Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Interdisciplinary modelling

This article examines one approach to promoting creative and flexible use of mathematical ideas within an interdisciplinary context in the primary curriculum, namely, through modelling. Three classes of fifth-grade children worked on a modelling problem, The First Fleet (Australia’s settlement), situated within the curriculum domains of science and studies of society and environment. Reported here are the cycles of development displayed by one group of children as they worked the problem, together with the range of models created across the classes. Children developed mathematisation processes that extended beyond their regular curriculum, including identifying and prioritising key problem elements, exploring relationships among elements, quantifying qualitative data, ranking and aggregating data, and creating and working with weighted scores. Aspects of Goldin’s (2000, 2007) affective structures also appeared to play an important role in the children's mathematical developments.

Comprehension as social and intellectual practice : rebuilding curriculum in low socioeconomic and cultural minority schools

This article reframes the concept of comprehension as a social and intellectual practice. It reviews current approaches to reading instruction for linguistically and culturally diverse and low socioeconomic students, noting an emphasis on comprehension as autonomous skills. The Four Resources model (Freebody & Luke, 1990) is used to make the case for the integration of comprehension instruction with an emphasis on student cultural and community knowledge, and substantive intellectual and sociocultural content in elementary school curricula. Illustrations are drawn from research underway on the teaching of literacy in primary schools in low SES communities.

Curriculum design innovation in flexible science teaching

In this paper you will be introduced to a number of principles which can be used to inform good teaching practice and rigorous curriculum design. Principles relate to: * Application of a common sequence of events for how learners learn; * Accommodating different learning styles; * Adopting a purposeful approach to teaching and learning; * Using assessment as a central driving force in the curriculum and as an organising structure leading to coherence of teaching and learning approach; and * The increasing emphasis that is being placed on the development of generic graduate competencies over and above discipline content knowledge. The principles are particularly significant in relation to adult learning. The paper will use three specific applications as illustrations to help you to learn how these principles can be applied. The illustrations are taken from a second year subject in supercomputing that uses scientific case studies. The subject has been developed (with support from Silicon Graphics Inc. and Intel) to be taught entirely via the Internet.

Teaching middle years : rethinking curriculum, pedagogy and assessment [2nd. ed.]

The middle years of schooling are increasingly recognised as a crucial stage in students' lives, one that has significant consequences for ongoing educational success. International research indicates that young adolescents benefit from programs designed especially for their needs. Teaching Middle Years offers a systematic overview of the philosophy, principles and issues in middle schooling. It includes contributions from academics and school-based practitioners on intellectual and emotional development in early adolescence, pedagogy, curriculum and assessment of middle years students. This second edition is fully revised to reflect the latest research findings. It includes new chapters on students with diverse needs, school partnerships with families and community, and effective team teaching. Also new to this edition is a chapter that brings middle schooling concepts to life by providing real examples of reform in action.

Teaching middle years : rethinking curriculum, pedagogy and assessment [1st ed.]

The middle years of schooling are increasingly recognised as a crucial stage in students' lives, one that has significant consequences for ongoing educational success. International research indicates that young adolescents benefit from programs designed especially for their needs, and the middle years have become an important reform issue for education systems. Teaching Middle Years offers a systematic overview of the philosophy, principles and issues in middle schooling. It includes contributions from academics and school-based practitioners on intellectual and emotional development in early adolescence, pedagogy, curriculum and assessment of middle years students. Written for teachers, student teachers, education leaders and policy makers, Teaching Middle Years is an essential resource for anyone involved in educating young adolescents. Teaching Middle Years is the first comprehensive Australian book to match and surpass the quality of many overseas publications.'

Trailblazers

A recent study in the United Kingdom (Ofsted Report 2008) provides strong evidence that well-organized activities outside the classroom contribute significantly to the quality and depth of children's learning, including their personal, social, and emotional development. Outdoor math trails supply further evidence of such enhanced learning: They are meaningful, stimulating, challenging, and exciting for children. Most important, these trails invite all students, irrespective of their classroom achievement level, to participate successfully in the problem activities and gain a sense of pride in the mathematics they create. Additionally, Math trails empower lifelong learning. Integrating "outside" mathematics with "inside" classroom mathematics can sow the seeds to develop flexible, creative, future-oriented mathematical thinkers and problem solvers. Here, English et al discuss how to design and implement math trails to promote active, meaningful, real-world mathematical learning beyond the classroom walls.

Curriculum in postcolonial contexts

This entry uses postcolonial perspectives to interrogate relations of power in the curriculum that are deeply influenced by the aftermath of European colonialism. The insights gained help to analyze continuing inequity in material, cultural, ideological and social aspects of the curriculum. This is a starting point for working out strategies of change and identifying the complexities and contestations which accompany change. The entry provides an introduction to key aspects of postcolonial theory, examines various aspects of the curriculum which are problematized by postcolonial perspectives, and explores ways in which curriculum decolonization is advocated in terms of social equity, race, cultural and gender identity, language and knowledge paradigms.

Will the Australian national curriculum up the intellectual ante in classrooms?

A critical review of the current and potential impacts of the Australian National Curriculum on the enacted curriculum in primary schools, with specific attention to issues of equity and social justice.

Comprehension and content : planning literacy curriculum in low socioeconomic and culturally diverse schools

This article reframes comprehension as a social and intellectual practice. It reviews literature on current approaches to reading instruction for linguistically and culturally diverse and low socioeconomic students, noting the current policy emphasis on the teaching of comprehension as autonomous skills and ‘strategies’. The Four Resources model (Freebody & Luke, 1990) is used to situate comprehension instruction with an emphasis on student cultural and community knowledge, and substantive intellectual and sociocultural content in elementary and middle school curricula. Illustrations are drawn from research underway on the teaching of literacy in low socioeconomic schools.

Curriculum evaluation : approaches and methodologies

Curriculum evaluation, as a field of study, is dynamic. For over the years it has been responsive to the developments in the conceptualization of curriculum and the associated processes of curriculum change. The concept of curriculum is integral to curriculum evaluation and can be defined in terms of what can and shall be taught to whom, when, where, how, and why. Much of the decision making relates to what knowledge is to be selected for inclusion in the curriculum.

The development of a "Good Practice Guide" for first year curriculum development, revision and evaluation : a moving feast

Since 2002 QUT has sponsored a range of first year-focussed initiatives, most recently the Transitions In Project (TIP) which was designed to complement the First Year Experience Program and be a capacity building initiative. A primary focus of TIP was The First Year Curriculum Project: the review, development, implementation and evaluation of first year curriculum which has culminated in the development of a “Good Practice Guide” for the management of large first year units. First year curriculum initiates staff-student relationships and provides the scaffolding for the learning experience and engagement. Good practice in first year curriculum is within the control of the institution and can be redesigned and reviewed to improve outcomes. This session will provide a context for the First Year Curriculum Project and a concise overview of the suite of resources developed that have culminated in the Good Practice Guide.