Action research for contexts of change and inequality

Undoubtedly, the past half-century has witnessed an escalation of changes in the social, political, economic and educational structures in many societies around the world. Some have seen change as a challenge and hope while, for many others, it is a source of concern and worry. Some have adopted change with gusto, while for many it is something to be resisted. Some say we live in a world and times with an increasing awareness that “times are changing”, while for some “the more things change, the more they stay the same”.

A thematic approach to integrating maths and science for pre-service primary teachers via sustainability

Efforts to improve mathematics and science content knowledge have in many institutions required redefining teacher education through new teaching and learning. See, for example, Peard & Pumadevi (2007) for an account of one such attempt involving the development of a Foundations Unit, Scientific and Quantitative Literacy. This unit is core for all first year pre-service primary teacher education students at Queensland University of Technology (QUT) and two Education Institutes in Malaysia, Institute Perguruan Raja Melewar (IPRM), and Institute Perguruan Teknik (IPT) Kuala Lumpur. Since then, QUT has modified the unit to adopt a thematic approach to the same content. An aim of the unit rewrite was the development of a positive attitude and disposition to the teaching and learning of mathematics and science, with a curiosity and willingness to speculate about and explore the world. Numeracy was specifically identified within the mathematics encountered and appropriately embedded in the science learning area. The importance of the ability to engage in communication of and about mathematics and science was considered crucial to the development of pre-service primary teachers. Cognisance was given to the appropriate selection and use of technology to enhance learning - digital technologies were embedded in the teaching, learning and assessment of the unit to avoid being considered as an optional extra. This was achieved around the theme of “the sustainable school”. This „sustainability‟ theme was selected due to its prominence in Australia‟s futures-oriented National Curriculum which will be implemented in 2011. This paper outlines the approach taken to the implementation of the unit and discusses early indicators of its effectiveness.

A thematic approach to integrating maths and science for pre-service primary teachers via sustainability

Efforts to improve mathematics and science content knowledge have in many institutions required redefining teacher education through new teaching and learning. See, for example, Peard & Pumadevi (2007) for an account of one such attempt involving the development of a Foundations Unit, Scientific and Quantitative Literacy. This unit is core for all first year pre-service primary teacher education students at Queensland University of Technology (QUT) and two Education Institutes in Malaysia, Institute Perguruan Raja Melewar (IPRM), and Institute Perguruan Teknik (IPT) Kuala Lumpur. Since then, QUT has modified the unit to adopt a thematic approach to the same content. An aim of the unit rewrite was the development of a positive attitude and disposition to the teaching and learning of mathematics and science, with a curiosity and willingness to speculate about and explore the world. Numeracy was specifically identified within the mathematics encountered and appropriately embedded in the science learning area. The importance of the ability to engage in communication of and about mathematics and science was considered crucial to the development of pre-service primary teachers. Cognisance was given to the appropriate selection and use of technology to enhance learning - digital technologies were embedded in the teaching, learning and assessment of the unit to avoid being considered as an optional extra. This was achieved around the theme of “the sustainable school”. This ‘sustainability’ theme was selected due to its prominence in Australia’s futures-oriented National Curriculum which will be implemented in 2011. This paper outlines the approach taken to the implementation of the unit and discusses early indicators of its effectiveness.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Kindergarten students' understanding of probability concepts

This study explored kindergarten students’ intuitive strategies and understandings in probabilities. The paper aims to provide an in depth insight into the levels of probability understanding across four constructs, as proposed by Jones (1997), for kindergarten students. Qualitative evidence from two students revealed that even before instruction pupils have a good capacity of predicting most and least likely events, of distinguishing fair probability situations from unfair ones, of comparing the probability of an event in two sample spaces, and of recognizing conditional probability events. These results contribute to the growing evidence on kindergarten students’ intuitive probabilistic reasoning. The potential of this study for improving the learning of probability, as well as suggestions for further research, are discussed.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Pedagogical practice after the information age

These chapters bare witness to various manifestations of an emerging global mind set that is marked not by coherence and a single story but by multiple and layered possibility. The authors all see, from often quite different positions, that the future health of society lies in diversity and a social activism that is grounded in the local actions of individuals. Education will play a central role in empowering this activism and it is to this multiple future that this book turns its attention.

Strategies for comparing decimal numbers with the same whole-number part

The strategies employed by 130 Grade 5 Brisbane students in comparing decimal numbers which have the same whole-number part were compared with those identified in similar studies conducted in the USA, France and Israel. Three new strategies were identified. Similar to USA results, the most common comparison errors stemmed from the incorrect whole-number strategy in which length is confused with size. The findings of this present study tend to support Resnick et al.’s (1989) hypothesis that the introduction of decimal-fraction recording before common-fraction recording seems to promote better comparison of decimal numbers.

Year 8, 9 and 10 students’ understanding and access of percent knowledge

This paper reports on Years 8, 9 and 10 students’ knowledge of percent problem types, use of diagrams, and type of solution strategy. Non- and semi-proficient students displayed the expected inflexible formula approach to solution but proficient students used a flexible mixture of estimation, number sense and trial and error instead of expected schema based methods.

Construction of multiplicative abstract schema for decimal-number numeration

This paper reports on an intervention study planned to help Year 6 students construct the multiplicative structure underlying decimal-number numeration. Three types of intervention were designed from a numeration model developed from a large study of 173 Year 6 students’ decimal-number knowledge. The study found that students could acquire multiplicative structure as an abstract schema if instruction took account of prior knowledge as informed by the model.

Reunitising hundredths: prototypic and nonprototypic representations

This paper reports on a study in which 29 Year 6 students (selected from the top 30% of 176 Year 6 students) were individually interviewed to explore their ability to reunitise hundredths as tenths (Behr, Harel, Post & Lesh, 1992) when represented by prototypic (PRO) and nonprototypic (NPRO) models. The results showed that 55.2% of the students were able to unitise both models and that reunitising was more successful with the PRO model. The interviews revealed that many of these students had incomplete, fragmented or non-existent structural knowledge of the reunitising process and often relied on syntactic clues to complete the tasks. The implication for teaching is that instruction should not be limited to PRO representations of the part/whole notion of fraction and that the basic structures (equal parts, link between name and number of equal parts) of the part/whole notion needs to be revisited often.

Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Place value, multiplicativity, reunitizing and effective classroom teaching of decimal numeration

Student understanding of decimal number is poor (e.g., Baturo, 1998; Behr, Harel, Post & Lesh, 1992). This paper reports on a study which set out to determine the cognitive complexities inherent in decimal-number numeration and what teaching experiences need to be provided in order to facilitate an understanding of decimal-number numeration. The study gave rise to a theoretical model which incorporated three levels of knowledge. Interview tasks were developed from the model to probe 45 students’ understanding of these levels, and intervention episodes undertaken to help students construct the baseline knowledge of position and order (Level 1 knowledge) and an understanding of multiplicative structure (Level 3 knowledge). This paper describes the two interventions and reports on the results which suggest that helping students construct appropriate mental models is an efficient and effective teaching strategy.

Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.