Le développement d’une séquence d’enseignement/apprentissage basée sur l’histoire de la numération pour des élèves du troisième cycle du primaire

Notre contexte pratique — nous enseignons à des élèves doués de cinquième année suivant le programme international — a grandement influencé la présente recherche. En effet, le Programme primaire international (Organisation du Baccalauréat International, 2007) propose un enseignement par thèmes transdisciplinaires, dont un s’intitulant Où nous nous situons dans l’espace et le temps. Aussi, nos élèves sont tenus de suivre le Programme de formation de l’école québécoise (MÉLS Ministère de l'Éducation du Loisir et du Sport, 2001) avec le développement, notamment, de la compétence Résoudre une situation-problème et l’introduction d’une nouveauté : les repères culturels. Après une revue de la littérature, l’histoire des mathématiques nous semble tout indiquée. Toutefois, il existe peu de ressources pédagogiques pour les enseignants du primaire. Nous proposons donc d’en créer, nous appuyant sur l’approche constructiviste, approche prônée par nos deux programmes d’études (OBI et MÉLS). Nous relevons donc les avantages à intégrer l’histoire des mathématiques pour les élèves (intérêt et motivation accrus, changement dans leur façon de percevoir les mathématiques et amélioration de leurs apprentissages et de leur compréhension des mathématiques). Nous soulignons également les difficultés à introduire une approche historique à l’enseignement des mathématiques et proposons diverses façons de le faire. Puis, les concepts mathématiques à l’étude, à savoir l’arithmétique, et la numération, sont définis et nous voyons leur importance dans le programme de mathématiques du primaire. Nous décrivons ensuite les six systèmes de numération retenus (sumérien, égyptien, babylonien, chinois, romain et maya) ainsi que notre système actuel : le système indo-arabe. Enfin, nous abordons les difficultés que certaines pratiques des enseignants ou des manuels scolaires posent aux élèves en numération. Nous situons ensuite notre étude au sein de la recherche en sciences de l’éducation en nous attardant à la recherche appliquée ou dite pédagogique et plus particulièrement aux apports des recherches menées par des praticiens (un rapprochement entre la recherche et la pratique, une amélioration de l’enseignement et/ou de l’apprentissage, une réflexion de l’intérieur sur la pratique enseignante et une meilleure connaissance du milieu). Aussi, nous exposons les risques de biais qu’il est possible de rencontrer dans une recherche pédagogique, et ce, pour mieux les éviter. Nous enchaînons avec une description de nos outils de collecte de données et rappelons les exigences de la rigueur scientifique. Ce n’est qu’ensuite que nous décrivons notre séquence d’enseignement/apprentissage en détaillant chacune des activités. Ces activités consistent notamment à découvrir comment différents systèmes de numération fonctionnent (à l’aide de feuilles de travail et de notations anciennes), puis comment ces mêmes peuples effectuaient leurs additions et leurs soustractions et finalement, comment ils effectuaient les multiplications et les divisions. Enfin, nous analysons nos données à partir de notre journal de bord quotidien bonifié par les enregistrements vidéo, les affiches des élèves, les réponses aux tests de compréhension et au questionnaire d’appréciation. Notre étude nous amène à conclure à la pertinence de cette séquence pour notre milieu : l’intérêt et la motivation suscités, la perception des mathématiques et les apprentissages réalisés. Nous revenons également sur le constructivisme et une dimension non prévue : le développement de la communication mathématique.

The potentials of student initiated netspeak in a middle primary science-inspired mutliliteracies project

There is no denying that the information technology revolution of the late twentieth century has arrived. Whilst not equitably accessible for many, others hold high expectations for the contributions online activity will make to student learning outcomes. Concurrently, and not necessarily consequentially, the number of science and technology secondary school and university graduates throughout the world has declined substantially, as has their motivation and engagement with school science (OECD, 2006). The aim of this research paper is to explore one aspect of online activity, that of forum-based netspeak (Crystal, 2006), in relation to the possibilities and challenges it provides for forms of scientific learning. This paper reports findings from a study investigating student initiated netspeak in a science inspired multiliteracies (New London Group, 2000) project in one middle primary (aged 7-10 years) multi-age Australian classroom. Drawing on the theoretical description of the Five phases of enquiry proposed by Bybee (1997), an analytic framework is proffered that allows identification of student engagement, exploration, explanation, elaboration and evaluation of scientific enquiry. The findings provide insight into online forums for advancing learning in and motivation for science in the middle primary years.

The differential recognition of children’s cultural practices in middle primary literacy classrooms

This paper argues that teachers’ recognition of children’s cultural practices is an important positive step in helping socio-economically disadvantaged children engage with school literacies. Based on twenty-one longitudinal case studies of children’s literacy development over a three-year period, the authors demonstrate that when children’s knowledges and practices assembled in home and community spheres are treated as valuable material for school learning, children are more likely to invest in the work of acquiring school literacies. However they show also that whilst some children benefit greatly from being allowed to draw on their knowledge of popular culture, sports and the outdoors, other children’s interests may be ignored or excluded. Some differences in teachers’ valuing of home and community cultures appeared to relate to gender dimensions.

Investigating literacy years 4-9 : a pilot. Final report.

Investigating Literacy Years 4-9: A pilot acknowledges that the literacy required of students in the middle years of schooling changes as they begin to read and write to learn across the subject areas using various resources and media. Teachers begin to look for evidence of understanding of concepts, content details, appropriate genre uses and the capacity to work with extended and complex texts. Yet, in comparison to the early years, there has been relatively little research conducted during this period of schooling, especially Years 4-7 of primary schooling (Comber et al, 2002). However, evidence suggests that gaps between those who perform highly and those who perform poorly on standardised measures of literacy increase rather than decrease, and these gaps relate to social background. Hence there is a need to investigate how different school communities with diverse student populations design rich curriculum at these stages of schooling and explicitly teach young people to handle new and changing literacy demands.

Surveying the field: Primary school teachers’ conceptions of the literacy capabilities of recently graduated primary school teachers

In 2015, ALEA National Council provided funds to support the implementation of a research project which was undertaken by a group of teacher educators and researchers from a range of universities across three Australian states. Stage one of the project, which is reported on here, examined primary school teachers’ perceptions of the personal and professional literacy capabilities of recently graduated primary school teachers. This stage of the project also examined primary school teachers’ perceptions of the impact of initial teacher education on the personal and professional literacy capabilities of recently graduated primary school teachers. The project team, led by Associate Professor Beryl Exley (Queensland University of Technology), included Chief Investigators Dr Eileen Honan (The University of Queensland), Associate Professor Lisa Kervin (University of Wollongong), Associate Professor Alyson Simpson (University of Sydney) and Dr Muriel Wells (Deakin University), with Dr Sandy Muspratt as the Statistical Analyst and Lesley Friend as the Research Assistant with primary responsibility for the publication of the online survey.

Addressing diversity and inclusion in the early years in conflict-affected societies: A case study of the Media Initiative for Children – Northern Ireland

This article reports on the development and systematic evaluation of an innovative early years programme aimed at encouraging young children to respect differences within a deeply-divided society that is emerging out of a prolonged period of violent conflict. The programme, the Media Initiative for Children – Northern Ireland, has been the product of a partnership between an US-based organisation (the Peace Initiatives Institute) and NIPPA – The Early Years Organisation and has been supported by academic research and the efforts of a range of voluntary and statutory organisations. It has attempted to encourage young children to value diversity and be more inclusive of those who are different to themselves through the use of short cartoons designed for and broadcast on television as well as specially-prepared curricular materials for use in pre-school settings. To date the programme has been delivered through 200 settings to approximately 3,500 pre-school children across Northern Ireland. This article describes how the programme was developed and implemented as well as the rigorous approach taken to evaluating its effects on young children’s attitudes and awareness. Key lessons from this are identified and discussed in relation to future work in this area.

Apendicitis aguda perforada en adultos; aproximación a las inequidades sociales en salud, Bogotá 2012

La perforación del apéndice es una complicación temprana de la apendicitis aguda, demoras en el diagnóstico o tratamiento incrementan la tasa de perforación. Se desconoce si la perforación dl apéndice es un reflejo de inequidades sociales. Se pretendió determinar la asociación de la apendicitis aguda perforada en adultos y la equidad en acceso a salud. Estudio tipo cohorte retrospectivo documental, de historias clínicas de pacientes con apendicitis aguda; el análisis se realizó con Stata 11.1 y Epi-info. Los resultados se presentaron en tablas y figuras. Se incluyeron 540 casos (292 hombre y 248 mujeres), el grupo de edad que aporto más datos fue el de 18 a 49 años (391 pacientes); el tiempo medio de síntomas a consulta fue de 37,45 horas, y de 5,3 horas para el paso a cirugía desde el ingreso, fueron solicitadas 76 ecografías y 53 tomografías, 50 interconsultas a urología y 10 a ginecología hasta el diagnostico. El grupo de mayores de 49 años, el estrato socioeconómico tres y la tomografía fueron factores de riesgo independientes para perforación del apéndice. El análisis multivariado mostró asociación lineal entre el estrato socioeconómico y tiempo de síntomas al ingreso, tiempo para paso a cirugía, solicitud de ayudas diagnósticas e interconsultas, con buena significación estadística. La apendicitis aguda perforada en adultos, podría ser un indicador de inequidad en salud. Se requiere de estudios multi-céntricos, con mayor tiempo de evaluación y muestra para demostrar si el apéndice perforado es un trazador de inequidades en salud en Colombia.

Fun or profit : primary students' perceptions of mathematics and science

As the number of students pursuing mathematics and science in higher education decline, it becomes imperative· that we look for the causes of the decline. As part of the Australian Improving Middle Years Mathematics and Science (IMYMS) project, students were asked to rate their perceptions of classroom practice in mathematics and science and their attitudes to these subjects. Results of this survey reveal little difference in perceptions of classroom practice, but significant differences in students' attitudes between mathematics and science. Differences were particularly evident for items relating to the usefulness of mathematics and science (mathematics was more useful) and enjoyment of the subjects (science is more fun). If teachers are aware of such perspectives, it may be possible to change students' attitudes.

Effective student engagement depends on students enjoying their studies in mathematics and science, being confident in their ability and recognising the relevance of these subjects to everyday life, now and in the future.
(Education Training Committee, 2006, p. xvii)

Science and technology are the widely acknowledged foundation of Australia's future development. Underpinning these are the key learning areas of mathematics and science. However, Australia is experiencing a decline in numbers of mathematics and science students in higher education. Moreover, studies over the last two decades have shown a general decline in Australian students' interest and enjoyment of science across the compulsory secondary school years, with a particularly sharp decline across the primary to secondary school transition (e.g. Adams, Doig, & Rosier 1991; Goodrum, Hackling, & Rennie, 200 I) and a decline in the numbers of students studying' advanced mathematical courses in upper secondary school (Thomas, 2000).

Improving teaching and learning in the middle years of schooling (Years 5 to 9) is receiving particular attention because of the coincidence of the disengagement of students with the significance of these years for the preparation of students for their future role in society. Thus the Improving Middle Years Mathematics and Science: The role of subject cultures in school and teacher change (IMYMS) project, which is the source of data for this paper, is investigating the role of mathematics and science' knowledge and subject cultures in mediating change processes in the middle years of schooling.

Mathematics and science are sometimes seen as "love-hate" subjects, rating highest for subjects disliked, but also rating relatively highly among preferred subjects (Hendley & Stables, 1996). Students, even primary aged students, can often shed light on what constitutes good practice (see, for example, 'van den Heuvel-Panhuizen, 2005). Students' attitudes towards mathematics and science and their perceptions of what they regard as positive aspects of classroom practice have been shown to decline from the primary years to junior secondary (Race, 2000). The decline in interest in science in the early years of secondary school is of particular concern, since it is in these years that attitudes to the pursuit of science subjects and careers are formed (Speering & Rennie, 1996). Students' negative attitude towards the relevance of science ,content for their lives was a strong theme in the report by Goodrum, Hackling, & Rennie (2001) on the status and quality of teaching and learning of science.

As part of the IMYMS project, the IMYMS Student Survey was administered to all students in 2004 and 2005. The survey included a 36 item section on students' perceptions of classroom practice and attitudes towards mathematics and science, and a 24 item section on students' learning preferences. Students completed separate, parallel surveys for mathematics and science.

This paper focuses on students' perceptions and attitudes. It explores the differences in 700 Year 5 and 6 students' perceptions of their learning environment and their attitudes to mathematics and science during 2005, the second (and final) year of schools , involvement in the IMYMS project.

Putting literacy in the middle: key learnings from the middle years literacy research project

This article discusses the Middle Years Literacy Research Project and its design. The authors report on key findings and recommendations from the research. In particular the authors look at what is distinctive about teaching adolescent learners in middle years and what does the research show that is distinctive about teaching, the ways that literacy is understood and talked about, its various positioning in the middle years and, connections between effective literacy and effective learning. The article describes a Four Resources model as a framework for literacy teaching and learning for middle year education; literacy leadership, coordination, professional development and collaborative partnerships; and, what school strategies have the most potential to bring about long-term change and improvement in students' literacy and learning outcomes.

A Jaworskian analysis of four senior class primary teachers endeavouring to teach mathematics from a constructivist-compatible perspective

A constructivist philosophy underlies the Irish primary mathematics curriculum. As constructivism is a theory of learning its implications for teaching need to be addressed. This study explores the experiences of four senior class primary teachers as they endeavour to teach mathematics from a constructivist-compatible perspective with primary school children in Ireland over a school-year period. Such a perspective implies that children should take ownership of their learning while working in groups on tasks which challenge them at their zone of proximal development. The key question on which the research is based is: to what extent will an exposure to constructivism and its implications for the classroom impact on teaching practices within the senior primary mathematics classroom in both the short and longer term? Although several perspectives on constructivism have evolved (von Glaserfeld (1995), Cobb and Yackel (1996), Ernest (1991,1998)), it is the synthesis of the emergent perspective which becomes pivotal to the Irish primary mathematics curriculum. Tracking the development of four primary teachers in a professional learning initiative involving constructivist-compatible approaches necessitated the use of Borko’s (2004) Phase 1 research methodology to account for the evolution in teachers’ understanding of constructivism. Teachers’ and pupils’ viewpoints were recorded using both audio and video technology. Teachers were interviewed at the beginning and end of the project and also one year on to ascertain how their views had evolved. Pupils were interviewed at the end of the project only. The data were analysed from a Jaworskian perspective i.e. using the categories of her Teaching Triad of management of learning, mathematical challenge and sensitivity to students. Management of learning concerns how the teacher organises her classroom to maximise learning opportunities for pupils. Mathematical challenge is reminiscent of the Vygotskian (1978) construct of the zone of proximal development. Sensitivity to students involves a consciousness on the part of the teacher as to how pupils are progressing with a mathematical task and whether or not to intervene to scaffold their learning. Through this analysis a synthesis of the teachers’ interpretations of constructivist philosophy with concomitant implications for theory, policy and practice emerges. The study identifies strategies for teachers wishing to adopt a constructivist-compatible approach to their work. Like O’Shea (2009) it also highlights the likely difficulties to be experienced by such teachers as they move from utilising teacher-dominated methods of teaching mathematics to ones in which pupils have more ownership over their learning.

Two of everything: developing functional thinking in the primary grades through children's literature

Traditionally algebra has been regarded as the domain of the secondary school years in Australia and many other countries. Non-mathematics teachers, parents and students often narrowly regard algebra as the manipulation of symbols adhering to tightly prescribed rules (Serow, Callingham & Muir, 2013). It is now recognised, however, that foundational ideas associated with algebraic thinking can, and should be, included in mathematics curricula in the pre-school and primary years (Bobis, Mulligan & Lowrie, 2009). This stance is reflected in the Australian Curriculum: Mathematics (Australian Curriculum Assessment & Reporting Authority, 2012) which extends key algebraic ideas to patterns and generalisations, and acknowledges that number and algebra are developed together as each enriches the study of the other. This article explores the concept of functional thinking and demonstrates how the story, ‘Two of Everything’ (Hong, 1993) is employed as a springboard for developing functional thinking with students from the early years through to upper primary schooling.

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

(Re)focusing the Lens to Make Diversity and Difference Visible : Teaching for Quality and Equity

Despite the evidence that Australia’s children are learning literacy, there is also significant evidence that the poorest and most disadvantaged children are being left behind. To date our understanding of the place of transitions in this has been limited, although there has been work on the fourth grade slump (Gee, 2000, 2008), the transition from primary years to secondary years (e.g. Bahr & Pendergast, 2007; Pendergast & Bahr, 2005, 2010), and transitions when changing schools (Henderson, 2008). In this chapter, we consider the notion of transitioning, as we unpack issues related to recognising and valuing student diversity and difference. We want to highlight ways of providing high quality and high equity literacy pedagogy and literacy outcomes for middle years students. We will also discuss the importance of recognising that students transit to schools and school learning from other significant contexts, each with their own combinations of literacy practices, rituals and values.

Teachers' conceptions of how to engage students through inquiry learning : foundations for STEM

The advocacy for inquiry-based learning in contemporary curricula assumes the principle that students learn in their own way by drawing on direct experience fostered by the teacher. That students should be able to discover answers themselves through active engagement with new experiences was central to the thinking of eminent educators such as Pestalozzi, Dewey and Montessori. However, even after many years of research and practice, inquiry learning as a referent for teaching still struggles to find expression in the average teachers' pedagogy. This study drew on interview data from 20 primary teachers. A phenomenographic analysis revealed three conceptions of teaching that support inquiry learning in science in the primary years of schooling: (a) The Experience-centred conception where teachers focused on providing interesting sensory experiences to students; (b) The Problem-centred conception where teachers focused on challenging students with engaging problems; and (c) The Question-centred conception where teachers focused on helping students to ask and answer their own questions. Understanding teachers' conceptions of teaching has implications for both the enactment of inquiry teaching in the classroom as well as the uptake of new teaching behaviours during professional development, with enhanced outcomes for engaging students in STEM.

Cooperative education through a large scale industry-school partnership

In most of the advanced economies, students are losing interest in careers especially in en¬gineering and related industries. Hence, western economies are confronting a critical skilled labour shortage in areas of technology, science and engineering. Decisions about career pathways are made as early as the primary years of schooling and hence cooperation be¬tween industry and schools to attract students to the professions is crucial. The aim of this paper is to document how the organisational and institutional elements of one industry-school partnerships initiative — The Gateway Schools Program — contribute to productive knowledge sharing and networking. In particular this paper focuses on an initiative of an Australian State government in response to a perceived crisis around the skills shortage in an economy transitioning from a localised to a global knowledge production economy. The Gateway Schools initiative signals the first sustained attempt in Australia to incorporate schools into production networks through strategic partnerships linking them to partner organisations at the industry level. We provide case examples of how four schools opera¬tionalise the partnerships with the minerals and energy industries and how these partner¬ships as knowledge assets impact the delivery of curriculum and capacity building among teachers. Our ultimate goal is to define those characteristics of successful partnerships that do contribute to enhanced interest and engagement by students in those careers that are currently experiencing critical shortages.