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.

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.

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.

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.

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.

An instrument for assessing primary students’ knowledge of information graphics in mathematics

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in-depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics; and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross-curriculum applications in learning about graphics, and the need to explicate the links among graphics.

Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

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.

A preliminary analysis of teacher perceptions of the effects of NAPLAN on pedagogy and curriculum

This paper reports preliminary survey findings of Western Australian and South Australian teacher perceptions of the impact of NAPLAN on curriculum and pedagogy in their classroom and school. The paper examines how teachers perceive the effects of NAPLAN on curriculum and pedagogy and whether these perceptions mediated by the teacher’s gender, the socioeconomics of the school, the State and the school system in which the teacher works. Teachers report that they are either choosing or being instructed to teach to the test, that this results in less time being spent on other curriculum areas and that these effects contribute in a negative way to the class environment and the engagement of students. This largely agrees with a body of international research that suggests that high-stakes literacy and numeracy tests often results in unintended consequences such as a narrow curriculum focus, a return to teacher-centred instruction and a decrease in motivation. Analysis suggests there is a relationship between participant responses to the effect of NAPLAN on curriculum based on the characteristics of which State the teacher taught in, the socioeconomic status of the school and the school system in which they were employed (State, Catholic, and Independent).

The effects of NAPLAN: Teacher perceptions of the impact of NAPLAN on pedagogy and curriculum

This paper reports preliminary findings of a survey of in-service teachers in WA and SA conducted in 2012. Participants completed an online survey open to all teachers in WA and SA. The survey ran for three months from April to June 2012. One section of the survey asked teachers to report their perceptions of the impact that NAPLAN has had on the curriculum and pedagogy of their classroom and school. Two principal research questions were addressed in this preliminary analysis. First what are teacher perceptions of the effects on NAPLAN on curriculum and pedagogy? Second, are there any interaction effects between gender, socioeconomics status, location and school system on teachers perceptions? Statistical analyses examined one- and two-way MANOVA to assess main effects and interaction effects on teachers' global perceptions. These were followed by a series of exploratory one- and two-way ANOVA of specific survey items to suggest potential sources for differences among teachers from different socioeconomic regions, states and systems. Teachers report that they are either choosing or being instructed to teach to the test, that this results in less time being spent on other curriculum areas and that these effects contribute in a negative way on the engagement of students. This largely agrees with a body of international research that suggests that high-stakes literacy and numeracy tests often results in unintended consequences such as a narrow curriculum focus (Au, 2007), a return to teacher-centred instruction (Barret, 2009) and a decrease in motivation (Ryan & Wesinstein, 2009). Preliminary results from early survey respondents suggests there is a relationship between participant responses to the effect of NAPLAN on curriculum and pedagogy based on the characteristics of which State the teacher taught in, their perceptions of the socioeconomic status of the school and the school system in which they were employed (State, Catholic, and Independent).

Understanding of BRCA1/2 genetic tests results:the importance of objective and subjective numeracy

Background: The majority of women (71%) who undergo BRCA1/2 testing—designed to identify genetic mutations associated with increased risk of cancer—receive results that are termed ‘ambiguous’ or ‘uninformative negative’. How women interpret these results and the association with numerical ability was examined. Methods: In this study, 477 women at increased risk for breast and ovarian cancer were recruited via the Cancer Genetics Network. They were presented with information about the four different possible BRCA1/2 test results—positive, true negative, ambiguous and uninformative negative—and asked to indicate which of six options represents the best response. Participants were then asked which treatment options they thought a woman receiving the results should discuss with her doctor. Finally, participants completed measures of objective and subjective numeracy. Results: Almost all of the participants correctly interpreted the positive and negative BRCA1/2 genetic test results. However, they encountered difficulties interpreting the uninformative and ambiguous BRCA1/2 genetic test results. Participants were almost equally likely to think either that the woman had learned nothing from the test result or that she was as likely to develop cancer as the average woman. Highly numerate participants were more likely to correctly interpret inconclusive test results (ambiguous, OR = 1.62; 95% CI [1.28, 2.07]; p < 0.001; uninformative, OR = 1.40; 95% CI [1.10, 1.80]). Discussion: Given the medical and psychological ramifications of genetic testing, healthcare professionals should consider devoting extra effort to ensuring proper comprehension of ambiguous and uninformative negative test results by women. Copyright © 2014 John Wiley & Sons, Ltd.

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.

Student understandings of numeracy problems: Semantic alignment and analogical reasoning

Despite compulsory mathematics throughout primary and junior secondary schooling, many schools across Australia continue in their struggle to achieve satisfactory numeracy levels. Numeracy is not a distinct subject in school curriculum, and in fact appears as a general capability in the Australian Curriculum, wherein all teachers across all curriculum areas are responsible for numeracy. This general capability approach confuses what numeracy should look like, especially when compared to the structure of numeracy as defined on standardised national tests. In seeking to define numeracy, schools tend to look at past NAPLAN papers, and in doing so, we do not find examples drawn from the various aspects of school curriculum. What we find are more traditional forms of mathematical worded problems.

Attention and basic literacy and numeracy in children with Autism Spectrum Disorder: a one-year follow-up study

Little is known about the link between Executive Functioning (EF) and academic performance in children with Autism Spectrum Disorder (ASD) and how such links develop over time. This study examined word reading, basic mathematics, attention switching, sustained attention and their development. Two age, gender and perceptual IQ matched groups of cognitively able 7-12 year olds (ASD N = 40; typical developing [TYP] N = 40) were assessed at baseline and one year later, completing Word Reading and Numerical Operations tests and computerized tasks tapping attention switching and sustained attention. Children with ASD had similar word reading and numerical operations performance and similar development of these skills relative to TYP children. A delay in attention switching but similar development was found in children with ASD relative to TYP children. The EF tasks were correlated with reading and mathematics in ASD children only, however, in regression analyses these factors were not significant predictors of Time 2 reading and mathematics after accounting for Time 1 reading and mathematics scores. These findings indicate similar word reading and mathematics development but atypical attention profiles in cognitively able children with ASD. Implications for educators are discussed.