James A Russo
Monash University, Faculty of Education, Faculty Member
- Sociology of Education, Educational Psychology, Mathematics Education, Mathematics Education at Primary Schools, Primary School Education, Teacher Education, and 29 moreTeaching Thinking Skills, Metacognition, Metacognitive Learning Strategies, Metacognition and its development, Math Education in Early Childhood Education, Elementary Mathematics Education, Primary School, Mathematics Education Pedagogy, Interpretative Phenomenological Analysis, Education Research, Mindfulness Meditation, Mindfulness and well being, Classroom Interaction, Meditation, Social Justice, Classroom environment, Play and Creativity in the Curriculum, Narrative Psychology, Effective Teaching, Social Emotional Learning, Early Childhood Curriculum, Learning Design, Self-regulated Learning, Creativity studies, Self-Regulated Learning (Education), Learning Sciences, Group Creativity, Creativity and Consciousness, and Conceptual Frameworkedit
Productive struggle is a vital aspect of mathematics learning; consequently, how teacher educators can effectively communicate the power of this idea to classroom teachers should in itself be an important consideration. We argue that... more
Productive struggle is a vital aspect of mathematics learning; consequently, how teacher educators can effectively communicate the power of this idea to classroom teachers should in itself be an important consideration. We argue that providing teachers with firsthand experience of learning mathematics through structured inquiry approaches (e.g., launch-explore-summarise/review) is vital for supporting their appreciation of productive struggle. To facilitate this, during professional learning workshops with primary school teachers and education support workers, we have introduced a reflective template (the "Confuse-ometer") to enhance educator awareness of their own journey from "confusion to clarity" as work on a task unfolds. In this current Illustration of Practice, we draw on data collected from several workshops we recently facilitated, which focussed on introducing challenging tasks and the launch-explore-summarise/review lesson structure. Our purpose is both to demonstrate the importance of providing educators with first-hand experience of productive struggle, and to illustrate how the reflective template designed supports this process.
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Mathematical games are widely employed by primary school teachers in many countries to support mathematics instruction. Despite broad usage, teacher decision making in relation to both why they choose to use mathematical games as a... more
Mathematical games are widely employed by primary school teachers in many countries to support mathematics instruction. Despite broad usage, teacher decision making in relation to both why they choose to use mathematical games as a pedagogical tool more generally, and which games they choose to use in their classrooms specifically, has received scant attention in the research literature. For example, although digital and non-digital games have both been shown to be effective for supporting student engagement in mathematics, little is known about educator preferences for a particular game mode (i.e., digital versus non-digital), and the factors that influence these preferences. Similarly, given the abundance of different game variations potentially available to teachers, it is valuable to have a deeper understanding of the context in which teachers might choose games of one particular structure over another (e.g., competitive games versus collaborative games). To shed light on these issues, and to assist in bridging this gap between research and practice, this lecture (and associated paper) discusses a series of studies focusing on Australian primary school teachers' use of mathematical games. Collectively, these studies have assisted us in taking initial steps towards deepening our community's understanding of this potentially powerful, and undeniably prevalent, pedagogical tool.
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Both digital and non-digital games have been shown to be effective for supporting student engagement in mathematics. However, little is known about educator preferences for a particular game mode (i.e. digital versus non-digital), and... more
Both digital and non-digital games have been shown to be effective for supporting student engagement in mathematics. However, little is known about educator preferences for a particular game mode (i.e. digital versus non-digital), and what factors influence these preferences. To address this gap, 111 Australian primary school educators completed a questionnaire reporting on their usage of, and preferences for using, digital compared with non-digital games to support mathematics instruction. Participants were considerably more likely to use non-digital games than digital games in their classrooms, and the majority indicated a clear preference for using non-digital games. Thematic analysis revealed several themes that explained why many participants preferred non-digital games, with the most frequently coded theme being for pedagogical reasons such as: that they were better for promoting collaboration and communication; that they
afforded opportunities for students to use manipulatives; and that they were easily adapted and differentiated for specific groups of students. Other notable themes included: assessment, in particular, the perception that when students played non-digital games it was easier to observe their understanding; access to, and limited awareness of, suitable digital resources; and managing the setup and delivery of the game. Implications of the findings are discussed.
afforded opportunities for students to use manipulatives; and that they were easily adapted and differentiated for specific groups of students. Other notable themes included: assessment, in particular, the perception that when students played non-digital games it was easier to observe their understanding; access to, and limited awareness of, suitable digital resources; and managing the setup and delivery of the game. Implications of the findings are discussed.
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In this paper we explored primary school teachers preference for different game modes to support mathematics teaching and learning. Eighty-four teachers played digital and non-digital addition and subtraction games that were functionally... more
In this paper we explored primary school teachers preference for different game modes to support mathematics teaching and learning. Eighty-four teachers played digital and non-digital addition and subtraction games that were functionally equivalent during professional learning workshops. Most teachers indicated that they would be more likely to use the non-digital mode; despite more mixed views around perceived effectiveness for supporting learning and anticipated student preferences. Key reasons as to why teachers tended to prefer non-digital or digital games are examined.
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Australian primary school teachers have reported that they use games frequently in teaching mathematics. In this paper, the authors discuss the game mechanics of five types of mathematical games that can be particularly powerful for... more
Australian primary school teachers have reported that they use games frequently in teaching mathematics. In this paper, the authors discuss the game mechanics of five types of mathematical games that can be particularly powerful for supporting mathematical thinking and student engagement in mathematics.
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Despite primary school teachers demonstrating strong preferences for using non-digital games over digital games to support mathematics instruction, much of the research review literature has focused on learning outcomes associated with... more
Despite primary school teachers demonstrating strong preferences for using non-digital games over digital games to support mathematics instruction, much of the research review literature has focused on learning outcomes associated with digital mathematical games. To address this gap, the current systematic literature review focuses on non-digital, games-based, empirical studies in the primary mathematics classroom over the past two decades from 2003 to 2022. The Preferred Reporting Items for Systematic Reviews (PRISMA) statement was employed as a guideline for the data-collection process. The review presents an analysis and synthesis of 34 manuscripts, representing 32 distinct studies. Over three-quarters of manuscripts employed quantitative methodologies and around half qualitative methodologies, whilst studies focused exclusively on student, as opposed to teacher, outcomes. Despite Australia and Indonesia being comparatively overrepresented, the studies in scope were notable for both their geographic diversity and the eclectic range of game types and structures incorporated; although they did tend to disproportionately focus on number and operations, as opposed to other mathematical content areas. Moreover, the impact of mathematical games was generally positive across the broad range of outcomes considered, suggesting that mathematical games are potentially effective for both developing mathematical proficiencies, as well as improving dispositions towards mathematics. Future research directions are discussed.
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Students enjoy mathematics less as they move through their schooling and this may be reflective of more negative attitudes towards learning mathematics in general; although not necessarily less valuing of mathematics as a discipline.... more
Students enjoy mathematics less as they move through their schooling and this may be reflective of more negative attitudes towards learning mathematics in general; although not necessarily less valuing of mathematics as a discipline. However, little is known about how stage of schooling influences the relationship between viewing mathematics as problem solving and student attitudes towards mathematics. To address this gap, 123 Australian primary and secondary students identified by their teachers as underachieving in mathematics completed a questionnaire exploring their attitudes towards, and views of, mathematics. We found that although attitudes towards mathematics became more negative as year level increased, this was entirely driven by students enjoying mathematics less; neither their valuing of mathematics, nor their ability to cope with mathematics declined. Similarly, the extent to which students held a problem-solving view of mathematics was unrelated to stage of schooling. ...
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Integrating mathematics and science can enrich student learning by providing relevant, meaningful, and engaging learning experiences that promote positive attitudes towards both subjects. However, despite reported benefits in relation to... more
Integrating mathematics and science can enrich student learning by providing relevant, meaningful, and engaging learning experiences that promote positive attitudes towards both subjects. However, despite reported benefits in relation to student learning, various barriers to integration have also been identified, including limited teacher content and pedagogical content knowledge, and the need for professional learning support with planning and implementing integrated lessons. In this article, we report on one phase of a project in which mathematics and science education researchers and primary teachers collaborated to design two sequences of integrated mathematics and science lessons. We focus on the processes considered critical for success, including how knowledge was co-constructed by the design team to develop the integrated lesson sequences. Findings are communicated as a set of guidelines to support teachers and educators interested in replicating the process to integrate mat...
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In this article, the authors from Monash University and the University of Sydney have collaborated to present a research-informed model to support the planning and teaching of mathematics, using a student centred structured inquiry... more
In this article, the authors from Monash University and the University of Sydney have collaborated to present a research-informed model to support the planning and teaching of mathematics, using a student centred structured inquiry approach.
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In this article, the authors emphasise the importance of purposeful mathematical discussion and using sequences of connected, cumulative, and challenging tasks in advancing students' spatial reasoning in the early years of schooling.
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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... more
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.
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Traditionally Australian primary school teachers have been viewed as generalists responsible for instruction across all content areas. Adopting self-determination theory as a lens, the aim of the study was to explore the extent to which... more
Traditionally Australian primary school teachers have been viewed as generalists responsible for instruction across all content areas. Adopting self-determination theory as a lens, the aim of the study was to explore the extent to which generalist primary school teachers are interested in becoming subject matter specialists. Questionnaire data were collected from 104 early years primary school teachers. Findings suggest that two-thirds of these generalist teachers expressed an interest in specialising in either English, mathematics, and to a far lesser extent, science, such that they would be responsible for exclusively teaching this subject. Preferences for specialisation were based on teachers’ self-perceived content and pedagogical expertise and/ or their enjoyment of teaching in this content area. By contrast, the one-third of teachers who would choose to remain generalists referred to the value in a variety of teaching experiences, teaching from a whole child perspective and co...
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In this paper, we propose a new, theoretical account of why many children persist with using counting strategies to solve single-digit addition problems. We hypothesise that, in some contexts, teaching approaches favour a phonological... more
In this paper, we propose a new, theoretical account of why many children persist with using counting strategies to solve single-digit addition problems. We hypothesise that, in some contexts, teaching approaches favour a phonological route for strengthening problem-answer associations in memory, which disadvantages children who have weaker skills with phonological memory. Furthermore, we hypothesise that more children will develop retrieval-based strategies if they are provided with opportunities to practice using tools that strengthen problem-answer associations in memory via a visual-spatial processing route. We also describe a new tool that we designed to help test these hypotheses, called the Keyboard. The Keyboard models a mental number line and makes use of children’s subitising skills.
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Students enjoy mathematics less as they move through their schooling and this may be reflective of more negative attitudes towards learning mathematics in general; although not necessarily less valuing of mathematics as a discipline.... more
Students enjoy mathematics less as they move through their schooling and this may be reflective of more negative attitudes towards learning mathematics in general; although not necessarily less valuing of mathematics as a discipline. However, little is known about how stage of schooling influences the relationship between viewing mathematics as problem solving and student attitudes towards mathematics. To address this gap, 123 Australian primary and secondary students identified by their teachers as underachieving in mathematics completed a questionnaire exploring their attitudes towards, and views of, mathematics. We found that although attitudes towards mathematics became more negative as year level increased, this was entirely driven by students enjoying mathematics less; neither their valuing of mathematics, nor their ability to cope with mathematics declined. Similarly, the extent to which students held a problem-solving view of mathematics was unrelated to stage of schooling. Interestingly, however, we also found that students who viewed mathematics as being fundamentally about problem solving were more likely to value mathematics as a discipline, and that this was particularly the case for secondary school students. We discuss how providing opportunities for secondary school students, including underachieving students, to engage with open-ended problem-solving tasks may lead to perceptions of mathematics as useful, purposeful, and important.
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There has been considerable research into how children solve single-digit addition problems for more than a century now, which has brought about significant changes to the ways teachers' support children to retrieve single-digit... more
There has been considerable research into how children solve single-digit addition problems for more than a century now, which has brought about significant changes to the ways teachers' support children to retrieve single-digit addition facts. In this project, we examine what makes an addition problem difficult to retrieve in light of contemporary teaching approaches, based on both student performance and teacher perceptions. Australian primary school students in Years 3 and 4 (n = 166) solved 36 single-digit addition problems under two different conditions during a structured interview. These data were then used to create the Difficulty Retrieving Addition Facts (DRAF) measure, which we propose as a contemporary measure of singledigit addition problem difficulty to supersede older measures developed in a different era of instruction. We then invited Australian primary school teachers (n = 49) to complete a questionnaire asking them to estimate the percentage of students who would be able to rapidly retrieve these same 36 single-digit addition problems to facilitate comparison between student performance and teacher perceptions. We found that although teachers were generally accurate in discerning which addition problems students would find relatively easy to retrieve and which they would find more difficult, they tended to overestimate student capacity to retrieve addition facts in general, particularly when the addition fact was comparatively difficult. We suggest that this overestimation resulted from teacher responses being shaped by curriculum expectations, which states that students should be able to recall single-digit addition facts by the end of Year 3.
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The notion of equivalence is a very important concept for students and should be developed from a young age. This article demonstrates how students can deepen their relational understanding of the equals sign by exploring inequalities... more
The notion of equivalence is a very important concept for students and should be developed from a young age. This article demonstrates how students can deepen their relational understanding of the equals sign by exploring inequalities within a dice game based on familiar children's literature.
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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... more
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’.
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Non-digital games are frequently used to support primary mathematics instruction. Moreover, we know from the literature that to increase the likelihood that a chosen mathematical game is educationally rich it should reflect specific... more
Non-digital games are frequently used to support primary mathematics instruction. Moreover, we know from the literature that to increase the likelihood that a chosen mathematical game is educationally rich it should reflect specific principles, such as offering a balance between skill and luck and ensuring that a key mathematical focus is central to gameplay. However, there is limited research informing us, from a teacher’s perspective, of the specific characteristics of mathematical games that are most indicative of a game’s value for supporting learning, and the likelihood that teachers will use the game with students in the future. To help address this gap, the current study invited 122 educators to complete an on-line questionnaire, including 20 Likert-scale items designed to assess the characteristics of educationally-rich mathematical games (CERMaGs) that aligned with six ‘good practice’ principles previously identified in the literature, in relation to a specific mathematical...
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We report on questionnaire data gathered from teacher participants (n = 100) following their participation in the project, Exploring Mathematical Sequences of Connected, Cumulative and Challenging Tasks. Teachers shared their views about... more
We report on questionnaire data gathered from teacher participants (n = 100) following their participation in the project, Exploring Mathematical Sequences of Connected, Cumulative and Challenging Tasks. Teachers shared their views about the effectiveness of various instructional approaches to support differentiation in mathematics, including those illuminated through the project, and a description of a lesson involving effective differentiation.
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Non-digital games are frequently used to support primary mathematics instruction. Moreover, we know from the literature that to increase the likelihood that a chosen mathematical game is educationally rich it should reflect specific... more
Non-digital games are frequently used to support primary mathematics instruction. Moreover, we know from the literature that to increase the likelihood that a chosen mathematical game is educationally rich it should reflect specific principles, such as offering a balance between skill and luck and ensuring that a key mathematical focus is central to gameplay. However, there is limited research informing us, from a teacher's perspective, of the specific characteristics of mathematical games that are most indicative of a game's value for supporting learning, and the likelihood that teachers will use the game with students in the future. To help address this gap, the current study invited 122 educators to complete an on-line questionnaire, including 20 Likert-scale items designed to assess the characteristics of educationally-rich mathematical games (CERMaGs) that aligned with six 'good practice' principles previously identified in the literature, in relation to a specific mathematical game of their choosing. In total, educators chose a broad range of mathematical games to be evaluated (n = 53). On average, they reported that their chosen game was highly valuable for supporting mathematics learning and that they were very likely to use this game with students if given the opportunity. Our results revealed that the extent to which educators perceived a game to be suitably challenging, engaging, enjoyable, modifiable to support different learners, and transformable into an investigation or broader mathematical inquiry, were particularly important characteristics associated with perceptions of a game's educational value. Similarly, perceived levels of student enjoyment, engagement and a game's potential to lead to a rich mathematical investigation were important characteristics for evaluating the likelihood that an educator would use a particular game in the future with students if given the opportunity, as was the capacity of a game to support mathematical discussion. The implications of these findings for supporting classroom practice and teacher professional learning are discussed.
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There has been considerable research into how children solve single-digit addition problems for more than a century now, which has brought about significant changes to the ways teachers' support children to retrieve single-digit addition... more
There has been considerable research into how children solve single-digit addition problems for more than a century now, which has brought about significant changes to the ways teachers' support children to retrieve single-digit addition facts. In this project, we examine what makes an addition problem difficult to retrieve in light of contemporary teaching approaches, based on both student performance and teacher perceptions. Australian primary school students in Years 3 and 4 (n = 166) solved 36 single-digit addition problems under two different conditions during a structured interview. These data were then used to create the Difficulty Retrieving Addition Facts (DRAF) measure, which we propose as a contemporary measure of singledigit addition problem difficulty to supersede older measures developed in a different era of instruction. We then invited Australian primary school teachers (n = 49) to complete a questionnaire asking them to estimate the percentage of students who would be able to rapidly retrieve these same 36 single-digit addition problems to facilitate comparison between student performance and teacher perceptions. We found that although teachers were generally accurate in discerning which addition problems students would find relatively easy to retrieve and which they would find more difficult, they tended to overestimate student capacity to retrieve addition facts in general, particularly when the addition fact was comparatively difficult. We suggest that this overestimation resulted from teacher responses being shaped by curriculum expectations, which states that students should be able to recall single-digit addition facts by the end of Year 3.
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Traditionally Australian primary school teachers have been viewed as generalists responsible for instruction across all content areas. Adopting self-determination theory as a lens, the aim of the study was to explore the extent to which... more
Traditionally Australian primary school teachers have been viewed as generalists responsible for instruction across all content areas. Adopting self-determination theory as a lens, the aim of the study was to explore the extent to which generalist primary school teachers are interested in becoming subject matter specialists. Questionnaire data were collected from 104 early years primary school teachers. Findings suggest that two-thirds of these generalist teachers expressed an interest in specialising in either English, mathematics, and to a far lesser extent, science, such that they would be responsible for exclusively teaching this subject. Preferences for specialisation were based on teachers’ self-perceived content and pedagogical expertise and/ or their enjoyment of teaching in this content area. By contrast, the one-third of teachers who would choose to remain generalists referred to the value in a variety of teaching experiences, teaching from a whole child perspective and content integration. Implications for educational policy are discussed.
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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... more
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 through a challenging tasks approach. A qualitative coding process was undertaken to analyse the written responses of 59 Year 2 students resulting in the development of a 7-point marking key to identify levels of progress. The marking key proved effective in supporting the interpretation of the written responses and identifying future learning pathways.
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The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their... more
The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their participation in a professional learning project. Findings suggest that teachers': view prompts as important when teaching with challenging tasks; generally prepare prompts in advance of the lesson; consistently allow students to engage with the core task before making prompts available; and consider prompts equally valuable for augmenting learning across all content areas.
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Just as students experience productive struggle or spend time in the ‘zone of confusion’ when engaging with challenging tasks, teachers also experience similar difficulties and periods of confusion when engaging with new pedagogical... more
Just as students experience productive struggle or spend time in the ‘zone of confusion’ when engaging with challenging tasks, teachers also experience similar difficulties and periods of confusion when engaging with new pedagogical approaches. Prior to a 19-week lockdown due to Coronavirus (COVID-19) during 2020, two Foundation teachers implemented a student-centred pedagogical approach when teaching with challenging tasks. While they had some initial success implementing the pedagogical approach and a three-phase lesson structure, they struggled to do so online during the lockdown. It is the experiences of these teachers, in particular their experience of confusion relating to aspects of the pedagogical approach, and how this confusion was overcome, that is reported in this paper. Central to our findings is the importance of teachers reflecting on their own experiences of struggle and the impact this had on their professional learning, as well as the notion that adversity can be a catalyst for change.
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How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school’s experience in considering an... more
How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school’s experience in considering an approach to mathematics instruction that could support teachers in addressing this question, specifically pursuing structured inquiry in a multi-age setting.
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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... more
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 involved in a professional learning initiative focused on teaching mathematics through sequences of challenging tasks completed a questionnaire inviting them to compare the two settings. Drawing on a mixed-methods approach, we found that teachers were more positive about the value of student struggle in classroom-based settings compared with remote learning settings. Qualitative analysis of open-ended responses revealed four themes capturing why teachers viewed efforts to support productive struggle in a remote learning setting as potentially problematic: absence of a teacher-facilitated, synchronous, learning environment; parents’ negativ...
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Build students' estimation skills is critical for developing their number sense. These games encourage students to use estimation, rather than calculation, when making decisions. Versions of the Rolling to the Target game and the... more
Build students' estimation skills is critical for developing their number sense. These games encourage students to use estimation, rather than calculation, when making decisions. Versions of the Rolling to the Target game and the grade bands for which they are appropriate include the following:
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The following series of challenging tasks are built around three wonderful picture story books by author/illustrator Oliver Jeffers. We suggest reading each book and tackling these tasks.
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This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. ‘Hopping to 100’ is a strategy-based game which exposes students to skip-counting from... more
This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. ‘Hopping to 100’ is a strategy-based game which exposes students to skip-counting from non-zero starting points. The mathematics in the activity is suitable for students in Years 2, 3 and 4, with more mathematically capable students encouraged to employ their knowledge of multiplication facts and mental strategies for adding two-digit numbers, rather than skip-counting. Upper primary students could also enjoy the game, focusing more on optimal strategy than the specific mathematics involved.
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91 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... more
91 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.
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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... more
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...
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Setting students problem-solving tasks that are simultaneously engaging and mathematically important is central to primary mathematics instruction. Often an attempt to develop engaging tasks involves first determining the meaningful... more
Setting students problem-solving tasks that are simultaneously engaging and mathematically important is central to primary mathematics instruction. Often an attempt to develop engaging tasks involves first determining the meaningful mathematics to be learnt, and then creating a ‘mini-narrative’ as a vehicle for exploring these concepts. However, in our experience, the more familiar, enjoyable and deeply developed the narrative, the more engaging the task is for students. Consequently, we demonstrate how there might be value in inverting the process- that is, beginning with rich narratives, and mapping on the mathematics- through creating mathematical tasks embedded in examples of well-known children’s literature. This is termed the Narrative-First Approach. We discuss one specific text – Fish Out of Water – and an associated mathematical investigation in some depth, including commenting on student work samples and student post-lesson reflections.
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This article outlines two interrelated challenging tasks which encourage students to make connections between different counting sequences. These tasks can be used to expose younger students to ideas such as factors and multiples.
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The current investigation systematically contrasted teaching with cognitively demanding (challenging) tasks using a task-first lesson structure with that of a teach-first lesson structure in a primary school setting (Year 1 and 2). The... more
The current investigation systematically contrasted teaching with cognitively demanding (challenging) tasks using a task-first lesson structure with that of a teach-first lesson structure in a primary school setting (Year 1 and 2). The findings indicate that there is more than one way of incorporating challenge tasks into mathematics lessons to produce sizeable learning gains. Analyses of interviews with teachers and students regarding their perceptions of learning with challenging tasks suggest that each type of lesson structure has distinct strengths. It is concluded that teachers should consider varying the structure of the lesson to provide a range of learning experiences for students.
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The current study compared the rate at which problem-based practice increased the use of retrieval-based strategies for students identified as displaying accurate min-counting with students identified as displaying almost proficient... more
The current study compared the rate at which problem-based practice increased the use of retrieval-based strategies for students identified as displaying accurate min-counting with students identified as displaying almost proficient performance. The findings supported the prediction that the rate at which problem-based practice promoted retrieval use was lower for students in the accurate min-counting group; in fact, it had no effect on their retrieval development. Implications for teaching practice are discussed, in particular, the notion that such students may require exposure to different problem representations (e.g., visual imagery) to move them away from conceptualising addition as counting.
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Engaging students in a challenging (cognitively demanding) task and launching a mathematics lesson with a task prior to instruction are two characteristics of a reform-oriented approach to mathematics instruction often considered... more
Engaging students in a challenging (cognitively demanding) task and launching a mathematics lesson with a task prior to instruction are two characteristics of a reform-oriented approach to mathematics instruction often considered together. The current investigation systematically contrasted teaching with challenging tasks using a task-first lesson structure (Task-First Approach) with that of a teach-first lesson structure (Teach-First Approach) through the delivery of two programs of mathematics instruction to 75 Year 1 and 2 students (7 and 8 year olds). The investigation adopted a quasi-experimental design and included three studies. Study One was quantitative in nature and involved analysing pre- and post- program student outcome data. A series of Mixed Design ANOVAs revealed that both teaching approaches resulted in large gains in student mathematical performance. Moreover, there was no evidence that problem-solving performance differed by lesson structure, although the Teach-First Approach was somewhat more effective in improving mathematical fluency. Study Two was qualitative in nature and involved semi-structured interviews with teacher-participants. Analysis of interview data suggested that there appear to be distinct advantages to both the task-first and teach-first lesson structures. Specifically, teacher-participants perceived that the Teach-First Approach was more focused and efficient, whilst the Task-First Approach was viewed as empowering students, and providing an opportunity to build persistence whilst fostering student mathematical creativity. Despite these differences, there was evidence that the most dramatic shift in teaching practice for teacher-participants would be the incorporation of more cognitively demanding tasks into their mathematics instruction in any capacity. Study Three was also predominantly qualitative and involved semi-structured interviews with student-participants. In line with teacher perceptions of the student experience (Study Two), analysis of student-participant interviews indicated that students generally embraced struggle and persisted when engaged in mathematics lessons involving challenging tasks. In addition, many students described enjoying the process of being challenged. Although most students reported preferring the Teach-First Approach when learning with challenging tasks because it provided opportunities for cognitive activation, a substantial minority (41%) of students preferred the Task-First Approach, in part because they relished the higher level of cognitive demand involved. The findings do not support the assumption that for students to learn from cognitively demanding tasks, lessons must begin with these tasks. Given that each approach was revealed to be effective and to possess distinct strengths, it is recommended that early primary teachers give consideration to incorporating both Task-First Approaches and Teach-First Approaches into future mathematics instruction.