Articles by Jill Fielding
Teaching and Teacher Education, 2022
Strengthening Initial Teacher Education (ITE) students' capabilities to implement challenging mat... more Strengthening Initial Teacher Education (ITE) students' capabilities to implement challenging mathematical tasks is a focus for policy and curriculum internationally. In this article, we report on motivational aspects of ITE students' engagement with challenging mathematical tasks as an outcome of an explorative study involving 41 Australian ITE students in their third year of a four-year program. Data collection instruments consisted of pre- and post-surveys and a focus group interview. The study was interpretive, utilizing both quantitative and qualitative techniques. Findings suggest ITE student motivation was most closely associated with situational interest and challenge served to both motivate and demotivate students.
Instructional Science, 2022
Conceptual challenge is often considered a necessary ingredient for promoting deep learning in an... more Conceptual challenge is often considered a necessary ingredient for promoting deep learning in an inquiry-based environment. However, challenge alone does not support conceptual development. In this paper, we draw on complexity theory as a theoretical lens to explore how a primary teacher facilitated students’ conceptual change through repeated cycles of challenge and support to develop increasingly robust concepts. Data are drawn from a primary class as they were developing initial understandings of distribution, informal statistical inference and sampling variability in the process of solving an extended mathematical inquiry problem. Data included classroom video, researcher journal and student work samples. The findings suggest two benefits to guiding students through multiple iterations of challenge and guidance: the opportunity to provoke and guide richer mathematical concepts; and the opportunity to provide earlier exposure to advanced mathematical concepts. Building on this research, we argue for the value of multiple iterations of challenge-support phases to develop increasingly robust understanding over time.
International Journal of STEM Education, 2022
The recommendation from national documents and reports to promote inquiry-related science activit... more The recommendation from national documents and reports to promote inquiry-related science activities has not been supported by recent studies, which have found the overall frequency of inquiry activities to be negatively associated with student learning outcomes. This study was inspired by such conflicting reports and aimed to clarify the associations of science-specific, inquiry-related activities and epistemological beliefs with students’ mathematical and scientific literacies. Results A secondary analysis of the database from the Programme for International Student Assessment 2015 of Australia ( N 1 = 14,530) and Taiwan ( N 2 = 7708) utilizing structural equation modelling revealed that these two countries exhibited similar data patterns. Results suggested that open-inquiry activities (such as debating and planning experiments) had a negative relationship with secondary students’ mathematical and scientific literacies. Structured inquiry learning (such as students explaining their ideas and teacher explaining how an idea can be applied to different phenomena) and epistemological beliefs about science were significant and positive predictors of student mathematical and scientific literacy performance. Conclusions The current study further highlights and provides empirical evidence that the teacher’s role in structured inquiry (especially pertaining to the relevance and applicability of these ideas) appears to be essential to the development of student literacy. Educational implications and recommendations are discussed.
The Australian and International Journal of Rural Education, 2017
This paper provides initial evidence of the effectiveness of an educational program in a Tasmania... more This paper provides initial evidence of the effectiveness of an educational program in a Tasmanian regional community that has experienced ongoing industrial restructuring. In response to these changes, community and civic leaders adopted a multifaceted strategic plan to address employment needs and opportunities. Part of this plan involved targeting school children to help them explore a broader range of educational and career options. The program, Aspire High, involves Year 5 children visiting workplaces, the local Year 11 and 12 college, the local technical college, and a local university campus. This paper reports results from student interviews and surveys. While it is difficult to attribute changes in students’ attitudes and aspirations solely to Aspire High, it is evident that they were enthusiastic about the program. Secondary findings showed that students become less positive towards school by Year 8, and that boys are less likely to be positive towards school and more like...
The Australian and International Journal of Rural Education, 2017
This paper analyses a community-based educational program involving private and public sector par... more This paper analyses a community-based educational program involving private and public sector partners instituted in a small city in northern Tasmania. The program represents part of a state-wide initiative to challenge the persistence of structural educational disadvantage and what is understood to be an entrenched “culture” that is insufficiently attuned to the necessity of further education. In this paper, we analyse this program from the perspective of key community partners drawing on a series of semi-structured interviews. We offer an analytic framework that suggests an integrated approach to thinking about supporting educational achievement, attainment and retention in regional Australia. It is our view while there is much that regional communities struggling with change can learn from this program, there are conceptual limitations in the way the problem of educational achievement is understood that should be enhanced by a more comprehensive understanding.
Australian Journal of Teacher Education
International Journal of STEM Education, 2022
Background: The recommendation from national documents and reports to promote inquiry-related sci... more Background: The recommendation from national documents and reports to promote inquiry-related science activities has not been supported by recent studies, which have found the overall frequency of inquiry activities to be negatively associated with student learning outcomes. This study was inspired by such conflicting reports and aimed to clarify the associations of science-specific, inquiry-related activities and epistemological beliefs with students' mathematical and scientific literacies. Results: A secondary analysis of the database from the Programme for International Student Assessment 2015 of Australia (N 1 = 14,530) and Taiwan (N 2 = 7708) utilizing structural equation modelling revealed that these two countries exhibited similar data patterns. Results suggested that open-inquiry activities (such as debating and planning experiments) had a negative relationship with secondary students' mathematical and scientific literacies. Structured inquiry learning (such as students explaining their ideas and teacher explaining how an idea can be applied to different phenomena) and epistemological beliefs about science were significant and positive predictors of student mathematical and scientific literacy performance. Conclusions: The current study further highlights and provides empirical evidence that the teacher's role in structured inquiry (especially pertaining to the relevance and applicability of these ideas) appears to be essential to the development of student literacy. Educational implications and recommendations are discussed.
Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather ... more Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for proportional reasoning in later years. In this paper, excerpts from a classroom case study of a fourth-grade classroom (students aged 9) are presented as they address an inquiry problem that required proportional reasoning. As the inquiry unfolded, students' additive strategies were progressively seen to shift to proportional thinking to enable them to answer the question that guided their inquiry. In wrestling with the challenges they encountered, their emerging proportional reasoning was supported by the inquiry model used to provide a structure, a classroom culture of inquiry and argumentation, and the proportionality embedded in the problem context.
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, "How 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 practices.
Previous research into the knowledge required for teaching has focused primarily on pre-service a... more Previous research into the knowledge required for teaching has focused primarily on pre-service and in-service teachers’ knowledge. What is less researched, however, is the role of the teacher educator in helping pre-service teachers (PSTs) develop the knowledge needed in order to teach mathematics to students. The focus thus shifts from examining school teachers’ knowledge for teaching mathematics to school students, to studying teacher educators’ knowledge for teaching teachers. This raises the question of what is the nature of this knowledge as required by teacher educators, and how evident is it in their practice? This paper documents the interactions among two teacher educators and two cohorts of PSTs enrolled in a unit designed to teach mathematics pedagogy to early childhood and primary PSTs. Over one semester, two teacher educators observed each other’s classes, engaged in reflective professional conversations, and surveyed PSTs about lesson material and delivery. The results indicated there were a number of issues faced by the teacher educators that could be interpreted through the use of a teacher knowledge framework, with examples for this study focussing on a representative lesson. The findings add to the field of research into teacher educator knowledge and have implications for mathematics teacher educators and the pre-service teachers they teach.
This paper analyses a community-based educational program involving private and public sector par... more This paper analyses a community-based educational program involving private and public sector partners instituted in a small city in northern Tasmania. The program represents part of a statewide initiative to challenge the persistence of structural educational disadvantage and what is understood to be an entrenched " culture " that is insufficiently attuned to the necessity of further education. In this paper, we analyse this program from the perspective of key community partners drawing on a series of semi-structured interviews. We offer an analytic framework that suggests an integrated approach to thinking about supporting educational achievement, attainment and retention in regional Australia. It is our view while there is much that regional communities struggling with change can learn from this program, there are conceptual limitations in the way the problem of educational achievement is understood that should be enhanced by a more comprehensive understanding.
This paper provides initial evidence of the effectiveness of an educational program in a Tasmania... more This paper provides initial evidence of the effectiveness of an educational program in a Tasmanian regional community that has experienced ongoing industrial restructuring. In response to these changes, community and civic leaders adopted a multifaceted strategic plan to address employment needs and opportunities. Part of this plan involved targeting school children to help them explore a broader range of educational and career options. The program, Aspire High, involves Year 5 children visiting workplaces, the local Year 11 and 12 college, the local technical college, and a local university campus. This paper reports results from student interviews and surveys. While it is difficult to attribute changes in students' attitudes and aspirations solely to Aspire High, it is evident that they were enthusiastic about the program. Secondary findings showed that students become less positive towards school by Year 8, and that boys are less likely to be positive towards school and more likely to choose a traditionally gendered occupation.
Book Chapters by Jill Fielding
Children’s informal reasoning about uncertainty can be considered a product of their beliefs, lan... more Children’s informal reasoning about uncertainty can be considered a product of their beliefs, language, and experiences, much of which is formed outside of formal schooling. As a result, students can adopt informal intuitions that are incompatible with formal reasoning. Although the creation of cognitive conflict has been considered as one means of challenging students’ understandings, prior research in probability suggests that students may simultaneously hold multiple, incompatible understandings without conflict arising. Design-based methodology was adopted to investigate young (7–8 years old) students’ inferential reasoning under uncertainty, using an inquiry-based unit developed around addition bingo. This paper selectively reports on students’ inferences that initially suggested they were tacitly working from a uniform distribution (equiprobability bias), but shifted as students collected empirical data (from a discrete symmetric triangular distribution). Their inferences were...
International Handbook of Research in Statistics Education
What is an appropriate structure for reporting a study of educators’ perceptions of cultural well... more What is an appropriate structure for reporting a study of educators’ perceptions of cultural wellbeing, following an interpretive paradigm, and a grounded theory methodology?
Statistics in the early years is often limited to the construction and ‘reading’ of simple data r... more Statistics in the early years is often limited to the construction and ‘reading’ of simple data representations as distinct from employing statistical inquiries that engage students with data in more authentic and meaningful contexts. One of the challenges of engaging with data inquiries is the extent to which students struggle with the lack of structure and direction, thus requiring additional support, or scaffolding. This chapter details the framework used for introducing statistical inquiry to young students and then provides insights that emerged from observation and analysis of a class of 5–6 year olds engaged in their own data investigation to illustrate. The findings suggest that considerable teacher scaffolding is required to progress students through inquiries and this was largely achieved through questioning employed to focus students on both the inquiry process and the statistical content to be addressed.
The purpose of this chapter is to develop an inclusive and coherent discussion about research dev... more The purpose of this chapter is to develop an inclusive and coherent discussion about research developments within numeracy while, at the same time, highlighting the contributions of its different facets. These facets include two broad contexts in which numeracy development and practices take place, schooling/initial teacher education and the workplace, and two centred on specific areas of mathematical content, statistical and financial literacy. Research in this review is analysed through the dimensions of the Model of Numeracy for the 21st Century—contexts, mathematical knowledge, tools, dispositions and critical orientation. The chapter concludes with a discussion of potential new directions for numeracy research.
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Articles by Jill Fielding
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, "How 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.
Book Chapters by Jill Fielding
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, "How 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.
mainly on research at the school level. After introducing several frameworks for the
practice, research is summarized in relation to posing and refining statistical questions
for investigation, to planning for and collecting appropriate data, to analyzing
data through visual representations, to analyzing data by summarizing them with
specific measures, and to making decisions acknowledging uncertainty. The importance of combining these stages through complete investigations is then stressed both in terms of student learning and of the needs of teachers for implementation. The need for occasional backtracking is also acknowledged, and more research in relation to complete investigations is seen as a priority. Having considered the Practice of Statistics as an active engagement by learners, the chapter reviews presentations of the Big Ideas underlying the practice, with a call for research linking classroom investigations with the fundamental understanding of the Big Ideas. The chapter ends with a consideration of the place of statistical literacy in relation to the Practice of Statistics and the question of the responsibility of the school curriculum to provide understanding and proficiency in both.
understandings without conflict arising. Design-based methodology was adopted to investigate young (7–8 years old) students’ inferential reasoning under uncertainty, using an inquiry-based unit developed around addition bingo. This paper selectively reports on students’ inferences that initially suggested they were tacitly working from a uniform distribution (equiprobability bias), but shifted as students
collected empirical data (from a discrete symmetric triangular distribution). Their inferences were challenged using an argumentation framework, with particular emphasis on the need for defensible evidence. Initial findings suggest potential for argumentation and inferential approaches that make students’ conceptions explicit through ‘visibilizing’ their knowledge.
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.
The authors, all leading mathematics educators and researchers, explore many familiar picture books to identify the key mathematical 'big ideas' inherent. They anticipate the misconceptions and difficulties students may have, and share planning frameworks which show how lessons can be enacted and extended.
Each chapter explores one powerful mathematical idea, such as place value, measurement concepts, and data handling and statistics. Find out how Six-dinner Sid can help with ordering numbers, One is a snail, ten is a crab with partitioning, Diary of a wombat with time, Knuffle Bunny with spatial sense, Sophie's Prize with big and small numbers, and Rooster's off to see the world with growing patterns.
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.
Abstract:
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.
More Info: Teacher Resource
Abstract: 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.
More Info: Teacher Resource
ISBN 978-1-86295-829-6