Abstract: We introduce the Berlin Numeracy Test, a new psychometrically sound instrument that quickly assesses statistical numeracy and risk literacy. We present 21 studies (n=5336) showing robust psychometric discriminability across 15 countries (e.g., Germany, Pakistan, Japan, USA) and diverse samples (e.g., medical professionals, general populations, Mechanical Turk web panels). Analyses demonstrate desirable patterns of convergent validity (e.g., numeracy, general cognitive abilities), discriminant validity (e.g., personality, motivation), and criterion validity (e.g., numerical and nonnumerical questions about risk). The Berlin Numeracy Test was found to be the strongest predictor of comprehension of everyday risks (e.g., evaluating claims about products and treatments; interpreting forecasts), doubling the predictive power of other numeracy instruments and accounting for unique variance beyond other cognitive tests (e.g., cognitive reflection, working memory, intelligence). The Berlin Numeracy Test typically takes about three minutes to complete and is available in multiple languages and formats, including a computer adaptive test that automatically scores and reports data to researchers (www.riskliteracy.org). The online forum also provides interactive content for public outreach and education, and offers a recommendation system for test format selection. Discussion centers on construct validity of numeracy for risk literacy, underlying cognitive mechanisms, and applications in adaptive decision support.

Abstract: When making decisions, people must frequently take into account numerical information, but not all individuals have the ability to understand and use numbers. Less numerate individuals comprehend less numerical information; but numeracy goes beyond comprehension, relating systematically to psychological mechanisms. In particular, greater numeracy has been associated with reduced susceptibility to framing effects, less influence of nonnumerical information such as mood states, and greater sensitivity to different levels of numerical risk. This greater number sensitivity has been linked with number-related affective reactions reported by the highly numerate. I briefly discuss methods to increase number use in decisions and policy implications of numeracy research.

Abstract: Despite evidence that individual differences in numeracy affect judgment and decision making, the precise mechanisms underlying how such differences produce biases and fallacies remain unclear. Numeracy scales have been developed without sufficient theoretical grounding, and their relation to other cognitive tasks that assess numerical reasoning, such as the Cognitive Reflection Test (CRT), has been debated. In studies conducted in Brazil and in the USA, we administered an objective Numeracy Scale (NS), Subjective Numeracy Scale (SNS), and the CRT to assess whether they measured similar constructs. The Rational-Experiential Inventory, inhibition (go/no-go task), and intelligence were also investigated. By examining factor solutions along with frequent errors for questions that loaded on each factor, we characterized different types of processing captured by different items on these scales. We also tested the predictive power of these factors to account for biases and fallacies in probability judgments. In the first study, 259 Brazilian undergraduates were tested on the conjunction and disjunction fallacies. In the second study, 190 American undergraduates responded to a ratio-bias task. Across the different samples, the results were remarkably similar. The results indicated that the CRT is not just another numeracy scale, that objective and subjective numeracy scales do not measure an identical construct, and that different aspects of numeracy predict different biases and fallacies. Dimensions of numeracy included computational skills such as multiplying, proportional reasoning, mindless or verbatim matching, metacognitive monitoring, and understanding the gist of relative magnitude, consistent with dual-process theories such as fuzzy-trace theory.

Abstract: Women typically participate less than men in the stock market, while also scoring lower on financial literacy. We explore the link between the gender gap in stock market participation and financial literacy. Using survey data on a random sample of 1,300 individuals that is representative of the Swedish population, we show that controlling for basic financial literacy, essentially a measure of numeracy that does not require knowledge about the stock market, may explain a large part of the gender gap in stock market participation. We also find that women report being less risk taking than men. This gender gap in risk attitudes remains significant also when controlling for financial literacy.

Abstract: Financial decisions, be they related to asset building or debt management, require the capacity to do calculations, including some complex ones. But how numerate are individuals, in particular when it comes to calculations related to financial decisions? Studies and surveys implemented in both the United States and in other countries that are described in this paper show the level of numeracy among the population to be very low. Moreover, lack of numeracy is not only widespread but is particularly severe among some demographic groups, such as women, the elderly, and those with low educational attainment. This has potential consequences for individuals and for society as a whole because numeracy is found to be linked to many financial decisions. Now more than ever, numeracy and financial literacy are lifetime skills necessary to succeed in today's complex economic environment.

Abstract: High stakes testing in Australia was introduced in 2008 by way of the National Assessment Program – Literacy and Numeracy (NAPLAN). Currently, every year all students in Years 3, 5, 7 and 9 are ass...

Abstract: NBER WORKING PAPER SERIESNUMERACY, FINANCIAL LITERACY, AND FINANCIAL DECISION-MAKINGAnnamaria LusardiWorking Paper 17821http://www.nber.org/papers/w17821NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts AvenueCambridge, MA 02138February 2012This paper was invited to be written for Numeracy, the open-access, peer-review journal of the NationalNumeracy Network. I would like to thank Dorothy Wallace, from the department of Mathematicsat Dartmouth College, for encouraging me to write this review article. Audrey Brown provided excellentresearch assistance. All errors are my own. The views expressed herein are those of the author anddo not necessarily reflect the views of the National Bureau of Economic Research.NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.© 2012 by Annamaria Lusardi. All rights reserved. Short sections of text, not to exceed two paragraphs,may be quoted without explicit permission provided that full credit, including © notice, is given tothe source.

Abstract: Attention is construed as multicomponential, but the roles of its distinct subfunctions in shaping the broader developing cognitive landscape are poorly understood. The current study assessed 3- to 6-year-olds (N = 83) to: (a) trace developmental trajectories of attentional processes and their structure in early childhood and (b) measure the impact of distinct attention subfunctions on concurrent and longitudinal abilities related to literacy and numeracy. Distinct trajectories across attention measures revealed the emergence of 2 attentional factors, encompassing “executive” and “sustained–selective” processes. Executive attention predicted concurrent abilities across domains at Time 1, whereas sustained–selective attention predicted basic numeracy 1 year later. These concurrent and longitudinal constraints cast a broader light on the unfolding relations between domain-general and domain-specific processes over early childhood.

Abstract: While research demonstrates the importance of numeracy-related activities performed at home for young children's mathematics achievement, few studies involve observational studies of the processes which support children's mathematical learning at home. On this premise, this study reports evidence from numeracy-related interactions between parents and their four-year-old child during cookery sessions at home. Numeracy group parents who received instructions to incorporate additional mathematics into the activity provided significantly more numeracy guidance and also created more opportunities for their children to practice advanced mathematics. Comparison group parents provided enough numeracy guidance to complete the recipe but rarely provided extensive or advanced numeracy guidance. Children in the numeracy group generated significantly more correct math responses during the activity than comparison group children, though there were no significant differences on the post-test. The findings sugge...

Abstract: Purpose: To evaluate the effectiveness of a video modelling package to teach a 5 year-old boy diagnosed with an autism spectrum disorder (ASD) basic numeracy skills. The treatment package consisted of iPad-based video modelling, gradual fading of video prompts, reinforcement, in vivo prompting and forward chaining.Methods: A single subject multiple baseline across numerals design with generalization and maintenance observational measures.Results: Clear gains were evident in the participant's ability to identify and write the Arabic numerals 1–7 and comprehend the quantity each numeral represents in association with the lagged intervention. Generalization and maintenance data demonstrated the robustness of the treatment effects.Conclusions: IPad-based video modelling, when used in a package, can be an effective technique for teaching numeracy skills to children with an ASD. Systematic replication of this study with different participants is warranted.

Abstract: This paper explores how mandated literacy assessment is reorganising teachers' work in the context of Australia's National Assessment Program – Literacy and Numeracy, which was implemented in 2008 Students in Years 3, 5, 7 and 9 are tested annually, with school results publicly available The wider policy context and the emergence of different forms of interconnected educational work associated with the testing phenomenon are described Taking an institutional ethnography approach, the local effects of the federal policy regime are examined through a case study of one school What mandated literacy assessment does to educators' work in a culturally diverse low-socioeconomic school community is discussed Key themes include strategic exclusions of students from the testing process, appropriations and adaptations of literacy theory, work intensification and ethical mediation of results Questions concerning equity are raised about the differential effects of policy in different school contexts

Abstract: There is evidence of a relation between numeracy and wealth held outside of pensions and Social Security. With pensions and Social Security accounting for half of wealth at retirement, and evidence that those with pensions save more in other forms, one would expect to find knowledge of pensions and Social Security influencing retirement saving. Yet we find no evidence that knowledge of pensions and Social Security is related to nonpension, non-Social Security wealth, to numeracy, or that it plays an intermediate role in the numeracy-wealth relation. Our findings raise questions about policies that would enhance numeracy to increase retirement saving.

Abstract: Diabet. Med. 29, 662–669 (2012) Abstract Aims To assess the numeracy and literacy skills of individuals with Type 1 diabetes and determine if there is a relationship with achieved glycaemic control independent of their duration of diabetes, diabetes education, demographic and socio-economic factors. Methods One hundred and twelve patients completed the study (mean current age 43.8 ± 12.5 years, 47% male, mean duration of diabetes 22.0 ± 13.2 years) out of 650 randomly selected patients from the Bournemouth Diabetes and Endocrine Centre’s diabetes register. The Skills for Life Initial Assessments were used to measure numeracy and literacy. These indicate skills levels up to level 2, equivalent to the national General Certificate of Secondary Education grades A*–C. HbA1c was also measured. Pearson’s correlation was used to measure the correlation of numeracy and literacy scores with HbA1c. To compare mean HbA1c between those with or without level 2 skills, t-tests were used, and multiple linear regression was used to investigate whether any differences were independent of duration of diabetes, diabetes education, demographic and socio-economic factors. Results Literacy was not associated with achieved HbA1c. In contrast, participants with numeracy skills at level 2 or above achieved an HbA1c lower than those with numeracy skills below level 2 (P = 0.027). Although higher socio-economic status was associated with lower mean HbA1c, the relationship between numeracy and HbA1c appeared to be independent of socio-economic factors. Conclusions Low numeracy skills were adversely associated with diabetes control. Assessment of numeracy skills may be relevant to the structure of diabetes education programmes.

Abstract: The 25-item Health Literacy Skills Instrument (HLSI) was designed to measure the ability to read and understand text and locate and interpret information in documents (print literacy), to use quantitative information (numeracy), to listen effectively (oral literacy), and to seek information through the Internet (navigation). It is a publically available measure that can be used in surveillance activities, to evaluate interventions, and in research examining the relation between health literacy and health outcomes. The authors developed a 10-item, short form (SF) version of the HLSI, the HLSI-SF, using data gathered for the development of the longer form. The authors selected 10 items for inclusion in the HLSI-SF and conducted a confirmatory factor analysis and item response theory analyses, then computed Cronbach's alpha. The HLSI-SF demonstrated acceptable internal consistency reliability (α = .70) for use in group-level comparisons. The HSLI-SF has many of the same advantages of the longer version with the additional benefit of taking only approximately 5 to 10 min to administer. The HLSI-SF offers researchers and practitioners a valid and reliable measure of health literacy skills.

Abstract: Seeking health information can be a complicated process for a patient. Patients must know the topic of interest, where to look or ask, how to assess and comprehend, and how to evaluate the credibility and trustworthiness of the sources. In this study, the authors describe preferences of patients with multiple risk factors for cardiovascular disease with varying health literacy and numeracy abilities for receiving health information. Participants were recruited from 2 health care systems. Health literacy and numeracy were assessed and participants completed an orally administered survey consisting of open-ended questions about obtaining health information and preferences for health information. In-depth interviews were conducted with a subset of participants. A diverse sample of 150 individuals (11.3% Latino, 37.3% African American, 44.7% with income less than $15,000/year) participated. Most participants had adequate functional health literacy, while 65% had low numeracy skills. Regardless of health literacy or numeracy ability, participants overwhelmingly preferred to receive health information during a face-to-face conversation with their health care provider. While individuals with adequate functional health literacy identified a variety of health information sources, actions are needed to ensure multiple modalities are available and are in plain, clear language that reinforces patients' understanding and application of information to health behavior.

Abstract: Recent research has begun to recognize the important influence of literacy levels and how they affect health and wellbeing, especially in older adults Our study focuses on health and financial literacy, two domains of literacy which previous research has suggested may be significantly related to health and wellbeing Our study examines the relation of health and financial literacy with health promoting behaviors and health status among community-based older persons We conducted a cross-sectional study using data from the Rush Memory and Aging Project, a community-based cohort study of aging in northeastern Illinois The study consisted of 556 older persons without dementia, each determined by a clinical evaluation Health and financial literacy were measured using a series of questions designed to assess the ability to understand and process health and financial information, concepts, and numeracy; the two scores were averaged to yield a total literacy score Health promoting behaviors, including engagement in cognitive, physical, and social activities, were assessed using self report measures Indicators of heath status, including cognition (global cognition and five specific cognitive abilities), functional status (basic and instrumental activities of daily living, mobility disability), and mental health (depressive symptoms, loneliness) were assessed In a series of regression models adjusted for age, sex, and education, higher total literacy scores were associated with more frequent participation in health promoting behaviors, including cognitive, physical and social activities (all p values <005) Higher total literacy scores were associated with higher cognitive function, less disability, and better mental health (all p values < 005) Literacy remained associated with health promoting behaviors and health status in fully adjusted models that also controlled for income and the number of chronic medical conditions Most of the findings were similar for health and financial literacy except that health literacy was more strongly associated with health promoting behaviors whereas financial literacy was more strongly associated with mental health Health and financial literacy are associated with more frequent engagement in health promoting behaviors and better health status in older persons without dementia

Abstract: Parent guidance for numeracy activities and preschoolers' numeracy performance were examined in the context of playing a board game in three sessions over a two-week period. Twenty-eight parent–child dyads were randomly assigned to a numeracy awareness group in which parents were provided with suggested numeracy activities to incorporate into the games, or a comparison group provided with no numeracy instructions. Parents in the numeracy awareness group provided guidance for basic and more complex numeracy skills at approximately twice the rate of parents in the comparison group. Children exposed to more numeracy questions during the games generated more correct responses. These results support the view that activities occurring in children's daily lives can be used by parents to enhance children's exposure to numeracy-related content and enrich socio-cultural interactions related to numeracy.

Abstract: This paper explores how mandated literacy assessment is reorganising teachers’ work in the context of Australia’s National Assessment Program – Literacy and Numeracy (NAPLAN), which was implemented in 2008. Students in Years 3, 5, 7 and 9 are tested annually, with school results publicly available. The wider policy context and the emergence of different forms of interconnected educational work associated with the testing phenomenon are described. Taking an Institutional Ethnography approach, the local effects of the federal policy regime are examined through a case study of one school. What mandated literacy assessment does to educators’ work in a culturally diverse low socioeconomic school community is discussed. Key themes include strategic exclusions of students from the testing process, appropriations and adaptations of literacy theory, work intensification, and ethical mediation of results. Questions concerning equity are raised about the differential effects of policy in different school contexts.

Abstract: Financial decisions, be they related to asset building or debt management, require the capacity to do calculations, including some complex ones. But how numerate are individuals, in particular when it comes to calculations related to financial decisions? Studies and surveys implemented in both the United States and in other countries that are described in this paper show the level of numeracy among the population to be very low. Moreover, lack of numeracy is not only widespread but is particularly severe among some demographic groups, such as women, the elderly, and those with low educational attainment. This has potential consequences for individuals and for society as a whole because numeracy is found to be linked to many financial decisions. Now more than ever, numeracy and financial literacy are lifetime skills necessary to succeed in today's complex economic environment.

Abstract: Purpose – The purpose of this article is to explore the role and importance of numeracy skills in graduate recruitment within a diversity of employment sectorsDesign/methodology/approach – The results of a mixed‐methods study, involving three online surveys (including an employer survey), student focus group sessions and interviews with tutors, are presentedFindings – The results reveal the importance that employers attach to graduates’ numeracy skills and the extent to which employers use numeracy tests in graduate recruitment They thus highlight the potential for poor numeracy skills to limit any graduate's acquisition of employment, irrespective of their degree subject; especially since numeracy tests are used predominantly in recruitment to the types of jobs commensurate with graduates’ career aspirations and within sectors that attract graduates from across the diversity of academic disciplines, including the arts and humanitiesResearch limitations/implications – Since participants were self‐sele

Abstract: Vocational Education and Training (VET) in high schools has had positive effects on the retention of Indigenous students, providing important pathways into further education and the workforce. However, low-level literacy (and numeracy) skills can make successful completion difficult, especially for students who speak Standard Australian English as an additional language or dialect. This article describes research undertaken to inform the development of a second language and literacy needs analysis model designed for high school VET teachers to address the needs of Indigenous students. The study draws on second language acquisition research, which demonstrates the value of using tasks as the basis for language teaching syllabus design, with needs analysis as a fundamental aspect of this. The project centred on Aboriginal high school VET students from remote and rural communities in Western Australia, who speak English as an additional language/dialect. Data collected included: individual and focus group interviews, training materials, and observation field notes on the language and literacy practices in classrooms and workplaces. The major findings focus on the development of oral language (for both job-oriented and social interactions in the workplace) and literacy skills, as well as the need to overcome ‘shame’ and develop confidence for speaking to non-Aboriginal people.

Abstract: Background: Limited literacy skills are common in the United States (US) and are related to lower HIV knowledge and worse health behaviors and outcomes. The extent of these associations is unknown in countries like Mozambique where no rigorously validated literacy and numeracy measures exist. Methods: A validated measure of literacy and numeracy the Wide Range Achievement Test version 3 (WRAT-3) was translated into Portuguese adapted for a Mozambican context and administered to a cross-section of female heads-of-household during a provincially representative survey conducted from August 8 to September 25 2010. Construct validity of each subscale was examined by testing associations with education income and possession of socioeconomic assets stratified by Portuguese speaking ability. Multivariable regression models estimated the association among literacy/numeracy and HIV knowledge self-reported HIV testing and utilization of prenatal care. Results: Data from 3557 women were analyzed; 1110 (37.9%) reported speaking Portuguese. Respondents mean age was 31.2; 44.6% lacked formal education and 34.3% reported no income. Illiteracy was common (50.4% of Portuguese speakers 93.7% of non-Portuguese speakers) and the mean numeracy score (10.4) corresponded to US kindergarten-level skills. Literacy or numeracy was associated (p<0.01) with education income age and other socioeconomic assets. Literacy and numeracy skills were associated with HIV knowledge in adjusted models but not with HIV testing or receipt of clinic-based prenatal care. Conclusion: The adapted literacy and numeracy subscales are valid for use with rural Mozambican women. Limited literacy and numeracy skills were common and associated with lower HIV knowledge. Further study is needed to determine the extent to which addressing literacy/numeracy will lead to improved health outcomes.

Abstract: Learning objectives By engaging with the text in this chapter, students will be able to: describe the general capabilities framework in the new Australian Curriculum apply the elements of the general capabilities framework to the health and physical education learning entitlement understand how information and communication technology (ICT) can be effectively incorporated into health and physical education teaching and learning practice to support the learning of students with diverse needs describe social justice principles relevant to access to ICT in terms of gender, ability, social class and ethnicity. Casey is in her first year of teaching at the local early childhood centre. The director of the centre has called a meeting to discuss the implications of the impending Australian Curriculum. The centre will be required to encourage the children to be literate across a range of areas. Casey recalls her pre-service teacher educator presented many different approaches to teaching health and physical education, but she didn’t see many ways of modelling how to use ICT for the young children in the preschool. In fact, screen time was noted as a factor in the increasing levels of overweight and obesity among children. How can play be accommodated with ICT? Alternatively, how can ICT progress children’s development around the issue of play? Jennie has been working with Year 4 this year. Although some sporty children are in her class, the gap is widening between the skilled and those disinterested in the game play. Jennie is seeking new ways of teaching physical education to close this gap in students’ attitudes and skill levels and avoid as much as possible the behaviour management challenges arising in her active lessons. How can she incorporate ICT into her teaching to engage the disinterested and poorly skilled? Is that possible or will ‘PE’ be just a ‘busy, happy, fun’ alternative to engaging students in the challenge of skill acquisition?

Abstract: A case study approach was adopted to investigate two thinking skills programmes for a maximum variation sample of five- to six-year-olds in four schools, in two local authorities (LAs), in England and Wales, using multiple methods. School staff interviewed felt that thinking skills programmes enhanced critical thinking skills and improved use of language, attentive listening, social cooperation, confidence and independence. Welsh staff indicated that the programmes had a whole-school impact, reflecting national policy, intensive training, coaching and monitoring and leading to transfer to other lessons, such as mathematics. Without a national curriculum mandate, the English thinking-skills practice was vulnerable to disruption and lack of continuity. Observation showed that teachers' delivery varied in open questioning and challenge, group work and pupil talk. Pupils' verbal reasoning and numerical attainments showed modest evidence of change and development. Conditions supporting change and sust...

Abstract: The purpose of this study was to extend the research on the Tests of Early Numeracy Curriculum-Based Measurement (TEN-CBM) tools by examining concurrent and predictive relations from kindergarten through third grade. Using a longitudinal sample of 535 students, this study included logistic regression, latent cluster, and latent transition analyses to examine the patterns and trends of student performance on all four TEN-CBM measures in kindergarten and first grade, math CBM (M-CBM) in first grade, and mathematics performance on a statewide high-stakes assessment in third grade. Results suggest that two of the TEN-CBM tools, Quantity Discrimination and Missing Number, are most robust at predicting later math performance. Longitudinal analysis indicated that students who are low performing in early numeracy at the beginning of kindergarten tend to be low performing in math at third grade. Low-achieving students also demonstrated a greater decrease in math skills over summer months when compared to higher-ac...