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Challenging mathematical tasks

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James Russo
added a research item
Understanding exponential growth is a fundamental aspect of developing critical numeracy skills; however, typically, exponential growth is introduced in curricular documents to secondary students. Moreover, such introductions tend to be in the context of formal mathematical modeling, divorced from a sense of quantity. We argue that, given its importance, elementary-age children should be presented with opportunities to explore exponential growth patterns and to develop an appreciation for the power of this idea. We put forward four principles of task design that should underpin the development of such learning experiences for elementary-age children and introduce tasks that have been trialed in elementary classrooms that capture these principles.
James Russo
added a research item
Teaching mathematics through problem solving is central to contemporary approaches to mathematics instruction, whilst augmenting problem-solving tasks through enabling and extending prompts ensures that a diverse community of learners are provided with opportunities to be optimally challenged, supporting an inclusive classroom environment. However, it has been frequently assumed that teachers should determine when a student should access an enabling prompt, perhaps in part due to concerns that students might be reluctant to seek prompts themselves because of social stigma associated with help seeking. In this paper, we argue that getting students to access prompts of their own volition should be central to teaching mathematics in this manner. One hundred and thirty-two Year 3-6 students completed a questionnaire disclosing their attitudes towards enabling prompts in classroom environments where they were expected to access prompts themselves. Most students consistently reported that enabling prompts empowered them as learners, allowing them to both take responsibility for, and have success with, their mathematics learning. In particular, students valued being able to access prompts when they were stuck on a task, felt that prompts had the power to increase their understanding, and to approach mathematical tasks with more confidence. Students generally did not associate accessing enabling prompts with being ‘bad’ at mathematics and acknowledged that even strong mathematicians might use a prompt sometimes. There was almost no evidence of any stigma or embarrassment associated with accessing enabling prompts. The implication is that classroom teachers can rapidly establish a culture where students access enabling prompts themselves to support learning mathematics through problem solving.
James Russo
added a research item
In response to increasing teacher interest in how to design and implement effective challenging tasks, James presents the Launch/Explore/Discuss model that builds on the work of leading Australian educators and researchers Peter Sullivan, Doug Clarke, and Charles Lovitt.
James Russo
added a research item
In this paper we report on changes to teachers’ practices as a result of their participation in a research-based program of professional learning focused on challenging tasks. Seventy early years teachers responded to a survey at the end of a year-long program asking them to nominate and describe the teaching practices that changed most as a result of their involvement in the program. The majority of teachers nominated each of ‘Allowing students time to struggle’ and ‘to share their thinking’ as the two practices that changed most. Qualitative responses are used to interpret the nature of and reasons for these reported changes in practice.
James Russo
added a research item
Encouraging teachers to incorporate challenging tasks into mathematics instruction is frequently implored by mathematics educators, due to its potential impact on student learning and persistence. However, there is evidence that teaching with such tasks is pedagogically demanding, particularly for less expert teachers. To support a developing dialogue around the experience of teaching with challenging tasks, I document my experience of teaching 84 lessons involving challenging tasks to three grades of year 1 and 2 students as part of a research project. Adopting a 'practitioner inquiry' lens, I analyse my reflective journal to reveal five themes: classroom management, maintaining and managing cognitive demand, time management, tensions between discussion objectives and tensions in task design. Implications for teacher professional learning are discussed.
James Russo
added a research item
This article reports on a project which involved introducing challenging tasks in the early years’ classrooms of twenty Victorian primary schools. The obstacles teachers encountered and how they overcame those obstacles are discussed.
James Russo
added a research item
In this article we focus on ways that the documented curriculum can inform the construction and implementation of planned sequences of experiences to support mathematics learning. We report on the early stages of a research project which is examining ways that thoughtfully created, cumulative, challenging and connected experiences can both initiate and consolidate mathematics learning. It is intended that through an iterative cycle of design-test-redesign-retest we will ultimately transform the documented curriculum into a set of refined and empirically developed sequences of learning experiences that are accessible by a diverse range of students.
James Russo
added a research item
This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. In this article, I briefly overview how to teach with Challenging Tasks. I then demonstrate how three Challenging Tasks exploring counting sequences can be used to expose young students to prime and composite numbers.
James Russo
added a research item
Teaching with challenging tasks in the early and middle years of primary school can support the development of student reasoning and unleash critical and creative mathematical thinking; however, teaching with challenging tasks can be challenging. Some issues that might arise for teachers when considering teaching with such tasks are: How do you develop (and use) appropriate enabling and extending prompts to support and extend all learners? How should you structure lessons involving challenging tasks? How do you introduce challenging tasks without creating classroom management issues? Although all of these questions are important and warrant examination, the focus of the current paper is on unpacking enabling and extending prompts. The author draws on his firsthand experience of teaching challenging tasks to students in Foundation to Year 4 to explore this issue.
James Russo
added a research item
This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. James Russo shares his experiences of exploring proof with a group of 8-and 9-year old students in an Australian primary school.
James Russo
added a research item
This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. Have students engage in these challenging questions relating to informal and formal measurement concepts, based around these images of the Melbourne Luna Park Moon Man.
James Russo
added a research item
Following an overview of teaching with challenging tasks, we explore the nexus between using both challenging and consolidating tasks to simultaneously develop conceptual understanding and procedural fluency. In particular, we argue that it is critical that students are provided with parallel opportunities to work on consolidating tasks, in order to connect conceptual understanding to improved strategy efficiency. This discussion makes reference to the Big Ideas in (primary) mathematics (Charles & Carmel, 2005) and provides three examples of challenging and consolidating tasks, each of which support students in grappling with a different ‘Big Idea’.
James Russo
added a research item
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.
James Russo
added 8 research items
This theoretical paper argues that the reform in mathematics towards more problem-based learning can be made consistent with cognitive load theory through the use of carefully designed challenging tasks. It is argued that such tasks can provide the benefits of problem-based approaches whilst being cognisant of the issue of cognitive overload. Possible directions for future research are suggested.
This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. Can your students work out how many Smarties there might be in the Smarties-box? The Smarties-Box Challenge encourages students to apply several different mathematical capabilities and concepts—such as, estimation, multiplication, and the notion of being systematic—to solve a complex, multistep problem.
This article provides a brief overview of challenging tasks, describing what they are, how teachers can use them in classrooms and introduces two example tasks.