Natalie Brown | University of Tasmania (original) (raw)

Conference presentations (refereed) by Natalie Brown

Sharing practice 10th Teaching Matters Annual Conference 22nd-23rd November, Hobart, Tasmania, Nov 23, 2011

The WIL Project was undertaken in 2010 to develop a new Work Integrated Learning (WIL) Policy usi... more The WIL Project was undertaken in 2010 to develop a new Work Integrated Learning (WIL) Policy using the staged University Policy Development Cycle. This cyclerepresents an adaptation of the stepped policy development process depicted in the AustralianPolicy Cycle (Althaus, Bridgman and Davis, 2007). This paper examines the processundertaken to examine two key research questions – What is the University of Tasmania’sposition regarding WIL; and How should these guiding principles be reflected in formalpolicy documentation? The project involved a number of elements, including a WIL ProjectManager, a WIL Working Party, a literature review, data collection, benchmarking as policylearning (Lundvall and Tomlinson, 2002; Paasi, 2005), WIL Discussion Forums, and anextensive series of interviews. The project dovetailed with the Centre for the Advancement of Learning and Teaching (CALT) WIL Provocations Symposium. Consultations anddeliberations involved collegial governance structures. This paper reveals the diversity inwork-related curriculum offerings and disciplinary approaches at Australian universities, andsuggests that establishing clear definitions is an important step towards developing minimumacademic standards or obligations. This paper reports tensions between University-wideumbrella policy provisions and requirements by local academic sections for a high degree of specificity. This paper suggests that the process of asking complex academic policy questionsis self-perpetuating, as more questions are raised which demand policy responses. Finally, indeveloping a uniquely University of Tasmania approach to work integrated learning, theproject confirmed the importance of ongoing dialogue and collegial governance to guide learning and teaching policy development.

Tertiary Education Management Conference Refereed Papers, pp. 73-94, 2013

The Australian federal government now requires higher education institutions to provide evidence ... more The Australian federal government now requires higher education institutions to provide evidence of effective development, implementation and review of institutional policies, however little attention has been given to policy implementation evaluation and policy review. This paper presents a case study of the development of a comprehensive policy implementation evaluation framework proposed for the University of Tasmania’s new Casual Teaching Staff Policy. The proposed policy implementation evaluation framework reflects concepts utilised in the policy development process arising from research regarding good practices with respect to university casual teaching staff.

Papers by Natalie Brown

The activities suggested in this article are intended for use with lowersecondary school students... more The activities suggested in this article are intended for use with lowersecondary school students. The Australian Curriculum: Mathematics states that students in lower secondary school should “investigate the rela-tionship between features of circles such as circumference, area, radius and diameter ” and “use formulas to solve problems involving circumference and area ” (Australian Curriculum, Assessment and Reporting Authority (ACARA), 2010, p. 39). It is suggested, however, that teachers may need to work together to plan for the background and level of the students they teach and decide upon intended learning outcomes suited to their own students. The investigations presented here were used by the authors during a half-day professional learning session with middle school teachers from five rural schools in southern Tasmania (as a part of the ARC-funded research project “Mathematics in an Australian Reform-Based Learning Environment ” [MARBLE]). The investigations are likely to be ...

More than ever, pharmacy graduates require broad-ranging knowledge, skills and attitudes (compete... more More than ever, pharmacy graduates require broad-ranging knowledge, skills and attitudes (competency) to enable them to be responsive and adaptable professionals in a rapidly changing Australian healthcare system - a system reliant on individuals working in interdisciplinary teams managing an increasing chronic health burden. These workplace competencies are declared through pharmacists’ registration requirements and the National Competency Standards Framework for Pharmacists in Australia (NCS). To ensure practice readiness, learning must be grounded in the essential competencies defined by the profession. The Tertiary Education Quality Standards Agency and Australian Pharmacy Council mandate that Australian pharmacy courses evidence that the NCS inform their curricula. Literature suggests international pharmacy curricula are also informed by competency standards. Interviews with key stakeholders were analysed using thematic analysis to offer an insight into Australian pharmacy educ...

Pharmacy, 2017

As medication experts, pharmacists are key members of the patient's healthcare team. Pharmacists ... more As medication experts, pharmacists are key members of the patient's healthcare team. Pharmacists must maintain their competence to practice to remain responsive to the increasingly complex healthcare sector. This paper seeks to determine how competence training for pharmacists may enhance quality in their professional development. Results of two separately administered surveys (2012 and 2013) were compared to examine the reported continued professional development (CPD) practices of Australian pharmacists. Examination of results from both studies enabled a focus on how the competency standards inform CPD practice. In the survey administered in 2012, 91% (n = 253/278) pharmacists reported that they knew their current registration requirements. However, in the survey administered in 2013, only 43% (n = 46/107) reported utilization of the National Competency Standards Framework for Pharmacists in Australia (NCS) to self-asses their practice as part of their annual re-registration requirements. Fewer, 23% (n = 25/107), used the NCS to plan their CPD. This may be symptomatic of poor familiarity with the NCS, uncertainty around undertaking self-directed learning as part of a structured learning plan and/or misunderstandings around what CPD should include. This is supported by thematic analysis of pharmacists' social media comments. Initial and ongoing competence training to support meaningful CPD requires urgent attention in Australia. The competence (knowledge, skills and attributes) required to engage in meaningful CPD practice should be introduced and developed prior to entry into practice; other countries may find they are in a similar position.

Journal of Learning Design, 2016

The Traffic Light Report (TLR) project is an educational intervention designed for pharmacy under... more The Traffic Light Report (TLR) project is an educational intervention designed for pharmacy undergraduates. This paper reports on analysis of TLR data specifically focusing on its potential as an innovative tool which combines Miller's pyramid, technology and student voice to examine a curriculum for Assurance of Learning (AoL). In 2014, educators mapped each summative assessment to the relevant National Competency Standards Framework for Pharmacists in Australia (NCS) alongside levels of expected performance on Miller's pyramid of clinical competence (Knows, Knows how, Shows how, Does). Simultaneously, students were invited to self-reflect using the same performance levels. The Miller's scale enabled a comparison between students' and their educators' understanding of the performance level demanded by assessments. Analysis highlighted a disconnect between students' and their educators' interpretations of the same assessed curriculum. The TLR facilitates quality enhancement by providing educators and their students with a logical meeting point for discussing foundation, scaffolding and integration of assessment across a course for AoL. This has portability to other professional disciplines.

The International journal of pharmacy practice, Jan 21, 2016

To determine the extent of use and perceived relevance of the National Competency Standards Frame... more To determine the extent of use and perceived relevance of the National Competency Standards Framework for Pharmacists in Australia (NCS). Based on these findings, to suggest approaches for the enhancement of pharmacy education for the profession locally and globally. Convenience sampling techniques were employed between November 2013 and June 2014 in conducting an online survey with Australian pharmacy students, interns, pharmacists and educators. Data from 527 participants were included in the final analysis. Fewer students (52%, 96/183) and interns 78% (69/88) knew the NCS framing pharmacy practice compared with pharmacists (86%, 115/134). Despite knowledge that the NCS existed most participants reported poor familiarity with and use of the NCS. Registered pharmacists reported annual use but not for Continuing Professional Development (CPD) plans or annual re-registration requirements. Respondents reported that practical use of NCS (e.g. mentoring interns) increased their use for ...

"Students are at their most vulnerable in the first year in terms of their likelihood of aca... more "Students are at their most vulnerable in the first year in terms of their likelihood of academic failure and they are most at risk with respect to a range of potential social, emotional, health and financial problems" (McInnis, 2001, p. 106). In 2001, Richard James edited a special edition of Higher Education Research & Development dedicated to the theme of the first year of higher education. In doing so he outlined the increasing focus on the first year experience (FYE) as a subfield of higher education research, and as a "central organising point for student support and development within universities" (James, 2001, p. 101). Eight years on, the FYE is still very much on the agenda for the higher education sector, and in much the same ways. Attention to the FYE in Australia in the last decade has included national surveys and research reports (e.g., Krause, Hartley, James, & McInnis, 2005; McInnis & Hartley, 2002; McInnes, James, & Hartley, 2000), documenting of institutional responses (e.g., Ballantyne, Todd & Olm, 2007; Burnett, 2006; Cameron & Tesoriero, 2004; Pitkethly & Prosser, 2001) and case studies presented through various fora such as dedicated conferences and journals, as well as more broadly in the higher education literature. A recent impetus to this field was the awarding of a senior Australian Learning and Teaching Council (ALTC) fellowship to Sally Kift for the project Articulating a transition pedagogy to scaffold and enhance the first year learning experience in Australian Higher Education. Adopting a case study approach, Professor Kift has interrogated good practice exemplars through expert commentary and theoretical frameworks in order to arrive at a set of ‘Guiding Principles for a Transition Pedagogy’ (ALTC, 2008; 2009). A recent forum (February, 2009), convened as part of this program, drew 450 participants, highlighting its relevance, impact and currency (ALTC, 2009).

Australian Journal of Teacher Education, 2015

Educational Research and Professional Learning in Changing Times, 2012

The extended case study in this chapter is based on four problem solving sessions held with nine ... more The extended case study in this chapter is based on four problem solving sessions held with nine high ability Year 5/6 students and their three teachers from a K-6 primary school in the MARBLE project. The students were interviewed at the beginning and end of the project and the teachers provided feedback after each session.

The Australian federal government now requires higher education institutions to provide evidence ... more The Australian federal government now requires higher education institutions to provide evidence of effective development, implementation and review of institutional policies,however little attention has been given to policy implementation evaluation and policy review. This paper presents a case study of the development of a comprehensive policy implementation evaluation framework proposed for the University of Tasmania’s new Casual Teaching Staff Policy. The proposed policy implementation evaluation framework reflects concepts utilised in the policy development process arising from research regarding good practices with respect to university casual teaching staff.

Educational Research and Professional Learning in Changing Times, 2012

There is an old saying that “there is more than one way to skin a cat.” Such is the case with fin... more There is an old saying that “there is more than one way to skin a cat.” Such is the case with finding the height of tall objects, a task that people have been approximating for centuries. Following Chapter 17, which presents methods appropriate for primary students, this chapter presents two more methods that are appropriate for middle school students who are beginning to learn about the trigonometric functions.

Educational Research and Professional Learning in Changing Times, 2012

Among the practical applications of statistics is the collection of data from manufacturing proce... more Among the practical applications of statistics is the collection of data from manufacturing processes. Often collected in the form of a time series, data collected from a series of measurements show the variation in those measurements, such as mass of a product manufactured. Limits are set for quality control and if these are exceeded then a decision is made about the process; perhaps it is halted and adjustments made to create a more uniform product over time. Can turning the primary (or middle school) classroom into a “food production line” promote learning outcomes that assist students in appreciating the essence of the statistics and probability curriculum: variation (Moore, 1990; Watson, 2007a)?

Educational Research and Professional Learning in Changing Times, 2012

The activities reported in this chapter were undertaken as part of a case study in a rural K-10 s... more The activities reported in this chapter were undertaken as part of a case study in a rural K-10 school in the MARBLE project. It was aimed at designing and trialling challenging activities for a group of relatively high achieving Year 5-8 students in the school. The focus and design of the case study were determined collaboratively between the researcher and the school’s middle school leader.

Educational Research and Professional Learning in Changing Times, 2012

This chapter describes a case study implemented at one MARBLE primary school where teachers negot... more This chapter describes a case study implemented at one MARBLE primary school where teachers negotiated with the researchers to develop a framework for the teaching of numeracy in the school, drawing on curriculum support materials and teachers’ understanding of the school context. The underpinnings to this case study lay at the intersection of pragmatic and participatory research paradigms (Creswell, 2003). Steeped in the “real world” of the teacher making everyday decisions about curriculum content, the researchers adopted a collaborative approach with the teacher participants, involving them in design, collection of data and data analysis.

Educational Research and Professional Learning in Changing Times, 2012

Two aspects of teachers’ perceptions of the success of the MARBLE professional learning program a... more Two aspects of teachers’ perceptions of the success of the MARBLE professional learning program are presented in this chapter. Any of the teachers who left the project early were asked to fill in an Exit Survey (Appendix J). As well, in the year following the completion of the project, fifteen teachers were interviewed individually in their schools about their involvement in MARBLE.

Educational Research and Professional Learning in Changing Times, 2012

The introduction of negative numbers should mean that mathematics can be twice as much fun, but u... more The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. As one teacher observed, “All of a sudden there are these concepts in maths where half the numbers are negatives and they’ve got no idea what it’s all about …” Despite the confusion that working with negative numbers can cause for middle school students there is evidence that the concept of numbers less than zero is not difficult. In fact the NCTM (2000) recommended that “in grades 3-5 all students should explore numbers less than 0 by extending the number line and through familiar applications.” Simple games that involve losing as well as gaining points or experiences with debt can facilitate quite young children believing that it is possible to have less than nothing and that such amounts are less than zero. In the Australian curriculum (ACARA, 2010a) although the continuation of number patterns is mentioned from Year 1 and could lead to the discovery of negative numbers they are not specifically mentioned until Year 6. In the middle years, particularly Years 7 and 8 students need to build on their intuitive understandings in order to use negative and positive integers to represent and compare quantities and extend number properties developed with positive integers to negative integers as well (NCTM, 2000).

Educational Research and Professional Learning in Changing Times, 2012

This chapter has three major sections. In order to illustrate the importance of teachers’ knowled... more This chapter has three major sections. In order to illustrate the importance of teachers’ knowledge of students in relation to teachers’ pedagogical content knowledge (PCK), the first section analyses one part of the initial teacher profile. In this part teachers were asked how their students would solve a fraction problem, both appropriately and inappropriately. They were then asked to explain how they would address the inappropriate answers. Their responses are then discussed in relation to students’ actual performance on the fraction question. The initial characterisation of teachers’ PCK is described in the second section based on the Rasch analysis carried out. Four hierarchical levels of ability are summarised. The final section discusses the analysis of teacher change in aspects of PCK from the initial to the final teacher profile for various subgroups of teachers who took part in the professional learning program.

Educational Research and Professional Learning in Changing Times, 2012

This chapter describes the strategies that students in a Year 5/6 class used for placing a set of... more This chapter describes the strategies that students in a Year 5/6 class used for placing a set of fractions on a number line. This aspect of fraction understanding was a key aim of teaching conducted as part of a case study in a rural K-10 school in one of three Year 5/6 classes. The three Year 5/6 teachers had agreed to divide their classes according to ability for several mathematics lessons each week and all were participants in professional learning associated with the MARBLE project throughout the period of the case study. All three classes were working with fractions and Rachel (pseudonym) who, along with her class, participated in the case study, was teaching the 27 students who comprised the middle group in terms of ability as perceived by the teachers.

Sharing practice 10th Teaching Matters Annual Conference 22nd-23rd November, Hobart, Tasmania, Nov 23, 2011

The WIL Project was undertaken in 2010 to develop a new Work Integrated Learning (WIL) Policy usi... more The WIL Project was undertaken in 2010 to develop a new Work Integrated Learning (WIL) Policy using the staged University Policy Development Cycle. This cyclerepresents an adaptation of the stepped policy development process depicted in the AustralianPolicy Cycle (Althaus, Bridgman and Davis, 2007). This paper examines the processundertaken to examine two key research questions – What is the University of Tasmania’sposition regarding WIL; and How should these guiding principles be reflected in formalpolicy documentation? The project involved a number of elements, including a WIL ProjectManager, a WIL Working Party, a literature review, data collection, benchmarking as policylearning (Lundvall and Tomlinson, 2002; Paasi, 2005), WIL Discussion Forums, and anextensive series of interviews. The project dovetailed with the Centre for the Advancement of Learning and Teaching (CALT) WIL Provocations Symposium. Consultations anddeliberations involved collegial governance structures. This paper reveals the diversity inwork-related curriculum offerings and disciplinary approaches at Australian universities, andsuggests that establishing clear definitions is an important step towards developing minimumacademic standards or obligations. This paper reports tensions between University-wideumbrella policy provisions and requirements by local academic sections for a high degree of specificity. This paper suggests that the process of asking complex academic policy questionsis self-perpetuating, as more questions are raised which demand policy responses. Finally, indeveloping a uniquely University of Tasmania approach to work integrated learning, theproject confirmed the importance of ongoing dialogue and collegial governance to guide learning and teaching policy development.

Tertiary Education Management Conference Refereed Papers, pp. 73-94, 2013

The Australian federal government now requires higher education institutions to provide evidence ... more The Australian federal government now requires higher education institutions to provide evidence of effective development, implementation and review of institutional policies, however little attention has been given to policy implementation evaluation and policy review. This paper presents a case study of the development of a comprehensive policy implementation evaluation framework proposed for the University of Tasmania’s new Casual Teaching Staff Policy. The proposed policy implementation evaluation framework reflects concepts utilised in the policy development process arising from research regarding good practices with respect to university casual teaching staff.

The activities suggested in this article are intended for use with lowersecondary school students... more The activities suggested in this article are intended for use with lowersecondary school students. The Australian Curriculum: Mathematics states that students in lower secondary school should “investigate the rela-tionship between features of circles such as circumference, area, radius and diameter ” and “use formulas to solve problems involving circumference and area ” (Australian Curriculum, Assessment and Reporting Authority (ACARA), 2010, p. 39). It is suggested, however, that teachers may need to work together to plan for the background and level of the students they teach and decide upon intended learning outcomes suited to their own students. The investigations presented here were used by the authors during a half-day professional learning session with middle school teachers from five rural schools in southern Tasmania (as a part of the ARC-funded research project “Mathematics in an Australian Reform-Based Learning Environment ” [MARBLE]). The investigations are likely to be ...

More than ever, pharmacy graduates require broad-ranging knowledge, skills and attitudes (compete... more More than ever, pharmacy graduates require broad-ranging knowledge, skills and attitudes (competency) to enable them to be responsive and adaptable professionals in a rapidly changing Australian healthcare system - a system reliant on individuals working in interdisciplinary teams managing an increasing chronic health burden. These workplace competencies are declared through pharmacists’ registration requirements and the National Competency Standards Framework for Pharmacists in Australia (NCS). To ensure practice readiness, learning must be grounded in the essential competencies defined by the profession. The Tertiary Education Quality Standards Agency and Australian Pharmacy Council mandate that Australian pharmacy courses evidence that the NCS inform their curricula. Literature suggests international pharmacy curricula are also informed by competency standards. Interviews with key stakeholders were analysed using thematic analysis to offer an insight into Australian pharmacy educ...

Pharmacy, 2017

As medication experts, pharmacists are key members of the patient's healthcare team. Pharmacists ... more As medication experts, pharmacists are key members of the patient's healthcare team. Pharmacists must maintain their competence to practice to remain responsive to the increasingly complex healthcare sector. This paper seeks to determine how competence training for pharmacists may enhance quality in their professional development. Results of two separately administered surveys (2012 and 2013) were compared to examine the reported continued professional development (CPD) practices of Australian pharmacists. Examination of results from both studies enabled a focus on how the competency standards inform CPD practice. In the survey administered in 2012, 91% (n = 253/278) pharmacists reported that they knew their current registration requirements. However, in the survey administered in 2013, only 43% (n = 46/107) reported utilization of the National Competency Standards Framework for Pharmacists in Australia (NCS) to self-asses their practice as part of their annual re-registration requirements. Fewer, 23% (n = 25/107), used the NCS to plan their CPD. This may be symptomatic of poor familiarity with the NCS, uncertainty around undertaking self-directed learning as part of a structured learning plan and/or misunderstandings around what CPD should include. This is supported by thematic analysis of pharmacists' social media comments. Initial and ongoing competence training to support meaningful CPD requires urgent attention in Australia. The competence (knowledge, skills and attributes) required to engage in meaningful CPD practice should be introduced and developed prior to entry into practice; other countries may find they are in a similar position.

Journal of Learning Design, 2016

The Traffic Light Report (TLR) project is an educational intervention designed for pharmacy under... more The Traffic Light Report (TLR) project is an educational intervention designed for pharmacy undergraduates. This paper reports on analysis of TLR data specifically focusing on its potential as an innovative tool which combines Miller's pyramid, technology and student voice to examine a curriculum for Assurance of Learning (AoL). In 2014, educators mapped each summative assessment to the relevant National Competency Standards Framework for Pharmacists in Australia (NCS) alongside levels of expected performance on Miller's pyramid of clinical competence (Knows, Knows how, Shows how, Does). Simultaneously, students were invited to self-reflect using the same performance levels. The Miller's scale enabled a comparison between students' and their educators' understanding of the performance level demanded by assessments. Analysis highlighted a disconnect between students' and their educators' interpretations of the same assessed curriculum. The TLR facilitates quality enhancement by providing educators and their students with a logical meeting point for discussing foundation, scaffolding and integration of assessment across a course for AoL. This has portability to other professional disciplines.

The International journal of pharmacy practice, Jan 21, 2016

To determine the extent of use and perceived relevance of the National Competency Standards Frame... more To determine the extent of use and perceived relevance of the National Competency Standards Framework for Pharmacists in Australia (NCS). Based on these findings, to suggest approaches for the enhancement of pharmacy education for the profession locally and globally. Convenience sampling techniques were employed between November 2013 and June 2014 in conducting an online survey with Australian pharmacy students, interns, pharmacists and educators. Data from 527 participants were included in the final analysis. Fewer students (52%, 96/183) and interns 78% (69/88) knew the NCS framing pharmacy practice compared with pharmacists (86%, 115/134). Despite knowledge that the NCS existed most participants reported poor familiarity with and use of the NCS. Registered pharmacists reported annual use but not for Continuing Professional Development (CPD) plans or annual re-registration requirements. Respondents reported that practical use of NCS (e.g. mentoring interns) increased their use for ...

"Students are at their most vulnerable in the first year in terms of their likelihood of aca... more "Students are at their most vulnerable in the first year in terms of their likelihood of academic failure and they are most at risk with respect to a range of potential social, emotional, health and financial problems" (McInnis, 2001, p. 106). In 2001, Richard James edited a special edition of Higher Education Research & Development dedicated to the theme of the first year of higher education. In doing so he outlined the increasing focus on the first year experience (FYE) as a subfield of higher education research, and as a "central organising point for student support and development within universities" (James, 2001, p. 101). Eight years on, the FYE is still very much on the agenda for the higher education sector, and in much the same ways. Attention to the FYE in Australia in the last decade has included national surveys and research reports (e.g., Krause, Hartley, James, & McInnis, 2005; McInnis & Hartley, 2002; McInnes, James, & Hartley, 2000), documenting of institutional responses (e.g., Ballantyne, Todd & Olm, 2007; Burnett, 2006; Cameron & Tesoriero, 2004; Pitkethly & Prosser, 2001) and case studies presented through various fora such as dedicated conferences and journals, as well as more broadly in the higher education literature. A recent impetus to this field was the awarding of a senior Australian Learning and Teaching Council (ALTC) fellowship to Sally Kift for the project Articulating a transition pedagogy to scaffold and enhance the first year learning experience in Australian Higher Education. Adopting a case study approach, Professor Kift has interrogated good practice exemplars through expert commentary and theoretical frameworks in order to arrive at a set of ‘Guiding Principles for a Transition Pedagogy’ (ALTC, 2008; 2009). A recent forum (February, 2009), convened as part of this program, drew 450 participants, highlighting its relevance, impact and currency (ALTC, 2009).

Australian Journal of Teacher Education, 2015

Educational Research and Professional Learning in Changing Times, 2012

The extended case study in this chapter is based on four problem solving sessions held with nine ... more The extended case study in this chapter is based on four problem solving sessions held with nine high ability Year 5/6 students and their three teachers from a K-6 primary school in the MARBLE project. The students were interviewed at the beginning and end of the project and the teachers provided feedback after each session.

The Australian federal government now requires higher education institutions to provide evidence ... more The Australian federal government now requires higher education institutions to provide evidence of effective development, implementation and review of institutional policies,however little attention has been given to policy implementation evaluation and policy review. This paper presents a case study of the development of a comprehensive policy implementation evaluation framework proposed for the University of Tasmania’s new Casual Teaching Staff Policy. The proposed policy implementation evaluation framework reflects concepts utilised in the policy development process arising from research regarding good practices with respect to university casual teaching staff.

Educational Research and Professional Learning in Changing Times, 2012

There is an old saying that “there is more than one way to skin a cat.” Such is the case with fin... more There is an old saying that “there is more than one way to skin a cat.” Such is the case with finding the height of tall objects, a task that people have been approximating for centuries. Following Chapter 17, which presents methods appropriate for primary students, this chapter presents two more methods that are appropriate for middle school students who are beginning to learn about the trigonometric functions.

Educational Research and Professional Learning in Changing Times, 2012

Among the practical applications of statistics is the collection of data from manufacturing proce... more Among the practical applications of statistics is the collection of data from manufacturing processes. Often collected in the form of a time series, data collected from a series of measurements show the variation in those measurements, such as mass of a product manufactured. Limits are set for quality control and if these are exceeded then a decision is made about the process; perhaps it is halted and adjustments made to create a more uniform product over time. Can turning the primary (or middle school) classroom into a “food production line” promote learning outcomes that assist students in appreciating the essence of the statistics and probability curriculum: variation (Moore, 1990; Watson, 2007a)?

Educational Research and Professional Learning in Changing Times, 2012

The activities reported in this chapter were undertaken as part of a case study in a rural K-10 s... more The activities reported in this chapter were undertaken as part of a case study in a rural K-10 school in the MARBLE project. It was aimed at designing and trialling challenging activities for a group of relatively high achieving Year 5-8 students in the school. The focus and design of the case study were determined collaboratively between the researcher and the school’s middle school leader.

Educational Research and Professional Learning in Changing Times, 2012

This chapter describes a case study implemented at one MARBLE primary school where teachers negot... more This chapter describes a case study implemented at one MARBLE primary school where teachers negotiated with the researchers to develop a framework for the teaching of numeracy in the school, drawing on curriculum support materials and teachers’ understanding of the school context. The underpinnings to this case study lay at the intersection of pragmatic and participatory research paradigms (Creswell, 2003). Steeped in the “real world” of the teacher making everyday decisions about curriculum content, the researchers adopted a collaborative approach with the teacher participants, involving them in design, collection of data and data analysis.

Educational Research and Professional Learning in Changing Times, 2012

Two aspects of teachers’ perceptions of the success of the MARBLE professional learning program a... more Two aspects of teachers’ perceptions of the success of the MARBLE professional learning program are presented in this chapter. Any of the teachers who left the project early were asked to fill in an Exit Survey (Appendix J). As well, in the year following the completion of the project, fifteen teachers were interviewed individually in their schools about their involvement in MARBLE.

Educational Research and Professional Learning in Changing Times, 2012

The introduction of negative numbers should mean that mathematics can be twice as much fun, but u... more The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. As one teacher observed, “All of a sudden there are these concepts in maths where half the numbers are negatives and they’ve got no idea what it’s all about …” Despite the confusion that working with negative numbers can cause for middle school students there is evidence that the concept of numbers less than zero is not difficult. In fact the NCTM (2000) recommended that “in grades 3-5 all students should explore numbers less than 0 by extending the number line and through familiar applications.” Simple games that involve losing as well as gaining points or experiences with debt can facilitate quite young children believing that it is possible to have less than nothing and that such amounts are less than zero. In the Australian curriculum (ACARA, 2010a) although the continuation of number patterns is mentioned from Year 1 and could lead to the discovery of negative numbers they are not specifically mentioned until Year 6. In the middle years, particularly Years 7 and 8 students need to build on their intuitive understandings in order to use negative and positive integers to represent and compare quantities and extend number properties developed with positive integers to negative integers as well (NCTM, 2000).

Educational Research and Professional Learning in Changing Times, 2012

This chapter has three major sections. In order to illustrate the importance of teachers’ knowled... more This chapter has three major sections. In order to illustrate the importance of teachers’ knowledge of students in relation to teachers’ pedagogical content knowledge (PCK), the first section analyses one part of the initial teacher profile. In this part teachers were asked how their students would solve a fraction problem, both appropriately and inappropriately. They were then asked to explain how they would address the inappropriate answers. Their responses are then discussed in relation to students’ actual performance on the fraction question. The initial characterisation of teachers’ PCK is described in the second section based on the Rasch analysis carried out. Four hierarchical levels of ability are summarised. The final section discusses the analysis of teacher change in aspects of PCK from the initial to the final teacher profile for various subgroups of teachers who took part in the professional learning program.

Educational Research and Professional Learning in Changing Times, 2012

This chapter describes the strategies that students in a Year 5/6 class used for placing a set of... more This chapter describes the strategies that students in a Year 5/6 class used for placing a set of fractions on a number line. This aspect of fraction understanding was a key aim of teaching conducted as part of a case study in a rural K-10 school in one of three Year 5/6 classes. The three Year 5/6 teachers had agreed to divide their classes according to ability for several mathematics lessons each week and all were participants in professional learning associated with the MARBLE project throughout the period of the case study. All three classes were working with fractions and Rachel (pseudonym) who, along with her class, participated in the case study, was teaching the 27 students who comprised the middle group in terms of ability as perceived by the teachers.

Educational Research and Professional Learning in Changing Times, 2012

The activities suggested in this chapter are intended for use with lower secondary school student... more The activities suggested in this chapter are intended for use with lower secondary school students. The Australian Curriculum: Mathematics states that students in lower secondary school should “investigate the relationship between features of circles such as circumference, area, radius and diameter and generalise these to solve problems involving circumference and area” and “use formulas to solve problems involving circumference and area” (ACARA, 2010a, p. 39). In the US, the NCTM (2000) recommends a similar mix of topics in its Geometry Standard (p. 232) and Measurement Standard (p. 240) for Years 6 to 8. As well it suggests that students “recognize and use connections among mathematical ideas” in its Connections Standard across all year levels (p. 402).

Educational Research and Professional Learning in Changing Times, 2012

The case study described in this chapter took place in a rural district school (Years K-10) with ... more The case study described in this chapter took place in a rural district school (Years K-10) with Year 7 teacher Jenny (pseudonym) and her mathematics class. During the previous year Jenny and a different Year 7 class had taken part in a related case study (Watson, 2008a) that arose from the desire of the statistics education research community to provide a meaningful bridge to formal inference, which many students will meet at the senior secondary or tertiary level. As well there was the desire to provide students who do not go on to formal statistics with intuitions about the inferential process without the theoretical assumptions and more complex mathematics required in formal statistics courses. The school curriculum provided direction on some of the ingredients required, such as data representation in graphs and data reduction with averages, but often did not signal the purpose of decision making with uncertainty based on samples representing populations. The NCTM (2000) included “develop and evaluate inferences and predictions” in its Standards at all levels but there was concern on the part of statistics educators about how this should be implemented, especially in acknowledging the uncertainty in the evaluation process.