Mathematical Discourse that Breaks Barriers and Creates Space for Marginalized Learners, 2018
This chapter considers how best to support the teaching and learning of early algebra, as well as... more This chapter considers how best to support the teaching and learning of early algebra, as well as the discourses in this area, for young, marginalised Indigenous students. In particular, the consideration that needs to be given to how these students construct their knowledge and mathematical discourse to act as a platform for reaching mathematical generalisations. This is especially important in the cultural context of Indigenous students given mathematical discourse is a social practice
Na Austrália, os alunos provenientes de meios socialmente desfavorecidos continuam a revelar um a... more Na Austrália, os alunos provenientes de meios socialmente desfavorecidos continuam a revelar um atraso de um ou dois anos relativamente aos colegas oriundos de outros meios no que se refere a testes de numeracia, tanto nacionais como internacionais. Os resultados da investigação indicam claramente que a qualidade dos professores faz a diferença. Este estudo foca-se no impacto de um modelo de aprendizagem profissional, o modelo RoleM (RPL), numa escola, ao longo de três anos. Os professores participantes (n = 12) lecionavam os primeiros três anos de escolaridade (desde a Educação Pré-escolar ao segundo ano; alunos de 4/5 a 8 anos de idade). Para avaliar a eficácia do RPL, os professores foram entrevistados três vezes por ano. Os resultados indicam que um ensino de qualidade se relaciona com a disponibilização de recursos de qualidade e com uma aprendizagem profissional igualmente de qualidade. À medida que os professores evoluem no sentido de manifestarem características de professor...
Building Better Schools with Evidence-based Policy
How to use this policy Excellence in Indigenous education uses a strengths-based approach to impl... more How to use this policy Excellence in Indigenous education uses a strengths-based approach to implementing broader Indigenous education policy imperatives. This policy incorporates the goals of a broad range of current Indigenous education policies into an applied way of addressing school-based issues associated with persisting Indigenous education disparities. This new policy will reframe much of the broader policy impetus into school-based approaches to Indigenous education informed by concepts of excellence, strength and aspiration that centres the voices and leadership of Indigenous peoples. Underpinned by Indigenous Research Theory (Rigney, 2006), Critical Race Theory (Ladson Billings, 2005) and Postcolonial Theory (Gandhi, 2019), the policy takes an evidence-based approach to Indigenous policy reform and will provide schools with a streamlined approach to doing Indigenous education that is orientated to Indigenous agency, partnerships and reciprocity. By using the process of co-design (Australian Government, 2020), schools will be able to provide spaces for meaningful community and school partnerships and collaborations to transpire. School leaders and staff will be provided with a framework to work in collaboration with Indigenous students, their families and communities to co-design and localise programs to address education goals that are aimed at enhancing the learning of all students in Australian classrooms. [INSERT name of school] Excellence in Indigenous education Rationale The field of Aboriginal and Torres Strait Islander education is saturated with literature that reinforces a bleak outlook in relation to educational outcomes for Indigenous peoples. Amongst the most researched peoples on the planet, there continues to be an abundance of research taking place on the "subject" of Indigenous peoples (Tuhiwai Smith, 2012). Much of this research continues to be undertaken by predominantly non-Indigenous researchers and without
International Journal of Science and Mathematics Education
Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of ... more Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of access to mathematics achievement and putting educational policy into practice. New Zealand has the largest group of Pāsifika people in the Western world, a multi-ethnic group of indigenous people from Pacific Island nations who have differing cultural values and experiences than the dominant Pākehā (Maori term commonly used to refer to European New Zealanders) population. This study aims to explore how patterning tasks based on indigenous patterns can support young diverse students to develop understanding of growing patterns. Two case studies are presented which show the results of an exploratory teaching experiment undertaken with one classroom of culturally diverse Year 2 students (6-year-olds) situated in an urban low socioeconomic area. Data drawn for this paper includes video-recorded classroom observations, written responses from students, and reflective notes from the researcher and teacher from two lessons of a series of 10 lessons on growing patterns. Data analysis involved an iterative approach of repeated refinement cycles focusing on early algebraic thinking and the pedagogical actions of the teacher. Findings revealed that the use of indigenous patterns in conjunction with pedagogical actions drawing on cultural values was successful in engaging these students in early algebraic reasoning.
Mathematics Education Research Group of Australasia, 2012
This paper presents the results from an initial lesson in a series of design experiments focusing... more This paper presents the results from an initial lesson in a series of design experiments focusing on young Indigenous students’ understandings of growing patterns. Indigenous students in Year 2 and 3 (n=16) participated in pre lesson activities and a 45 minute lesson on growing patterns. Tentative findings from this study suggest that; (a) Year 2 and 3 Indigenous students are capable of working with growing patterns; (b) contextual artefacts assisted with communication; and (c) gesture played an important two-fold role in the lessons and communication of the mathematics experienced.
This paper reports on the preliminary findings from the researchers’ thesis exploring how young A... more This paper reports on the preliminary findings from the researchers’ thesis exploring how young Australian Indigenous students engage in mathematical generalisation tasks. Six students (8.5 years) were purposely selected to participate in one on one Piagetian clinical interview to explore how they engage and express generalisations with growing patterns. Initial findings of the study suggest that these young students can generalise contextual growing patterns. Representing the patterns with concrete materials and kinaesthetically engaging with tasks enhanced their ability to reach generalisations. In addition, using patterns where the relationship between the two variables was visually explicit assisted students to express this relationship in general terms. Interestingly, cultural gestures (both verbal and non-verbal) were apparent throughout the interviews. These gave insight into how Indigenous students engage in one-on-one settings in contrast to whole class interactions.
Mathematics Education Research Group of Australasia, 2015
The aim of this study was to determine the role of semiotics in assisting young Indigenous studen... more The aim of this study was to determine the role of semiotics in assisting young Indigenous students to engage with and identify the general structure of growing patterns. The theoretical perspective of semiotics underpinned the study. Data are drawn from two Year 3 students, including analysis of pretest questions and two conjecture-driven lessons. Results indicate that particular semiotic signs (iconic signs) contribute to how young Indigenous students attend to, and identify the structure of growing patterns.
Mathematics Education Research Group of Australasia, 2016
This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route t... more This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n=18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n=3). A case study of one student is presented as a representative of high achieving students’ progression and shifts in learning. Results suggest that students are capable of functional thinking, which contradicts the notion of young students can only engage with recursive pattern sequences. In addition, particular teaching actions assisted in promoting shifts in developing students’ capability to generalise growing patterns.
Mathematics Education Research Group of Australasia, 2017
In this paper, we present data from a study exploring the use of coding to promote mathematical t... more In this paper, we present data from a study exploring the use of coding to promote mathematical thinking. A teaching experiment was undertaken with 40 Year 2 students participating in six 45-minute lessons of coding (one lesson per week for six weeks). All lessons were video-recorded and analysed to determine students’ mathematical thinking. Insights from the study reveal that coding contexts promoted higher levels of mathematical thinking for Year 2 students including measuring angles, orientation and perspectivetaking, and deducing repeating patterns.
Mathematics Education Research Group of Australasia, 2014
This paper explores how young Indigenous students’ (Year 2 and 3) generalise growing patterns. Pi... more This paper explores how young Indigenous students’ (Year 2 and 3) generalise growing patterns. Piagetian clinical interviews were conducted to determine how students articulated growing pattern generalisations. Two case studies are presented displaying how students used gesture to support and articulate their generalisations of growing patterns. This paper presents a hypothesised cultural learning semiotic model that was a result of the interactions that occurred between the non-Indigenous researcher, the Indigenous students and the Indigenous Education Officers.
Both Pasifika and Maori cultures have a rich background of mathematics including a strong emphasi... more Both Pasifika and Maori cultures have a rich background of mathematics including a strong emphasis on patterns used within craft design (Finau and Stillman, 1995), however there have been limited studies which have investigated young Pasifika and Maori students' understanding of growing patterns. The aim of this study was to explore how contextual Pasifika and Maori patterning tasks can potentially support young children to develop their understanding of algebraic growing patterns. A teaching experiment was undertaken with 27 Year 2 students (6-year-old) participating in 10 lessons focusing on growing patterns. Analysis of the data reveal that the contextual growing tasks assisted these young students to generalise growing patterns.
Future Alternatives for Educational Leadership, 2021
The book chapter stems from two funded research projects, ‘Doing things right way: Dimensions of ... more The book chapter stems from two funded research projects, ‘Doing things right way: Dimensions of excellence in Indigenous education in Queensland secondary schools’ and ‘Indigenous education excellence in flexi schools’. This chapter focuses specifically on the role of leadership in the pursuit of Indigenous excellence in educational settings. Focusing on data from three sites from our data set, one urban, one regional, and one remote school setting, we present a comparative analysis of leadership principles and practices across these three school settings. Central to this research is an examination of perspectives, understandings, aspirations, and experiences of Indigenous and non-Indigenous educators and leaders to make visible what they see as excellence in Indigenous education and to begin to conceptualise and theorise a practice and policy framework that reflects these aspirations. The questions framing the study are: How is excellence in Indigenous Education defined by Indigen...
Strengthening the personal mathematical capabilities of initial teacher education students is an ... more Strengthening the personal mathematical capabilities of initial teacher education students is an international priority. In this paper, we report on an aspect of a study that investigated the potential of challenging online tasks to meet this goal. Here, we focus on the analysis of survey data in the form of student feedback on trialled tasks from the perspective of motivation theory. Findings of this aspect of the study are reported along with implications for the design of challenging online mathematical tasks and their implementation in teacher education programs.
The gap between young Indigenous and non-Indigenous students' capability within mathematics i... more The gap between young Indigenous and non-Indigenous students' capability within mathematics is widely acknowledged. This gap is conjectured to exist at all levels of schooling, including pre-school, and widens as students mature. Most of these findings are based on research relating to students' understanding of number and space. Little is known about what knowledge Indigenous students bring to early years' settings with regard to patterning, an area that is widely acknowledged as fundamental to the development of concepts, process and knowledge of mathematics. One on one interviews were conducted with 35 Indigenous students (average age 4 years and 4 months) as they entered kindergarten. The results indicate that these students enter these settings with some intuitive understanding of repeating pattern, and that this knowledge is at odds with the hypothesised learning trajectory (Sarama and Clements, 2009) for repeating patterns. The results also begin to delineate the ...
The Early Years Generalising Project involves Australian students, Years 1–4 (age 5–9), and explo... more The Early Years Generalising Project involves Australian students, Years 1–4 (age 5–9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focussing on the identification, prediction and justification of function rules. It reports on students attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks. The Early Years Generalising Project (EYGP) 1 is a series of cross-sectional studies of cohorts of students from Year 1 to Year 4 (age 5 to 9) that aims to build theories regarding young students’ ability to grasp and express generalisations, the two components of the act o...
Mathematical Discourse that Breaks Barriers and Creates Space for Marginalized Learners, 2018
This chapter considers how best to support the teaching and learning of early algebra, as well as... more This chapter considers how best to support the teaching and learning of early algebra, as well as the discourses in this area, for young, marginalised Indigenous students. In particular, the consideration that needs to be given to how these students construct their knowledge and mathematical discourse to act as a platform for reaching mathematical generalisations. This is especially important in the cultural context of Indigenous students given mathematical discourse is a social practice
Na Austrália, os alunos provenientes de meios socialmente desfavorecidos continuam a revelar um a... more Na Austrália, os alunos provenientes de meios socialmente desfavorecidos continuam a revelar um atraso de um ou dois anos relativamente aos colegas oriundos de outros meios no que se refere a testes de numeracia, tanto nacionais como internacionais. Os resultados da investigação indicam claramente que a qualidade dos professores faz a diferença. Este estudo foca-se no impacto de um modelo de aprendizagem profissional, o modelo RoleM (RPL), numa escola, ao longo de três anos. Os professores participantes (n = 12) lecionavam os primeiros três anos de escolaridade (desde a Educação Pré-escolar ao segundo ano; alunos de 4/5 a 8 anos de idade). Para avaliar a eficácia do RPL, os professores foram entrevistados três vezes por ano. Os resultados indicam que um ensino de qualidade se relaciona com a disponibilização de recursos de qualidade e com uma aprendizagem profissional igualmente de qualidade. À medida que os professores evoluem no sentido de manifestarem características de professor...
Building Better Schools with Evidence-based Policy
How to use this policy Excellence in Indigenous education uses a strengths-based approach to impl... more How to use this policy Excellence in Indigenous education uses a strengths-based approach to implementing broader Indigenous education policy imperatives. This policy incorporates the goals of a broad range of current Indigenous education policies into an applied way of addressing school-based issues associated with persisting Indigenous education disparities. This new policy will reframe much of the broader policy impetus into school-based approaches to Indigenous education informed by concepts of excellence, strength and aspiration that centres the voices and leadership of Indigenous peoples. Underpinned by Indigenous Research Theory (Rigney, 2006), Critical Race Theory (Ladson Billings, 2005) and Postcolonial Theory (Gandhi, 2019), the policy takes an evidence-based approach to Indigenous policy reform and will provide schools with a streamlined approach to doing Indigenous education that is orientated to Indigenous agency, partnerships and reciprocity. By using the process of co-design (Australian Government, 2020), schools will be able to provide spaces for meaningful community and school partnerships and collaborations to transpire. School leaders and staff will be provided with a framework to work in collaboration with Indigenous students, their families and communities to co-design and localise programs to address education goals that are aimed at enhancing the learning of all students in Australian classrooms. [INSERT name of school] Excellence in Indigenous education Rationale The field of Aboriginal and Torres Strait Islander education is saturated with literature that reinforces a bleak outlook in relation to educational outcomes for Indigenous peoples. Amongst the most researched peoples on the planet, there continues to be an abundance of research taking place on the "subject" of Indigenous peoples (Tuhiwai Smith, 2012). Much of this research continues to be undertaken by predominantly non-Indigenous researchers and without
International Journal of Science and Mathematics Education
Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of ... more Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of access to mathematics achievement and putting educational policy into practice. New Zealand has the largest group of Pāsifika people in the Western world, a multi-ethnic group of indigenous people from Pacific Island nations who have differing cultural values and experiences than the dominant Pākehā (Maori term commonly used to refer to European New Zealanders) population. This study aims to explore how patterning tasks based on indigenous patterns can support young diverse students to develop understanding of growing patterns. Two case studies are presented which show the results of an exploratory teaching experiment undertaken with one classroom of culturally diverse Year 2 students (6-year-olds) situated in an urban low socioeconomic area. Data drawn for this paper includes video-recorded classroom observations, written responses from students, and reflective notes from the researcher and teacher from two lessons of a series of 10 lessons on growing patterns. Data analysis involved an iterative approach of repeated refinement cycles focusing on early algebraic thinking and the pedagogical actions of the teacher. Findings revealed that the use of indigenous patterns in conjunction with pedagogical actions drawing on cultural values was successful in engaging these students in early algebraic reasoning.
Mathematics Education Research Group of Australasia, 2012
This paper presents the results from an initial lesson in a series of design experiments focusing... more This paper presents the results from an initial lesson in a series of design experiments focusing on young Indigenous students’ understandings of growing patterns. Indigenous students in Year 2 and 3 (n=16) participated in pre lesson activities and a 45 minute lesson on growing patterns. Tentative findings from this study suggest that; (a) Year 2 and 3 Indigenous students are capable of working with growing patterns; (b) contextual artefacts assisted with communication; and (c) gesture played an important two-fold role in the lessons and communication of the mathematics experienced.
This paper reports on the preliminary findings from the researchers’ thesis exploring how young A... more This paper reports on the preliminary findings from the researchers’ thesis exploring how young Australian Indigenous students engage in mathematical generalisation tasks. Six students (8.5 years) were purposely selected to participate in one on one Piagetian clinical interview to explore how they engage and express generalisations with growing patterns. Initial findings of the study suggest that these young students can generalise contextual growing patterns. Representing the patterns with concrete materials and kinaesthetically engaging with tasks enhanced their ability to reach generalisations. In addition, using patterns where the relationship between the two variables was visually explicit assisted students to express this relationship in general terms. Interestingly, cultural gestures (both verbal and non-verbal) were apparent throughout the interviews. These gave insight into how Indigenous students engage in one-on-one settings in contrast to whole class interactions.
Mathematics Education Research Group of Australasia, 2015
The aim of this study was to determine the role of semiotics in assisting young Indigenous studen... more The aim of this study was to determine the role of semiotics in assisting young Indigenous students to engage with and identify the general structure of growing patterns. The theoretical perspective of semiotics underpinned the study. Data are drawn from two Year 3 students, including analysis of pretest questions and two conjecture-driven lessons. Results indicate that particular semiotic signs (iconic signs) contribute to how young Indigenous students attend to, and identify the structure of growing patterns.
Mathematics Education Research Group of Australasia, 2016
This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route t... more This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n=18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n=3). A case study of one student is presented as a representative of high achieving students’ progression and shifts in learning. Results suggest that students are capable of functional thinking, which contradicts the notion of young students can only engage with recursive pattern sequences. In addition, particular teaching actions assisted in promoting shifts in developing students’ capability to generalise growing patterns.
Mathematics Education Research Group of Australasia, 2017
In this paper, we present data from a study exploring the use of coding to promote mathematical t... more In this paper, we present data from a study exploring the use of coding to promote mathematical thinking. A teaching experiment was undertaken with 40 Year 2 students participating in six 45-minute lessons of coding (one lesson per week for six weeks). All lessons were video-recorded and analysed to determine students’ mathematical thinking. Insights from the study reveal that coding contexts promoted higher levels of mathematical thinking for Year 2 students including measuring angles, orientation and perspectivetaking, and deducing repeating patterns.
Mathematics Education Research Group of Australasia, 2014
This paper explores how young Indigenous students’ (Year 2 and 3) generalise growing patterns. Pi... more This paper explores how young Indigenous students’ (Year 2 and 3) generalise growing patterns. Piagetian clinical interviews were conducted to determine how students articulated growing pattern generalisations. Two case studies are presented displaying how students used gesture to support and articulate their generalisations of growing patterns. This paper presents a hypothesised cultural learning semiotic model that was a result of the interactions that occurred between the non-Indigenous researcher, the Indigenous students and the Indigenous Education Officers.
Both Pasifika and Maori cultures have a rich background of mathematics including a strong emphasi... more Both Pasifika and Maori cultures have a rich background of mathematics including a strong emphasis on patterns used within craft design (Finau and Stillman, 1995), however there have been limited studies which have investigated young Pasifika and Maori students' understanding of growing patterns. The aim of this study was to explore how contextual Pasifika and Maori patterning tasks can potentially support young children to develop their understanding of algebraic growing patterns. A teaching experiment was undertaken with 27 Year 2 students (6-year-old) participating in 10 lessons focusing on growing patterns. Analysis of the data reveal that the contextual growing tasks assisted these young students to generalise growing patterns.
Future Alternatives for Educational Leadership, 2021
The book chapter stems from two funded research projects, ‘Doing things right way: Dimensions of ... more The book chapter stems from two funded research projects, ‘Doing things right way: Dimensions of excellence in Indigenous education in Queensland secondary schools’ and ‘Indigenous education excellence in flexi schools’. This chapter focuses specifically on the role of leadership in the pursuit of Indigenous excellence in educational settings. Focusing on data from three sites from our data set, one urban, one regional, and one remote school setting, we present a comparative analysis of leadership principles and practices across these three school settings. Central to this research is an examination of perspectives, understandings, aspirations, and experiences of Indigenous and non-Indigenous educators and leaders to make visible what they see as excellence in Indigenous education and to begin to conceptualise and theorise a practice and policy framework that reflects these aspirations. The questions framing the study are: How is excellence in Indigenous Education defined by Indigen...
Strengthening the personal mathematical capabilities of initial teacher education students is an ... more Strengthening the personal mathematical capabilities of initial teacher education students is an international priority. In this paper, we report on an aspect of a study that investigated the potential of challenging online tasks to meet this goal. Here, we focus on the analysis of survey data in the form of student feedback on trialled tasks from the perspective of motivation theory. Findings of this aspect of the study are reported along with implications for the design of challenging online mathematical tasks and their implementation in teacher education programs.
The gap between young Indigenous and non-Indigenous students' capability within mathematics i... more The gap between young Indigenous and non-Indigenous students' capability within mathematics is widely acknowledged. This gap is conjectured to exist at all levels of schooling, including pre-school, and widens as students mature. Most of these findings are based on research relating to students' understanding of number and space. Little is known about what knowledge Indigenous students bring to early years' settings with regard to patterning, an area that is widely acknowledged as fundamental to the development of concepts, process and knowledge of mathematics. One on one interviews were conducted with 35 Indigenous students (average age 4 years and 4 months) as they entered kindergarten. The results indicate that these students enter these settings with some intuitive understanding of repeating pattern, and that this knowledge is at odds with the hypothesised learning trajectory (Sarama and Clements, 2009) for repeating patterns. The results also begin to delineate the ...
The Early Years Generalising Project involves Australian students, Years 1–4 (age 5–9), and explo... more The Early Years Generalising Project involves Australian students, Years 1–4 (age 5–9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focussing on the identification, prediction and justification of function rules. It reports on students attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks. The Early Years Generalising Project (EYGP) 1 is a series of cross-sectional studies of cohorts of students from Year 1 to Year 4 (age 5 to 9) that aims to build theories regarding young students’ ability to grasp and express generalisations, the two components of the act o...
In this paper, we present data from a study exploring the use of coding to promote mathematical t... more In this paper, we present data from a study exploring the use of coding to promote mathematical thinking. A teaching experiment was undertaken with 40 Year 2 students participating in six 45-minute lessons of coding (one lesson per week for six weeks). All lessons were video-recorded and analysed to determine students’ mathematical thinking. Insights from the study reveal that coding contexts promoted higher levels of mathematical thinking for Year 2 students including measuring angles, orientation and perspective taking, and deducing repeating patterns.
Strengthening Initial Teacher Education (ITE) students' capabilities to implement challenging mat... more Strengthening Initial Teacher Education (ITE) students' capabilities to implement challenging mathematical tasks is a focus for policy and curriculum internationally. In this article, we report on motivational aspects of ITE students' engagement with challenging mathematical tasks as an outcome of an explorative study involving 41 Australian ITE students in their third year of a four-year program. Data collection instruments consisted of pre- and post-surveys and a focus group interview. The study was interpretive, utilizing both quantitative and qualitative techniques. Findings suggest ITE student motivation was most closely associated with situational interest and challenge served to both motivate and demotivate students.
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