La programmation informatique dans la recherche et la formation en mathématiques au niveau universitaire

Une étude récente auprès de 302 mathématiciens canadiens révèle un écart intriguant : tandis que 43% des sondés utilisent la programmation informatique dans leur recherche, seulement 18% indiquent qu'ils emploient cette technologie dans leur enseignement (Buteau et coll., 2014). La première donnée reflète le potentiel énorme qu'a la programmation pour faire et apprendre des mathématiques. La deuxième donnée a inspiré ce mémoire : pourquoi existe-t-il un tel écart ? Pour répondre à cette question, nous avons mené une étude exploratoire qui cherche à mieux comprendre la place de la programmation dans la recherche et la formation en mathématiques au niveau universitaire. Des entrevues semi-dirigées ont été conduites avec 14 mathématiciens travaillant dans des domaines variés et à différentes universités à travers le pays. Notre analyse qualitative nous permet de décrire les façons dont ces mathématiciens construisent des programmes informatiques afin d'accomplir plusieurs tâches (p.e., simuler des phénomènes réels, faire des mathématiques « expérimentales », développer de nouveaux outils puissants). Elle nous permet également d'identifier des moments où les mathématiciens exposent leurs étudiants à certains éléments de ces pratiques en recherche. Nous notons toutefois que les étudiants sont rarement invités à concevoir et à écrire leurs propres programmes. Enfin, nos participants évoquent plusieurs contraintes institutionnelles : le curriculum, la culture départementale, les ressources humaines, les traditions en mathématiques, etc. Quelques-unes de ces contraintes, qui semblent limiter l'expérience mathématique des étudiants de premier cycle, pourraient être revues.

Etnomatemática quilombola: as relações dos saberes da matemática dialógica com as práticas socioculturais dos remanescentes de quilombo do Mola-Itapocu/PA

A pesquisa, etnomatemática quilombola: as relações dos saberes da matemática dialógica com as práticas socioculturais dos remanescentes de quilombo do Mola-Itapocu/PA, realizada de junho de 2003 a dezembro de 2004, foi norteada no estudo de caso etnográfico. O questionamento básico dessa dissertação expressa a preocupação de como se estabelecer relações entre as práticas socioculturais das teias de saberes matemáticos com a matemática escolar, sem negar os seus significados e o(s) seu(s) sentido(s), que são vivenciados na (re)construção das memórias cotidianas dos remanescentes de quilombo molense? Esta investigação teve como objetivos: identificar os significados, atribuídos pelos molenses, às suas práticas socioculturais, conectadas aos saberes matemáticos da cultura local, e estabelecer algumas relações entre a matemática escolar e a matemática praticada pelos remanescentes de quilombo do Mola-Itapocu/PA, sem dispensar os seus significados e o(s) sentido(s) das memórias das vivências cotidianas do contexto particular. No capítulo I, teço reflexões críticas acerca das relações entre as práticas da vida cotidiana e os saberes etnomatemáticos, relacionadas às memórias das vivências dos remanescentes de quilombo do Mola. Inicio tecendo memórias da matemática não escolar, seguidas dos saberes plurais das práticas matemáticas; depois, lanço olhares por dentro das investidas positivistas, para evidenciar como teias investidas negam a vida cotidiana dos saberes etnomatemáticos, por último, visito os olhares escolares lançados sobre os saberes etnomatemáticos. No capítulo II, faço uma breve análise das diferentes racionalidades presentes nas (etno)ciências, desvelando as faces da etnociência, ciência moderna e da ciência pós-moderna. No terceiro capítulo, construo a análise sob as convergências e as divergências entre os saberes matemáticos e a matemática escolar, vinculadas às teias: caminhando em terrenos áridos da lógica formal matemática; aos saberes etnomatemáticos; as reentrâncias das etnomatemáticas com a complexidade da vida e a lógica dialógica da etnomatemática. No quarto, evidencio as diferenças existentes entre a pesquisa experimental positivista e a pesquisa qualitativa, para, em seguida, tecer as possíveis relações dialógicas da pesquisa etnográfica com a etnomatemática, e no quinto, com base nas falas e nas observações das vivências socioculturais e os saberes matemáticos dos informantes, estabeleço algumas relações entre os saberes locais da matemática molense e a matemática escolar. Neste contexto, começo revisitando brevemente a história da educação do campo; seguida das teias das relações entre as práticas socioculturais e a matemática dialógica dos molenses; por último, teço a alfabetização das teias de saberes matemáticos e de saberes das práticas socioculturais. A etnomatemática quilombola, incessantemente, construída nas relações da matemática dialógica com as práticas educativas molenses, evidenciou a linguagem, as memórias e as representações dos saberes matemáticos e etnocientífico, articulada às possíveis relações com os saberes da matemática escolar do ensino multisseriado.

Práticas algébricas no contexto da modelagem compreendida como proposta pedagógica

Pós-graduação em Educação Matemática - IGCE

Achieving growth in NAPLAN: characteristics of successful schools

Since 2008, Australian students in Years 3, 5, 7 and 9 have been assessed through the National Assessment Program – Literacy and Numeracy (NAPLAN). In 2015, the Office of the Chief Scientist commissioned a study into the processes used by schools that demonstrated successful outcomes in NAPLAN numeracy. A team of researchers across Australia conducted a total of 55 case studies in order to identify practices and policies that were consistent between successful schools. Data were gathered through surveys, classroom observations and interviews conducted with school leaders, teachers, students, and parents. Overall findings indicated there were a number of characteristics that were common to schools who achieved sustained growth in NAPLAN results. These characteristics included the development and implementation of policies that specifically supported numeracy learning and teaching, use of a variety of data sources to develop and refine mathematics teaching programs, team planning, strong numeracy leadership and a consistent school approach to teaching mathematics. This paper presents the findings from three case study schools as illustrative examples of how the identified characteristics were enacted in practice. The study has particular implications for policy makers and school leaders who may be seeking ways to develop consistent and effective mathematical practices in their own schools.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

Student identities in a mathematical community of practice : radical visible pedagogy and the teacher collective

This study investigated the practices of two teachers in a school that was successful in enabling the mathematical learning of students in Years 1 and 2, including those from backgrounds associated with low mathematical achievement. The study explained how the practices of the teachers constituted a radical visible pedagogy that enabled equitable outcomes. The study also showed that teachers’ practices have collective power to shape students’ mathematical identities. The role of the principal in the school was pivotal because she structured curriculum delivery so that students experienced the distinct practices of both teachers.

Rich and purposeful mathematical knowledge of mothers and children in a Torres Strait Islander community

This paper focuses on a pilot study that explored the situated mathematical knowledge of mothers and children in one Torres Strait Islander community in Australia. The community encouraged parental involvement in their children’s learning and schooling. The study explored parents’ understandings of mathematics and how their children came to learn about it on the island. A funds of knowledge approach was used in the study. This approach is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being (Moll, 1992). The participants, three adults and one child are featured in this paper. Three separate events are described with epiphanic or illuminative moments analysed to ascertain the features that enabled an understanding of the nature of the mathematical events. The study found that Indigenous ways of knowing of mathematics were deeply embedded in rich cultural practices that were tied to the community. This finding has implications for teachers of children in the early years. Where school mathematics is often presented as disembodied and isolated facts with children seeing little relevance, learning a different perspective of mathematics that is tied to the resources and practices of children’s lives and facilitated through social relationships, may go a long way to improving the engagement of children and their parents in learning and schooling.

Early mathematical learning: Number processing skills and executive function at 5 and 8 years of age

This research investigated differences and associations in performance in number processing and executive function for children attending primary school in a large Australian metropolitan city. In a cross-sectional study, performance of 25 children in the first full-time year of school, (Prep; mean age = 5.5 years) and 21 children in Year 3 (mean age = 8.5 years) completed three number processing tasks and three executive function tasks. Year 3 children consistently outperformed the Prep year children on measures of accuracy and reaction time, on the tasks of number comparison, calculation, shifting, and inhibition but not on number line estimation. The components of executive function (shifting, inhibition, and working memory) showed different patterns of correlation to performance on number processing tasks across the early years of school. Findings could be used to enhance teachers’ understanding about the role of the cognitive processes employed by children in numeracy learning, and so inform teachers’ classroom practices.

Building teachers' pedagogy practices in reasoning, to improve students' dispositions towards mathematics

Drawing on participatory action research, this study identifies the pedagogies necessary to advance reasoning, which is one of the proficiencies from the Australian Curriculum Mathematics, and explores how reasoning leads to greater productive disposition. With the current emphasis on STEM in schools, this research is timely. This thesis makes an original and substantive contribution to the understanding of why and how teachers can most effectively advance student proficiency in reasoning through targeted instructional strategies and style of instruction. The study explores the ways in which teacher practices, when focused on reasoning, enhance the disposition of students towards greater mathematical proficiency.

Intervention strategies on teachers focused on creating meaningful educational environments for mathematical abilities development

This article describes an intervention process undertaken in a training program for preschool and first grade teachers from public schools in Cali, Colombia. The objective of this process is to provide a space for teachers to reflect on pedagogical practices which allow them to generate educational processes that foster children’s understanding of mathematical knowledge in the classroom. A set of support strategies was presented for helping teachers in the design, analysis and implementation of learning environments as meaningful educational spaces. Furthermore, participants engaged in an analysis of their own intervention modalities to identify which modalities facilitate the development of mathematical abilities in children. In order to ascertain the transformations in the teachers’ learning environments, the mathematical competences and cognitive processes underlying the activities proposed in the classroom, as well as teacher intervention modalities and the types of student participation in classroom activities were examined both before and after the intervention process. Transformations in the teachers’ conceptions about the children’s abilities and their own practices in teaching mathematics in the classroom were evidenced.

Risk pricing practices in finance, insurance and construction

A review of current risk pricing practices in the financial, insurance and construction sectors is conducted through a comprehensive literature review. The purpose was to inform a study on risk and price in the tendering processes of contractors: specifically, how contractors take account of risk when they are calculating their bids for construction work. The reference to mainstream literature was in view of construction management research as a field of application rather than a fundamental academic discipline. Analytical models are used for risk pricing in the financial sector. Certain mathematical laws and principles of insurance are used to price risk in the insurance sector. construction contractors and practitioners are described to traditionally price allowances for project risk using mechanisms such as intuition and experience. Project risk analysis models have proliferated in recent years. However, they are rarely used because of problems practitioners face when confronted with them. A discussion of practices across the three sectors shows that the construction industry does not approach risk according to the sophisticated mechanisms of the two other sectors. This is not a poor situation in itself. However, knowledge transfer from finance and insurance can help construction practitioners. But also, formal risk models for contractors should be informed by the commercial exigencies and unique characteristics of the construction sector.

Communities of mathematical inquiry : a primary pedagogy in peril

This paper outlines some examples from an Australian education system, and its classrooms, that provide evidence of practices that are considered as antithetical to establishing and maintaining Communities of Mathematical Inquiry (CoMI). Although some possible solutions are posed, implementation is left open for readers to consider, as contexts vary widely from jurisdiction to jurisdiction.

Assessment of mathematical development in early childhood : some views of preschool practitioners in regional and rural Australia

As part of the project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice directors, teachers, and assistants in prior-to-school settings from regional and rural eastern Australia were interviewed to ascertain their beliefs and practices concerning early childhood mathematics. This paper reports the responses to  uestions about their assessment of children’s mathematical activity and development. The practitioners provided examples of both incidental and planned assessment activities, the different forms these took, methods of recording, and how the results were used.

Mathematical thinking of preschool children in rural and regional Australia : research and practice

At what age do young children begin thinking mathematically? Can young children work on mathematical problems? How do early childhood educators ensure young children feel good about mathematics? Where do early childhood educators learn about suitable mathematics activities?

A good early childhood start in mathematics is critical for later mathematics success. Parents, carers and early childhood educators are teaching mathematics, either consciously or unconsciously, in any social interaction with a child.

Mathematical Thinking of Preschool Children in Rural and Regional Australia is an extension of a conference of Australian and New Zealand researchers that identified a number of important problems related to the mathematical learning of children prior to formal schooling. A project team of 11 researchers from top Australian universities sought to investigate how early childhood education can best have a positive influence on early mathematics learning.

The investigation complements and extends the work of Project Good Start by focusing attention on critical aspects of parents, carers and early childhood educators who care for young children. Early childhood educators from regional and rural New South Wales, Queensland and Victoria were interviewed, following a set of structured questions. The questions focused on: children’s mathematics learning; support for mathematics teaching; use of technology; attitudes to mathematics; and assessment and record keeping.

The researchers also reviewed research focusing on the mathematical capacities and potential foundations for further mathematical development in young children (0–5 years) published in the last decade and produced an annotated bibliography. This should provide a good basis for further research and reading.

Based upon the results of this investigation, the researchers make 11 recommendations for improving the practices of early childhood education centres in relation to young children’s mathematical thinking and development. The implications for policy and decision makers are outlined for teacher education, the provision of resources and further research.

Distinguishing between mathematics classrooms in Australia, China, Japan, Korea and the USA through the lens of the distribution of responsibility for knowledge generation : public oral interactivity and mathematical orality

The research reported in this paper examined spoken mathematics in particular well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA from the perspective of the distribution of responsibility for knowledge generation in order to identify similarities and differences in classroom practice and the implicit pedagogical principles that underlie those practices. The methodology of the Learner’s Perspective Study (LPS) documented the voicing of mathematical ideas in public discussion and in teacher-student conversations and the relative priority accorded by different teachers to student oral contributions to classroom activity. Significant differences were identified among the classrooms studied, challenging simplistic characterisations of ‘the Asian classroom’ as enacting a single pedagogy, and suggesting that, irrespective of cultural similarities, local pedagogies reflect very different assumptions about learning and instruction. We have employed spoken mathematical terms as a form of surrogate variable, possibly indicative of the location of the agency for knowledge generation in the various classrooms studied (but also of interest in itself). The analysis distinguished one classroom from another on the basis of “public oral interactivity” (the number of utterances in whole class and teacher-student interactions in each lesson) and “mathematical orality” (the frequency of occurrence of key mathematical terms in each lesson). Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. In particular, the results suggest that one characteristic that might be identified with a national norm of practice could be the level of mathematical orality: relatively high mathematical orality characterising the mathematics classes in Shanghai with some consistency, while lessons in Seoul and Hong Kong consistently involved much less frequent spoken mathematical terms. The relative contributions of teacher and students to this spoken mathematics provided an indication of how the responsibility for knowledge generation was shared between teacher and student in those classrooms. Specific analysis of the patterns of interaction by which key mathematical terms were introduced or solicited revealed significant differences. It is suggested that the empirical investigation of mathematical orality and its likely connection to the distribution of the responsibility for knowledge generation are central to the development of any theory of mathematics instruction.