What does the review of the Australian Curriculum mean for History in the Primary Years?

The recent introduction of the Australian Curriculum: History as a timetabled school subject has enhanced the teaching of history in the primary years. Previously, history was integrated with geography, economics and civics and citizenship; however, in the new curriculum students are introduced to history from their first year at school. The review addresses significant concerns about the scope and content in history in an over-crowded primary curriculum (Donnelly & Wiltshire, 2014; APPA, 2014). However, the history curriculum provides a rare opportunity to explore distinctive content and develop agency by investigating personal, local, national and international contexts. This paper examines the recommendations of the review and the implications for history in the primary years.

A model eliciting framework for integrating mathematics and robotics learning

Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile round for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

Will they know enough? Pre-service primary teachers' knowledge base for teaching intergrated social sciences

A significant issue in primary teacher education is developing a knowledge base which prepares teachers to teach in a range of subject areas. In Australia, the problem in primary social science education is compounded by the integrated nature of the key learning area of Studies of Society and Environment (SOSE). Recent debates on teaching integrated social sciences omit discussions on the knowledge base for teaching. In this paper, a case study approach is used to investigate primary pre-service teachers’ approaches to developing a knowledge base in designing a SOSE curriculum unit. Data from five teacher-educators who taught primary SOSE curriculum indicates that novice teachers’ subject content knowledge, as revealed through their curriculum planning, lacked a disciplinary basis. However, understanding of inquiry learning, which is fundamental to social science education, was much stronger. This paper identifies a gap in the scholarship on teaching integrated social science and illustrates the need to support and develop primary teachers’ disciplinary knowledge in teacher education.

Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

Implementing dance in a Queensland primary school : a descriptive case study

This research documents and analyses the modes of implementation of the Dance component of The Arts Essential Learnings in a Queensland school. The research identifies what makes good practice in dance education and the multiple modes of implementation that support this practice. The primary purpose of this research is to describe the factors that influence dance education, as it is delivered, in a Queensland primary school to inform the development of further support for primary teachers and to improve the quality of dance education in Prep -7 schooling. The literature review investigates dance education both in Queensland, Australia and internationally, identifying current issues related to the delivery of dance in a primary school environment including barriers to implementation of dance, authentic learning and integrated approaches to learning. Based on Engestrom.s reformulation of Vygotsky.s theory of socially mediated learning, the implementation of dance education curriculum was explored through descriptive case study method. The case study was conducted in a regional Queensland school identified as delivering the dance curriculum in a variety of ways. The research project provided opportunities to observe, document and analyse how teachers deal with pedagogical dilemmas and solve logistical problems associated with teaching the dance component of the Arts curriculum in this school. Teachers. practices were contextualised through investigation of the whole school context of dance curriculum development. The findings revealed a range of teaching approaches that influenced teachers. interpretation and children.s experience of the dance curriculum. The features of a supportive whole school and cultural environment for dance were identified. These have been captured in a reworked version of Engestrom.s Second Generation Activity Theory that can be applied to the implementation of dance education in primary schools.

Jabberwocky : the complexities of mathematical English

Mathematical English is a unique language based on ordinary English, with the addition of highly stylised formal symbol systems. Some words have a redefined status. Mathematical English has its own lexicon, syntax, semantics and literature. It is more difficult to understand than ordinary English. Ability in basic interpersonal communication does not necessarily result in proficiency in the use of mathematical English. The complex nature of mathematical English may impact upon the ability of students to succeed in mathematical and numeracy assessment. This article presents a review of the literature about the complexities of mathematical English. It includes examples of more than fifty language features that have been shown to add to the challenge of interpreting mathematical texts. Awareness of the complexities of mathematical English is an essential skill needed by mathematics teachers when teaching and when designing assessment tasks.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.

The power of percent

Which statistic would you use if you were writing the newspaper headline for the following media release: "Tassie’s death rate of deaths arising from transport-related injuries was 13 per 100,000 people, or 50% higher than the national average”? (Martain, 2007). The rate “13 per 100,000” sounds very small whereas “50% higher” sounds quite large. Most people are aware of the tendency to choose between reporting data as actual numbers or using percents in order to gain attention. Looking at examples like this one can help students develop a critical quantitative literacy viewpoint when dealing with “authentic contexts” (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2013a, p. 37, 67). The importance of the distinction between reporting information in raw numbers or percents is not explicitly mentioned in the Australian Curriculum: Mathematics (ACARA, 2013b, p. 42). Although the document specifically mentions making “connections between equivalent fractions, decimals and percentages” [ACMNA131] in Year 6, there is no mention of the fundamental relationship between percent and the raw numbers represented in a part-whole fashion. Such understanding, however, is fundamental to the problem solving that is the focus of the curriculum in Years 6 to 9. The purpose of this article is to raise awareness of the opportunities to distinguish between the use of raw numbers and percents when comparisons are being made in contexts other than the media. It begins with the authors’ experiences in the classroom, which motivated a search in the literature, followed by a suggestion for a follow-up activity.

Successful outcomes in vocational education and training courses and mathematics: how pedagogy and expectations influence achievement

This paper reports on a four year Australian Research Council funded Linkage Project titled Skilling Indigenous Queensland, conducted in regional areas of Queensland, Australia from 2009 to 2013. The project sought to investigate Vocational Education and Training (VET) and teaching, Indigenous learners’ needs, employer culture and expectations and community culture and expectations to identify best practice in numeracy teaching for Indigenous VET learners. Specifically it focused on ways to enhance the teaching and learning of courses and the associated mathematics in such courses to benefit learners and increase their future opportunities of employment. To date thirty - nine teachers/trainers/teacher aides and two hundred and thirty - one students consented to participate in the project. Nine VET courses offered in schools and Technical and Further Education Institutes (TAFE) were nominated to be the focus on the study. This paper focuses on student questionnaire responses and interview responses from teachers/trainers one high school principal and five students as a result of these processes, the findings indicated that VET course teachers work hard to adopt contextualising strategies to their teaching; however this process is not always straight forward because of the perceptions of how mathematics has been taught and learned by trainers and teachers. Further teachers, trainers and students have high expectations of one another with the view to successful outcomes from the courses.

Primary schools and the delivery of relationships and sexuality education : the experience of Queensland teachers

Primary school provides an appropriate opportunity for children to commence comprehensive relationships and sexuality education (RSE), yet many primary school teachers avoid teaching this subject area. In the absence of teacher confidence and competence, schools have often relied on health promotion professionals, external agencies and/or one-off issue related presentations rather than cohesive, systematic and meaningful health education. This study examines the implementation of a ten-lesson pilot RSE unit of work and accompanying assessment task in two primary schools in South-East Queensland, Australia. Drawing predominantly from qualitative data, this research explores the experiences of primary school teachers as they engage with RSE curriculum resources and content delivery. The results show that the provision of a high quality RSE curriculum resource grounded in contemporary educational principles and practices enables teachers to feel more confident to deliver RSE and minimises potential barriers such as parental objections and fear of mishandling sensitive content.