This study explores the generative artificial intelligence (GAI) prompting practices of Australian primary and secondary educators in the first year following the advent of OpenAI's ChatGPT. Following a brief training workshop on prompting GAI for pedagogical purposes, 38 teachers uploaded 252 prompts they deemed 'pedagogically useful' and 19…

Drawing upon principles of participatory action research, this study collected input from secondary school stakeholders (teachers, students, caregivers, alumni, staff, and administrators) to create a local definition of quality teaching for students at an urban charter school in the northeastern United States. Analysis of stakeholder input…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

Through an extended commentary on the empirical articles in this special issue 'Signature Assessment and Feedback Practices in the Disciplines' we elaborate the concepts of signature assessment and signature feedback practices by developing a new taxonomy of their elements. We propose that signature assessments focus on conceptual,…

We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of…

In an increasingly complex interconnected world, STEAM practices have gained attention in Higher Education (HE). The integration of Sciences, Technology, Engineering and Mathematics pedagogies with those from the Arts takes many forms with myriad intentions, processes and outcomes. Common aspirations pertain to equipping students with…

The quest to improve teaching on a wide scale is an enduring challenge globally. Yet demonstrable improvement in teaching quality is both elusive and slow. In this essay, I explore some of the complexities that contribute to the slow pace of change, including: the slippage between teachers and teaching as the object of improvement; the poorly…

The term blended learning is used frequently, but there is ambiguity about what is meant. What do we mean by blended learning? What, how and why are we blending? In this paper different definitions, models and conceptualizations of blended learning and their implications are discussed. Inclusive definitions and models, and diverse…

Reviewing the literature is an important part of academic work, as it helps readers see what has come before, what has and has not worked, and situates the author's place in the ongoing discussion. Accepting this view, extensive reading literature often points to Day and Bamford (1988) as identifying Kelly (1969) as crediting Palmer (1921) as the…

Empirical evidence is insufficient on the specific roles GIS learning plays in developing students' understanding various spatial concepts. The present study aims to draw attention to common struggles of learning some spatial concepts in geography and offer directions for future research on GIS learning and the development of student spatial…

In this paper, we explore second-level students' understanding of the concept of creativity and the implications for their engagement in class-based assessments. We propose that creativity represents an important outcome of education, particularly at second level. We use a single case study, with data presented from a series of semi-structured…

Big ideas, sometimes referred to as key, core, fundamental or threshold concepts, are widely applicable concepts at the heart of disciplines that are or have been central and influential for their fields. Attention here is particularly directed to meta-concepts common to sister disciplines in the sciences. "Learning thresholds",…

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 purpose of the present article is to investigate the definition of matrix multiplication as a central issue in linear algebra courses. Applying both historical and pedagogical approaches, it focuses on the philosophy of generating the usual matrix multiplication, as a special binary operation, with its partly unexpected form compared with the…

While a mutually agreed-upon definition of STEM education remains elusive, there is no doubt that instructional models and ideas put forward with the STEM label have had a tremendous impact on thinking, debate, and practice in schools worldwide. At issue is the degree to which some or all the STEM disciplines must be taught in a concurrent or…