Jill Wells - Academia.edu (original) (raw)

Papers by Jill Wells

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 result...

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?

What is Next in Educational Research?, 2016

What is Next in Educational Research? enables the reader to peek into research at the forefront o... more What is Next in Educational Research? enables the reader to peek into research at the forefront of a diverse range of education fields as it is being conducted by beginning researchers. The book illustrates the extensive range of research being undertaken in education through a broad range of issues, topics and methodologies that will underpin and provoke research well into the future. The five sections address a range of topics, including: issues in design and methodology, social integration, language education, leadership, and issues in contemporary education. Each chapter makes a valuable contribution to existing educational research, and is a testament to the potential of these researchers to lead innovative educational research projects. Both higher degree by research students and their supervisors will find this book particularly useful and interesting as it provides examples of quality research higher degree writing, illustrates a variety of contemporary methodologies, and supports the early publication of student work.

Every scientific discipline needs a solid research base on which to build theory and areas of inq... more Every scientific discipline needs a solid research base on which to build theory and areas of inquiry. In education, this research base is also crucial in that it provides a foundation for understanding and improving teaching and learning. Unlike other disciplines, such as mathematics education or science education, the research related to statistics spans many areas of scholarship and teaching, such as mathematics, psychology, and science. Synthesizing research from these different areas has been challenging, due to different terminology, focus, methodology, and target population. At the Fourth International Conference on Teaching Statistics (ICOTS-4), held in 1998 in Singapore, it became clear that there was a need to form a coherent research community to allow scholars studying the teaching and learning of statistics to not only share and discuss their work in detail, but also explore ways to coordinate their research discourse, questions and methods. At that time there were two major challenges to these goals. First, it was difficult to gather researchers from around the world except for ICOTS, which was held only every four years, and even at ICOTS, there was limited time to present and almost no time to discuss research in a deep way. The second challenge had to do with the way researchers used terms to describe important student learning reasoning and outcomes. In particular, there seemed to be no agreement on the definitions of statistical literacy, reasoning and thinking, despite the growing interest in research studying or assessing each of these learning outcomes. xv xvi FOREWORD As we recognized this need and tried to come up with possible solutions, the idea for SRTL was born. We wondered: If we held a small, invitational research forum and invited our colleagues to come, independent of a professional organization or conference, but offering the opportunity to share rich segments of video recorded interviews and observations of students, would anyone come? At that time, Dani lived on Kibbutz Be'eri in the south of Israel, and he offered his kibbutz as a place for us to host such a gathering. We obtained a type of endorsement from the informal International Study Group for the Teaching and Learning of Probability and Statistics, then chaired by Carmen Batanero, at the University of Granada, Spain. Dani was also able to get support from the Weizmann Institute of Science, where he had been working for several years, and Joan was able to secure a small amount of funding from her department chair (Mary McEvoy) at the University of Minnesota. We sent out an invitation, and held our breath. Would anyone come? Luckily, the answer was yes. In the summer of 1999, we had 16 scholars from Australia, Belgium, Ireland, Israel, the UK, and the US come to the kibbutz to meet for an intense five days of presentations and discussions. Along with the research we were immersed in, Dani provided outings to enable us to get to know his country, its history and diversity. By the end of SRTL-1, we were an enthusiastic group that saw not only the enormous opportunities and challenges ahead of us, but also the joy of forming a research community with a shared passion for learning how students come to understand and learn statistical concepts and methods. Today, the International Collaboration for Research in Statistical Reasoning, Thinking, and Literacy offers scientific gatherings for statistics education researchers every two years. The SRTL research forums, foster collaborative and innovative research studies that examine the nature and development of statistical literacy, reasoning, and thinking, and to explore how educators can develop these desired learning goals for students. The SRTL research forums have led to many publications that present new research, synthesize and build on previous research, and form connections among related work in other disciplines (see table below). SRTL Forums and Contributions to Statistics Education Primary Forum Theme Host/Venue Date Publication(s) SRTL-1 Statistical reasoning, thinking, and literacy Kibbutz Be'eri, Israel July 18-23, 1999 SRTL-2 The challenges in describing, teaching, and assessing statistical reasoning, thinking, and literacy

International Handbook of Research in Statistics Education

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 d...

Students come to formal schooling with prior probabilistic conceptions developed through informal... more Students come to formal schooling with prior probabilistic conceptions developed through informal experiential events. One such concept is that of chance outcomes being inherently equiprobable, even when not the case. In the design-based research described here, a class of 3rd Grade students was posed an inquiry problem embedded with non-equiprobable outcomes: What is the best addition bingo card? Argumentation was employed as a pedagogic approach to challenging students’ equiprobable beliefs, with students supported to develop an evidence-based argument in response. Students initially experienced conflict with the realisation of unequal frequencies, then developed representations to act as theoretical evidence. A shift from conceptualizing equiprobable outcomes towards responses reflecting theoretical distribution was observed. This exploratory research suggests potential for an evidentiary focus to challenge probabilistic conceptions.

Mathematics Education Research Journal, 26 (1), 1-31, 2014

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 pr...

Argumentation in mathematics teaching has potential to move students beyond tacit understanding o... more Argumentation in mathematics teaching has potential to move students beyond tacit understanding of mathematical concepts and procedures towards articulation and justification of their ideas; a practice in which evidence is central. Design-based research was used to examine the nature of evidence used by a class of primary students through levels of argument and explanation. Results of this exploratory study indicate that evidence put forward became increasingly sophisticated as students’ conceptions became public and therefore open to increased potential challenge.

Presented at the …, 2010

An overview of many primary programs demonstrates the passivity of statistical learning in the ju... more An overview of many primary programs demonstrates the passivity of statistical learning in the junior years. Students are usually provided clean, orderly, simplistic data, or data representations, with which to work. When students are encouraged to collect their own data, it is limited to that which could be expected to cause little difficulty. The focus on contrived and unsophisticated data collection and analysis denies younger students the opportunity to design their own statistical investigations. The research reported here derives from the introduction of the statistical investigative cycle (Wild and Pfannkuch, 1999) to a classroom of 9-10 year old students. The students initially experienced difficulty envisioning the investigation process, despite both explicit instruction and multiple prior experiences with investigative learning. A focus on connecting problems and conclusions to evidence enabled students to plan investigations more efficiently.

Most educational research on argumentation comes from science, with argumentation in mathematics ... more Most educational research on argumentation comes from science, with argumentation in mathematics tending to focus on proof. We contend that argumentation can be used productively in learning mathematics even at the primary level. A research study was designed to explore children's development of argumentation in an Australian primary mathematics classroom. The classroom of 23 children (aged 9-10) had regularly used an inquiry-based approach to address extended, complex, ill-structured problems. The ...

AARE 2008 International Education Conference Brisbane: Changing Climates: Education for Sustainable Futures, 2008

The mathematical sciences are fundamental to the well-being of all nations. They drive the data a... more The mathematical sciences are fundamental to the well-being of all nations. They drive the data analysis, forecasting, modelling, decision-making, management, design and technological principles that underpin every sector of modern enterprise. Mathematics is the foremost enabling science which underpins research, development and innovation in every aspect of society, from business and science through to health and national security (Australian Academy of Science, 2006; 18). The importance of a supply of capable ...

Despite its importance for the discipline, the statistical investigation cycle is given little at... more Despite its importance for the discipline, the statistical investigation cycle is given little attention in schools. Teachers face unique challenges in teaching statistical inquiry, with elements unfamiliar to many mathematics classrooms: Coping with uncertainty, encouraging debate and competing interpretations, and supporting student collaboration. This chapter highlights ways for teacher educators to support teachers’ learning to teach statistical inquiry. Results of two longitudinal studies are used to formulate recommendations to develop teachers’ proficiency in this area.

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 result...

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?

What is Next in Educational Research?, 2016

What is Next in Educational Research? enables the reader to peek into research at the forefront o... more What is Next in Educational Research? enables the reader to peek into research at the forefront of a diverse range of education fields as it is being conducted by beginning researchers. The book illustrates the extensive range of research being undertaken in education through a broad range of issues, topics and methodologies that will underpin and provoke research well into the future. The five sections address a range of topics, including: issues in design and methodology, social integration, language education, leadership, and issues in contemporary education. Each chapter makes a valuable contribution to existing educational research, and is a testament to the potential of these researchers to lead innovative educational research projects. Both higher degree by research students and their supervisors will find this book particularly useful and interesting as it provides examples of quality research higher degree writing, illustrates a variety of contemporary methodologies, and supports the early publication of student work.

Every scientific discipline needs a solid research base on which to build theory and areas of inq... more Every scientific discipline needs a solid research base on which to build theory and areas of inquiry. In education, this research base is also crucial in that it provides a foundation for understanding and improving teaching and learning. Unlike other disciplines, such as mathematics education or science education, the research related to statistics spans many areas of scholarship and teaching, such as mathematics, psychology, and science. Synthesizing research from these different areas has been challenging, due to different terminology, focus, methodology, and target population. At the Fourth International Conference on Teaching Statistics (ICOTS-4), held in 1998 in Singapore, it became clear that there was a need to form a coherent research community to allow scholars studying the teaching and learning of statistics to not only share and discuss their work in detail, but also explore ways to coordinate their research discourse, questions and methods. At that time there were two major challenges to these goals. First, it was difficult to gather researchers from around the world except for ICOTS, which was held only every four years, and even at ICOTS, there was limited time to present and almost no time to discuss research in a deep way. The second challenge had to do with the way researchers used terms to describe important student learning reasoning and outcomes. In particular, there seemed to be no agreement on the definitions of statistical literacy, reasoning and thinking, despite the growing interest in research studying or assessing each of these learning outcomes. xv xvi FOREWORD As we recognized this need and tried to come up with possible solutions, the idea for SRTL was born. We wondered: If we held a small, invitational research forum and invited our colleagues to come, independent of a professional organization or conference, but offering the opportunity to share rich segments of video recorded interviews and observations of students, would anyone come? At that time, Dani lived on Kibbutz Be'eri in the south of Israel, and he offered his kibbutz as a place for us to host such a gathering. We obtained a type of endorsement from the informal International Study Group for the Teaching and Learning of Probability and Statistics, then chaired by Carmen Batanero, at the University of Granada, Spain. Dani was also able to get support from the Weizmann Institute of Science, where he had been working for several years, and Joan was able to secure a small amount of funding from her department chair (Mary McEvoy) at the University of Minnesota. We sent out an invitation, and held our breath. Would anyone come? Luckily, the answer was yes. In the summer of 1999, we had 16 scholars from Australia, Belgium, Ireland, Israel, the UK, and the US come to the kibbutz to meet for an intense five days of presentations and discussions. Along with the research we were immersed in, Dani provided outings to enable us to get to know his country, its history and diversity. By the end of SRTL-1, we were an enthusiastic group that saw not only the enormous opportunities and challenges ahead of us, but also the joy of forming a research community with a shared passion for learning how students come to understand and learn statistical concepts and methods. Today, the International Collaboration for Research in Statistical Reasoning, Thinking, and Literacy offers scientific gatherings for statistics education researchers every two years. The SRTL research forums, foster collaborative and innovative research studies that examine the nature and development of statistical literacy, reasoning, and thinking, and to explore how educators can develop these desired learning goals for students. The SRTL research forums have led to many publications that present new research, synthesize and build on previous research, and form connections among related work in other disciplines (see table below). SRTL Forums and Contributions to Statistics Education Primary Forum Theme Host/Venue Date Publication(s) SRTL-1 Statistical reasoning, thinking, and literacy Kibbutz Be'eri, Israel July 18-23, 1999 SRTL-2 The challenges in describing, teaching, and assessing statistical reasoning, thinking, and literacy

International Handbook of Research in Statistics Education

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 d...

Students come to formal schooling with prior probabilistic conceptions developed through informal... more Students come to formal schooling with prior probabilistic conceptions developed through informal experiential events. One such concept is that of chance outcomes being inherently equiprobable, even when not the case. In the design-based research described here, a class of 3rd Grade students was posed an inquiry problem embedded with non-equiprobable outcomes: What is the best addition bingo card? Argumentation was employed as a pedagogic approach to challenging students’ equiprobable beliefs, with students supported to develop an evidence-based argument in response. Students initially experienced conflict with the realisation of unequal frequencies, then developed representations to act as theoretical evidence. A shift from conceptualizing equiprobable outcomes towards responses reflecting theoretical distribution was observed. This exploratory research suggests potential for an evidentiary focus to challenge probabilistic conceptions.

Mathematics Education Research Journal, 26 (1), 1-31, 2014

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 pr...

Argumentation in mathematics teaching has potential to move students beyond tacit understanding o... more Argumentation in mathematics teaching has potential to move students beyond tacit understanding of mathematical concepts and procedures towards articulation and justification of their ideas; a practice in which evidence is central. Design-based research was used to examine the nature of evidence used by a class of primary students through levels of argument and explanation. Results of this exploratory study indicate that evidence put forward became increasingly sophisticated as students’ conceptions became public and therefore open to increased potential challenge.

Presented at the …, 2010

An overview of many primary programs demonstrates the passivity of statistical learning in the ju... more An overview of many primary programs demonstrates the passivity of statistical learning in the junior years. Students are usually provided clean, orderly, simplistic data, or data representations, with which to work. When students are encouraged to collect their own data, it is limited to that which could be expected to cause little difficulty. The focus on contrived and unsophisticated data collection and analysis denies younger students the opportunity to design their own statistical investigations. The research reported here derives from the introduction of the statistical investigative cycle (Wild and Pfannkuch, 1999) to a classroom of 9-10 year old students. The students initially experienced difficulty envisioning the investigation process, despite both explicit instruction and multiple prior experiences with investigative learning. A focus on connecting problems and conclusions to evidence enabled students to plan investigations more efficiently.

Most educational research on argumentation comes from science, with argumentation in mathematics ... more Most educational research on argumentation comes from science, with argumentation in mathematics tending to focus on proof. We contend that argumentation can be used productively in learning mathematics even at the primary level. A research study was designed to explore children's development of argumentation in an Australian primary mathematics classroom. The classroom of 23 children (aged 9-10) had regularly used an inquiry-based approach to address extended, complex, ill-structured problems. The ...

AARE 2008 International Education Conference Brisbane: Changing Climates: Education for Sustainable Futures, 2008

The mathematical sciences are fundamental to the well-being of all nations. They drive the data a... more The mathematical sciences are fundamental to the well-being of all nations. They drive the data analysis, forecasting, modelling, decision-making, management, design and technological principles that underpin every sector of modern enterprise. Mathematics is the foremost enabling science which underpins research, development and innovation in every aspect of society, from business and science through to health and national security (Australian Academy of Science, 2006; 18). The importance of a supply of capable ...

Despite its importance for the discipline, the statistical investigation cycle is given little at... more Despite its importance for the discipline, the statistical investigation cycle is given little attention in schools. Teachers face unique challenges in teaching statistical inquiry, with elements unfamiliar to many mathematics classrooms: Coping with uncertainty, encouraging debate and competing interpretations, and supporting student collaboration. This chapter highlights ways for teacher educators to support teachers’ learning to teach statistical inquiry. Results of two longitudinal studies are used to formulate recommendations to develop teachers’ proficiency in this area.