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…

Pedagogical Content Knowledge (PCK) is a fundamental component for effective teaching and plays a crucial role in teacher education. Even though pre-service teachers are engaged in training to improve their PCK, the literature reveals that most of their difficulties in practicum courses stem from their PCK. The purpose of this research is to…

Function is a multifaceted and essential concept in mathematics that includes various complex ideas such as mapping, relations between variables, algebra, input-output, and rule. Pre-service mathematics teachers' (PMTs) should have a rich understanding of these ideas for their future teaching practices. However, research showed that PMTs had a…

The paper introduces the notion of collateral creativity as an unintended outcome of the appropriate use of technology, both physical and digital, in the teaching of mathematics. The notion is motivated by Dewey's conceptual framework of collateral learning which enables one gaining knowledge beyond the intent of the traditional curriculum.…

Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply…

Problem posing is an indispensable constituent of mathematical thinking, which makes it a requisite ability for students of all grades. Therefore, pre- and in-service teachers should carry out problem posing activities of high quality, and having them pose non-routine problems may be a good way to make this happen. In this context, this study…

Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

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…

We are four academics teaching mathematics at three different higher education institutions over two continents. Through fortnightly meetings to research how our practices changed as a result of the COVID-19 lockdowns, we formed a community of practice. The process of articulating our experiences and ideas, and reflecting on the recorded meetings…

Academic integrity at our small Canadian college is informed by several key frameworks and centred around teaching, learning, and proactive education. Mathematics assessments were quickly moved through various learning environments over the past year, showing that some assessment design strategies were no longer feasible if they instead centred on…

Peer-Assisted Learning (PAL) schemes typically involve student volunteers (PAL Leaders) designing and delivering sessions that support groups of students in lower years with their studies. This paper discusses three different PAL schemes, within Mathematics degrees at Sheffield Hallam University (a Post-92 University) and The University of York (a…

In this classroom note, we outline a system of assessment used by the authors since 2020 to deliver individualized summative assessments to students from first- and second-year mathematics courses. Our system comprises three modular components allowing a mix-and-match of different technological approaches and mathematical question types. First is…

During the COVID-19 pandemic, the teaching of programming for undergraduate mathematicians was moved online. This was delivered asynchronously, with students working through notes and exercises and asking for help from staff via online messages as needed. Staff delivery time was redirected from content delivery into a formal system of formative…

Through the global pandemic, the single greatest challenge at universities has been the move towards digital assessment. In this classroom note, we describe our new no-exam assessment setup in a Statistics course for third-year bachelor Mechanical Engineering students. The main idea is to assess the students based on self-generated problems.…

In March 2020, COVID-19 restrictions required our university courses to be offered in online mode only. This quick transition meant that lecturers were suddenly tasked with adapting their classroom-based teaching approaches and materials to the online space. For mathematics teacher educators (MTEs), whose on-campus classes were characterized by…