Articles and Book Chapters by Kevin Larkin
Australian Primary Mathematics Classroom, 2022
This article proposes a way of engaging students in mathematical open inquiry using a video
clip ... more This article proposes a way of engaging students in mathematical open inquiry using a video
clip as stimulus. It discusses findings from a recent study conducted in a Year 5 (9-10 years
old) classroom in which the students’ problem-posed and developed personal mathematical
inquiries based on a video prompt. The article highlights the benefits for teachers and students
in using video stimulus for open inquiry in Primary Mathematics classrooms.
Journal of Research on Technology in Education, 2022
This article describes the conceptual development of a learning app,
“Representations”, developed... more This article describes the conceptual development of a learning app,
“Representations”, developed for preschool children (4-5 years of age).
In this article we analyse how the app supported the development of
logical reasoning via a variety of decoding, encoding, conditionals and
debugging activities, which were supported in the game play by the
children’s own user generated content (UGC). Research such as this is
important as logical reasoning in young children correlates positively
with later mathematics achievement. The learning app is used within a
broader program, which also included a range of off-device learning.
Data indicates the success of our design and implementation in terms of
children’s engagement with the app and in terms of their early learning
of important logical reasoning concepts.
Mathematical Thinking and Learning, 2022
Patterns are a fundamental component of mathematics, and the patterning ability of
young children... more Patterns are a fundamental component of mathematics, and the patterning ability of
young children has been well researched; however, this research has largely been
conducted with relatively small cohorts (+/- 70) and in an interventionist way (in
laboratory settings or with researchers directly intervening in educational contexts).
The current study examines the patterning skills of approximately3 200 children in a
naturalistic setting. As part of a larger, early years’ STEM engagement program,
children were provided patterning opportunities across one school term. The data
presented here relates to the children’s performance on the tablet-based activities
embedded in the program. Findings indicate that 3 to 4 year old children were
able to copy, extend, insert missing elements, fix, and create patterns, using a range of
two, three or four elements pattern structures. These findings, from a large-scale
naturalistic setting, confirm some aspects of the existing laboratory-based research,
whilst also indicating that some children are more capable in terms of creating patterns
than the existing research suggests. These findings have implications for educators
when they are planning play-based patterning activities with preschool children.
Journal of Mathematics Teacher Education, 2021
This qualitative survey study set out to investigate in-service and pre-service primary
school te... more This qualitative survey study set out to investigate in-service and pre-service primary
school teachers’ perceived barriers to and enablers for the integration of children’s literature in mathematics teaching and learning in an Australian educational context. While
research over the past three decades have documented pedagogical benefts of teaching
mathematics using children’s literature, research into teachers’ perceptions regarding the
use of such resources is virtually non-existent. The study thus flled this research gap by
drawing responses from open-ended survey questions of 94 in-service and 82 pre-service
teachers in Australia. A thematic analysis revealed 13 perceived barriers classifed under
fve themes with Lack of Pedagogical Knowledge and Confdence, and Time Constraint,
representing 75% of all perceived barriers. Moreover, 14 perceived enablers were identifed
and classifed under fve themes with Pedagogical Benefts and Love of Stories representing around 70% of all perceived enablers. Findings also showed that most of the teachers in
the study (around 75%) never or infrequently used children’s literature in their mathematics classrooms. The study highlights the role of professional learning and teacher training
in ensuring that both in- and pre-service teachers have the necessary pedagogical knowledge, experience and confdence in using children’s literature to enrich their mathematics
teaching.
Mathematics Teacher Education and Development, 2020
This paper investigates, using a case study methodology, the impact of formative video feedback o... more This paper investigates, using a case study methodology, the impact of formative video feedback on
the educational experiences of early childhood and primary preservice teachers (PST) completing a
pedagogically focused mathematics education unit in a fully online mode. Given the trend over the
past 10 years towards the delivery of university mathematics education courses online, this research
is important. It is particularly timely given the current world health crisis, where universities are
hurriedly rolling out online courses. We argue, based on the findings of this initial pilot, that the use
of regular, formative video feedback has a positive effect on PST learning, and on the way PSTs
perceive and engage with the feedback provided in video form, and on the affective connection this
platform provides between the PST and the lecturer. We suggest that these themes have the potential
to positively impact on PSTs’ knowledge of content and pedagogy in the context of university
mathematics education.
STEM Education across the learning continuum, 2020
Engaging young learners in STEM practices such as robotics and coding gives students the opportun... more Engaging young learners in STEM practices such as robotics and coding gives students the opportunity to
use new and emerging technologies to solve problems while extending their own knowledge and
understanding of mathematics. In Australia, a digital technologies curriculum was introduced in 2014 to
assist with making connections between Technology and areas such as mathematics. Drawing on examples
from Australia, British Columbia, the United Kingdom and New Zealand, this chapter examines how the
introduction of a new curriculum intersects with existing curricula. As an example of an authentic activity
that successfully combines elements of both curricula to support STEM learning, findings of a research
project that has been conducted with Year 2 students (n = 153) from two Australian primary schools are
presented. It appears as young students engage in robotics and coding (Technology) to learn mathematics
concepts, they demonstrate learning that moves beyond their curriculum year level, creating a possible
conflict between the digital technologies and mathematics curricula with their tightly prescribed sequence
of content.
Australian Primary Mathematics Classroom, 2019
This article builds upon earlier work by mathematics
colleagues (e.g. Bailey, 2015; Hartnett, 201... more This article builds upon earlier work by mathematics
colleagues (e.g. Bailey, 2015; Hartnett, 2018; Rogers,
2012) published in the APMC journal regarding the
fundamental importance of place value (PV) understanding.
In this paper we explore the utility of an iPad
app, Place Value Chart, which was custom-designed
to support the development of student PV understanding
across all primary school year levels. This article
also describes an international collaborative effort to
support teachers’ Mathematics Content Knowledge
(MCK) and Mathematics Pedagogical Content
Knowledge (MPCK) through the creation of a
25-page teachers’ guide outlining the use of the app.
Traversing the Doctorate. Palgrave Studies in Education Research Methods., 2019
This chapter explores how the transition from doctoral student to Early Career Academic (ECA)
res... more This chapter explores how the transition from doctoral student to Early Career Academic (ECA)
resolved many of the perturbations - tensions and contradictions - inherent in the doctoral
degree by focusing on my experiences of recently completing this journey. These perturbations
are conceptualised, via an ‘Activity Systems’ approach, the disquieting transition of the author
from a doctoral student to ECA., My various perturbing experiences of this journey provide the
‘dataset’ for this chapter. As an initial position, Engestrom’s (1987) Activity Systems are utilised
to situate me in a university Community of Practice (CoP).
These perturbations are analysed using Active Subjectivities (Valsiner & Van Der Veer, 2000) as
a conceptual tools. This approach identifies the agentic activity of an active subject, who chooses
from a range of available roles (student, researcher, author, lecturer or colleague) in response
to a range of intellectually disquieting discourses within a particular context. The resolution of
my perturbations in the transition from doctoral student to ECA is a consequence of personal
transformation whilst simultaneously acknowledging that individual agentic action in a CoP
shapes this transformation at a more granular level than can solely be explained by Activity
Systems. A new conceptual model incorporating these perturbations, offering a relational
approach to the individual and social dichotomy evident in workplaces (Billett, 2006), is
suggested.
International Journal of Education Management, 2019
Purpose – The authors argue that middle leaders are the key educators in school-based educational... more Purpose – The authors argue that middle leaders are the key educators in school-based educational
development. Schools often secure small-scale funding to engage in government or systemic initiatives, and
these projects require a leadership “close to the classroom” if they are to realise sustainable educational gains.
This leadership often comes from the middle leaders – those who practice their leading in and around
classrooms. The paper aims to discuss this issue.
Design/methodology/approach – A single case study methodology is used to investigate two middle
leaders, leading a small-scale project. Their leading practices are examined using the “theory of practice
architectures”, to identify how these practices were enacted within their educational context.
Findings – While principals play a crucial role in enacting change, it is the middle leaders who are closer to
the classroom than most principals, and whose practices more directly impact teaching and learning as they
are best placed to ensure that meagre resources are well used to improve student learning. They do this by
ensuring that development is collegial and a response to evidence-based needs.
Practical implications – First, middle leaders need support in facilitating educational development.
Second, their leading practice is crucial for sustainable school-based development. Third, site-based
educational development occurs most effectively when it is evidence-based. Finally, this form of educational
development requires high-level collegiality.
Originality/value – This paper is original in two key ways: first, it addresses the under-researched practices
of middle leaders; and, second it employs the practice theory to understand school leadership and development.
British Journal of Educational Technology, 2019
This article presents an heuristic that underpinned the development of a range of early years app... more This article presents an heuristic that underpinned the development of a range of early years applications (apps) as part of the Early Learning STEM Australia (ELSA) project (2016-2019). The heuristic was developed to address a range of challenges that accompany the use of digital technologies in the year before formal schooling. These include the role of digital technologies in play-based learning environments, screen time, and the importance of agency when young children are using digital technologies. In an increasingly digital world, the issue of screen time looms large as a particularly contested aspect of technology use by
young children. The ELSA project responded to this challenge by developing a pedagogical framework that embedded digital technologies into context-rich, play-based STEM learning. The Experience, Represent, Apply (ERA) heuristic discussed in this article is a component of the project’s overall pedagogical framework, and provides early years educators with the opportunity, and the know-how, to integrate digital technologies into STEM activities through intentional teaching and play-based engagement. It was evident, from educator feedback at the four days of workshops we delivered, and in other comments throughout the
year long trial, that the educators were able to embrace the cyclic nature of the ERA heuristic and ensure that the time spent on the tablet (Represent) was connected to contextualised learning opportunities (Experience and Apply). Importantly, the tablets provided affordances for the children to utilise User Generated Content (UGC) to support
active engagement when using the tablets.
Digital Experiences in Mathematics Education, 2018
It is an increasingly common phenomenon that elementary school students are using
mobile applicat... more It is an increasingly common phenomenon that elementary school students are using
mobile applications (apps) in their mathematics classrooms. Classroom teachers, who
are using apps, require a tool, or a set of tools, to help them determine whether or not
apps are appropriate and how enhanced educational outcomes can be achieved via their
use. In this article we investigate whether Artifact Centric Activity Theory (ACAT) can
be used to create a useful tool for evaluating apps, present a review guide based on the
theory and test it using a randomly selected geometry app [Pattern Shapes] built upon
different (if any at all) design principles. In doing so we broaden the scope of ACAT by
investigating a geometry app that has additional requirements in terms of accuracy of
external representations, and depictions of mathematical properties (e.g. reflections and
rotations), than is the case for place value concepts in [Place Value Chart] which was
created using ACAT principles and has been the primary app evaluated using ACAT.
We further expand the use of ACAT via an independent assessment of a second app
[Click the Cube] by a novice, using the ACAT review guide. Based on our latest
research, we argue that ACAT is highly useful for evaluating any mathematics app and
this is a critical contribution if the evaluation of apps is to move beyond academic
circles and start to impact student learning and teacher pedagogy in mathematics.
Free online version available at https://protect-au.mimecast.com/s/4ZGUC2xZzgHWA8B6HB_fFm?domain=em.rdcu.be
Teaching Primary Years: Rethinking curriculum, pedagogy and assessment. Allen & Unwin. Crows Nest, NSW. , 2019
Learning mathematics is an important and integral part of the primary school curriculum. For many... more Learning mathematics is an important and integral part of the primary school curriculum. For many, mathematics achievement is typically associated with skills and formulae application. However, an unintended outcome of learning mathematics in the primary years of schooling is that many students learn to dislike mathematics and regard it as dull and useless (Attard, Ingram, Forgasz, Leder, & Grootenboer, 2016). Indeed, this remains one of the consistent problems in primary school education, as it seems to resist change despite intense focus and effort. Due to the persistence of negative attitudes towards mathematics (Grootenboer & Marshman, 2017; Jorgensen & Larkin, 2017), primary school teachers need to appreciate that, in addition to the need to teach mathematical concepts and ideas well, they also need to ensure that students find that the learning of mathematics is enjoyable and interesting, and that they regard it as useful. Therefore, in this chapter we will discuss the who of mathematics education (i.e., the students), the how of mathematics education (i.e., the teaching, or pedagogy) and the what of mathematics education (i.e., the curriculum).
Mathematical applications (apps) are becoming commonplace in educational settings. Despite their ... more Mathematical applications (apps) are becoming commonplace in educational settings. Despite their increasing use, limited quantitative research has been undertaken that might support teachers in making appropriate pedagogical decisions regarding their use, nor how teachers might go about selecting appropriate apps from the multitudes available at iTunes or Google Play. This chapter explores how cluster analysis can be used to identify homogeneity among elements within apps, thus assisting teachers to make decisions regarding which apps might be most appropriate. Based upon selection criteria and rankings generated via a number of scales, the cluster structure of 53 apps to support geometry learning in elementary mathematics classrooms is reported. The chapter concludes by exploring the homogeneity and heterogeneity of these clusters of apps and suggests how to use these apps to enhance student mathematical learning.
In this article we critique, disrupt and resist the taken for granted use of the term fun in lear... more In this article we critique, disrupt and resist the taken for granted use of the term fun in learning; specifically as it is used to justify mathematics education apps that purport to portray maths learning as a fun experience. We accomplish this critique through the creation of a digital artwork called Arithmomania. This artwork challenges how users interact with education apps by employing the aesthetic of the glitch, an aesthetic characterized by reifying disorder and malfunction. Arithmomania shows fun as a miasma to learning, rather than the nostrum it is believed to be.
The growth in interest in science, technology, engineering and mathematics (STEM) education has b... more The growth in interest in science, technology, engineering and mathematics (STEM) education has been the catalyst for this book. There has been a worldwide trend to focus on the teaching of STEM across all sectors of schooling, and this is evidenced by the geographical spread of the authors in this book. The initial intent of STEM education was to build strengths in science, technology, engineering and mathematics due to the declining number of students undertaking these courses of study in high school or at university, a perceived decline in the quality of teaching, and an increased recognition that STEM is a key driver in advancing societies (see Han et al. 2015). Most societies have taken the urgency to develop STEM in schools and in the labour market very seriously, with many nations developing productive strategies to boost STEM in schools and in the workplace. While increased emphasis has occurred overall, within the four STEM elements, there is a disparity in the amount of attention each element receives, with science and mathematics remaining the main focus. Daugherty et al. (2014), for example, argue that technology and engineering education continue to struggle to maintain a foothold in secondary education and that, despite some curriculum initiatives in the USA (e.g. Project Lead the Way, Engineering by Design), the “influence of technology and engineering education curriculum at junior high and high schools across America is clearly less than it was just 20 years ago” (p. 45).
One of the key drivers underpinning mathematics education in general, and more specifically mathe... more One of the key drivers underpinning mathematics education in general, and more specifically mathematics education at a university level, is the use of Web 2.0 technologies to support the delivery of courses to undergraduate, primary pre-service teachers (PSTs) who often form part of large cohorts of students studying education. It is now unusual to find a mathematics education courses at Australian universities that do not incorporate online course delivery elements. Unfortunately, the drive online has not always been matched with a complementary drive to support developments in online pedagogy, and thus, mathematics educators are often in the position of delivering online content with little or no professional development to support a new form of pedagogy required in this context. This chapter examines the use of various combinations of online lectures (namely, full video, part video or no video) to support the development of content and pedagogical knowledge of PSTs. In addition, and just as critically, the lectures were a component of a course that had the second aim of enhancing the affective experience of mathematics for these PSTs. Data to support the claims made in this chapter are from PST feedback using an anonymous online survey and also from data collected by EchoCapture software, a component of the learning management system (LMS) used by the university in which this research took place.
In this article, we argue the need to use inter-disciplinary paradigms to make
sense of a range o... more In this article, we argue the need to use inter-disciplinary paradigms to make
sense of a range of findings from a research project. We developed a methodology using iPad diaries to uncover young students’ thinking—mathematical, social and affective—so as to better understand their experiences of mathematics. These students, predominantly from year 3 to year 6, were drawn from economically and socially distinct schools in Queensland and New South Wales, Australia. This article builds on
previous research, where we outlined the unique methodology that we developed over three iterations to collect student attitudinal comments regarding mathematics. The comments we collected gave significant insights into the experiences of, and possibilities for, the mathematics education of young learners. Here, we use these findings to explore the value of two paradigms to explain student experiences towards mathematics among primary school students from different social backgrounds. In so doing, we develop an explanatory model for the socially differentiated outcomes in students’ responses and then use this explanatory model to analyse student responses from the two most socially disparate schools in our research.
This chapter examines changes to the online component of core primary mathematics education cours... more This chapter examines changes to the online component of core primary mathematics education courses for pre-service teachers (PSTs) offered in blended mode (a mixture of online and face-to-face lectures, workshops and tutorials). It also reports upon the impact these changes had on students’ attitudes towards, and experiences of, the course in terms of their connection with the lecturer, the content, and each other. One of the current drivers in tertiary mathematics education is the use of digital technologies to support mixed mode delivery. Unfortunately, this movement has not always been matched with a drive to resolve issues arising from online education for PSTs, teaching staff and course content. Although there are many elements that constitute a successful experience, the focus here is on a specific aspect, i.e. the use of online lectures and how modifications to these lectures were made to maximise PSTs connectedness. The chapter has twin foci; first, the impact of the online lectures on PSTs engagement with the course material and their learning relationship with the course convenor (the author); and, second, the impact of the online lectures on my experience of teaching the courses. The dataset for the chapter includes formal university student evaluation of course and evaluation of teaching feedback; data collected via the Learning Management System (LMS) regarding online engagement; and the personal reflections of the convenor. The chapter contributes knowledge regarding the use of digital pedagogies with adult learners and highlights the need for lecturers to consider the various learning needs of PSTs, particularly in the building of rapport and engagement with the discipline and with each other.
The aim of this paper is propositional and is based on research findings which suggest that succe... more The aim of this paper is propositional and is based on research findings which suggest that success in mathematics teaching and reform is contingent upon having key personnel in schools to lead curriculum reform. Based on the outcomes of a large national study on successful practice in the teaching of numeracy for some of Australia’s most disadvantaged learners, it was found that, among other practices, the appointment of a numeracy leader alongside the use of effective and appropriate digital tools (in particular apps) supported teachers to implement strong and effective numeracy practices. This paper presents a rationale for a renewed focus on practices that will enable success for all Australian students, but most particularly those who are most at risk of mathematical mortality.
The teaching and learning of Geometry has been identified in much of the literature as being prob... more The teaching and learning of Geometry has been identified in much of the literature as being problematic and the mathematics strand where many teachers feel least knowledgeable and least confident to teach. This paper describes a school-based project which sought to develop teacher knowledge and confidence in this strand via the use of Professional Learning Communities (DuFour & Reeves, 2016) and Instructional Coaching.
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Articles and Book Chapters by Kevin Larkin
clip as stimulus. It discusses findings from a recent study conducted in a Year 5 (9-10 years
old) classroom in which the students’ problem-posed and developed personal mathematical
inquiries based on a video prompt. The article highlights the benefits for teachers and students
in using video stimulus for open inquiry in Primary Mathematics classrooms.
“Representations”, developed for preschool children (4-5 years of age).
In this article we analyse how the app supported the development of
logical reasoning via a variety of decoding, encoding, conditionals and
debugging activities, which were supported in the game play by the
children’s own user generated content (UGC). Research such as this is
important as logical reasoning in young children correlates positively
with later mathematics achievement. The learning app is used within a
broader program, which also included a range of off-device learning.
Data indicates the success of our design and implementation in terms of
children’s engagement with the app and in terms of their early learning
of important logical reasoning concepts.
young children has been well researched; however, this research has largely been
conducted with relatively small cohorts (+/- 70) and in an interventionist way (in
laboratory settings or with researchers directly intervening in educational contexts).
The current study examines the patterning skills of approximately3 200 children in a
naturalistic setting. As part of a larger, early years’ STEM engagement program,
children were provided patterning opportunities across one school term. The data
presented here relates to the children’s performance on the tablet-based activities
embedded in the program. Findings indicate that 3 to 4 year old children were
able to copy, extend, insert missing elements, fix, and create patterns, using a range of
two, three or four elements pattern structures. These findings, from a large-scale
naturalistic setting, confirm some aspects of the existing laboratory-based research,
whilst also indicating that some children are more capable in terms of creating patterns
than the existing research suggests. These findings have implications for educators
when they are planning play-based patterning activities with preschool children.
school teachers’ perceived barriers to and enablers for the integration of children’s literature in mathematics teaching and learning in an Australian educational context. While
research over the past three decades have documented pedagogical benefts of teaching
mathematics using children’s literature, research into teachers’ perceptions regarding the
use of such resources is virtually non-existent. The study thus flled this research gap by
drawing responses from open-ended survey questions of 94 in-service and 82 pre-service
teachers in Australia. A thematic analysis revealed 13 perceived barriers classifed under
fve themes with Lack of Pedagogical Knowledge and Confdence, and Time Constraint,
representing 75% of all perceived barriers. Moreover, 14 perceived enablers were identifed
and classifed under fve themes with Pedagogical Benefts and Love of Stories representing around 70% of all perceived enablers. Findings also showed that most of the teachers in
the study (around 75%) never or infrequently used children’s literature in their mathematics classrooms. The study highlights the role of professional learning and teacher training
in ensuring that both in- and pre-service teachers have the necessary pedagogical knowledge, experience and confdence in using children’s literature to enrich their mathematics
teaching.
the educational experiences of early childhood and primary preservice teachers (PST) completing a
pedagogically focused mathematics education unit in a fully online mode. Given the trend over the
past 10 years towards the delivery of university mathematics education courses online, this research
is important. It is particularly timely given the current world health crisis, where universities are
hurriedly rolling out online courses. We argue, based on the findings of this initial pilot, that the use
of regular, formative video feedback has a positive effect on PST learning, and on the way PSTs
perceive and engage with the feedback provided in video form, and on the affective connection this
platform provides between the PST and the lecturer. We suggest that these themes have the potential
to positively impact on PSTs’ knowledge of content and pedagogy in the context of university
mathematics education.
use new and emerging technologies to solve problems while extending their own knowledge and
understanding of mathematics. In Australia, a digital technologies curriculum was introduced in 2014 to
assist with making connections between Technology and areas such as mathematics. Drawing on examples
from Australia, British Columbia, the United Kingdom and New Zealand, this chapter examines how the
introduction of a new curriculum intersects with existing curricula. As an example of an authentic activity
that successfully combines elements of both curricula to support STEM learning, findings of a research
project that has been conducted with Year 2 students (n = 153) from two Australian primary schools are
presented. It appears as young students engage in robotics and coding (Technology) to learn mathematics
concepts, they demonstrate learning that moves beyond their curriculum year level, creating a possible
conflict between the digital technologies and mathematics curricula with their tightly prescribed sequence
of content.
colleagues (e.g. Bailey, 2015; Hartnett, 2018; Rogers,
2012) published in the APMC journal regarding the
fundamental importance of place value (PV) understanding.
In this paper we explore the utility of an iPad
app, Place Value Chart, which was custom-designed
to support the development of student PV understanding
across all primary school year levels. This article
also describes an international collaborative effort to
support teachers’ Mathematics Content Knowledge
(MCK) and Mathematics Pedagogical Content
Knowledge (MPCK) through the creation of a
25-page teachers’ guide outlining the use of the app.
resolved many of the perturbations - tensions and contradictions - inherent in the doctoral
degree by focusing on my experiences of recently completing this journey. These perturbations
are conceptualised, via an ‘Activity Systems’ approach, the disquieting transition of the author
from a doctoral student to ECA., My various perturbing experiences of this journey provide the
‘dataset’ for this chapter. As an initial position, Engestrom’s (1987) Activity Systems are utilised
to situate me in a university Community of Practice (CoP).
These perturbations are analysed using Active Subjectivities (Valsiner & Van Der Veer, 2000) as
a conceptual tools. This approach identifies the agentic activity of an active subject, who chooses
from a range of available roles (student, researcher, author, lecturer or colleague) in response
to a range of intellectually disquieting discourses within a particular context. The resolution of
my perturbations in the transition from doctoral student to ECA is a consequence of personal
transformation whilst simultaneously acknowledging that individual agentic action in a CoP
shapes this transformation at a more granular level than can solely be explained by Activity
Systems. A new conceptual model incorporating these perturbations, offering a relational
approach to the individual and social dichotomy evident in workplaces (Billett, 2006), is
suggested.
development. Schools often secure small-scale funding to engage in government or systemic initiatives, and
these projects require a leadership “close to the classroom” if they are to realise sustainable educational gains.
This leadership often comes from the middle leaders – those who practice their leading in and around
classrooms. The paper aims to discuss this issue.
Design/methodology/approach – A single case study methodology is used to investigate two middle
leaders, leading a small-scale project. Their leading practices are examined using the “theory of practice
architectures”, to identify how these practices were enacted within their educational context.
Findings – While principals play a crucial role in enacting change, it is the middle leaders who are closer to
the classroom than most principals, and whose practices more directly impact teaching and learning as they
are best placed to ensure that meagre resources are well used to improve student learning. They do this by
ensuring that development is collegial and a response to evidence-based needs.
Practical implications – First, middle leaders need support in facilitating educational development.
Second, their leading practice is crucial for sustainable school-based development. Third, site-based
educational development occurs most effectively when it is evidence-based. Finally, this form of educational
development requires high-level collegiality.
Originality/value – This paper is original in two key ways: first, it addresses the under-researched practices
of middle leaders; and, second it employs the practice theory to understand school leadership and development.
young children. The ELSA project responded to this challenge by developing a pedagogical framework that embedded digital technologies into context-rich, play-based STEM learning. The Experience, Represent, Apply (ERA) heuristic discussed in this article is a component of the project’s overall pedagogical framework, and provides early years educators with the opportunity, and the know-how, to integrate digital technologies into STEM activities through intentional teaching and play-based engagement. It was evident, from educator feedback at the four days of workshops we delivered, and in other comments throughout the
year long trial, that the educators were able to embrace the cyclic nature of the ERA heuristic and ensure that the time spent on the tablet (Represent) was connected to contextualised learning opportunities (Experience and Apply). Importantly, the tablets provided affordances for the children to utilise User Generated Content (UGC) to support
active engagement when using the tablets.
mobile applications (apps) in their mathematics classrooms. Classroom teachers, who
are using apps, require a tool, or a set of tools, to help them determine whether or not
apps are appropriate and how enhanced educational outcomes can be achieved via their
use. In this article we investigate whether Artifact Centric Activity Theory (ACAT) can
be used to create a useful tool for evaluating apps, present a review guide based on the
theory and test it using a randomly selected geometry app [Pattern Shapes] built upon
different (if any at all) design principles. In doing so we broaden the scope of ACAT by
investigating a geometry app that has additional requirements in terms of accuracy of
external representations, and depictions of mathematical properties (e.g. reflections and
rotations), than is the case for place value concepts in [Place Value Chart] which was
created using ACAT principles and has been the primary app evaluated using ACAT.
We further expand the use of ACAT via an independent assessment of a second app
[Click the Cube] by a novice, using the ACAT review guide. Based on our latest
research, we argue that ACAT is highly useful for evaluating any mathematics app and
this is a critical contribution if the evaluation of apps is to move beyond academic
circles and start to impact student learning and teacher pedagogy in mathematics.
Free online version available at https://protect-au.mimecast.com/s/4ZGUC2xZzgHWA8B6HB_fFm?domain=em.rdcu.be
sense of a range of findings from a research project. We developed a methodology using iPad diaries to uncover young students’ thinking—mathematical, social and affective—so as to better understand their experiences of mathematics. These students, predominantly from year 3 to year 6, were drawn from economically and socially distinct schools in Queensland and New South Wales, Australia. This article builds on
previous research, where we outlined the unique methodology that we developed over three iterations to collect student attitudinal comments regarding mathematics. The comments we collected gave significant insights into the experiences of, and possibilities for, the mathematics education of young learners. Here, we use these findings to explore the value of two paradigms to explain student experiences towards mathematics among primary school students from different social backgrounds. In so doing, we develop an explanatory model for the socially differentiated outcomes in students’ responses and then use this explanatory model to analyse student responses from the two most socially disparate schools in our research.
clip as stimulus. It discusses findings from a recent study conducted in a Year 5 (9-10 years
old) classroom in which the students’ problem-posed and developed personal mathematical
inquiries based on a video prompt. The article highlights the benefits for teachers and students
in using video stimulus for open inquiry in Primary Mathematics classrooms.
“Representations”, developed for preschool children (4-5 years of age).
In this article we analyse how the app supported the development of
logical reasoning via a variety of decoding, encoding, conditionals and
debugging activities, which were supported in the game play by the
children’s own user generated content (UGC). Research such as this is
important as logical reasoning in young children correlates positively
with later mathematics achievement. The learning app is used within a
broader program, which also included a range of off-device learning.
Data indicates the success of our design and implementation in terms of
children’s engagement with the app and in terms of their early learning
of important logical reasoning concepts.
young children has been well researched; however, this research has largely been
conducted with relatively small cohorts (+/- 70) and in an interventionist way (in
laboratory settings or with researchers directly intervening in educational contexts).
The current study examines the patterning skills of approximately3 200 children in a
naturalistic setting. As part of a larger, early years’ STEM engagement program,
children were provided patterning opportunities across one school term. The data
presented here relates to the children’s performance on the tablet-based activities
embedded in the program. Findings indicate that 3 to 4 year old children were
able to copy, extend, insert missing elements, fix, and create patterns, using a range of
two, three or four elements pattern structures. These findings, from a large-scale
naturalistic setting, confirm some aspects of the existing laboratory-based research,
whilst also indicating that some children are more capable in terms of creating patterns
than the existing research suggests. These findings have implications for educators
when they are planning play-based patterning activities with preschool children.
school teachers’ perceived barriers to and enablers for the integration of children’s literature in mathematics teaching and learning in an Australian educational context. While
research over the past three decades have documented pedagogical benefts of teaching
mathematics using children’s literature, research into teachers’ perceptions regarding the
use of such resources is virtually non-existent. The study thus flled this research gap by
drawing responses from open-ended survey questions of 94 in-service and 82 pre-service
teachers in Australia. A thematic analysis revealed 13 perceived barriers classifed under
fve themes with Lack of Pedagogical Knowledge and Confdence, and Time Constraint,
representing 75% of all perceived barriers. Moreover, 14 perceived enablers were identifed
and classifed under fve themes with Pedagogical Benefts and Love of Stories representing around 70% of all perceived enablers. Findings also showed that most of the teachers in
the study (around 75%) never or infrequently used children’s literature in their mathematics classrooms. The study highlights the role of professional learning and teacher training
in ensuring that both in- and pre-service teachers have the necessary pedagogical knowledge, experience and confdence in using children’s literature to enrich their mathematics
teaching.
the educational experiences of early childhood and primary preservice teachers (PST) completing a
pedagogically focused mathematics education unit in a fully online mode. Given the trend over the
past 10 years towards the delivery of university mathematics education courses online, this research
is important. It is particularly timely given the current world health crisis, where universities are
hurriedly rolling out online courses. We argue, based on the findings of this initial pilot, that the use
of regular, formative video feedback has a positive effect on PST learning, and on the way PSTs
perceive and engage with the feedback provided in video form, and on the affective connection this
platform provides between the PST and the lecturer. We suggest that these themes have the potential
to positively impact on PSTs’ knowledge of content and pedagogy in the context of university
mathematics education.
use new and emerging technologies to solve problems while extending their own knowledge and
understanding of mathematics. In Australia, a digital technologies curriculum was introduced in 2014 to
assist with making connections between Technology and areas such as mathematics. Drawing on examples
from Australia, British Columbia, the United Kingdom and New Zealand, this chapter examines how the
introduction of a new curriculum intersects with existing curricula. As an example of an authentic activity
that successfully combines elements of both curricula to support STEM learning, findings of a research
project that has been conducted with Year 2 students (n = 153) from two Australian primary schools are
presented. It appears as young students engage in robotics and coding (Technology) to learn mathematics
concepts, they demonstrate learning that moves beyond their curriculum year level, creating a possible
conflict between the digital technologies and mathematics curricula with their tightly prescribed sequence
of content.
colleagues (e.g. Bailey, 2015; Hartnett, 2018; Rogers,
2012) published in the APMC journal regarding the
fundamental importance of place value (PV) understanding.
In this paper we explore the utility of an iPad
app, Place Value Chart, which was custom-designed
to support the development of student PV understanding
across all primary school year levels. This article
also describes an international collaborative effort to
support teachers’ Mathematics Content Knowledge
(MCK) and Mathematics Pedagogical Content
Knowledge (MPCK) through the creation of a
25-page teachers’ guide outlining the use of the app.
resolved many of the perturbations - tensions and contradictions - inherent in the doctoral
degree by focusing on my experiences of recently completing this journey. These perturbations
are conceptualised, via an ‘Activity Systems’ approach, the disquieting transition of the author
from a doctoral student to ECA., My various perturbing experiences of this journey provide the
‘dataset’ for this chapter. As an initial position, Engestrom’s (1987) Activity Systems are utilised
to situate me in a university Community of Practice (CoP).
These perturbations are analysed using Active Subjectivities (Valsiner & Van Der Veer, 2000) as
a conceptual tools. This approach identifies the agentic activity of an active subject, who chooses
from a range of available roles (student, researcher, author, lecturer or colleague) in response
to a range of intellectually disquieting discourses within a particular context. The resolution of
my perturbations in the transition from doctoral student to ECA is a consequence of personal
transformation whilst simultaneously acknowledging that individual agentic action in a CoP
shapes this transformation at a more granular level than can solely be explained by Activity
Systems. A new conceptual model incorporating these perturbations, offering a relational
approach to the individual and social dichotomy evident in workplaces (Billett, 2006), is
suggested.
development. Schools often secure small-scale funding to engage in government or systemic initiatives, and
these projects require a leadership “close to the classroom” if they are to realise sustainable educational gains.
This leadership often comes from the middle leaders – those who practice their leading in and around
classrooms. The paper aims to discuss this issue.
Design/methodology/approach – A single case study methodology is used to investigate two middle
leaders, leading a small-scale project. Their leading practices are examined using the “theory of practice
architectures”, to identify how these practices were enacted within their educational context.
Findings – While principals play a crucial role in enacting change, it is the middle leaders who are closer to
the classroom than most principals, and whose practices more directly impact teaching and learning as they
are best placed to ensure that meagre resources are well used to improve student learning. They do this by
ensuring that development is collegial and a response to evidence-based needs.
Practical implications – First, middle leaders need support in facilitating educational development.
Second, their leading practice is crucial for sustainable school-based development. Third, site-based
educational development occurs most effectively when it is evidence-based. Finally, this form of educational
development requires high-level collegiality.
Originality/value – This paper is original in two key ways: first, it addresses the under-researched practices
of middle leaders; and, second it employs the practice theory to understand school leadership and development.
young children. The ELSA project responded to this challenge by developing a pedagogical framework that embedded digital technologies into context-rich, play-based STEM learning. The Experience, Represent, Apply (ERA) heuristic discussed in this article is a component of the project’s overall pedagogical framework, and provides early years educators with the opportunity, and the know-how, to integrate digital technologies into STEM activities through intentional teaching and play-based engagement. It was evident, from educator feedback at the four days of workshops we delivered, and in other comments throughout the
year long trial, that the educators were able to embrace the cyclic nature of the ERA heuristic and ensure that the time spent on the tablet (Represent) was connected to contextualised learning opportunities (Experience and Apply). Importantly, the tablets provided affordances for the children to utilise User Generated Content (UGC) to support
active engagement when using the tablets.
mobile applications (apps) in their mathematics classrooms. Classroom teachers, who
are using apps, require a tool, or a set of tools, to help them determine whether or not
apps are appropriate and how enhanced educational outcomes can be achieved via their
use. In this article we investigate whether Artifact Centric Activity Theory (ACAT) can
be used to create a useful tool for evaluating apps, present a review guide based on the
theory and test it using a randomly selected geometry app [Pattern Shapes] built upon
different (if any at all) design principles. In doing so we broaden the scope of ACAT by
investigating a geometry app that has additional requirements in terms of accuracy of
external representations, and depictions of mathematical properties (e.g. reflections and
rotations), than is the case for place value concepts in [Place Value Chart] which was
created using ACAT principles and has been the primary app evaluated using ACAT.
We further expand the use of ACAT via an independent assessment of a second app
[Click the Cube] by a novice, using the ACAT review guide. Based on our latest
research, we argue that ACAT is highly useful for evaluating any mathematics app and
this is a critical contribution if the evaluation of apps is to move beyond academic
circles and start to impact student learning and teacher pedagogy in mathematics.
Free online version available at https://protect-au.mimecast.com/s/4ZGUC2xZzgHWA8B6HB_fFm?domain=em.rdcu.be
sense of a range of findings from a research project. We developed a methodology using iPad diaries to uncover young students’ thinking—mathematical, social and affective—so as to better understand their experiences of mathematics. These students, predominantly from year 3 to year 6, were drawn from economically and socially distinct schools in Queensland and New South Wales, Australia. This article builds on
previous research, where we outlined the unique methodology that we developed over three iterations to collect student attitudinal comments regarding mathematics. The comments we collected gave significant insights into the experiences of, and possibilities for, the mathematics education of young learners. Here, we use these findings to explore the value of two paradigms to explain student experiences towards mathematics among primary school students from different social backgrounds. In so doing, we develop an explanatory model for the socially differentiated outcomes in students’ responses and then use this explanatory model to analyse student responses from the two most socially disparate schools in our research.
dimensions of engagement; emotional, behavioural, and cognitive, and these were used to
structure the data collection and analysis vis- -vis learning mathematics outdoors. This
comparative case study involved 34 students from two Year 6 classes at a Queensland state
primary school. The findings indicate that the students were engaged in their mathematics
learning in the outdoor context. However, there was no compelling evidence that suggested
the outdoor environment was any more emotionally, behaviourally, or cognitively engaging
than the indoor context.
number understanding for young children. In this paper we investigate the usefulness
of a purpose built app in supporting children’s understanding in German and
Australian contexts. In particular, we investigate whether the app supports the
development of bundling and unbundling. Our findings indicate positive and negative
aspects of the use, which have implications for both teachers and app designers.
Keywords: apps, place value, curriculum, professional development
primary school teachers’ beliefs concerning the integration of children’s literature in
their mathematics learning and teaching. The thematic and content analyses were drawn
from self-reported beliefs of 33, third- and fourth-year pre-service teachers in Queensland.
Findings from this pilot study reveal several gaps in knowledge, as well as misconceptions
held by them, concerning the use of children’s literature in mathematics learning and
teaching. These findings suggest the need for mathematics teacher educators to do more to
address these gaps and misconceptions, also possibly held by the pre-service teachers they
teach, in order for this future generation of teachers to become more knowledgeable in their
approach to the use of children’s literature.
Preschools. The majority of the literature points to overwhelmingly positive outcomes for
young children when digital technology is thoughtfully used in play based learning contexts.
However, despite the wealth of evidence that the use of tablets can be beneficial to preschool
students, early childhood teachers often report being uncomfortable in teaching STEM. We
suggest that, if accompanied by suitable professional development, tablets are an important
addition to early childhood contexts.
STEM Australia (ELSA) project. It provided educators with an approach that embeds digital
technologies in play-based learning in such a way that the focus of the learning remains on
the child and not on the device. This paper reports on the experiences of early years educators
and indicates that the ERA heuristic was instrumental in helping educators to integrate digital
technologies in their everyday activities to promote engagement with STEM.
program. The conceptual framework is developed from STEM practices, rather than from
play-based investigations derived from traditional understandings of content within the four
STEM disciplines. One of these core STEM practices is spatial reasoning—a practice that
not only has strong associations with mathematics but is also the best predictor of an
individual choosing a STEM-related profession beyond schooling.
suggest a pedagogical framework to underpin mathematics learning using mapping as an exemplar, and then explain how we will use a design based approach to create apps that support learning in Mathematics.
particularly the case for Geometry apps where accurate and dynamic representations are critical in enhancing mathematical learning. This paper provides findings from an initial critique of 53 Geometry apps. Early findings indicate that the majority of these apps were limited in their ability to assist students in developing Geometrical conceptual understanding; however, all is not lost as a number of apps were highly appropriate.
relations. This paper explores a method using iPads and a video diary technique not dissimilar to the ‘Big Brother” room with which many children are familiar. We describe the development of the tool and process when implemented in a primary school setting. We allude to both the enabling prospects of the technique as well as some of the limitations we found when implementing the method.
cyclical process to achieve course objectives.
apps for mathematics education. The ease of access and the fact that they are generally low cost, often free, means that they are readily available to the general population but this raises questions as to their quality and what is being learned through the use of these apps.
Using two quantitative measures and one qualitative measure, this article evaluates 142 apps which met initial search criteria, and recommends 34 mathematics apps for further evaluation and trial with primary school teachers and students.
This study sought to determine whether or not ubiquitous access to netbook computers equated to ubiquitous usage of the devices and whether or not varying the pattern and ratio of access affected the uptake and impact of netbook usage. It also sought to determine whether or not netbooks were an appropriate computing device for early adolescent learners, and whether or not the use of the netbooks affected the classroom environment. Specifically, it examined the impact of the netbooks on student productivity, social activity, teacher control and individual learning. It also sought to further establish whether or not Activity Theory (AT) was an appropriate methodological and conceptual framework for classroom based research. Four classrooms received the netbooks in one of the following four patterns:
1:1 student to netbook access - 5 days per week for 6 weeks;
1:1 student to netbook access - 3 days per week for 10 weeks;
1:2 student to netbook access - 5 days per week for 6 weeks; and,
1:2 student to netbook access - 3 days per week for 10 weeks.
The study drew upon AT as the conceptual framework and employed a mixed method methodology.
The study, conducted in a South East Queensland Catholic Primary School, involved 120 Year 7 students and four classroom teachers. Throughout the 2009 school year data were collected about the students, the teachers, and the classroom environments via interviews, student forums, surveys, questionnaires, data logging software, researcher diary and classroom observations. Questionnaire data relating to classroom environments were analysed using SPSS and statistical significance determined using t-tests and correlational analysis. Interview, survey and observational data were initially coded using six Activity Theory nodes (Subject, Object, Tools, Division of Labour, Community and Rules and the eight NCEI sub-scales (Involvement, Innovation, Teacher Control, Teacher Support, Order and Organisation, Competition, Affiliation and Group Work. As analysis continued, further nodes emerged including student productivity, Technological Pedagogical Content Knowledge (TPACK) and the crowded curriculum. NVivo was utilised to assist in this analysis.
The study found that ubiquitous access did not equate to ubiquitous use with average daily use of the netbooks of between 60 – 90 minutes. The netbooks were considered as an appropriate computing device by the students and teachers in this study and provided a balance between mobility and functionality. Statistically significant changes occurred in three classrooms. These changes related to Order and Organisation in one classroom and Teacher Control and Involvement in two classrooms. The use of the netbooks had significant impact on student productivity and social activity but no impact on individualised learning. Minor changes occurred to teacher pedagogy in two of the classrooms. Varying the pattern and ratio of use was a significant factor in the findings noted above and the study recommends the allocation of computers in a 1:2 rather that 1:1 ratio.
This research is significant as it can inform other primary schools as they determine the most effective means in which to utilise new mobile technologies. It is also relevant to informing secondary schools as they consider the implementation of the Digital Education Revolution (DER). This research also informs the broader debate as to whether or not 1:1 distribution of computers is most efficacious in terms of student outcomes and whether or not netbooks are an appropriate computing solution for early adolescent students.