The current paper overviews a nine-month PhD study that investigated the impact of learning mathematics through sequences of challenging tasks on the mathematical competence and attitudes of Year 2 students (n = 59). Adopting a Self-Determination Theory lens, a pragmatist paradigm and a mixed-method design, the study found that at all levels of…

Despite curriculum expectations, many students, including a disproportionate number of girls, do not 'just know' (retrieve) single-digit addition facts by Year 3. The current study employed structured interviews to explore which strategies Year 3/4 students (n = 166) used when solving more difficult addition combinations. Results revealed that…

Learning statistics can be challenging for many students, due to their inability to engage in statistical reasoning and application of techniques. This challenge becomes compounded in online learning contexts where students are spatially and temporally separated from the teacher. This paper describes and explains a case of theory-driven…

In cognitive load theory, the superiority of the Example-Problem sequence over the Problem-Example sequence has become a classic paradigm. The comparative effectiveness of these sequences, however, is subject to the influence of the factors of element interactivity and prior knowledge, and studies have examined these influences focused mostly on…

Making accurate judgements and interpretations about student growth and progress in mathematics can be problematic when using open-ended assessments. This study reports on the development of a class-based assessment instrument and marking key designed to assess Year 2 students' mathematics competence to reflect their learning of mathematics…

This study investigated the effectiveness of using a sequence of worked examples as part of the feedback cycle. Worked examples were either presented as full worked examples or partial worked examples (single-step and completion formats). In two experiments, grade 8 students completed a learning phase on a mathematics topic, which was immediately…

This collaborative inquiry between an academic (James Russo) and two school-based practitioners (Jessie McCosh and Travis Hewish) explores student attitudes towards learning mathematics through problem solving in a medium sized primary school in regional Victoria.

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

This paper reports the results of an investigation into the ways pre-service teachers engaged in structured problem solving as part of their first-year mathematics education course. The purpose of this study was to determine the preferred problem solving strategies of pre-service teachers and the types of difficulties they experienced. The written…

Given what is known about the importance of productive struggle for supporting student learning of mathematics at all levels, the current study sought to examine teacher attitudes towards student struggle when students learn mathematics in remote learning settings compared with classroom settings. Eighty-two Australian early years primary teachers…

This paper outlines a seven-step process for developing problem-solving tasks informed by cognitive load theory. Through an example of a task developed for Year 2 students, we show how this approach can be used to produce challenging mathematical tasks that aim to optimise cognitive load for each student.

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

Student learning is greatest in classrooms where students engage in problem solving tasks that are cognitively demanding. However, there are growing concerns that many Australian students are given limited opportunities to engage in these types of tasks. 108 upper primary school teachers were surveyed to examine task features and cognitive demand…

The application of skills and knowledge to a "real world" context entails a greater set of competencies than just technical proficiency, for both the student who sits the problem and the teacher who sets it. These competencies require unpacking. A greater understanding of these competencies would enable teachers to create tasks that test…

There have been many attempts to reform mathematics teaching in Australia to encourage teachers to use more cognitively demanding tasks that focus on problem solving and reasoning. However, there is limited specific advice for teachers on how best to do this. This paper reports on one set of survey items that examines 52 teachers' responses to…