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Teaching mathematics in primary schools with Challenging Tasks: The big not so friendly giant

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Teaching mathematics in primary schools with Challenging Tasks: The big not so friendly giant

Abstract

The use of enabling and extending prompts allows tasks to be both accessible and challenging within a classroom. This article provides an example of how to use enabling and extending prompts effectively when employing a challenging tasks in Year 2.
... Enabling prompts can be thought of as a type of 'reverse scaffold', whereby rather than support being removed as students become more competent and independent, support can be accessed by students on a 'just-in-time' basis when required. Enabling prompts provide an alternative to teacher telling (Sullivan et al., 2014), and are sometimes referred to in the classroom using the student-friendly term 'hint sheet' (Russo, 2016). By contrast, extending prompts expose students to an additional task that is more challenging but involves similar reasoning, conceptualizations and representations as the main task (Sullivan et al., 2006). ...
... Examples of the types of challenging tasks included in the current program have been published elsewhere (e.g. Russo, 2016;Russo & Hopkins, 2017a). 3 ...
... Indeed, it was apparent, particularly from Polly's and Rachel's accounts, that the early stages of the first unit of work were associated with high levels of teacher anxiety, as students began to navigate, some perhaps for the first time, what has been termed the Bzone of confusion^ (Clarke, Cheeseman, Roche & van der Schans, 2014, p. 58). It has been argued that teachers can facilitate student persistence through normalizing the concept of the zone of confusion in the mathematics classroom and providing students with avenues for taking constructive action when confronted with this state (Russo, 2016). The current study provides some support for this contention. ...
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Research suggests that teachers of mathematics are frequently reluctant to pose challenging tasks to students. Reasons for this reluctance include fears of negative student reactions, time and resource constraints, and a lack of relevant teacher content knowledge. The current study involved interviewing three early primary-grade (elementary) teachers to explore their perceptions of teaching with challenging tasks, following their observations of 2 units of mathematical work taught by the first author. Contrary to some other studies where classroom teachers were themselves observed teaching with such tasks and asked to reflect on the experience, we found that teacher-participants perceived that students responded positively to the 2 units of work. Specifically, teacher-participants described their students as autonomous, persistent and highly engaged. These positive student reactions were attributed to a variety of factors, including a classroom culture that embraced struggle, high teacher expectations, and consistent classroom routines. Despite these positive reflections, teacher-participants differed in their views of whether challenging tasks are a suitable means of differentiating instruction, with such evaluations apparently linked to how they defined student success.
... Challenging tasks are complex and absorbing mathematical problems with multiple solution pathways, whereby the whole class works on the same problem. The task is differentiated through the use of enabling and extending prompts (Sullivan & Mornane, 2013), the former of which are sometimes referred to as the 'hint sheet' (Russo, 2016a). Generally teaching with cognitively demanding tasks involves a three-stage process: launch, explore, discuss (with summary) (Stein et al., 2008). ...
... Teacher-participants observed the researcher deliver two units of work across Terms 2 and 3 of 2016: one unit of work relating to number patterns (Patterning Unit), and another unit of work relating to addition and missing addend problems (Addition Unit). Examples of some of the challenging tasks included in the units of work have been published elsewhere (e.g., Russo, 2015Russo, , 2016aRusso, , 2016bRusso, , 2016cRusso & Hopkins, 2017b). ...
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Despite reforms in mathematics education, many teachers remain reluctant to incorporate challenging (i.e., more cognitively demanding) tasks into their mathematics instruction. The current study examines how lesson structure shapes teacher perceptions of teaching with challenging tasks. Participants included three Year 1/2 classroom teachers who observed the researcher (first author) deliver two units of mathematical work. Teacher-participants were given an opportunity to observe the use of challenging tasks to both launch lessons (Task-First Approach) and extend student thinking (Teach-First Approach). It was revealed that teacher-participants perceived both the Task-First Approach and the Teach-First Approach to teaching with challenging tasks to have particular strengths. Specifically, the Task-First Approach was viewed as engaging and empowering for students, providing an opportunity to build student persistence whilst fostering student mathematical creativity. Teachers also placed value on the quality of the mathematical discussion which emerged, and the value of the Task-First Approach for supporting an authentic assessment of student mathematical knowledge. By contrast, the Teach-First Approach was viewed as highly focussed, and an efficient approach to learning. It was also perceived as providing an opportunity for lower-achieving and less confident students to be successful. Although there appear to be distinct advantages to both the Task-First and Teach-First Approaches, the study revealed that the most dramatic shift in teaching practice for some teachers may be the incorporation of more cognitively demanding tasks into their mathematics instruction in any capacity.
... One key feature of challenging tasks is their authenticity in the sense that they are characterized by a certain degree of complexity and they are not amenable to a ready-made solution (Diezman & Watters, 2000). Students should be engaged in challenging tasks for important pedagogical, psychological and social reasons (Powell et al., 2009) even in the early years of schooling when they possess a very small fraction of formal mathematical knowledge, thus allowing students at different levels to pursue the same learning objective (Russo, 2016). Challenging tasks "engage students in cognitive processes at the level of doing mathematics and engage students in high-level thinking and reasoning" (Henningsen & Stein, 1997, p. 546). ...
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Rich and challenging tasks can be the vehicle to bring mathematical challenge in classroom. Challenge emerges when you don’t know how to solve the task at first but you can figure out, that is when the solvers are not aware of certain tools to solve the tasks and they have therefore to invent some mathematical actions to proceed. Some challenging tasks in the paper-and-pencil as well as in a digital environment will be presented. The aim is to highlight their potential (i) in engaging students to actions that make sense for them from the mathematical point of view, (ii) to support students in their experimentation and development of problem-solving strategies, (iii) to foster creative mathematical thinking, and (iv) to provoke students’ curiosity as the starting point of meaning-making actions in mathematics.
... Equally, productive struggles ensue when students are given the support structure during problem-solving [7]. In classrooms, at the center of teaching and learning, teachers are expected to create a learning environment that values and promotes productive struggles among students by using challenging learning tasks that are nonetheless accessible to all students [18][19][20][21]. Productive struggle, which is stimulated by using challenging tasks during learning and teaching, supports students' cognitive growth and is essential for their learning of mathematics with understanding. ...
... This article looks at examples of challenging mathematical tasks designed to enable students of all abilities to experience productive struggle, and examines the lesson structure and teacher's role when implementing a challenging task, along with students' responses to being challenged through the tasks. It adds to existing research on challenging tasks, including in previous editions of APMC (e.g., Cheeseman, Clarke, Roche, & Walker, 2016;Roche & Clarke, 2014;Russo, 2016) through challenging tasks being used to evoke productive struggle, and illustrative examples of what productive struggle 'looks like'. ...
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Challenging mathematical tasks can be designed to allow students of all abilities to experience productive struggle. It is important for teachers to communicate with students that productive struggle is important and it is what mathematicians do
... rather than asking for support from the teacher). As part of this process, the teacher should ensure that all students know where the enabling prompts are in the room, and that there is no stigma associated with accessing an enabling prompt (e.g. an overly competitive classroom climate, where it is implicitly or explicitly assumed that 'good mathematicians don't need help') (Russo, 2016). ...
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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.
... The task must: have multiple solution pathways and may have multiple solutions; involve multiple mathematical steps; have at least one enabling prompt and one extending prompt; involve students spending considerable time, at least 10 minutes, on the task; involve students having primary control over how they are able to approach the task and when they are able to access enabling and extending prompts. In total, 28 challenging tasks were developed for the present study, several of which have subsequently been published in teacher practitioner journals (e.g., Russo, 2016aRusso, , 2016b. Two examples of challenging tasks are the following. ...
Article
Engaging students in a challenging (cognitively demanding) task and launching a mathematics lesson with a task before instruction are two characteristics of a reform-oriented approach to mathematics instruction often considered together. The authors systematically contrasted teaching with challenging tasks using a task-first lesson structure with that of a discussion-first lesson structure to three composite classes of first- and second-grade students (n = 73). Subsequent assessments of mathematical performance revealed that the discussion-first lesson structure was somewhat more efficacious in improving fluency performance but both structures similarly improved problem-solving performance. The findings suggest there is more than one way of incorporating challenging tasks into mathematics lessons to produce sizeable learning gains.
... For instance, the mean number of minutes students spent engaged with each task was 14.5 min for the patterning unit and 14.9 min for the addition unit. Examples of challenging tasks used in the current study have been published elsewhere (Russo, 2015(Russo, , 2016a(Russo, , 2016b(Russo, , 2016c, and some of these tasks are also included as an appendix to the current paper. In addition, a detailed account of the theoretical framework guiding the design and steps taken to construct the challenging tasks was provided by Russo and Hopkins (2017b). ...
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The current study considered young students’ (seven and eight years old) experiences and perceptions of mathematics lessons involving challenging (i.e., cognitively demanding) tasks. We used the Constant Comparative Method to analyse the interview responses (n=73) regarding what work artefacts students were most proud of creating and why. Five themes emerged that characterised student reflections: Enjoyment, Effort, Learning, Productivity and Meaningful Mathematics. Overall, there was evidence that students embraced struggle and persisted when engaged in mathematics lessons involving challenging tasks, and moreover that many students enjoyed the process of being challenged. In the second section of the paper, the lesson structure preferences of a subset of participants (n=23) when learning with challenging tasks are considered. Overall, more students preferred the teach-first lesson structure to the task-first lesson structure, primarily because it activated their cognition to prepare them for work on the challenging task. However, a substantial minority of students (42%) instead endorsed the task-first lesson structure, with several students explaining they preferred this structure precisely because it was so cognitively demanding. Other reasons for preferring the task-first structure included that it allowed the focus of the lesson to be on the challenging task and the subsequent discussion of student work. A key implication of these combined findings is that, for many students, work on challenging tasks appeared to remain cognitively demanding irrespective of the structure of the lesson.
Chapter
At first glance, Geography may seem a simple study concentrating on locating places and determining how near or far they are from each other. Indeed, the origin of the term supports this idea. The term ‘Geography’ combines two Greek words, ‘geo’ meaning Earth and graphia ‘meaning to draw or describe the earth’. (Gilbert & Hoepper, 2014) However, the contemporary discipline of Geography has a much more ambitious agenda. Modern geography is an all-encompassing discipline that seeks to understand the world and all of its human and natural complexities. It is now defined as the investigation and understanding of the earth and its features and distribution of life on earth. It is the study of the earth and its features, inhabitants and phenomena. Geography answers questions about why places have their particular environmental factors and/or human characteristics, looks to explain how and why these have changed and developed over time. These issues are investigated at all levels from local to global with an eye to management and sustainability (Taylor et al, 2012).
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