Vincent Geiger
Australian Catholic University, Faculty of Education, Faculty Member
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Based on theoretical considerations, a possible means of gaining a resolution of the long standing issues of problem formulation and specification and their successful mathematisation by relatively naive modellers is proposed. This is... more
Based on theoretical considerations, a possible means of gaining a resolution of the long standing issues of problem formulation and specification and their successful mathematisation by relatively naive modellers is proposed. This is based on empirical evidence having been provided for paradigmatic cases of the construct of implemented anticipation as proposed by Niss, that is, foreshadowing of future action projected back onto decisions about current action during ideal mathematisation. A Foreshadowing and Feedback Framework to Engage Beginning Modellers in Implemented Anticipation and its theoretical underpinnings are outlined and illustrated using empirical data.
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Research Interests: Psychology and Routledge
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This article developed from a request by a German mathematics educator (Rudolf) to an Australian colleague (Vince) for a language check of an international conference presentation. Because of a history of cooperation, Rudolf trusted that... more
This article developed from a request by a German mathematics educator (Rudolf) to an Australian colleague (Vince) for a language check of an international conference presentation. Because of a history of cooperation, Rudolf trusted that Vince could provide a faithful translation. Vince happily accepted but had two reservations: he did not wish to edit the text in a way that obscured Rudolf's voice, and he was concerned that he might diminish the richness of Rudolf's message. The subsequent conversation generated a number of points about English language usage, but also raised the challenges faced by English non-dominant-language authors when they attempt to publish in English language journals
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Numeracy refers to the use of mathematics in non-mathematical contexts. In this paper two approaches to conceptualising numeracy across the whole school curriculum are identified: one based on interdisciplinary inquiry and the other on... more
Numeracy refers to the use of mathematics in non-mathematical contexts. In this paper two approaches to conceptualising numeracy across the whole school curriculum are identified: one based on interdisciplinary inquiry and the other on embedding numeracy into each school subject. The latter approach informed a systematic audit of resources available to Australian teachers for understanding and enacting numeracy across the curriculum. It was found that few resources addressed the need for teachers to recognise and take advantage of the numeracy learning demands and opportunities within the subjects they teach.
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In this article, we report on a typology of the demands of statistical and mathematical products (StaMPs) embedded in media items related to the COVID-19 (coronavirus) pandemic. The typology emerged from a content analysis of a large... more
In this article, we report on a typology of the demands of statistical and mathematical products (StaMPs) embedded in media items related to the COVID-19 (coronavirus) pandemic. The typology emerged from a content analysis of a large purposive sample of diverse media items selected from digital news sources based in four countries. The findings encompass nine categories of StaMPs: (1) descriptive quantitative information, (2) models, predictions, causality and risk, (3) representations and displays, (4) data quality and strength of evidence, (5) demographics and comparative thinking, (6) heterogeneity and contextual factors, (7) literacy and language demands, (8) multiple information sources, and (9) critical demands. We illustrate these categories via selected media items, substantiate them through relevant research literature, and point to categories that encompass new or enhanced types of demands. Our findings offer insights into the rich set of capabilities that citizens (includ...
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Research Interests: Psychology and Routledge
Despite repeated calls for development of statistical literacy among citizens, in fact there is a dearth of recent systematic empirical research on the actual mathematical and statistical demands of mainstream media. Hence, this study... more
Despite repeated calls for development of statistical literacy among citizens, in fact there is a dearth of recent systematic empirical research on the actual mathematical and statistical demands of mainstream media. Hence, this study aimed to develop a typology of the content of mathematical and statistical products and demands in the COVID-19 pandemic media, given the criticality of such information to citizens and societies alike. We conducted content-analysis of a purposive sample of over 300 media items from digital news sources based in four countries with different profiles. The analysis generated nine categories of new or enhanced types of knowledge and skill demands evident in the media items analyzed, such as regarding models and causality, data quality and strength of evidence, comparative thinking, literacy and language, official data sources, critical interpretation, and more. We discuss implications for current conceptual models and for instructional efforts focused on...
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Research Interests: Psychology and Routledge
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In this article, we document the support provided by highly recognised journals in Mathematics Education in response to the challenges faced by English non-dominant language (EnDL) authors when they attempt to publish in English. To... more
In this article, we document the support provided by highly recognised journals in Mathematics Education in response to the challenges faced by English non-dominant language (EnDL) authors when they attempt to publish in English. To address this issue, we first conducted a synthesis of research literature related to those influences that direct EnDL authors’ publication efforts towards English language journals and the associated challenges that result. Second, we gathered survey and interview data from participant editors-in-chief of leading journals in Mathematics Education about the support, enacted and planned, provided by their journal for EnDL authors and associated challenges. Finally, we discuss the findings of the study from the perspective of heteroglossia. Findings indicate that while a range of initiatives have been employed to support EnDL authors, current journal policies lag somewhat behind the plans of editors-in-chief, which have been limited, to date, by available ...
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espanolEste articulo es una adaptacion al frances de la publicacion de Geiger & Straser (2015) : The challenge of publication of english non dominant-language authors in mathematics education, en For the Learning of Mathematics, 35(3),... more
espanolEste articulo es una adaptacion al frances de la publicacion de Geiger & Straser (2015) : The challenge of publication of english non dominant-language authors in mathematics education, en For the Learning of Mathematics, 35(3), 35-41 (escrito en ingles originalmente). La adaptacion del texto al frances ha requerido incluir algunas partes adicionales para hacer que el articulo sea comprensible. Estas fueron realizadas por Claire Margolinas y complementadas por algunas reflexiones de los autores que son especificas para el contexto de Recherches en Didactique des Mathematiques. Las notas a pie de pagina corresponden a las de la edicion original del articulo. EnglishThis paper is an annotated translation from English into French of an article by Geiger and Straser (2015) : The challenge of publication for English non dominant-language authors in mathematics education. This article was first published in For the Learning of Mathematics, 35(3), 35-41. The translation required ann...
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Of the three theories of intellectual development that have had greatest influence on school classrooms since the turn of last century, behaviourist, constructivism and socio-culturalism, all were initially conceptualised before digital... more
Of the three theories of intellectual development that have had greatest influence on school classrooms since the turn of last century, behaviourist, constructivism and socio-culturalism, all were initially conceptualised before digital technologies were available. Further, whereas current reform agendas that emphasise the importance of social aspects of learning can draw theoretical underpinnings from socio-cultural or socio-constructivist perspectives of knowledge acquisition and meaning making, theoretical frameworks that help explain the role of collaborative interaction in technology rich classrooms are only beginning to emerge. This paper will consider the emergence of recent developments in theorising collaborative practice that incorporate the use of digital tools from a socially orientated theoretical perspective and attempt to draw connections with this emergence from the history of ICMI's involvement in this area.
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This paper considers the potential of Computer Algebra Systems (CAS) to enhance the processes associated with mathematical modelling and application tasks. In doing so, the role of technology in the cyclical development of mathematical... more
This paper considers the potential of Computer Algebra Systems (CAS) to enhance the processes associated with mathematical modelling and application tasks. In doing so, the role of technology in the cyclical development of mathematical models is considered in relation to current literature in this area. The analysis of data drawn from a one year study of three different secondary school classrooms indicates that CAS enabled technologies have a role to play as provocateurs of productive student-student-teacher interaction in both small group and whole class settings. Background This paper investigates the nature of the potential partnership between two powerful thinking tools – mathematical modelling and computer algebra systems (CAS) – in teaching and learning mathematics in the senior secondary school. Mathematical modelling – formulating a mathematical representation of a real world situation, using mathematics to derive results, and interpreting the results in terms of the given ...
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Data from a pilot study concerned with pre-service teachers’ perceptions of the numeracy demands on Australian teachers are reported. The sample comprised 211 students enrolled in pre-service teacher education courses at a large... more
Data from a pilot study concerned with pre-service teachers’ perceptions of the numeracy demands on Australian teachers are reported. The sample comprised 211 students enrolled in pre-service teacher education courses at a large Australian university. While most recognised the importance of mathematics and its applications in everyday life, less than half considered there were mathematical demands on teachers beyond their teaching domain. NAPLAN-related information data was used to examine the group’s ability to access, apply, and interpret the statistical information.
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Research Interests: Psychology and Numeracy
This paper reports on a year long, state wide research project that aimed to assist primary and secondary teachers to improve their teaching and learning practices through engagement with a new model of numeracy. Data collection included... more
This paper reports on a year long, state wide research project that aimed to assist primary and secondary teachers to improve their teaching and learning practices through engagement with a new model of numeracy. Data collection included sequence maps of participants' development as teachers of numeracy as elements of the model became more prominent in their thinking and planning. Semi-structured interviews were also used to clarify and expand upon teachers' perceptions of their own development. Findings include a propensity to begin with the dispositions element of the model but responses showed that in most cases all elements were eventually addressed by each teacher.
Research Interests: Psychology and Numeracy
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The purpose of this paper is to describe the processes utilised to develop an online learning module within the Opening Real Science (ORS) project – Modelling the present: Predicting the future. The module was realised through an... more
The purpose of this paper is to describe the processes utilised to develop an online learning module within the Opening Real Science (ORS) project – Modelling the present: Predicting the future. The module was realised through an interdisciplinary collaboration, among mathematicians, scientists and mathematics and science educators that drew on the enquirybased approach underpinning ORS as well as structuring devices and working practices that emerged during the course of the module development. The paper is a precursor to further research that will investigate the effectiveness of the module in terms of students’ learning and attitudes as well as the module development team members’ perspectives on the interdisciplinary collaboration that took place.
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This paper is a reflective critique of practice within the field of mathematics education in relation to the challenges faced by non-first-language-English speaking academics when they attempt to publish in English language research... more
This paper is a reflective critique of practice within the field of mathematics education in relation to the challenges faced by non-first-language-English speaking academics when they attempt to publish in English language research outlets. Data for this study are drawn from communications between a German and an Australian academic as the Australian assisted the German in negotiating aspects of translation bound by syntactic, semiotic, cultural, and colloquial language considerations. The paper concludes by raising questions about the issue of the use of English as a universal language for the dissemination of new knowledge and offers possible solutions to the problem.
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Numeracy is a general capability to be developed in all leami11g areas of the Australian Curriculum. We evaluated the numeracy demands of the F -10 curriculum, using a model of numeracy that incorporates mathematical knowledge,... more
Numeracy is a general capability to be developed in all leami11g areas of the Australian Curriculum. We evaluated the numeracy demands of the F -10 curriculum, using a model of numeracy that incorporates mathematical knowledge, dispositions, tool s, contexts, and a critical orientation to the use of mathematics. Findings of the history curriculum audit, presented in this paper, highlight the distinction between the numeracy demands and opportunities of the curriculum, and uncover mismatches between claims made about numeracy in the curriculum materials.
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The purpose of this article is to provide insight into how teachers identify initial ideas for the design of numeracy tasks. A design-based research approach was employed utilising classroom observations, video-stimulated recall... more
The purpose of this article is to provide insight into how teachers identify initial ideas for the design of numeracy tasks. A design-based research approach was employed utilising classroom observations, video-stimulated recall techniques and semi-structured teacher interviews. Data collection and analysis were informed by a rich model of numeracy as well as generic principals of task design synthesised from relevant literature. Data analysis indicated that there were at least two approaches to generating ideas for numeracy tasks both of which were compatible with the principles of task design employed in this study.
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In this article, we describe the generation of a Design and Implementation Framework for Mathematical Modelling Tasks (DIFMT) through a researcher-teacher collaboration. The purpose of the framework is to support holistic approaches to... more
In this article, we describe the generation of a Design and Implementation Framework for Mathematical Modelling Tasks (DIFMT) through a researcher-teacher collaboration. The purpose of the framework is to support holistic approaches to instructional modelling competency. This framework is underpinned by principles drawn from theory and praxis which are informed by the anticipatory capabilities that teachers require for the design and effective implementation of quality modelling tasks in secondary classrooms. A draft DIFMT was developed from a synthesis of research literature and was refined through an iterative process of task development, implementation and observation, reflection through teacher/student interviews, and revision of the framework. Each iteration made use of the most recent refinement of the co-constructed DIFMT, building theory while simultaneously addressing a problem in educational practice, consistent with a design-based methodology. Thus, the DIMFT developed organically throughout the project. While initial modelling exemplars were researcher-designed, the locus of responsibility moved to teachers as the project progressed. The DIFMT consists of two major components—principles for modelling task design and pedagogical architecture—each of which is structured around dimensions that include elaborations which detail the knowledge required for modelling as well as teacher and student capabilities.
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1. Learning and teaching algebra 2. Sense and nonsense in algebra 3. Beginnings 4. Developing algebraic skills 5. Patterns with squares 6. Functions and graphs 7. Creating and solving equations 8. Proportionality, growth and decay 9.... more
1. Learning and teaching algebra 2. Sense and nonsense in algebra 3. Beginnings 4. Developing algebraic skills 5. Patterns with squares 6. Functions and graphs 7. Creating and solving equations 8. Proportionality, growth and decay 9. Links to geometry 10. Trigonometry and circular functions 11. Sequences and series 12. The calculus: differentiation and integration Index
This chapter presents the framework for conceptualising and assessing adult numeracy and developing a reporting scale for the direct assessment of numeracy as part of the OECD’s Programme for the International Assessment of Adult... more
This chapter presents the framework for conceptualising and assessing adult numeracy and developing a reporting scale for the direct assessment of numeracy as part of the OECD’s Programme for the International Assessment of Adult Competencies (PIAAC Cycle 2). Numeracy as described here refers to adults’ skills in accessing, using and reasoning critically with mathematical content, information and ideas represented in multiple ways in order to engage in and manage the mathematical demands of a range of situations in adult life. The framework describes the conceptual and theoretical foundations behind the adult numeracy construct and the principles applied for assessing numeracy in PIAAC and the distribution of the numeracy assessment items by a range of task characteristics.
Research Interests: Psychology and Numeracy
Increasingly, digital technologies are being utilised to provide opportunities for teacher professional learning (PL) in fully online, blended and face-to-face environments. Videos have been used extensively across the three modes of... more
Increasingly, digital technologies are being utilised to provide opportunities for teacher professional learning (PL) in fully online, blended and face-to-face environments. Videos have been used extensively across the three modes of delivery but there appears little research on the conceptual framing underpinning their development. This article describes and analyses a research-informed instructional design approach taken to develop an online resource to support teacher PL. The approach utilised a conceptual framework consisting of an audit framework and model of numeracy for the twenty-first century to guide an audit of existing resources, gap analysis and production of an online resource. The purpose of the resource audit was to establish how existing resources support teachers’ understanding and enactment of numeracy across the curriculum. Gaps where teachers might benefit from new resources were identified through the resource audit and subsequent interviews with stakeholders. The conceptual framework was employed to inform the development of a suite of six videos: one to enhance teachers’ understanding of the meaning of numeracy; four to demonstrate teachers’ embedding of numeracy in particular subjects; and one that captured a collaborative planning session. This article adds to new knowledge within the discipline by providing insight into instructional design processes that could be employed in other contexts related to the identification and/or development of resources for online PL that target specific learning needs of teachers.