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200 % of nothing. An eye-opening tour through the twists and turns of math abuse and innumeracy
... Outros autores (Best, 2001;Blastland & Dilnot, 2008;Dewdney, 1993;Huff, 1954) também se debruçam sobre o uso indevido de matemática, mas num contexto mais amplo de situações da vida diária (incluindo nos meios de comunicação). ...
... Comparando os jornais de referência com os populares, os dados indicam que, enquanto erros numéricos são os mais frequentes nos jornais de referência, os erros nos jornais populares são predominantemente estatísticos� Curiosamente, raramente se identificaram falácias de raciocínio nos cinco jornais, embora a literatura sugira estes erros são frequentes nas notícias (Blastland & Dilnot, 2008;Dewdney, 1993;Paulos, 1997 ...
... Outras autores, como Dewdney (1993), Best (2001), Blastland e Dilnot (2008) e Huff (1954), debruçam-se ainda sobre o uso e erros matemáticos comuns, cometidos em contexto de notícias e do quotidiano, sendo alguns desses erros semelhantes àqueles que se encontram em notícias. ...
... A grelha construída para recolher a informação foi desenvolvida antes da recolha dos dados e com base na literatura (Berry, 1967;Blankenburg, 1970;Azevedo, 2007;Gradim, 2000;Cohn & Cope, 2001;Paulos, 1997;Maier, 2000;Huff, 1954;Blastland & Dilnot, 2008;Dewdney, 1993;Best, 2001), optando-se assim por uma abordagem dedutiva, com o objetivo de sensibilizar os investigadores, à priori, para o tipo de conteúdo que poderiam encontrar. ...
... La capacidad de interpretar información presentada en tablas es un elemento clave de la cultura científica, y esto requiere una atención explícita como parte de la educación de todas las personas. Algunas personas no se desenvuelven adecuadamente frente a información cuantitativa, y pueden llegar a depender de la interpretación de otros, convirtiéndose en sujetos vulnerables a engaños intencionales o no (Dewdney, 1993), puesto que no han tomado conciencia que los datos pueden manipularse para apoyar ciertos puntos de vista. ...
The growing emphasis on the development of research abilities positions the presentation and interpretation of data as activities of increasing importance. Being competent in interpreting data representations is essential to understanding the modern world and to being a scientifically literate citizen. Tables are used daily, but it is not easy to understand the different cognitive processes that tables activate. It is important to know how to read, complete, build, and interpret tables. There is controversy about what to teach first with respect to graphs, but there is no controversy about what to teach regarding tables. Given subjects' difficulties with tables, the research centers on them and contributes to the school science curriculum and to teaching and learning practices. This article presents the state of the art regarding tables from 1977 to 2012. The search and revision of the statistics bibliography referring to tables included scientific articles, books, dissertations, talks in international conferences, and school curricula from some countries. This study shows tables apparent simplicity, proposes a generic table structure, and provides arguments and guidelines for tables being explicitly taught, given their broad insertion in our culture.
... In this realm it is important to note that humans perform rather weakly in comparing the differential impact of gains and losses [15]. For instance, many participants assumed that if they lose 33% of their invested capital, it would take a gain of 33% to recover their losses [16], which would need a much higher gain of 50%. This general fallacy seems to be not so substantial within low ranges of losses as in the given example; but it counts the stronger the higher the losses are. ...
In an experiment, we systematically tested the risk tolerance for trading stock shares that vary in the initial
price of the shares. Persons inexperienced with the stock market had to set the selling points for 60 stocks in the
case of (a) decreasing or (b) rising prices. First, a stronger risk aversion for falling compared to rising prices was
obtained. Second, the experiment revealed a dramatic increase in risk tolerance the lower the buying prices of the
stocks were; nearly perfectly following a power function (Pearson-R’s>.93). Furthermore, it seemed very difficult for
persons to grasp the consequences of share price neglect, namely that the initial share price has a significant impact
on the readiness to take higher risks, whether in a positive or negative direction. Therefore, we are also referring to
it as a “hidden risk tolerance”. This paper offers insights into irrational decision making in trading stocks. It allows
the formation of estimates regarding trading volume and share price potential on the basis of the initial share price.Furthermore, it provides clues for the consequent reduction of risk-seeking behavior.
... El anumerismo o la incompetencia en el uso correcto de las matemáticas en la vida (Pedoe, 1998) tiene nefastas consecuencias para la propia vida personal o para el propio progreso del entorno social donde se vive. La ausencia de matemáticas lleva necesariamente a errores de planteamiento y resolución de problemas (Dewdney, 1996) (Devlin 1999(Devlin , 2000. El uso inadecuado puede inducir a graves problemas ya sea por la formulación de un modelo precario en recursos o también por la formulación de un modelo excesivamente sofisticado para poder concluir soluciones que sean prácticas. ...
El presente trabajo focaliza la atención en el importante papel que el aprendizaje de las matemáticas, por medio de la modelización y las aplicaciones, puede jugar en la educación de los futuros ciudadanos, como tales. Se discute la necesidad de cambios y como introducir nuevos contenidos y competencias para la vida en el siglo XXI.
... At a functional level, it means being able to do mental arithmetic. But beyond this, a numerate person has an ability to analyse claims made using numbers (and related media, such as graphs); for example, knowing how statistics can be abused (see McFarlane, 1997: Chapter 7 andDewdney, 1996). A related belief is that teenagers should now be taught "financial literacy": how to manage money, recognising the impact of debt on their personal lives. ...
An exploration of information literacy and ICT skills education from the point of view of social and political theory. The author incorporates theories to argue why the idea of information literacy is so important in the 21st century, and also to develop teaching strategies to this end. The book argues that only through expanding the range of information literacy education taking it beyond just formal school and university education and into homes, friendship networks and workplaces can we construct an effective educational response to information technology in the 21st century. Information literacy includes, but transcends, ICT skills and ultimately is about being politically, socially and communicatively competent in an information society.
... La capacidad de interpretar información presentada en tablas es un elemento clave de la cultura científica, y esto requiere una atención explícita como parte de la educación de todas las personas. Algunas personas no se desenvuelven adecuadamente frente a información cuantitativa, y pueden llegar a depender de la interpretación de otros, convirtiéndose en sujetos vulnerables a engaños intencionales o no (Dewdney, 1993), puesto que no han tomado conciencia que los datos pueden manipularse para apoyar ciertos puntos de vista. ...
El creciente énfasis en el desarrollo de habilidades de investigación posiciona la presentación e interpretación de los datos como actividades cada vez más importantes. Tener competencia en interpretar representaciones de datos es esencial para comprender el mundo actual y ser un ciudadano científicamente alfabetizado. La tabla es usada cotidianamente, pero no es simple comprender los diferentes procesos cognitivos que activan las tablas. En el caso de las tablas es importante saber leerlas, completarlas, construirlas e interpretarlas. Existe controversia sobre qué enseñar primero respecto a cómo graficar; sin embargo, no existe controversia de qué enseñar respecto a las tablas. Debido a las dificultades de los sujetos con las tablas, la investigación en torno a ellas es un aporte al currículo científico escolar y a las prácticas de enseñanza y aprendizaje. Este artículo presenta el estado del arte sobre las tablas desde 1977 a 2012; la búsqueda y lectura de material bibliográfico del área de estadística referida a las tablas incluyó artículos científicos, libros, ponencias en congresos internacionales, tesis y currículo escolar de algunos países. Este estudio muestra la simplicidad aparente de las tablas, realiza una propuesta de estructura de tabla genérica, y entrega argumentos y lineamientos para que las tablas sean enseñadas explícitamente dadas su amplia inserción en nuestra cultura.
... Information asymmetry exists between consumers and the payday lenders. Many payday loan consumers as well as the general population do not have an accurate understanding of the APR process (Dewdney, 1993), and/or the industry has "incentive to stretch the truth" or "to outright lie" (Pappalardo, 2012, p. 327). Thus, consumers may not make "a reasonably" informed comparison of alternative forms of credit (e.g., J. Y. Campbell, Jackson, Madrian, & Tufano, 2011;Lusardi & Tufano, 2009;Martin, 2010). ...
Individuals with limited or no access to checking accounts rely on alternative financial services (AFS) to navigate today’s economy. One AFS product that arguably is the most controversial is the payday loan—a small, short-term, high-interest loan. Although potentially assisting financially fragile individuals to fulfill their short-term credit needs, payday loans likely expose them to greater financial vulnerability. Despite the significance of issues related to financially fragile individuals, payday lending is largely understudied in social work. This article describes the payday loan industry, payday loan consumers, the consequences of payday loan use, and implications for social work advocacy.
... • Users suffer from gaps in the education system. " Innumeracy " (as an analogous phenomenon to illiteracy; for the notion of innumeracy, see, e.g., Paulos 1989; Dewdney 1993; Schneeweiß 2001) contrasts with the trend of making growing use of statistical figures in the media, management, and the public sector. Though not as visible as illiteracy or general cultural ignorance, this type of mathematical illiteracy, it has recently been argued, has a considerable impact on everyday life (e.g., muddled government decisions, media coverage on complex phenomena). ...
One of the key principles of quality management in official statistics is user orientation. The types of users are manifold and the relationship between users and producers is very complex. This difficult situation requires much attention and will be one of the main fields of interest in the next years. One important reason for the great variety of user types lies in the fact that statistical information (as the main product of NSIs) has to be provided both as public good (informational infrastructure for democratic societies) and as a private good (tailor-made analyses on the demand of individual customers). Different types of users with different and (partly) conflicting requirements correspond to this distinction. In this respect the statistical product differs from many other products on the market. In addition to the diverse and partly conflicting user needs, the relationship of the producer with each single user is very complex in itself. A complex interaction between user and producer has to be established in order to achieve an optimum solution. In this user-producer dialogue, user and producer negotiate and define the statistical working system comprising the statistical programme as well as the products and the processes.
... La capacidad de interpretar información presentada en tablas es un elemento clave de la cultura científica, y esto requiere una atención explícita como parte de la educación de todas las personas. Algunas personas no se desenvuelven adecuadamente frente a información cuantitativa, y pueden llegar a depender de la interpretación de otros, convirtiéndose en sujetos vulnerables a engaños intencionales o no (Dewdney, 1993), puesto que no han tomado conciencia que los datos pueden manipularse para apoyar ciertos puntos de vista. ...
El creciente énfasis en el desarrollo de habilidades de investigación posiciona la presentación e interpretación de los datos como actividades cada vez más importantes. Tener competencia en interpretar representaciones de datos es esencial para comprender el mundo actual y ser un ciudadano científicamente alfabetizado. La tabla es usada cotidianamente, pero no es simple comprender los diferentes procesos cognitivos que activan las tablas. En el caso de las tablas es importante saber leerlas, completarlas, construirlas e interpretarlas. Existe controversia sobre qué enseñar primero respecto a cómo graficar; sin embargo, no existe controversia de qué enseñar respecto a las tablas. Debido a las dificultades de los sujetos con las tablas, la investigación en torno a ellas es un aporte al currículo científico escolar y a las prácticas de enseñanza y aprendizaje. Este artículo presenta el estado del arte sobre las tablas desde 1977 a 2012; la búsqueda y lectura de material bibliográfico del área de estadística referida a las tablas incluyó artículos científicos, libros, ponencias en congresos internacionales, tesis y currículo escolar de algunos países. Este estudio muestra la simplicidad aparente de las tablas, realiza una propuesta de estructura de tabla genérica, y entrega argumentos y lineamientos para que las tablas sean enseñadas explícitamente dadas su amplia inserción en nuestra cultura.
The growing emphasis on the development of research abilities positions the presentation and interpretation of data as activities of increasing importance. Being competent in interpreting data representations is essential to understanding the modern world and to being a scientifically literate citizen. Tables are used daily, but it is not easy to understand the different cognitive processes that tables activate. It is important to know how to read, complete, build, and interpret tables. There is controversy about what to teach first with respect to graphs, but there is no controversy about what to teach regarding tables. Given subjects' difficulties with tables, the research centers on them and contributes to the school science curriculum and to teaching and learning practices. This article presents the state of the art regarding tables from 1977 to 2012. The search and revision of the statistics bibliography referring to tables included scientific articles, books, dissertations, talks in international conferences, and school curricula from some countries. This study shows tables’ apparent simplicity, proposes a generic table structure, and provides arguments and guidelines for tables being explicitly taught, given their broad insertion in our culture.
... Mathematicians, statisticians, and mathematics educators consider probability and statistics to be valuable for people in understanding their everyday world (Borel, 1962;Dörlfer & McLone, 1986;Good, 1983;Jacobsen, 1989;McGervey, 1986). Dewdney (1993) and Paulos (1989Paulos ( , 1994 have argued that people who lack a basic understanding of probability and statistics are often functionally innumerate. Probability and statistics are also considered important for advanced post-secondary studies; for example in the natural and social sciences. ...
... One area in which individuals are susceptible to errors is changes in percentage rates. For instance, in standardized test scores in California, Dewdney (1993) found that participants liked a 60-per-cent decrease followed by a 70-per-cent increase, perceiving the net change to be positive when in fact it was a net decrease of 32 per cent. In the consumer domain, Paulos (1988) found that consumers mistakenly judge a 40-per-cent price discount followed by another 40-per-cent discount to be a total discount of 80 per cent, believing they could buy more in this situation than if the retailer provided a single but economically equivalent percentage discount of 64 per cent. ...
... Others have demonstrated the consequences of innumeracy-the lack of quantitative literacy-in many topics and settings. Indeed, a small genre of literature has emerged on the subject including Paulos's books, A Mathematician Reads the Newspaper (1996) and Innumeracy: Mathematical Illiteracy and Its Consequences (2001), Dewdney's (1993) 200% of Nothing: An Eye-Opening Tour Through the Twists and Turns of Math Abuse and Innumeracy, and Best's (2001) Damned Lies and Statistics: Untangling Numbers From the Media, Politicians, and Activists. Authors of these books all suggested that many people emerge from school ill-equipped to apply quantitative literacy skills to the kinds of questions central to functioning in modern society. ...
... It has come to light that despite the methodolgical sophistication associated with them, too many statistics are of fuzzy quality at best, too many stray widely from what they are meant to represent, and instead of fostering insight, too many simply produce a perceptual muddle. Many books and papers have documented these problems in varied fields (Crossen, 1996;Dewdney, 1993;Levi, 2001;Milibank, 2002;Paulos, 1990Paulos, , 1997. The case of the Iraq war is but a tip of a vast iceberg. ...
... "Math," after all, "is hard" (as one none-too politically correct "Talking Barbie" doll is reported to have said). And indeed, there is no shortage of findings that attest to the counterintuitiveness of many mathematical principles (Banks & Hill, 1974;Dewdney, 1993;Gigerenzer & Edwards, 2003;Gilovich, Vallone, & Tversky, 1985;Hoffrage, Lindsey, Hertwig, & Gigerenzer, 2000;Kahneman & Tversky, 1973;Kruger, Savitsky, & Gilovich, 1999;Tversky & Kahneman, 1971), percent included (Lembke & Reys, 1994;Parker, 1997;Parker & Leinhardt, 1995;Venezky & Bregar, 1998) Although doubtless part of the explanation, the results suggest that the bias is a product of more than mere innumeracy. In Experiment 5, for instance, we found that participants' math ability had little if any influence on their tendency to show the bias. ...
The present research investigated consumers' intuitions about percent differences. We found that the perceived difference between two quantities compared on a percent scale varies as a function of the target of the comparison. The subjective price difference between a 1000 moped, for instance, increased when the former was described as 50% more than the latter than when the latter was described as 33% less than the former (Experiment 1). This effect (1) is limited to comparisons made on a ratio scale, (2) varies as a function of the percent difference between the two quantities, and (3) applies not only to price but also to other quantifiable attributes (Experiments 2–4). Finally, Experiment 5 found that the bias was reduced (but not eliminated) with financial incentives for accuracy and persisted even among highly numerate individuals. Discussion focuses on the source and the implications of this bias.
... One study of Danish doctors even concluded that "the statistical knowledge of most doctors is so limited that they cannot be expected to draw the right conclusions from those statistical analyses which are found in papers in medical journals" 27 . While innumeracy pervades society as a whole 28 , we must not allow it to be rampant in the medical community. All medical professionals must have at least a basic understanding of how to interpret biostatistics and understand research methodology. ...
Myths are widely held beliefs that are false or of unverifiable existence. In medicine, they are not just unproven theories or mistaken conclusions, rather, they are fictitious ideas that weave their way throughout the profession. In order to prevent and treat medical myths, they need to be recognized as a disease that is harmful to patient care. Using established principles of medicine, the myths then can be medically managed and a cure attempted. To accomplish this, the myths need to be understood in terms of their etiology and pathopsychology. A firm understanding of biostatistics and the principles of evidence based medicine is essential to the prevention, management, and cure of medical myths.
Research question:
Temperature control within the IVF laboratory is an important aspect of a quality control system, helping to reduce environmental stress and ensure good-quality embryo development. Temperature fluctuations are probably more common than expected and the optimal temperature for embryo culture is not known. Modern incubators offer the opportunity to examine the impact of culture temperature on preimplantation embryo development while controlling for other variables within the system. The purpose of this study was to examine the effect of a range of temperatures during extended embryo culture on resulting mouse embryo development and morphokinetic timings.
Methods:
Using a single time-lapse incubator with six individual chambers, frozen-thawed one-cell mouse embryos were cultured individually at temperatures adjusted by 0.5°C between chambers to cover the range of 35.0-37.5°C. Resulting blastocyst formation and embryo morphokinetic timings were recorded and compared.
Results:
Changes in culture temperature had a significant impact on mouse blastocyst development and morphokinetic timings (P < 0.05). Under the conditions used in this study, blastocyst development was best at 37.0°C. Mouse preimplantation embryo mitotic cell divisions were generally slower at cooler temperatures and accelerated as the temperature increased from 35.0°C to 37.5°C.
Conclusion:
Incubator culture temperature must be carefully controlled, as even slight variations of 0.5°C in the temperature used for extended embryo culture can have significant impacts on embryo development and mitotic cell divisions. These data have potential implications for application of universal morphokinetic selection algorithms and may help explain differences in mitotic errors/embryo mosaicism between laboratories.
This proceedings report presents the outcomes from an international expert meeting to establish consensus guidelines on IVF culture conditions. Topics reviewed and discussed were: embryo culture - basic principles and interactions; temperature in the IVF laboratory; humidity in culture; carbon dioxide control and medium pH; oxygen tension for embryo culture; workstations - design and engineering; incubators - maintaining the culture environment; micromanipulation - maintaining a steady physcochemical environment; handling practices; assessment practices; culture media - buffering and pH, general composition and protein supplementation, sequential or single-step media for human embryo culture; use and management - cold chain and storage; test equipment - calibration and certification; and laboratory equipment and real-time monitoring. More than 50 consensus guideline points were established under these general headings.
Many factors are considered when a woman estimates her personal risk of breast cancer. Common to most decisions are four separate influences that have convinced the public and many health-care providers that breast cancer is the greatest concern for menopausal women and that menopausal hormone therapy (MHT) is generally responsible. Historically there have been well-documented situations in which big pharma and doctors have not put patient interests first. Conflicting reports about the safety of MHT and the media imperative to always increase readership by presenting a compelling scary story have created an underlying distrust of science, doctors, and MHT. Numerical and statistical illiteracy in the general population creates a situation where lotteries succeed despite astronomical odds and the risks of medical interventions are exaggerated by their description using relative, rather than absolute, risks. Finally, mammographic overdiagnosis contributing to improved breast cancer survival has contributed to the ‘popularity paradox’ (more screening – more enthusiasm) especially among survivors and advocacy groups. As a result, worry about breast cancer has overshadowed concern about cardiovascular diseases as the major cause of death and disability in the later years. The ongoing challenge for clinicians dealing with menopausal women is to bridge the gap in risk perception with evidence-based common-sense advice.
The authors present a quantitative content analysis to assess the use of mathematical information in the news of five generalist Portuguese newspapers during a three-month period. Misuses of mathematics were also studied in this context. Results show that only a small percentage of the news articles have mathematical information when compared to previous studies in the field. Furthermore, over 30% of the news articles containing mathematical information have some type of mathematical error. Different categories of errors are defined and reasons why these might occur are discussed.
Measurements are essential In medical practice. Throughout their training, doctors are taught the adage “meten is weten” (the knowledge is in the numbers). In this thesis we evaluated various diagnostic measurements in paediatrics – across a wide age range, from neonates to older children – aimed at clarifying (demystifying) these commonly used procedures. We discuss the general aspects of uncertainty in medicine, since uncertainty is a major reason for performing diagnostic tests in the first place. Furthermore we explain the way evidence-based medicine (EBM) may help doctors to deal with this feeling of uncertainty.
The measurements investigated in this thesis are: 1) test strips for measurement of glucosuria in neonates, 2) diagnostic value of various clinical signs, including glucosuria, in identifying late-onset sepsis in premature neonates, 3) fluid-balance charts in neonates, 4) clinical assessment of severity of dyspnoea in children and 5) viral tests to identify and isolate RSV-infected infants hospitalised for bronchiolitis, for the purpose of reducing nosocomial cross-infection.
Apart from the test strips for measurement of glucosuria, all measurements or procedures we have investigated appeared to be too imprecise or of insufficiently validity to allow for clinically meaningful use in clinical practice.
This is a list of mathematical mistakes made over and over by advertisers, the media, reporters, politicians, activists, and in general many non-math people. These come from many sources, which will appear in parenthesis. I will try to find an actual example of each for learning purposes. Note: In this document, I attack errors made by popular social organizations. I am not attacking their important causes, only their mathematical errors. I try to find errors from all political and social views. Any suggestions for better examples and new topics can be e-mailed to me: paul@mathmistakes.com Aftermath Counting (A. K. Dewdney)-What the press has a tendency to do after a major disaster. It is the counting of known casualties from the police, paramedics, hospitals, and morgues, without considering duplication. Example: After the San Francisco Earthquake in 1989, reported deaths skyrocketed to 255 before finally settling on the number 64 dead. Interestingly, the Oklahoma City bombing of 1995 kept the body count at only the number of bodies actually recovered, though the press reported as many as 300 missing (the final tally was 163). "All Disasters Come in Threes" Conjecture" -Also called the "All Celebrities Die in Threes" Conjecture. Essentially it is the mistake of grouping what is essentially a random occurrence.
Quantitative literacy is an important proficiency that pertains to "word problems" from science, history, and other fields. Unfortunately, teaching how to solve such problems is often relegated to math courses alone. This paper shows how quantitative literacy also involves concepts and skills from English composition and the substantive disciplines. It outlines a systematic approach to writing the answers to word problems – a fundamental skill that applies to ongoing education, everyday life, and the workplace.
For decades, there has been a heated debate about whether or not nuclear power plants contribute to childhood cancer in their respective neighbourhoods, with statisticians testifying on both sides. The present paper points to some flaws in the pro-arguments, taking a recent study prepared for the political party “Buendnis 90 /Gruene” as a specimen. Typical mistakes include an understatement of the size of tests of significance, disregard of important covariates and extreme reliance on very few selected data points.
When evaluating the net impact of a series of percentage changes, we predict that consumers may employ a "whole number" computational strategy that yields a systematic error in their calculation. We report on three studies conducted to examine this issue. In the first study we identify the computational error and demonstrate its consequences. In a second study, we identify several theoretically driven boundary conditions for the observed phenomenon. Finally we demonstrate in a real-world retail setting that, consistent with our premise, sequential percentage discounts generate more purchasers, sales, revenue, and profit than the economically equivalent single percentage discount. (c) 2007 by JOURNAL OF CONSUMER RESEARCH, Inc..
Odds and odds ratios are hard for many clinicians to understand. Odds are the probability of an event occurring divided by the probability of the event not occurring. An odds ratio is the odds of the event in one group, for example, those exposed to a drug, divided by the odds in another group not exposed. Odds ratios always exaggerate the true relative risk to some degree. When the probability of the disease is low (for example, less than 10%), the odds ratio approximates the true relative risk. As the event becomes more common, the exaggeration grows, and the odds ratio no longer is a useful proxy for the relative risk. Although the odds ratio is always a valid measure of association, it is not always a good substitute for the relative risk. Because of the difficulty in understanding odds ratios, their use should probably be limited to case-control studies and logistic regression, for which odds ratios are the proper measures of association.
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