Jane Watson | University of Tasmania (original) (raw)
Papers by Jane Watson
Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, interna... more Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice.
The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skill... more The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this paper reports on the preliminary phase of a large national study designed to move beyond the hypothetical and to provide an evidence-based foundation for learning progressions in mathematical reasoning in three key areas of the curriculum.
EJ765294 - Proportional Reasoning: Lessons from Research in Data and Chance.
S everal issues surround the continuing implementation of the Chance and Data component of the ma... more S everal issues surround the continuing implementation of the Chance and Data component of the mathematics curriculum in Australia. First is its survival. Second is the question of how far toward formal inference should the curriculum take students (assuming it survives). Third is what contexts are amenable for understanding the concepts in the curriculum. Fourth is what tools are available to save time and assist in the learning process. One of the ways of ensuring survival is to convince decision makers that Chance and Data can be taught and learned successfully.
Identities, cultures and learning …, 2006
This paper reports some initial results of a project that involved profiling middle school mathem... more This paper reports some initial results of a project that involved profiling middle school mathematics teachers and their students. Survey data concerning the teachers' confidence in relation to the mathematics topics that they teach, their beliefs about numeracy and effective teaching of ...
Curriculum reform in Tasmanian schools centres around the implementation of an Essential Learning... more Curriculum reform in Tasmanian schools centres around the implementation of an Essential Learnings framework. This framework has provided a catalyst for pedagogical change; for teachers to work collaboratively; in cross-curricular ways and; for assessment to be authentic and support learning. The place of numeracy in this reform-based learning environment is the focus of a research project which commenced in 2005. A professional learning program for middle years' teachers with a goal to improve student outcomes in numeracy has been co-constructed with participants and will be evaluated at several stages through the project. An important component of the project involves working with teachers as they continue to implement the Essential Learnings. This paper reports on the baseline data received via a teacher profile and discusses teachers' responses to questions on planning and implementing units of work in the area of numeracy.
As part of an interview protocol investigating teachers' pedagogical content knowledge (PCK) in s... more As part of an interview protocol investigating teachers' pedagogical content knowledge (PCK) in statistics, 40 teachers were presented with a newspaper article reporting a phonein survey about the legalisation of marijuana. The article and a question about the reliability of the sample had earlier been used in student surveys, and three student answers to the question were also presented to the teachers. Teachers' PCK was assessed based on responses to questions about the big ideas in the task, potential student appropriate and inappropriate answers, and how teachers would intervene in relation to the three student answers. The wide range of responses provided evidence for the potential of the task in a cross-curricular secondary classroom.
To capture aspects of pedagogical content knowledge (PCK) not illuminated in an earlier written s... more To capture aspects of pedagogical content knowledge (PCK) not illuminated in an earlier written survey, an interview protocol was used with 40 middle school teachers. The scenarios were intended to elicit teachers ’ understanding of the big ideas, ability to anticipate students ’ answers, and intervention strategies for the classroom. This was expected to be a straight-forward journey based on teachers ’ responses to three context-based scenarios regarding students ’ answers to questions. Instead we were surprised by teachers ’ responses that revealed their perceptions that their experiences teaching mathematics and teaching statistics are very different. This led to further analysis of the PCK tasks and a suggestion that the mathematics embedded in the tasks was sometimes an impediment for the teachers, especially in relation to intervention strategies in the classroom.
This report explores the development of student understanding in an open-ended problem solving si... more This report explores the development of student understanding in an open-ended problem solving situation intended to encourage higher order functioning by students who have not received specific instruction in the constructs involved
This paper considers the change in teachers' confidence, beliefs, and knowledge with respect ... more This paper considers the change in teachers' confidence, beliefs, and knowledge with respect to mathematics teaching across a 3-year collaborative intervention, which although planned in a reform-based learning environment, took place as the reforms were rolled back and a new view of curriculum introduced. Of 86 middle school teachers involved at some time during the project only 19 completed both the pre-and post-profiles and of these only 11 had been in the project since its beginning. Teacher change appears more likely to have been related to the length of time in the program than to the state-wide curriculum changes.
Of interest in this study, based in a class of 26 Year 5/6 students, is the way TinkerPlots facil... more Of interest in this study, based in a class of 26 Year 5/6 students, is the way TinkerPlots facilitated the development of statistical reasoning for students with no previous data handling experience. The class completed four lessons related to data collection, data representation, data summary, and data inference based on a sporting activity, where they had recorded their heart rates before and after the event and used the software TinkerPlots to analyse the data. A month later 12 of the students were individually interviewed with a three-part protocol using TinkerPlots to assess their reasoning in relation to comparing two data sets, to hypothesising relationships and providing evidence, and to interpreting differences in large data sets. The consolidation and transfer of reasoning evidenced in the student interviews demonstrated the value of employing TinkerPlots in the classroom. BACKGROUND The development of school students' reasoning in various areas of statistics has been...
This report details the underlying themes that contribute to the implementation of graphing curri... more This report details the underlying themes that contribute to the implementation of graphing curricula: • the history of graphing, both outside and inside the school curriculum; • the 21st century graphing technology, including what it does and does not offer; • research on the development of student understanding; • recognition of the close and critical relationship of graph creation and graph interpretation; and • the implications of graph understanding for Working Mathematically interpreted as facilitating decision-making. These themes contribute to the recommendations made for the implementation of a 21st century graphing curriculum.
This paper reports pilot data from an instrument devised as part of a large ARC funded project th... more This paper reports pilot data from an instrument devised as part of a large ARC funded project that aims, among other things, to investigate factors that influence the decisions of students in rural and/or disadvantaged areas to continue their schooling beyond Year 10. One section of the pilot student questionnaire comprised 42 items designed to reflect dimensions believed to influence these decisions. Participants responded on 5-point Likert scales indicating the extent of their agreement from Strongly Disagree to Strongly Agree with each of the items. We were interested in the extent to which the data supported the theoretical structure that underpinned the structure of the questionnaire and in testing the appropriateness of the language used. The large scale data collection will survey students from Years 5 to 11 with as few adaptations for differences in literacy levels across that range as possible. To this end, the pilot questionnaire was administered to Year 5 (n = 44) and Ye...
Although the creation of graphs to display data has been part of the school curriculum for some t... more Although the creation of graphs to display data has been part of the school curriculum for some time, the call in the new Australian Curriculum for " numeracy across the curriculum " provides both the opportunity and challenge to link the skills of graph creating with the understanding of context in order to produce meaningful interpretation of the messages held in graphs. This paper reports on classroom experiences of and follow-up interviews with 12 grade 5/6 students who were introduced to the software TinkerPlots to assist in graph creation. The focus is on their success at graph creation and interpretation in contexts that provide potential links to other subjects in the school curriculum. Implications for the curriculum and teaching are drawn from the students' experiences.
Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, interna... more Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice.
The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skill... more The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this paper reports on the preliminary phase of a large national study designed to move beyond the hypothetical and to provide an evidence-based foundation for learning progressions in mathematical reasoning in three key areas of the curriculum.
EJ765294 - Proportional Reasoning: Lessons from Research in Data and Chance.
S everal issues surround the continuing implementation of the Chance and Data component of the ma... more S everal issues surround the continuing implementation of the Chance and Data component of the mathematics curriculum in Australia. First is its survival. Second is the question of how far toward formal inference should the curriculum take students (assuming it survives). Third is what contexts are amenable for understanding the concepts in the curriculum. Fourth is what tools are available to save time and assist in the learning process. One of the ways of ensuring survival is to convince decision makers that Chance and Data can be taught and learned successfully.
Identities, cultures and learning …, 2006
This paper reports some initial results of a project that involved profiling middle school mathem... more This paper reports some initial results of a project that involved profiling middle school mathematics teachers and their students. Survey data concerning the teachers' confidence in relation to the mathematics topics that they teach, their beliefs about numeracy and effective teaching of ...
Curriculum reform in Tasmanian schools centres around the implementation of an Essential Learning... more Curriculum reform in Tasmanian schools centres around the implementation of an Essential Learnings framework. This framework has provided a catalyst for pedagogical change; for teachers to work collaboratively; in cross-curricular ways and; for assessment to be authentic and support learning. The place of numeracy in this reform-based learning environment is the focus of a research project which commenced in 2005. A professional learning program for middle years' teachers with a goal to improve student outcomes in numeracy has been co-constructed with participants and will be evaluated at several stages through the project. An important component of the project involves working with teachers as they continue to implement the Essential Learnings. This paper reports on the baseline data received via a teacher profile and discusses teachers' responses to questions on planning and implementing units of work in the area of numeracy.
As part of an interview protocol investigating teachers' pedagogical content knowledge (PCK) in s... more As part of an interview protocol investigating teachers' pedagogical content knowledge (PCK) in statistics, 40 teachers were presented with a newspaper article reporting a phonein survey about the legalisation of marijuana. The article and a question about the reliability of the sample had earlier been used in student surveys, and three student answers to the question were also presented to the teachers. Teachers' PCK was assessed based on responses to questions about the big ideas in the task, potential student appropriate and inappropriate answers, and how teachers would intervene in relation to the three student answers. The wide range of responses provided evidence for the potential of the task in a cross-curricular secondary classroom.
To capture aspects of pedagogical content knowledge (PCK) not illuminated in an earlier written s... more To capture aspects of pedagogical content knowledge (PCK) not illuminated in an earlier written survey, an interview protocol was used with 40 middle school teachers. The scenarios were intended to elicit teachers ’ understanding of the big ideas, ability to anticipate students ’ answers, and intervention strategies for the classroom. This was expected to be a straight-forward journey based on teachers ’ responses to three context-based scenarios regarding students ’ answers to questions. Instead we were surprised by teachers ’ responses that revealed their perceptions that their experiences teaching mathematics and teaching statistics are very different. This led to further analysis of the PCK tasks and a suggestion that the mathematics embedded in the tasks was sometimes an impediment for the teachers, especially in relation to intervention strategies in the classroom.
This report explores the development of student understanding in an open-ended problem solving si... more This report explores the development of student understanding in an open-ended problem solving situation intended to encourage higher order functioning by students who have not received specific instruction in the constructs involved
This paper considers the change in teachers' confidence, beliefs, and knowledge with respect ... more This paper considers the change in teachers' confidence, beliefs, and knowledge with respect to mathematics teaching across a 3-year collaborative intervention, which although planned in a reform-based learning environment, took place as the reforms were rolled back and a new view of curriculum introduced. Of 86 middle school teachers involved at some time during the project only 19 completed both the pre-and post-profiles and of these only 11 had been in the project since its beginning. Teacher change appears more likely to have been related to the length of time in the program than to the state-wide curriculum changes.
Of interest in this study, based in a class of 26 Year 5/6 students, is the way TinkerPlots facil... more Of interest in this study, based in a class of 26 Year 5/6 students, is the way TinkerPlots facilitated the development of statistical reasoning for students with no previous data handling experience. The class completed four lessons related to data collection, data representation, data summary, and data inference based on a sporting activity, where they had recorded their heart rates before and after the event and used the software TinkerPlots to analyse the data. A month later 12 of the students were individually interviewed with a three-part protocol using TinkerPlots to assess their reasoning in relation to comparing two data sets, to hypothesising relationships and providing evidence, and to interpreting differences in large data sets. The consolidation and transfer of reasoning evidenced in the student interviews demonstrated the value of employing TinkerPlots in the classroom. BACKGROUND The development of school students' reasoning in various areas of statistics has been...
This report details the underlying themes that contribute to the implementation of graphing curri... more This report details the underlying themes that contribute to the implementation of graphing curricula: • the history of graphing, both outside and inside the school curriculum; • the 21st century graphing technology, including what it does and does not offer; • research on the development of student understanding; • recognition of the close and critical relationship of graph creation and graph interpretation; and • the implications of graph understanding for Working Mathematically interpreted as facilitating decision-making. These themes contribute to the recommendations made for the implementation of a 21st century graphing curriculum.
This paper reports pilot data from an instrument devised as part of a large ARC funded project th... more This paper reports pilot data from an instrument devised as part of a large ARC funded project that aims, among other things, to investigate factors that influence the decisions of students in rural and/or disadvantaged areas to continue their schooling beyond Year 10. One section of the pilot student questionnaire comprised 42 items designed to reflect dimensions believed to influence these decisions. Participants responded on 5-point Likert scales indicating the extent of their agreement from Strongly Disagree to Strongly Agree with each of the items. We were interested in the extent to which the data supported the theoretical structure that underpinned the structure of the questionnaire and in testing the appropriateness of the language used. The large scale data collection will survey students from Years 5 to 11 with as few adaptations for differences in literacy levels across that range as possible. To this end, the pilot questionnaire was administered to Year 5 (n = 44) and Ye...
Although the creation of graphs to display data has been part of the school curriculum for some t... more Although the creation of graphs to display data has been part of the school curriculum for some time, the call in the new Australian Curriculum for " numeracy across the curriculum " provides both the opportunity and challenge to link the skills of graph creating with the understanding of context in order to produce meaningful interpretation of the messages held in graphs. This paper reports on classroom experiences of and follow-up interviews with 12 grade 5/6 students who were introduced to the software TinkerPlots to assist in graph creation. The focus is on their success at graph creation and interpretation in contexts that provide potential links to other subjects in the school curriculum. Implications for the curriculum and teaching are drawn from the students' experiences.
International Handbook of Research in Statistics Education, 2018
This chapter presents an overview of the Practice of Statistics focusing mainly on research at t... more This chapter presents an overview of the Practice of Statistics focusing
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.