Australian shows

This book is a reader for primary school students, stage 27-30 (fluent), incorporating mathematics themes. There is a fictional narrative, entitled "A Day at the Show", that describes the activities of Tess and Alex when visiting their local show. A non-fiction exposition, entitled "Supporting Australian Shows", explains more about Australian shows and why we should support them. Accompanying the book is a "building comprehension card" to assist teachers in their classroom use of the reader.

The flying doctors

This book is a reader for primary school students, stage 24-26 (fluent), incorporating mathematics themes. There is a fictional narrative, entitled "A Flying Visit", that describes Tess' and Alex's encounter with the Flying Doctor. A non-fiction recount, entitled "Fundraising for the Flying Doctors", describes the activities of a class group in raising money for the Flying Doctors. Accompanying the book is a "building comprehension card" to assist teachers in their classroom use of the reader.

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.

A framework for mathematics graphical tasks : The influence of the graphic element on student sense making

Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.

How can Australia sustain middle-schooling education?

Middle schooling is a crucial area of education where adolescents experiencing physiological and psychological hanges require expert guidance. As more research evidence is provided about adolescent learning, teachers are considered pivotal to adolescents’ educational development. The two levels of implementing reform measures need to be targeted, that is, at the inservice and preservice teacher levels. This quantitative study employs a 40-item, five-part Likert scale survey to understand preservice teachers’ (n=142) perceptions of their confidence to teach in the middle school at the conclusion of their tertiary education. The survey instrument was developed from the literature with connections to the Queensland College of Teachers professional standards. Results indicated that they perceived themselves as capable of creating a positive classroom environment with seven items greater than 80%, except with behaviour management (<80% for two items) and they considered their pedagogical knowledge to be adequate (i.e., 7 out of 8 items >84%). Items associated with implementing middle schooling curriculum had varied responses (e.g., implementing literacy and numeracy were 74% while implementing learning with real-world connections was 91%). This information may assist coursework designers. For example, if significant percentages of preservice teachers indicate they believe they were not well prepared for assessment and reporting in the middle school then course designers can target these areas more effectively.

A picture is worth a thousand words : an approach to learning about visuals

Students in the middle years encounter an increasing range of unfamiliar visuals. Visual literacy, the ability to encode and decode visuals and to think visually, is an expectation of all middle years curriculum areas and an expectation of NAPLAN literacy and numeracy tests. This article presents a multidisciplinary approach to teaching visual literacy that links the content of all learning areas and encourages students to transfer skills from familiar to unfamiliar contexts. It proposes a classification of visuals in six parts: one-dimensional; two-dimensional; map; shape; connection; and picture, based on the properties, rather than the purpose, of the visual. By placing a visual in one of these six categories, students learn to transfer the skills used to decode familiar visuals to unfamiliar cases in the same category. The article also discusses a range of other teaching strategies that can be used to complement this multi-disciplinary approach.

‘Wanna do more math’: engaging underachieving Indigenous learners the YuMi Deadly way.

The Accelerating Indigenous Mathematics (AIM) Program offered by the YuMi Deadly Centre from QUT accelerates the mathematics learning of underperforming students in Years 8 - 10 by a) apportioning Years 2-10 Australian Curriculum: Mathematics content into three years, and b) provides a teaching approach that accelerates the mathematical learning. The philosophy of the YuMi Deadly teaching approach for mathematics is one that requires a ‘body’, ‘hand’, ‘mind’ pedagogy. This presentation will provide examples of the “‘body’, ‘hand’, ‘mind’” mathematics pedagogy. In AIM classrooms, mathematics is presented this approach is having a positive impact. Students are willing ‘to have a go’ without shame; and they develop the desire to learn and improve their numeracy.

Get Into Vocational Education (GIVE) : motivating underperforming students

This study explores the effects of a vocational education-based program on academic motivation and engagement of primary school aged children. The Get Into Vocational Education (GIVE) program integrated ‘construction’ and the mathematics, English and science lessons of a Year 4 primary classroom. This paper focuses on investigating the components of the GIVE program that led to student changes in mathematical academic motivation and engagement resulting in outstanding gains in NAPLAN Numeracy results. The components proposed to have contributed to effectiveness of the GIVE program are: teacher and trainer expectations, task mastery and classroom relationships. These findings may be useful to researchers and educators who are interested in enhancing students’ mathematical academic motivation.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Funds of knowledge of sorting and patterning : networks of exchange in a Torres Strait Island community

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based 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. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through using a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can be used as foundations for future learnings for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

How can universities support beginning teachers?

Many beginning teachers struggle in teaching, consequently, tertiary education has been criticised for not preparing preservice teachers well enough. This qualitative study uses interviews and questionnaires to investigate 10 first-year teachers’ understandings of how universities can support them more effectively. The findings indicated that university preparation needed more literacy (particularly reading and spelling), numeracy, catering for lower socio-economic students, understanding behaviour differentiation, and communicating with parents. A two-prong approach may support beginning teachers: (1) timely induction and mentoring within school settings, and (2) research for advancing teacher education coursework to ensure currency of addressing beginning teachers’ needs.

Towards improving public understanding of judgement practice in standards-referenced assessment : an Australian perspective

Internationally there has been a move towards standards-referenced assessment with countries such as Australia developing a National Curriculum and Achievement Standards, New Zealand adopting National Standards for literacy and numeracy that involve schools making and reporting judgements about the reading, writing and mathematics achievement of children up to Year 8 (the end of primary school) and in Canada, classroom assessment standards aimed at the improvement of assessment practice of K-12 education are being formulated. Standards-driven reform has major implications for teachers’ work. The consequences of adopting a standards-driven approach to educational change by systems are often under-estimated with the unintended effects not fully understood by either the policy writers, and the public, including parents. It is for these reasons that the contention developed in this article relates to the teacher’s role, which it is argued remains central to policy focused on the improvement of the quality of education and educational standards.

Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.

Problem solving in the primary school (K-2)

This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten through college. Can children really solve problems that involve concepts (or skills) that they have not yet been taught? Can children really create important mathematical concepts on their own – without a lot of guidance from teachers? What is the relationship between problem solving abilities and the mastery of skills that are widely regarded as being “prerequisites” to such tasks?Can primary school children (whose toolkits of skills are limited) engage productively in authentic simulations of “real life” problem solving situations? Can three-person teams of primary school children really work together collaboratively, and remain intensely engaged, on problem solving activities that require more than an hour to complete? Are the kinds of learning and problem solving experiences that are recommended (for example) in the USA’s Common Core State Curriculum Standards really representative of the kind that even young children encounter beyond school in the 21st century? … This article offers an existence proof showing why our answers to these questions are: Yes. Yes. Yes. Yes. Yes. Yes. And: No. … Even though the evidence we present is only intended to demonstrate what’s possible, not what’s likely to occur under any circumstances, there is no reason to expect that the things that our children accomplished could not be accomplished by average ability children in other schools and classrooms.

Evaluation of the "reconceptualising early mathematics learning" project

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure enables mathematical thinking and simple forms of generalisation from an early age. The project aims to promote a strong foundation for mathematical development by focusing on critical, underlying features of mathematics learning. This paper provides an overview of key aspects of the assessment and intervention, and analyses of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in the evaluation throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ assessment and a Pattern and Structure Assessment (PASA) interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a relatively short period of time.