marks in the mathematics and statistics subjects investigated. The demographic information analysed included language spoken at home, age, socioeconomic status, international or domestic status, parents' education, full-time or part-time study, and pathway to university.

The two predictors of most interest are the level of mathematics studied, and the ranking within the state received, in the final two years of secondary school. Gender was the least significant of the demographic factors studied.

ABSTRACT. Universities around the world were suddenly confronted by the Covid 19 pandemic lockdown in 2020. Higher education students and teachers were thrust into an environment of emergency online teaching and learning. Within days higher education shifted to a new mode of delivery from face-to-face to an online platform in an attempt at connecting students, teachers and content via learning management systems. Online teaching is not a new discourse, however, the narratives of four mathematics educators showed that having digital tools does not necessary equip one with expertise to mediate online content delivery. Through an autoethnographic study, four mathematics teacher educators from Ghana, South Africa and New Zealand reflect on their practice across borders within the higher education context during this period of change. The responsive transition to online teaching meant an immediate shift in our practice and discourse as mathematics educators. Merging boundaries and having a wider reach are some of the unintentional consequences of remote online teaching. Regardless of the different demographics the transitional experiences of the four mathematics educators from on-campus face-to-face teaching to online teaching revealed that the challenges pertaining to teaching of mathematics online were the same. On the other hand, mathematics teaching and learning was no longer confined by the on-campus boundary. Could the far- reaching potential of online learning have implications for higher education across country borders for mathematics educators and researchers to reflect, connect and be inspired?

ABSTRACT. In the Covid era, online and open-book assessments were forced on universities. While this was intended to be a temporary and undesirable measure, several advantages of online, open-book examinations became apparent. These include resource savings as examination papers do not need to be printed, and the ease of sharing the scripts among a team of markers. This research is on appropriate types of questions to include in such examinations. We first discuss a survey of students and staff regarding their experience of online examination during the Covid lockdown. We then consider online, open-book, timed examinations for a first-year mathematics examination, and take-home, open-book, open-internet, untimed but set submission time examination for two higher level applied statistics units. Our experience dictates that such examinations are not only feasible but desirable. In particular, several graduate attributes for the applied statistics units cannot be tested in a traditional, timed, closed-internet examination.

ABSTRACT. Mathematics learning is significantly influenced by students' beliefs of mathematics. The importance of students' beliefs of mathematics has been shown repeatedly over many years by numerous researchers. Beliefs are founded on learning experiences and are an individualistic interpretation. This paper reflects on an investigation aimed at measuring first-year calculus students’ beliefs regarding mathematics. Using questions from the standardised Indiana Mathematical Belief Scale (IMBS), a quantitative measure of these beliefs was attained. The questionnaires were administered to 118 first-year calculus students at a South African university and descriptive analysis was performed on the data. These results pointed out that the highest mean value for the belief "Understanding", has considerably more significance than the belief of “Achieving the correct answer”. The results also demonstrated that this particular group of students strongly concur that making an effort and working hard can have an advantageous effect on mathematical abilities. However, it was unsettling to learn that students thought mathematics required step-by-step processes, as observed from the lowest mean for the belief “Steps”. Implications stemming from this contradiction are that students do not necessarily understand the difference between step-by-step procedures and conceptual understanding, which might indicate that even their belief systems about mathematics are conflicted.

ABSTRACT. Expert mathematicians use examples and visual representations as part of their informal mathematics reasoning when constructing proofs. In contrast, the ways undergraduates reason and work toward creating proofs is an open area of investigation, particularly in advanced mathematics. Furthermore, research on students’ reasoning in topology is largely unexplored. Building on findings from Gallagher [(2020). Identifying Structure in Introductory Topology: Diagrams, Examples, and Gestures. Doctoral Dissertation, West Virginia University, Morgantown, West Virginia. https://researchrepository.wvu.edu/etd/7599/ (MS #8610)], we present a case study of an undergraduate taking a first course in general topology and her use of generic examples in argumentation prior to producing formal proofs and counterexamples. We discuss patterns that emerged in her use of generic examples when proving true statements and disproving false claims. We compare and contrast this student’s generic examples with other generic examples in the literature from other content areas within mathematics, and we argue that generic examples are not one-size-fits-all but rather must be fit-for-purpose. Our results suggest that generic examples may be particularly useful for students writing proofs when they may not have access to specific examples.

IJMEST special issue: https://doi.org/10.1080/0020739X.2023.2256732

ABSTRACT. Students that classify as having growth mindsets rather than fixed mindsets enjoy greater academic success. This finding has been repeated in a variety of contexts and encourages teachers and researchers to develop growth mindsets in students. However, neutral and negative conclusions from some mindset intervention studies raise questions about the conditions in which growth mindsets develop. This study contributes evidence and suggestions to guide the development and assessment of growth mindsets in university students. The five-stage behaviour change model provides a framework to explain why mindset interventions may cause shifts that are not detected in the short term. Mindset assessment methods with original and adapted scales are presented and critiqued. I compare literature-sourced experiences used in growth mindset interventions with interview data from seven first-year engineering students at a South African university to help determine if growth mindset interventions for university students are worth implementing. I summarise implications for practice when assessing mindsets or using growth mindset interventions.

IJMEST special issue: https://doi.org/10.1080/0020739X.2023.2255212

Free version: https://www.researchgate.net/publication/374452164_Exploring_growth_mindset_experiences_in_university_students#fullTextFileContent 

For analysing PDF documents: PDFGear https://www.pdfgear.com/

For finding and analysing references: https://elicit.com

ABSTRACT. Motivation and Target Audience

Physical scientists and engineers are active and intensive users of mathematics. But the siloed nature of mathematics and applied departments often means that no courses are designed to bridge the gap; mathematics courses teach only the algebraic and calculus manipulations and applied courses assume that students already have experience applying those mathematics skills within scientific models. For over 25 years at Oregon State University we have been studying student reasoning and designing curriculum to bridge this gap (Paradigms Team, 2019–2023). One of the most powerful approaches that we have discovered is to emphasize the geometry of the physical situation, and one of the most powerful representations we employ is kinesthetic activities that ask students to use their bodies and their embodied cognition to model that geometry. Our target audience is teachers of single- and multi-variable calculus and/or complex numbers and researchers who study student reasoning in these contexts.

Workshop Content

Participants will explore two examples: complex numbers, with applications to both the time evolution of quantum spin systems and to quantum computing, and scalar line and surface integrals, with applications involving density, a concept common to multiple scientific disciplines.

The workshop will interweave kinesthetic activities, small group problem-solving, and discussions about implementation strategies. Participants will also learn how physical scientists and engineers use this content in applications.

A brief discussion of equity considerations for kinesthetic activities will be included. How might you accommodate people who cannot physically perform the kinesthetic activity? How might you accommodate people who are reluctant to participate publicly with the whole group?

ABSTRACT. The transition from high school to university has long been a challenge for mathematics students, with a widening gap in content comprehension and application. This study provides a comprehensive exploration of this gap, focusing on trigonometry and calculus, two pivotal areas in the mathematical curriculum. By analysing the National Senior Certificate (NSC) examination reports and first-year university mathematics results over a span of five years, the research delves deep into the challenges and opportunities presented in this educational transition. In this study we answer the following question, “What should be done to improve and align the mathematical content and teaching of calculus and trigonometry, to ease the transition to first-year university mathematics?”. The study is framed by the needs assessment theory and the Cultural-Historical Activity Theory (CHAT) and employs a mixed-methods approach to data collection. A mixed-methods approach is used to collect quantitative data from surveys and qualitative data from interviews. A sample of South African university lecturers teaching students who make the school-to-university transition is surveyed, to gather data on their perceptions of the transition gap. Additionally, interviews with the mathematics educators provide insights into their perspectives on the challenges and strategies for addressing the gap. Surveys were conducted with South African university lecturers who teach transitioning students, and interviews were held with mathematics educators. The findings reveal specific challenges faced by students in trigonometry and calculus, with underlying factors like prior educational experiences, socio-economic conditions, and cultural nuances playing significant roles. The study concludes with the emphasis on targeted interventions to bridge the transition gap, paving the way for a more equitable higher education landscape in South Africa.

ABSTRACT. This paper underscores the significance of adopting a holistic approach to support mathematics learners across both basic and higher education levels. While some may view this approach as a luxury, particularly in low-income settings, its pivotal role in promoting both academic achievement and overall student well-being is undeniable. Through a comprehensive rapid literature review, this paper delves into various studies concerning the holistic approach in mathematics education a subject that often induces apprehension among many learners. The aim of this holistic approach is to inspire students, consequently altering their perceptions and attitudes towards learning mathematics. A rigorous methodological approach was utilised to guarantee integrity and transparency. Initially, the study followed the Preferred Reporting Items for Systematic Reviews (PRISMA) guidelines. This procedure was augmented by Rayyan, an Artificial Intelligence (AI) tool tailored for collaborative systematic literature reviews. With Rayyan, authors were able to blindly screen titles and abstracts of prospective papers. Literature review was procured from three databases: Engineering Village, ERIC via EBSCOHost, and Scopus. From these sources, 95 papers were initially identified based on specified search keywords. Of the 95, a mere 30 met the exacting empirical research criteria. These selected papers then underwent categorisation via coding analysis, capturing all relevant themes. Among the key findings, this paper highlights the indispensability of academic support services, psychosocial interventions, and meeting basic needs such as housing and food security to create an environment conducive for effective learning. Drawing on these insights a conceptual framework aimed at enhancing the transition of students from school was formulated. It is recommended that by addressing the full spectrum of learner needs, potential academic setbacks can be circumvented, laying a solid foundation for the development of non-academic skills. This comprehensive approach resonates perfectly with the overarching goals of both basic and higher education institutions.

ABSTRACT. The advent of the COVID-19 pandemic and the consequent move to online education have impacted students enrolling in universities from 2021 onward. Many students in South Africa found themselves unable to engage with online education, resulting in a significant portion of the incoming first-year cohort lacking the essential digital skills required for their university learning, leaving them ill-equipped for their academic endeavours. The lecturers of two first-year courses became aware that several students had difficulties using a computer and could not solve problems involving mathematical content in real-life contexts. This paper presents the first stage of the action research cycle to diagnose the problematic situation experienced in the computing classroom. The diagnosis of the problem was done using reflective practice to gain an understanding of the experiences of the students. It was found that the students lack digital literacy such as keyboard and mouse skills as well as mathematical literacy. The paper concludes with potential strategies for the action planning phase to alleviate the literacy gap.

ABSTRACT. This paper seeks to explore the effect of remote teaching and learning on the challenges faced by preservice mathematics teachers when learning mathematics education during Covid 19 and remote teaching limited to four universities two in South Africa, one in Ghana, and one in New Zealand university. The study followed a quantitative research approach to select a survey research design. A total of 95 preservice mathematics teachers from four universities were randomly assigned to participate in the completion of an online survey. The participants signed the informed consent forms before completing the survey to comply with the ethical requirements. The study revealed two preservice mathematics teachers challenging factors during remote teaching and learning, data, and technological devices for learning. The findings revealed that there is no significant difference p < .000 between remote teaching and learning and the challenges faced by preservice mathematics teachers when learning during the Covid era, Therefore, the null hypothesis is rejected since p < .05 level of significance. The study concludes that the challenges were more on technological devices for learning. The recommendation is that relevant technological devices need to be provided for the learning of preservice mathematics teachers.

ABSTRACT. We’ve all heard of machine learning and artificial intelligence. But can we approach and explain this rapidly advancing field with fundamental mathematics? The answer is yes, and, in this workshop, we’ll show you how. A linear algebra inspired, digit recognition algorithm will be presented, based exclusively on linear algebra concepts studied in a 1^st linear algebra class taken by STEM students. We will walk the audience through the algorithm in detail and then wrap up with an interactive demonstration in MATLAB. [Sponsor Presentation: MathWorks]

ABSTRACT. In teaching large undergraduate statistics courses, we had previously followed a standard model of Lectures supplemented by Tutorials and Computer Lab classes. We undertook an extensive re-design of these classes to improve groupwork and collaboration, and to better utilise computing power for producing graphs and conducting analysis. Our re-design aimed to combine the strengths of both types of classes, while removing this artificial separation between types of tasks and building a more authentic learning experience. This was achieved as part of a pilot program trialling our Next Generation tutorial rooms - small-group teaching spaces trialling new electronic whiteboard technology equipped with a fully-featured Windows PC. While this technology has its advantages, most of the benefits are possible within a standard computer lab setting. We will discuss the materials/tasks themselves, what we learned through the process of developing them, and the evaluation of the materials for student learning.