National numeracy tests : a graphic tells a thousand words

Mandatory numeracy tests have become commonplace in many countries, heralding a new era in school assessment. New forms of accountability and an increased emphasis on national and international standards (and benchmarks) have the potential to reshape mathematics curricula. It is noteworthy that the mathematics items used in these tests are rich in graphics. Many of the items, for example, require students to have an understanding of information graphics (e.g., maps, charts and graphs) in order to solve the tasks. This investigation classifies mathematics items in Australia’s inaugural national numeracy tests and considers the effect such standardised testing will have on practice. It is argued that the design of mathematics items are more likely to be a reliable indication of student performance if graphical, linguistic and contextual components are considered both in isolation and in integrated ways as essential elements of task design.

Literacy, numeracy and learning in school-aged children identified as having speech and language impairment in early childhood

The progress of a nationally representative sample of 3632 children was followed from early childhood through to primary school, using data from the Longitudinal Study of Australian Children (LSAC). The aim was to examine the predictive effects of different aspects of communicative ability, and of early vs. sustained identification of speech and language impairment, on children's achievement and adjustment at school. Four indicators identified speech and language impairment: parent-rated expressive language concern; parent-rated receptive language concern; use of speech-language pathology services; below average scores on the adapted Peabody Picture Vocabulary Test-III. School outcomes were assessed by teachers' ratings of language/literacy ability, numeracy/mathematical thinking and approaches to learning. Comparison of group differences, using ANOVA, provided clear evidence that children who were identified as having speech and language impairment in their early childhood years did not perform as well at school, two years later, as their non-impaired peers on all three outcomes: Language and Literacy, Mathematical Thinking, and Approaches to Learning. The effects of early speech and language status on literacy, numeracy, and approaches to learning outcomes were similar in magnitude to the effect of family socio-economic factors, after controlling for child characteristics. Additionally, early identification of speech and language impairment (at age 4-5) was found to be a better predictor of school outcomes than sustained identification (at aged 4-5 and 6-7 years). Parent-reports of speech and language impairment in early childhood are useful in foreshadowing later difficulties with school and providing early intervention and targeted support from speech-language pathologists and specialist teachers.

Evaluation of the year 1 literacy and numeracy checkpoints assessments trial - 2010

The draft Year 1 Literacy and Numeracy Checkpoints Assessments were in open and supported trial during Semester 2, 2010. The purpose of these trials was to evaluate the Year 1 Literacy and Numeracy Checkpoints Assessments (hereafter the Year 1 Checkpoints) that were designed in 2009 as a way to incorporate the use of the Year 1 Literacy and Numeracy Indicators as formative assessment in Year 1 in Queensland Schools. In these trials there were no mandated reporting requirements. The processes of assessment were related to future teaching decisions. As such the trials were trials of materials and the processes of using those materials to assess students, plan and teach in year 1 classrooms. In their current form the Year 1 Checkpoints provide assessment resources for teachers to use in February, June and October. They aim to support teachers in monitoring children's progress and making judgments about their achievement of the targeted P‐3 Literacy and Numeracy Indicators by the end of Year 1 (Queensland Studies Authority, 2010 p. 1). The Year 1 Checkpoints include support materials for teachers and administrators, an introductory statement on assessment, work samples, and a Data Analysis Assessment Record (DAAR) to record student performance. The Supported Trial participants were also supported with face‐to‐face and on‐line training sessions, involvement in a moderation process after the October Assessments, opportunities to participate in discussion forums as well as additional readings and materials. The assessment resources aim to use effective early years assessment practices in that the evidence is gathered from hands‐on teaching and learning experiences, rather than more formal assessment methods. They are based in a model of assessment for learning, and aim to support teachers in the “on‐going process of determining future learning directions” (Queensland Studies Authority, 2010 p. 1) for all students. Their aim is to focus teachers on interpreting and analysing evidence to make informed judgments about the achievement of all students, as a way to support subsequent planning for learning and teaching. The Evaluation of the Year 1 Literacy and Numeracy Checkpoints Assessments Supported Trial (hereafter the Evaluation) aimed to gather information about the appropriateness, effectiveness and utility of the Year 1 Checkpoints Assessments from early years’ teachers and leaders in up to one hundred Education Queensland schools who had volunteered to be part of the Supported Trial. These sample schools represent schools across a variety of Education Queensland regions and include schools with:  - A high Indigenous student population; - Urban, rural and remote school locations; - Single and multi‐age early phase classes; - A high proportion of students from low SES backgrounds. The purpose of the Evaluation was to: Evaluate the materials and report on the views of school‐based staff involved in the trial on the process, materials, and assessment practices utilised. The Evaluation has reviewed the materials, and used surveys, interviews, and observations of processes and procedures to collect relevant data to help present an informed opinion on the Year 1 Checkpoints as assessment for the early years of schooling. Student work samples and teacher planning and assessment documents were also collected. The evaluation has not evaluated the Year 1 Checkpoints in any other capacity than as a resource for Year 1 teachers and relevant support staff.

Cracking the language code : NAPLAN numeracy tests in years 7 and 9

Focusing on the use of language is a crucial strategy in good mathematics teaching and a teacher’s guidance can assist students to master the language of mathematics. This article discusses the statements with reference to recent year 7 and 9 NAPLAN numeracy tests. It draws the readers’ attention to the complexities of language in the field of mathematics. Although this article refers to NAPLAN numeracy tests it also offers advice about good teaching practice.

Year 7 students’ approaches to understanding and solving NAPLAN numeracy problems

This study investigated how the interpretation of mathematical problems by Year 7 students impacted on their ability to demonstrate what they can do in NAPLAN numeracy testing. In the study, mathematics is viewed as a culturally and socially determined system of signs and signifiers that establish the meaning, origins and importance of mathematics. The study hypothesises that students are unable to succeed in NAPLAN numeracy tests because they cannot interpret the questions, even though they may be able to perform the necessary calculations. To investigate this, the study applied contemporary theories of literacy to the context of mathematical problem solving. A case study design with multiple methods was used. The study used a correlation design to explore the connections between NAPLAN literacy and numeracy outcomes of 198 Year 7 students in a Queensland school. Additionally, qualitative methods provided a rich description of the effect of the various forms of NAPLAN numeracy questions on the success of ten Year 7 students in the same school. The study argues that there is a quantitative link between reading and numeracy. It illustrates that interpretation (literacy) errors are the most common error type in the selected NAPLAN questions, made by students of all abilities. In contrast, conceptual (mathematical) errors are less frequent amongst more capable students. This has important implications in preparing students for NAPLAN numeracy tests. The study concluded by recommending that increased focus on the literacies of mathematics would be effective in improving NAPLAN results.

Developing a model of embedding academic numeracy in university programs : a case study from nursing

This is a study of the academic numeracy of nursing students. This study develops a theoretical model for the design and delivery of university courses in academic numeracy. The following objectives are addressed: 1. To investigate nursing students' current knowledge of academic numeracy; 2. To investigate how nursing students’ knowledge and skills in academic numeracy can be enhanced using a developmental psychology framework; and 3. To utilise data derived from meeting objectives 1 and 2 to develop a theoretical model to embed academic numeracy in university programs. This study draws from Valsiner’s Human Development Theory (Valsiner, 1997, 2007). It is a quasi-experimental intervention case study (Faltis, 1997) and takes a multimethod approach using pre- and post-tests; observation notes; and semi-structured teaching sessions to document a series of microgenetic studies of student numeracy. Each microgenetic study is centered on the lived experience of students becoming more numerate. The method for this section is based on Vygotsky’s double stimulation (Valsiner, 2000a; 2007). Data collection includes interviews on students’ past experience with mathematics; their present feelings and experiences and how these present feelings and experiences are transformed. The findings from this study have provided evidence that the course developed for nursing students, underpinned by an appropriate framework, does improve academic numeracy. More specifically, students improved their content knowledge of and confidence in mathematics in areas that were directly related to their degree. The study used Valsiner’s microgenetic approach to development to trace the course as it was being taught and two students’ personal academic numeracy journeys. It highlighted particularly troublesome concepts, then outlined scaffolding and pathways used to develop understanding. This approach to academic numeracy development was summarised into a four-faceted model at the university, program, course and individual level. This model can be applied successfully to similar contexts. Thus the thesis advances both theory and practice in this under-researched and under-theorised area.

Time limitations in NAPLAN numeracy tests

The article discusses evidence that time prevented many students from showing what they could do in the 2010 Year 7 and 9 NAPLAN numeracy tests. In addition to analysing the available data, the article discusses some NAPLAN numeracy questions that contribute to this problem. It is suggested that schools should investigate whether time limitation is a problem for their own students. The article discusses the implications of these findings for teachers preparing students for NAPLAN tests and for the developers of the tests.

Learning to think spatially : what do students 'see' in numeracy test items?

Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results showed that graphics were embedded in at least 50 % of test items across 3 year levels. The second investigation examined 11 – 12-year-olds’ performance on 2 mathematical tasks which required substantial interpretation of graphics and spatial thinking. The outcomes revealed that many students lacked proficiency in the basic spatial skills of visual memory and spatial perception and the more advanced skills of spatial orientation and spatial visualisation. This paper concludes with a reaffirmation of the importance of spatial thinking in mathematics and proposes ways to capitalize on graphics in learning to think spatially.

A multiple case study of NAPLAN numeracy testing of Year 9 students in three Queensland secondary schools

This thesis reports on a multiple case study of the actions of three Queensland secondary schools in the context of Year 9 NAPLAN numeracy testing, focusing on their administrative practices, curriculum, pedagogy and assessment. It was established that schools have found it both challenging and costly to operate in an environment of educational reform generally, and NAPLAN testing in particular. The lack of a common understanding of numeracy and the substantial demands of implementing the Australian Curriculum have impacted on schools' ability to prepare students appropriately for NAPLAN numeracy tests. It was concluded that there is scope for schools to improve their approaches to NAPLAN numeracy testing in a way that maximises learning as well as test outcomes.

Literacy and numeracy project: Final report 2009

Literacy and numeracy are critical for young people during and after their schooling. The subjects and courses that students undertake during their school years incorporate a range of academic literacy and numeracy practices which students must be able manage if they are to be successful. Pathways beyond schooling also require specific, and changing, understandings of, and proficiencies with, literacy and numeracy as new communication technologies increasingly impact on further study, work, and everyday life. Teaching and learning numeracy is a new emphasis in the SACE and as yet we have little understanding about the ways in which secondary schools handle this area. Students in Years 10 and 11 are at a crucial point in their educational and life pathways as they begin to refine their future aspirations. For those who have difficulty with academic literacies and numeracies – and often a long history of such problems – this period can be fraught unless teachers are able to provide specific support when it is needed, or students are able to access it from care-givers or community members. The School to Work Literacy and Numeracy Project involved teachers from nine schools across the three sectors and university researchers working together to design curriculum interventions for students with a history of low measurable achievement in literacy and/or numeracy. The project started from the premise that working with ‘rich tasks’, an approach to learning and assessment developed in the Productive Pedagogies work undertaken in Queensland (Hayes et al., 2006), would improve students’ motivation, engagement and learning and that this work could best be done by teachers working in school-based, cross-curriculum teams with a school leadership team member and a university researcher as mentor. A key idea in designing rich tasks is that students will have opportunities to demonstrate their learning in assessments which are aligned with the learning expectations (for example a film festival to publicly launch student-produced films, advertising to sell student-made cubby-houses, a household budget based on students’ likely incomes in future work). In other words the assessments should be designed to allow for authentic communication and displays of what the students have learned through serious engagement with the curriculum. The project was conducted from Term 1-4 2009, with follow-up checks with some project teachers in the early weeks of 2010.

Numeracy and statistical reasoning on entering university

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on mathematics anxiety. Gnaldi (2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning, basic numeracy skills, mathematics background and attitudes towards statistics. This work reports on some key relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Numeracy counts in the statistical reasoning equation

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on maths anxiety. Gnaldi (Gnaldi 2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning ability, basic numeracy skills and attitudes towards statistics. This work reports on the relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The new Australian Curriculum and national standardised testing have placed the teaching of numeracy across the curriculum at the forefront of what Australian schools must do. However, it has been left to schools to determine how they do this. Although there is a growing body of literature giving examples of pedagogies that embed numeracy in various learning areas, there are few studies of cross-curricular numeracy from the management perspective. This paper responds to the research question: How do selected Queensland secondary schools interpret and apply the Australian Curriculum requirement to embed numeracy throughout the curriculum? A multiple case study design was used to investigate the actions of the senior managers and mathematics teachers in three large secondary schools located in outer Brisbane. The numeracy practices in the three schools were interpreted from asocial constructivist perspective. The study found that in each school key managers had differing constructions of numeracy that led to confusion in administrative practices, policy development and leadership. The lack of coordinated cross-curricular action in numeracy in all three schools points to the difficulty that arises when teachers do not share the cross-curricular vision of numeracy present in the Australian Curriculum. The managers identified teachers’ commitment, understanding, or skills in relation to numeracy as significant barriers to the successful implementation of numeracy in their school. Adoption of the Australian Curriculum expectation of embedding numeracy across the curriculum will require school managers to explicitly commit to initiatives that require persistence,time and, most importantly, money.

Language Literacy and Numeracy in TAFE Diploma of Nursing (Enrolled/Division 2 Nursing)

This project aimed to identify current Language Literacy and Numeracy (LLN) and Inclusive Teaching and Learning Practices in a TAFE Diploma of Nursing (Enrolled/Division 2 Nursing). The key purpose of the study was to make recommendations for improving inclusive teaching practice and learning outcomes of students and for reducing student attrition, thereby increasing the employability of graduates in the health industry subsequent to course completion.

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The Australian Curriculum identified seven General Capabilities, including numeracy, to be embedded in all learning areas. However, it has been left to individual schools to manage this. Whilst there is a growing body of literature about pedagogies that embed numeracy in various learning areas, there are few studies from the management perspective. A social constructivist perspective and a multiple case study approach were used to explore the actions of school managers and mathematics teachers in three Queensland secondary schools, in order to investigate how they meet the Australian Curriculum requirement to embed numeracy throughout the curriculum. The study found a lack of coordinated cross-curricular approaches to numeracy in any of the schools studied. It illustrates the difficulties that arise when teachers do not share the Australian Curriculum cross-curricular vision of numeracy. Schools and curriculum authorities have not acknowledged the challenges for teachers in implementing cross-curricular numeracy, which include: limited understanding of numeracy; a lack of commitment; and inadequate skills. Successful embedding of numeracy in all learning areas requires: the commitment and support of school leaders, a review of school curriculum documents and pedagogical practices, professional development of teachers, and adequate funding to support these activities.