Katie Makar | The University of Queensland, Australia (original) (raw)

Books by Katie Makar

Mathematical inquiry challenges students to ask questions, create definitions and think very care... more Mathematical inquiry challenges students to ask questions, create definitions and think very carefully about how they are going to solve a problem.

With the emphasis on mathematical reasoning, judgement and problem-solving skills, the Thinking through Mathematics series requires students to investigate questions that are open-ended and ambiguous, rather than closed and defined. The process of reasoning is reinforced as students consider the parameters of their inquiry, formulate, trial and enact a plan, and share their thinking process alongside the results.Each book provides ten mathematical inquiry units, each posing a real-life, ambiguous question for inquiry.

Thinking through Mathematics provides a practical entry into inquiry-based mathematics learning which immerses students in solving authentic, complex problems.

Papers by Katie Makar

Statistics Education Research Journal, 2017

Measurement activities were designed in this study on the basis of authentic professional practic... more Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17-18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities? Analysis of students' reasoning during these activities in one classroom (N = 13) suggests that students considered variability in four ways: noticing and acknowledging variability, measuring variability, explaining variability, and using investigative strategies to handle variability. We conclude that the measurement tasks based on authentic professional practices helped students to reason with relevant aspects of variability. Finally, we discuss curricular and research implications.

One of the challenges in research is in understanding processes and systems that enable teachers ... more One of the challenges in research is in understanding processes and systems that enable teachers to build their expertise and commitment to reform-based pedagogies. A qualitative study documented the influence that a set of support mechanisms, or connection levers, had in assisting upper primary teachers over the course of a year in developing confidence in teaching mathematics through inquiry.

Early Mathematics Learning and Development

Recent literature in the early years has emphasised the benefits of introducing children to power... more Recent literature in the early years has emphasised the benefits of introducing children to powerful disciplinary ideas. Powerful ideas in statistics such as variability, aggregate, population, the need for data, data representation and statistical inquiry are generally introduced in the later years of schooling or university and therefore may be considered too difficult for young children. However, at an informal level, these ideas arise in contexts that are accessible to young children. The aim of this chapter is to theorise important relations between children’s contextual experiences and key structures in statistics. It introduces the notion of statistical context–structures, which characterise aspects of contexts that can expose children to important statistical ideas. A classroom case study involving statistical inquiry by children in their first year of schooling (ages 4–5) is included to illustrate characteristics of age-appropriate links between contexts and structures in statistics. Over time, engaging children in significant activities that rely on statistical context–structures can provide children with multiple opportunities to experience statistics as a coherent and purposeful discipline and develop rich networks of informal statistical concepts well before ideas are formalised. For teachers and curriculum writers, statistical context–structures provide a framework to design statistical inquiries that directly address learning intentions and curricular goals.

Mathematics Education Research Group of Australasia, 2016

An empirical study was conducted with the aim to develop teachers’ confidence and proficiency wit... more An empirical study was conducted with the aim to develop teachers’ confidence and proficiency with teaching mathematics through inquiry. The study followed 41 primary teachers and compared a regular mathematics lesson to a lesson taught using an inquiry approach; 19 of these teachers were also followed over three years. Lessons were coded on the extent of intellectual quality in the lesson across six dimensions. Higher order thinking showed the most gains over time. Implications for research and practice are given.

Informal statistical inference has gained increasing recognition as an effective approach to teac... more Informal statistical inference has gained increasing recognition as an effective approach to teaching statistics. Distinct from descriptive statistics, inference provides learners with access to the power of statistics by giving them tools to make predictions beyond their data. International research in this area has focused on students from primary school through university. A series of teaching experiments introduced informal statistical inference to very young children (aged 5-6). Although making predictions was familiar as an everyday task, initial attempts revealed challenges to teaching informal inferential reasoning to young learners. Prior to conducting a statistical inquiry involving inference, activities were designed to generate a need for recording and organising data, the language of uncertainty and using data as evidence. Results suggest that the activities prior to inquiry likely supported students in their emerging inferential practices.

Statistics Education Research Journal, 2009

Informal inferential reasoning has shown some promise in developing students’ deeper understandin... more Informal inferential reasoning has shown some promise in developing students’ deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference – eneralizations ‘beyond the data,’ probabilistic language, and data as evidence. The authors use primary school classroom episodes and excerpts of interviews with the teachers to illustrate the framework and reiterate the importance of embedding statistical learning within the context of statistical inquiry. Implications for the teaching of more powerful satistical concepts at the primary school level are discussed.

The Australian mathematics teacher, 2018

Suppose you were taught the game of soccer, but never put your skills to use in an actual game. I... more Suppose you were taught the game of soccer, but never put your skills to use in an actual game. In order to develop expertise in anything, we need to put our knowledge into practice. Playing a game of soccer develops a deeper understanding of our knowedge of the game and the ball-handling skills that we practised because we have to apply these knowledge and skills in messy, dynamic and unpredictable (non-routine) contexts. We have to adapt, combine, extend and even question our skills ‘in the moment’ of the game to respond to problems on the playing field that are new and not quite the same as those encountered in practice. As we gain experience in these non-routine situations, not only do we have a better understanding of our skills and when to use them, but we gain confidence to apply them in unpredictable situations. We begin to recognise approaches that worked before in similar situations. It is the knowledge of the game, the basic skills we practise and the non-routine experien...

A statistical question acknowledges that there is variability in data that needs to be accounted ... more A statistical question acknowledges that there is variability in data that needs to be accounted for in the conclusion. Accounting for variability is problematic if students do not have an understanding that a distribution shows patterns and can be described by the centre, spread and overall shape. TinkerPlots provides opportunities to build understandings of spread and measures of centre as students work with distributions, adding and manipulating dividers and hat plots. In this exploratory study, students in a middle school inquiry classroom used hat plots to compare distributions and write justified conclusions. Results suggest that the necessity to account for variability in data within their conclusions presented students with a purpose to transition from hat plots to box plots to provide evidence to answer the question. To answer a statistical question students are required to understand, explain, and quantify variability in data (Franklin et al., 2007). Unless students have a...

The aim of this paper is to extend and adapt Yackel and Cobb’s (JRME, 1996) identification of soc... more The aim of this paper is to extend and adapt Yackel and Cobb’s (JRME, 1996) identification of sociomathematical norms in mathematical inquiry to problems that are ill-structured. The background theory influenced the design and local theory development of the research. This paper uses excerpts from an upper primary classroom to address the ill-structured mathematical inquiry question, Which bubble gum is the best? Two norms are illustrated: (1) mathematising the ambiguity in an inquiry question, and (2) using the inquiry question to check progress towards a solution. Children demonstrated productive social norms and emergence of the sociomathematical inquiry norm of mathematising, but using the inquiry question was less prevalent. In both cases, children found it challenging to productively coordinate their everyday (relevant) and mathematical knowledge.

Mathematics Teacher Education and Development, 2007

Gaps between teaching practices and research recommendations have been well documented. One chall... more Gaps between teaching practices and research recommendations have been well documented. One challenge for research is in understanding the processes and systems that promote a bridging of these gaps. A year-long study with four primary teachers documented ten support mechanisms, or connection levers, that the teachers raised as important for building their expertise, commitment, and confidence in teaching mathematics and statistics through an inquiry-based approach. Their words provide insight into how support helps teachers to take on and commit to innovative practices.

Mathematics Education Research Group of Australasia, 2016

Intellectual risk is valued among 21st century skills. Three primary teachers who promoted positi... more Intellectual risk is valued among 21st century skills. Three primary teachers who promoted positive learning within mathematical inquiry collaborated with researchers to design and apply a rubric to assess children’s progress in taking intellectual risks twice during the year. Results suggest that handling setbacks and giving feedback to peers were the most challenging skills initially, but showed significant gains by the end of the year. Teacher interviews discussed challenges that students faced and how positive classroom culture encouraged intellectual risk.

Experience with statistical inquiry has been advocated in statistics education as vital for learn... more Experience with statistical inquiry has been advocated in statistics education as vital for learners’ understandings of statistical processes. Research has suggested, however, that practices at the school level have focused almost solely on graphs and procedures. While important, these skills do not develop learners’ abilities to cope with the decisions that arise in the face of uncertainties and ambiguities that accompany statistical investigations. A longitudinal study in Australia researched experienced primary teachers’ evolving experiences in teaching statistical inquiry. This paper will report on the uniqueness of teachers’ early experiences in teaching statistical inquiry, an issue that emerged in the first three years of the study. Critical skills that teachers need to develop to teach statistical investigations that are often neglected in teacher professional development are discussed, including implications for research and teacher education.

Little is known about the way that teachers articulate notions of variation in their own words. T... more Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of standard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the prospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined.

Several years ago, we characterized “informal statistical inference” as a claim that went beyond ... more Several years ago, we characterized “informal statistical inference” as a claim that went beyond the data, using the data as evidence and acknowledging uncertainty (Makar & Rubin, 2009). This characterization was intentionally ambiguous in order to provide a context for ongoing research on statistical reasoning (especially with younger learners and those without formal statistical training) and to provoke discussion among researchers whose uses of the term differed from one another. Since then, research about informal statistical inference has proliferated, from work with young children to tertiary settings. In this paper, we review recent research on informal statistical inference, investigating issues and new questions that have emerged around looking “beyond the data”, using “data as evidence” and “articulating uncertainty”.

International Handbook of Research in Statistics Education

This chapter reviews research on the learning of statistical inference, focusing in particular on... more This chapter reviews research on the learning of statistical inference, focusing in particular on recent research on informal statistical inference. The chapter begins by arguing for the importance of broader access to the power of statistical inference—which, until recently, has been accessible only to those with extensive knowledge of mathematics—and then traces the philosophical roots of inference. We outline the challenges that students have encountered in learning statistical inference and strategies to facilitate its learning that have capitalized on technological advances. We describe the emergence of informal statistical inference and how researchers have framed the idea over the past decade. Rather than consider formal and informal statistical inference dichotomously, we highlight a number of dimensions along which approaches to statistical inference may differ, providing a richer perspective on how formal and informal statistical inference are related. Cases from classroom research aimed at primary, secondary, and tertiary levels are used to illustrate how informal statistical inference has shaped new ways to approach the teaching and learning of statistical inference. Finally, we outline gaps in research on statistical inference and present our speculations on its future in light of new research on statistical modeling and big data.

International Journal of Educational Research

Curriculum ergonomics focuses on the “fit” between students and the curriculum, and how this “fit... more Curriculum ergonomics focuses on the “fit” between students and the curriculum, and how this “fit” extends students’ understanding of content. We argue that the opportunity for narrative in an inquiry-based learning environment in mathematics promotes this “fit” between students and the curriculum. This is in contrast to purely expository forms, which focus on description and facts. In this paper, we use Bruner’s concept of narrative to propose elements of a curriculum ergonomics design framework—connection, sharing of incomplete ideas and repeated experiences over time—that promotes opportunities for “fit” in implementing mathematics curriculum. We draw on data from a primary school classroom (ages 7–8) to illustrate how this fit is played out in a classroom that engages in learning mathematics through inquiry.

ZDM

Children have limited exposure to statistical concepts and processes, yet researchers have highli... more Children have limited exposure to statistical concepts and processes, yet researchers have highlighted multiple benefits of experiences in which they design and/or engage informally with statistical modelling. A study was conducted with a classroom in which students developed and utilised data-based models to respond to the inquiry question, Which origami animal jumps the furthest? The students used hat plots and box plots in Tinkerplots to make sense of variability in comparing distributions of their data and to support them to write justified conclusions of their findings. The study relied on classroom video and student artefacts to analyse aspects of the students' modelling experiences which exposed them to powerful statistical ideas, such as key repeatable structures and dispositions in statistics. Three principles-purpose, process and prediction-are highlighted as ways in which the problem context, statistical structures and inquiry dispositions and cycle extended students' opportunities to reason in sophisticated ways appropriate for their age. The research question under investigation was, How can an emphasis on purpose, process and prediction be implemented to support children's statistical modelling? The principles illustrated in the study may provide a simple framework for teachers and researchers to develop statistical modelling practices and norms at the school level.

Mathematics Education Research Journal

The 3-year study described in this paper aims to create new knowledge about inquiry norms in prim... more The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, BHow do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?^The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers' progressive development of classroom norms of mathematical inquiry and how they facilitate learning.

Mathematical inquiry challenges students to ask questions, create definitions and think very care... more Mathematical inquiry challenges students to ask questions, create definitions and think very carefully about how they are going to solve a problem.

With the emphasis on mathematical reasoning, judgement and problem-solving skills, the Thinking through Mathematics series requires students to investigate questions that are open-ended and ambiguous, rather than closed and defined. The process of reasoning is reinforced as students consider the parameters of their inquiry, formulate, trial and enact a plan, and share their thinking process alongside the results.Each book provides ten mathematical inquiry units, each posing a real-life, ambiguous question for inquiry.

Thinking through Mathematics provides a practical entry into inquiry-based mathematics learning which immerses students in solving authentic, complex problems.

Statistics Education Research Journal, 2017

Measurement activities were designed in this study on the basis of authentic professional practic... more Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17-18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities? Analysis of students' reasoning during these activities in one classroom (N = 13) suggests that students considered variability in four ways: noticing and acknowledging variability, measuring variability, explaining variability, and using investigative strategies to handle variability. We conclude that the measurement tasks based on authentic professional practices helped students to reason with relevant aspects of variability. Finally, we discuss curricular and research implications.

One of the challenges in research is in understanding processes and systems that enable teachers ... more One of the challenges in research is in understanding processes and systems that enable teachers to build their expertise and commitment to reform-based pedagogies. A qualitative study documented the influence that a set of support mechanisms, or connection levers, had in assisting upper primary teachers over the course of a year in developing confidence in teaching mathematics through inquiry.

Early Mathematics Learning and Development

Recent literature in the early years has emphasised the benefits of introducing children to power... more Recent literature in the early years has emphasised the benefits of introducing children to powerful disciplinary ideas. Powerful ideas in statistics such as variability, aggregate, population, the need for data, data representation and statistical inquiry are generally introduced in the later years of schooling or university and therefore may be considered too difficult for young children. However, at an informal level, these ideas arise in contexts that are accessible to young children. The aim of this chapter is to theorise important relations between children’s contextual experiences and key structures in statistics. It introduces the notion of statistical context–structures, which characterise aspects of contexts that can expose children to important statistical ideas. A classroom case study involving statistical inquiry by children in their first year of schooling (ages 4–5) is included to illustrate characteristics of age-appropriate links between contexts and structures in statistics. Over time, engaging children in significant activities that rely on statistical context–structures can provide children with multiple opportunities to experience statistics as a coherent and purposeful discipline and develop rich networks of informal statistical concepts well before ideas are formalised. For teachers and curriculum writers, statistical context–structures provide a framework to design statistical inquiries that directly address learning intentions and curricular goals.

Mathematics Education Research Group of Australasia, 2016

An empirical study was conducted with the aim to develop teachers’ confidence and proficiency wit... more An empirical study was conducted with the aim to develop teachers’ confidence and proficiency with teaching mathematics through inquiry. The study followed 41 primary teachers and compared a regular mathematics lesson to a lesson taught using an inquiry approach; 19 of these teachers were also followed over three years. Lessons were coded on the extent of intellectual quality in the lesson across six dimensions. Higher order thinking showed the most gains over time. Implications for research and practice are given.

Informal statistical inference has gained increasing recognition as an effective approach to teac... more Informal statistical inference has gained increasing recognition as an effective approach to teaching statistics. Distinct from descriptive statistics, inference provides learners with access to the power of statistics by giving them tools to make predictions beyond their data. International research in this area has focused on students from primary school through university. A series of teaching experiments introduced informal statistical inference to very young children (aged 5-6). Although making predictions was familiar as an everyday task, initial attempts revealed challenges to teaching informal inferential reasoning to young learners. Prior to conducting a statistical inquiry involving inference, activities were designed to generate a need for recording and organising data, the language of uncertainty and using data as evidence. Results suggest that the activities prior to inquiry likely supported students in their emerging inferential practices.

Statistics Education Research Journal, 2009

Informal inferential reasoning has shown some promise in developing students’ deeper understandin... more Informal inferential reasoning has shown some promise in developing students’ deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference – eneralizations ‘beyond the data,’ probabilistic language, and data as evidence. The authors use primary school classroom episodes and excerpts of interviews with the teachers to illustrate the framework and reiterate the importance of embedding statistical learning within the context of statistical inquiry. Implications for the teaching of more powerful satistical concepts at the primary school level are discussed.

The Australian mathematics teacher, 2018

Suppose you were taught the game of soccer, but never put your skills to use in an actual game. I... more Suppose you were taught the game of soccer, but never put your skills to use in an actual game. In order to develop expertise in anything, we need to put our knowledge into practice. Playing a game of soccer develops a deeper understanding of our knowedge of the game and the ball-handling skills that we practised because we have to apply these knowledge and skills in messy, dynamic and unpredictable (non-routine) contexts. We have to adapt, combine, extend and even question our skills ‘in the moment’ of the game to respond to problems on the playing field that are new and not quite the same as those encountered in practice. As we gain experience in these non-routine situations, not only do we have a better understanding of our skills and when to use them, but we gain confidence to apply them in unpredictable situations. We begin to recognise approaches that worked before in similar situations. It is the knowledge of the game, the basic skills we practise and the non-routine experien...

A statistical question acknowledges that there is variability in data that needs to be accounted ... more A statistical question acknowledges that there is variability in data that needs to be accounted for in the conclusion. Accounting for variability is problematic if students do not have an understanding that a distribution shows patterns and can be described by the centre, spread and overall shape. TinkerPlots provides opportunities to build understandings of spread and measures of centre as students work with distributions, adding and manipulating dividers and hat plots. In this exploratory study, students in a middle school inquiry classroom used hat plots to compare distributions and write justified conclusions. Results suggest that the necessity to account for variability in data within their conclusions presented students with a purpose to transition from hat plots to box plots to provide evidence to answer the question. To answer a statistical question students are required to understand, explain, and quantify variability in data (Franklin et al., 2007). Unless students have a...

The aim of this paper is to extend and adapt Yackel and Cobb’s (JRME, 1996) identification of soc... more The aim of this paper is to extend and adapt Yackel and Cobb’s (JRME, 1996) identification of sociomathematical norms in mathematical inquiry to problems that are ill-structured. The background theory influenced the design and local theory development of the research. This paper uses excerpts from an upper primary classroom to address the ill-structured mathematical inquiry question, Which bubble gum is the best? Two norms are illustrated: (1) mathematising the ambiguity in an inquiry question, and (2) using the inquiry question to check progress towards a solution. Children demonstrated productive social norms and emergence of the sociomathematical inquiry norm of mathematising, but using the inquiry question was less prevalent. In both cases, children found it challenging to productively coordinate their everyday (relevant) and mathematical knowledge.

Mathematics Teacher Education and Development, 2007

Gaps between teaching practices and research recommendations have been well documented. One chall... more Gaps between teaching practices and research recommendations have been well documented. One challenge for research is in understanding the processes and systems that promote a bridging of these gaps. A year-long study with four primary teachers documented ten support mechanisms, or connection levers, that the teachers raised as important for building their expertise, commitment, and confidence in teaching mathematics and statistics through an inquiry-based approach. Their words provide insight into how support helps teachers to take on and commit to innovative practices.

Mathematics Education Research Group of Australasia, 2016

Intellectual risk is valued among 21st century skills. Three primary teachers who promoted positi... more Intellectual risk is valued among 21st century skills. Three primary teachers who promoted positive learning within mathematical inquiry collaborated with researchers to design and apply a rubric to assess children’s progress in taking intellectual risks twice during the year. Results suggest that handling setbacks and giving feedback to peers were the most challenging skills initially, but showed significant gains by the end of the year. Teacher interviews discussed challenges that students faced and how positive classroom culture encouraged intellectual risk.

Experience with statistical inquiry has been advocated in statistics education as vital for learn... more Experience with statistical inquiry has been advocated in statistics education as vital for learners’ understandings of statistical processes. Research has suggested, however, that practices at the school level have focused almost solely on graphs and procedures. While important, these skills do not develop learners’ abilities to cope with the decisions that arise in the face of uncertainties and ambiguities that accompany statistical investigations. A longitudinal study in Australia researched experienced primary teachers’ evolving experiences in teaching statistical inquiry. This paper will report on the uniqueness of teachers’ early experiences in teaching statistical inquiry, an issue that emerged in the first three years of the study. Critical skills that teachers need to develop to teach statistical investigations that are often neglected in teacher professional development are discussed, including implications for research and teacher education.

Little is known about the way that teachers articulate notions of variation in their own words. T... more Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of standard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the prospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined.

Several years ago, we characterized “informal statistical inference” as a claim that went beyond ... more Several years ago, we characterized “informal statistical inference” as a claim that went beyond the data, using the data as evidence and acknowledging uncertainty (Makar & Rubin, 2009). This characterization was intentionally ambiguous in order to provide a context for ongoing research on statistical reasoning (especially with younger learners and those without formal statistical training) and to provoke discussion among researchers whose uses of the term differed from one another. Since then, research about informal statistical inference has proliferated, from work with young children to tertiary settings. In this paper, we review recent research on informal statistical inference, investigating issues and new questions that have emerged around looking “beyond the data”, using “data as evidence” and “articulating uncertainty”.

International Handbook of Research in Statistics Education

This chapter reviews research on the learning of statistical inference, focusing in particular on... more This chapter reviews research on the learning of statistical inference, focusing in particular on recent research on informal statistical inference. The chapter begins by arguing for the importance of broader access to the power of statistical inference—which, until recently, has been accessible only to those with extensive knowledge of mathematics—and then traces the philosophical roots of inference. We outline the challenges that students have encountered in learning statistical inference and strategies to facilitate its learning that have capitalized on technological advances. We describe the emergence of informal statistical inference and how researchers have framed the idea over the past decade. Rather than consider formal and informal statistical inference dichotomously, we highlight a number of dimensions along which approaches to statistical inference may differ, providing a richer perspective on how formal and informal statistical inference are related. Cases from classroom research aimed at primary, secondary, and tertiary levels are used to illustrate how informal statistical inference has shaped new ways to approach the teaching and learning of statistical inference. Finally, we outline gaps in research on statistical inference and present our speculations on its future in light of new research on statistical modeling and big data.

International Journal of Educational Research

Curriculum ergonomics focuses on the “fit” between students and the curriculum, and how this “fit... more Curriculum ergonomics focuses on the “fit” between students and the curriculum, and how this “fit” extends students’ understanding of content. We argue that the opportunity for narrative in an inquiry-based learning environment in mathematics promotes this “fit” between students and the curriculum. This is in contrast to purely expository forms, which focus on description and facts. In this paper, we use Bruner’s concept of narrative to propose elements of a curriculum ergonomics design framework—connection, sharing of incomplete ideas and repeated experiences over time—that promotes opportunities for “fit” in implementing mathematics curriculum. We draw on data from a primary school classroom (ages 7–8) to illustrate how this fit is played out in a classroom that engages in learning mathematics through inquiry.

ZDM

Children have limited exposure to statistical concepts and processes, yet researchers have highli... more Children have limited exposure to statistical concepts and processes, yet researchers have highlighted multiple benefits of experiences in which they design and/or engage informally with statistical modelling. A study was conducted with a classroom in which students developed and utilised data-based models to respond to the inquiry question, Which origami animal jumps the furthest? The students used hat plots and box plots in Tinkerplots to make sense of variability in comparing distributions of their data and to support them to write justified conclusions of their findings. The study relied on classroom video and student artefacts to analyse aspects of the students' modelling experiences which exposed them to powerful statistical ideas, such as key repeatable structures and dispositions in statistics. Three principles-purpose, process and prediction-are highlighted as ways in which the problem context, statistical structures and inquiry dispositions and cycle extended students' opportunities to reason in sophisticated ways appropriate for their age. The research question under investigation was, How can an emphasis on purpose, process and prediction be implemented to support children's statistical modelling? The principles illustrated in the study may provide a simple framework for teachers and researchers to develop statistical modelling practices and norms at the school level.

Mathematics Education Research Journal

The 3-year study described in this paper aims to create new knowledge about inquiry norms in prim... more The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, BHow do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?^The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers' progressive development of classroom norms of mathematical inquiry and how they facilitate learning.

Mathematics Education Research Journal, 2017

Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-str... more Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-structured problems set in authentic contexts. While IBL is gaining ground in Australia as an instructional practice, there has been little research that considers implications for student motivation and engagement. Expectancy-value theory (Eccles and Wigfield 2002) provides a framework through which children's beliefs about their mathematical competency and their expectation of success are able to be examined and interpreted, alongside students' perceptions of task value. In this paper, Eccles and Wigfield's expectancy-value model has been adopted as a lens to examine a complete unit of mathematical inquiry as undertaken with a class of 9-10-year-old students. Data were sourced from a unit (∼10 lessons) based on geometry and geometrical reasoning. The units were videotaped in full, transcribed, and along with field notes and student work samples, subjected to theoretical coding using the dimensions of Eccles and Wigfield's model. The findings provide insight into aspects of IBL that may impact student motivation and engagement. The study is limited to a single unit; however, the results provide a depth of insight into IBL in practice while identifying features of IBL that may be instrumental in bringing about increased motivation and engagement of students in mathematics. Identifying potentially motivating aspects of IBL enable these to be integrated and more closely studied in IBL practises.