- Kelvin Grove, Queensland, Australia
David Nutchey
Queensland University of Technology, Faculty of Education, Department Member
Research Interests:
This is the author’s version of a work that was submitted/accepted for pub-lication in the following source:
This is the author’s version of a work that was submitted/accepted for pub-lication in the following source:
Research Interests:
Contemporary mathematics education attempts to instil within learners the conceptualization of mathematics as a highly organized and inter-connected set of ideas. To support this, a means to graphically represent this organization of... more
Contemporary mathematics education attempts to instil within learners the conceptualization of mathematics as a highly organized and inter-connected set of ideas. To support this, a means to graphically represent this organization of ideas is presented which reflects the cognitive mechanisms that shape a learner’s understanding. This organisation of information may then be analysed, with the view to informing the design of mathematics instruction in face-to-face and/or computer-mediated learning environments. However, this analysis requires significant work to develop both theory and practice.
Research Interests:
Research Interests:
Early-number is a rich fabric of interconnected ideas that is often misunderstood and thus taught in ways that do not lead to rich understanding. In this presentation, a visual language is used to describe the organisation of this domain... more
Early-number is a rich fabric of interconnected ideas that is often misunderstood and thus taught in ways that do not lead to rich understanding. In this presentation, a visual language is used to describe the organisation of this domain of knowledge. This visual language is based upon Piaget’s notion of reflective abstraction (Dubinsky, 1991; Piaget, 1977/2001), and thus captures the epistemological associations that link the problems, concepts and representations of the domain. The constructs of this visual language are introduced and then applied to the early-number domain. The introduction to this visual language may prompt reflection upon its suitability and significance to the description of other domains of knowledge. Through such a process of analysis and description, the visual language may serve as a scaffold for enhancing pedagogical content knowledge and thus ultimately improve learning outcomes.
Research Interests:
Research Interests:
Research Interests:
This is the author’s version of a work that was submitted/accepted for pub-lication in the following source:
A mathematics classroom is comprised of many mathematicians with varying understanding of mathematics knowledge, including the teacher, students and sometimes researchers. To align with this conceptualisation of knowledge and... more
A mathematics classroom is comprised of many mathematicians with varying understanding of mathematics knowledge, including the teacher, students and sometimes researchers. To align with this conceptualisation of knowledge and understanding, the multi-faceted teaching experiment will be introduced as an approach to study all classroom participants’ interactions with the shared knowledge of mathematics. Drawing on the experiences of a large curriculum project, it is claimed that, unlike a multi-tiered teaching experiment, the multi-faceted teaching experiment provides a research framework that allows for the study of mathematicians’ building of knowledge in a classroom without privileging the experience of any one participant.
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Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the... more
Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging ...
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The authors have collaboratively used a graphical language to describe their shared knowledge of a small domain of mathematics, which has in turn scaffolded their re-development of a related curriculum for mathematics acceleration. This... more
The authors have collaboratively used a graphical language to describe their shared knowledge of a small domain of mathematics, which has in turn scaffolded their re-development of a related curriculum for mathematics acceleration. This collaborative use of the graphical language is reported as a simple descriptive case study. This leads to an evaluation of the graphical language’s usefulness as a tool to support the articulation of the structure of mathematics knowledge. In turn, implications are drawn for how the graphical language may be utilised as the detail of the curriculum is further elaborated and communicated to teachers.
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Science is often considered as one of the cornerstones of human advancement. Despite its importance in our society, science as a subject in schools appears to be losing ground. Lack of relevance, the nature of the curriculum and the... more
Science is often considered as one of the cornerstones of human advancement. Despite its importance in our society, science as a subject in schools appears to be losing ground. Lack of relevance, the nature of the curriculum and the pedagogical approach to teaching are some of the reasons which researchers believe are causing a “swing” away from science. This paper will argue for the effectiveness of simple science demonstrations as a feasible pedagogical option with a high task value and which has the potential to reengage and reinvigorate student interest in the subject. This paper describes a case study (N = 25) in which the Integrative problem based learning model for science was implemented in a year nine science class. The study was conducted at a secondary school in Australia. Teacher demonstrations were situated in classroom activities in a “Why is it so?” problem/question format. Qualitative data gathered from students demonstrated a number of benefits of this approach. Thi...
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Teacher professional learning is a complex activity based on the interaction of three sub-systems: the teacher, the school and the learning activity. Such learning evolves over time depending on salient outcomes and teacher value... more
Teacher professional learning is a complex activity based on the interaction of three sub-systems: the teacher, the school and the learning activity. Such learning evolves over time depending on salient outcomes and teacher value positions, and requires support that is responsive to the teacher’s growth. This phenomenon has been observed within a group of teachers tasked with implementing an innovative curriculum. The curriculum involved an unfamiliar pedagogical practice that was designed to accelerate the mathematics learning of low socio-economic status junior secondary students. Based upon the observations, implications are drawn for the types of support needed to enhance teachers’ capacity to engage with pedagogical and curricular changes, with the aim of sustained teacher professional growth.
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This study explores the effects of a vocational education-based program on academic motivation and engagement of primary school aged children. The Get Into Vocational Education (GIVE) program integrated ‘construction’ and the mathematics,... more
This study explores the effects of a vocational education-based program on academic motivation and engagement of primary school aged children. The Get Into Vocational Education (GIVE) program integrated ‘construction’ and the mathematics, English and science lessons of a Year 4 primary classroom. This paper focuses on investigating the components of the GIVE program that led to student changes in mathematical academic motivation and engagement resulting in outstanding gains in NAPLAN Numeracy results. The components proposed to have contributed to effectiveness of the GIVE program are: teacher and trainer expectations, task mastery and classroom relationships. These findings may be useful to researchers and educators who are interested in enhancing students’ mathematical academic motivation.
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Studio-based learning provides an environment in which a collaborative, problembased approach to learning Science, Technology, Engineering and Mathematics (STEM) is encouraged. In this project, the STEM Studio approach was used with... more
Studio-based learning provides an environment in which a collaborative, problembased approach to learning Science, Technology, Engineering and Mathematics (STEM) is encouraged. In this project, the STEM Studio approach was used with school students in formal and informal learning environments for preservice teacher education. Building on research from orchestration and learning analytics identifying stakeholders, and part of a nationally funded, multi-institutional project, we examine the complexity and diversity of communities in three STEM Studios. Using multiple data sources, the aim of this paper is to identify the stakeholders and the relationships between them in order to visualize the complexity of the networks and to compare (1) changes in networks over time; (2) differences between the learning contexts; and (3) the implications for preservice teacher education.
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To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of... more
To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed th...
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A continuum for describing the degree to which teachers interpret the various features of a curriculum is presented. The continuum has been developed based upon the observation of classroom practices and discussions with a group of... more
A continuum for describing the degree to which teachers interpret the various features of a curriculum is presented. The continuum has been developed based upon the observation of classroom practices and discussions with a group of teachers who are using an innovative junior secondary mathematics curriculum. It is anticipated that the ongoing use of the continuum will lead to its improvement as well as the refinement of the curriculum, more focussed support for the teachers,improved student learning, and the building of explanatory theory regarding mathematics teaching and learning.
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FIRST LEGO League, or FLL, is an international program designed to promote STEM-related learning and work amongst middle-school aged children. In Australia a new nation-wide curriculum has recently been introduced which is based upon the... more
FIRST LEGO League, or FLL, is an international program designed to promote STEM-related learning and work amongst middle-school aged children. In Australia a new nation-wide curriculum has recently been introduced which is based upon the development of seven so called General Capabilities. In this paper, a qualitative study that sought to ascertain FLL’s efficacy in developing these capabilities at one FLL site is reported upon. This study sought the perceptions of FLL team coaches, typically classroom teachers with knowledge of the Australian Curriculum, in regards to the FLL’s efficacy for developing these capabilities. These perceptions of FLL were compared to the descriptions of the seven General Capabilities as well as the broad intentions of FLL. From this study, implications are drawn regarding how the implementation of STEM-rich activities, such as FLL, might be aligned to the imperatives of the new curriculum.
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The Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students project aims to address the issues faced by very underperforming mathematics students as they enter high school. Its aim is to accelerate... more
The Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students project aims to address the issues faced by very underperforming mathematics students as they enter high school. Its aim is to accelerate learning of mathematics through a vertical curriculum to enable students to access Year 10 mathematics subjects, thus improving life chances. This paper reports upon the theory underpinning this project and illustrates it with examples of the curriculum that has been designed to achieve acceleration.
Adopting constructivist practices in mathematics without rejecting the integrity of fundamental structures of bathematical knowledge is acknowledged as a challenge of curriculum reform. This paper illustrates the use of an approach to... more
Adopting constructivist practices in mathematics without rejecting the integrity of fundamental structures of bathematical knowledge is acknowledged as a challenge of curriculum reform. This paper illustrates the use of an approach to operationalising constructivist theory that supports the description of both the structure of mathematical knowledge and the nature of individual’s idiosyncratic and changing understanding.
The Bhutanese mathematics curriculum has undergone substantial reform in recent years; however, little consideration has been given to its implementation. Effective implementation assumes that there is alignment between teachers’ beliefs... more
The Bhutanese mathematics curriculum has undergone substantial reform in recent years; however, little consideration has been given to its implementation. Effective implementation assumes that there is alignment between teachers’ beliefs about teaching mathematics and the principles articulated in the reformed curriculum. This paper reports on a study which set out to explore Bhutanese elementary teachers’ beliefs and their implemented practices after adoption of the new Curriculum. A survey was conducted with 80 respondents from 40 randomly selected elementary schools across the country. The survey comprised of questions that elicited demographic information, beliefs about mathematics and mathematics education, and a short planning task that involved the design of a sample learning activity. An analysis of the responses revealed that a majority of the respondents supported belief statements aligning with the social constructivist approach of teaching and learning of mathematics as ...
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This paper reports on the use of the RAMR framework within a curriculum project. Description of the RAMR framework’s theoretical bases is followed by two descriptions of students’ learning in the classroom. Implications include the need... more
This paper reports on the use of the RAMR framework within a curriculum project. Description of the RAMR framework’s theoretical bases is followed by two descriptions of students’ learning in the classroom. Implications include the need for the teacher to connect student activities in a structured sequence, although this may be predicated on the teacher’s own structural understanding of mathematics.
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Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile ground for... more
Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile ground for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper...