Education Commons^™

Calculus Of The Impossible: Review Of The Improbability Principle (2014) By David Hand And The Logic Of Miracles (2018) By Lásló Mérő, Samuel L. Tunstall

Numeracy

David J. Hand. 2014. The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day (New York, NY: Scientific American/Farrar, Straus and Giroux) 288 pp. ISBN: 978-0374175344.

Lásló Mérő. 2018. The Logic of Miracles: Making Sense of Rare, Really Rare, and Impossibly Rare Events (New Haven, CT: Yale University Press) 288 pp. ISBN: 978-0300224153.

David Hand and Lásló Mérő both grapple with the occurrence of seemingly impossible events in these two popular science books. In this comparative review, I describe the two books, and explain why I prefer Hand's treatment of the impossible.

Why I Believe People Need Painting By Numbers, Jason Makansi

Numeracy

Jason Makansi.2016. Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the Experts (Tucson AZ: Layla Dog Press). 196 pp. ISBN 978-0998425900.

This piece briefly introduces my Painting By Numbers, which aims to take the core messages of the QL/QR community from academic and professional circles to the rest of the citizenry. I describe the book in the context of the critical need for the most basic numeracy tools to help consumers of news, information, and analysis—delivered through traditional and contemporary social media outlets—determine where a reported numerical result lies on the scale from utter nonsense …

Using Visual Analogies To Teach Introductory Statistical Concepts, Jessica S. Ancker, Melissa D. Begg

Numeracy

Introductory statistical concepts are some of the most challenging to convey in quantitative literacy courses. Analogies supplemented by visual illustrations can be highly effective teaching tools. This literature review shows that to exploit the power of analogies, teachers must select analogies familiar to the audience, explicitly link the analog with the target concept, and avert misconceptions by explaining where the analogy fails. We provide guidance for instructors and a series of visual analogies for use in teaching medical and health statistics.

Attitudes Toward Statistics Studies Among Students With Learning Disabilities, Orly Lipka, Itay Hess

Numeracy

This study aims to examine the effectiveness of a support course to change attitudes toward statistics studies of post-secondary students who were diagnosed with learning disabilities (LD) and/or Attention Deficit Hyperactivity Disorder (ADHD). The participants were 22 students in a support course that was provided over a single academic term on a weekly basis. The design of the study was according to 'Pre-Post' comparison. The effects on attitudes toward statistics were examined quantitatively and qualitatively to provide a comprehensive methodology for the research purposes. Results suggest that the weekly support course model that was taught simultaneously to the on-line course …

Ucsmp Teachers’ Perspectives When Using Graphing Calculators In Advanced Mathematics, Ilyas Karadeniz

USF Tampa Graduate Theses and Dissertations

Nowadays, technology plays a fundamental role in education, in general, and in mathematics education in particular. The graphing calculator has been an important technological tool in mathematics classrooms since its invention and introduction in 1985 by Casio. As graphing calculators provided so many uses, their contribution to the teaching and learning process has been investigated by many researchers who have shown the use of such technology can have a significant effect on improving mathematics teaching and learning.

Investigating the impact of graphing calculators on student learning is important. It is also essential to research teachers’ perspectives on how using graphing …

Incorporating Quantitative Reasoning In Common Core Courses: Mathematics For The Ghost Map, John R. Jungck

Numeracy

How can mathematics be integrated into multi-section interdisciplinary courses to enhance thematic understandings and shared common readings? As an example, four forms of quantitative reasoning are used to understand and critique one such common reading: Steven Berlin Johnson’s "The Ghost Map: The Story of London's Most Terrifying Epidemic - and How it Changed Science, Cities and the Modern World" (Riverhead Books, 2006). Geometry, statistics, modeling, and networks are featured in this essay as the means of depicting, understanding, elaborating, and critiquing the public health issues raised in Johnson’s book. Specific pedagogical examples and resources are included to illustrate applications and …

Period Life Tables: A Resource For Quantitative Literacy, Thomas J. Pfaff, Stanley Seltzer

Numeracy

A period life table provides an estimate of the probability that a person will die at a particular age. Using data available online, we examine tables of expected years to live for males and females against age for three populations: the United States in 2007, the U.S. at the turn of the twentieth century, and the Roman Empire. Scatter plots of males and females for each population show how life expectancy increases with age (e.g., U.S. 2007: 50 year-old female > 40 year-old female > 45 year-old male). The three data sets allow historical comparisons (e.g., of gender disparity, larger now; of …

Constructivist And Behaviorist Approaches: Development And Initial Evaluation Of A Teaching Practice Scale For Introductory Statistics At The College Level, Rossi A. Hassad

Numeracy

This study examined the teaching practices of 227 college instructors of introductory statistics from the health and behavioral sciences. Using primarily multidimensional scaling (MDS) techniques, a two-dimensional, 10-item teaching-practice scale, TISS (Teaching of Introductory Statistics Scale), was developed. The two dimensions (subscales) are characterized as constructivist and behaviorist; they are orthogonal. Criterion validity of the TISS was established in relation to instructors’ attitude toward teaching, and acceptable levels of reliability were obtained. A significantly higher level of behaviorist practice (less reform-oriented) was reported by instructors from the U.S., as well as instructors with academic degrees in mathematics and engineering, whereas …

Quantitative Literacy At Michigan State University, 2: Connection To Financial Literacy, Dennis Gilliland, Vince Melfi, Alla Sikorskii, Edward Corcoran, Eleanor Melfi

Numeracy

The lack of capability of making financial decisions has been recently described for the adult United States population. A concerted effort to increase awareness of this crisis, to improve education in quantitative and financial literacy, and to simplify financial decision-making processes is critical to the solution. This paper describes a study that was undertaken to explore the relationship between quantitative literacy and financial literacy for entering college freshmen. In summer 2010, incoming freshmen to Michigan State University were assessed. Well-tested financial literacy items and validated quantitative literacy assessment instruments were administered to 531 subjects. Logistic regression models were used to …

Quantitative Literacy At Michigan State University, 1: Development And Initial Evaluation Of The Assessment, Alla Sikorskii, Vince Melfi, Dennis Gilliland, Jennifer Kaplan, Suzie Ahn

Numeracy

Development, psychometric testing, and the results of the administration of a quantitative literacy (QL) assessment to undergraduate students are described. Three forms were developed covering a wide range of skills, contexts, and quantitative information presentation formats. Following item generation and revision based on preliminary testing and cognitive interviewing, a total of 3,701 consented undergraduate students at Michigan State University completed one of the three forms. Two of the forms contained 14 multiple-choice items, and one form contained 17 multiple-choice items. All forms were completed by students in less than 30 minutes. Evidence of validity and reliability were obtained for the …

A Quantitative Literacy View Of Natural Disasters And Nuclear Facilities, C. B. Connor

Numeracy

The March 11, 2011 earthquake, tsunami, and nuclear disaster in Tohoku, Japan, highlights the need to improve quantitative literacy (QL) in natural hazard assessment. A critical understanding of natural hazard assessments requires a sophisticated perspective on the mathematical and statistical tools used to estimate the odds of disaster, and the roles of data quality, model development, and subjective probability in estimation of uncertainty. Thus, improved QL is a basic requirement for improved decision-making about the safety of critical infrastructure, such as nuclear facilities.

A Leap Forward For Quantitative Literacy, H. L. Vacher

Numeracy

The Association of American College and Universities’ Learning Education and America’s Promise (LEAP) initiative has identified quantitative literacy (QL) as one of its Essential Learning Outcomes and classified it amongst five other Intellectual and Practical Skills such as inquiry and analysis, critical and creative thinking, and written and oral communication. This brings to mind a spreadsheet in which these transdisciplinary intellectual and practical skills are rows and academic disciplines are columns. With the view that the learning outcome QL is a row crossing mathematics and other disciplinary columns, this editorial considers how the papers in this and previous issues of …

Personal And Professional Numeracy: A Unit For Pre-Service Teachers At The University Of Tasmania, Jane M. Watson

Numeracy

This paper addresses issues associated with the development of a unit preparing pre-service teachers to be quantitatively literate in three respects. These issues surround (i) the need to be aware of numeracy demands across the curriculum, (ii) the need to model numerate behavior in all interactions of teachers, and (iii) the need to be able to interpret and use system data provided from local and national testing programs. The context for the unit described is Australia, where a national testing program for literacy and numeracy requires teachers to analyze extensive data on their students, a national curriculum requires teachers of …

Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman

Numeracy

This paper offers an alternative curriculum for high school mathematics. It proposes replacing the Algebra-Geometry-Algebra rush to calculus model with one which focuses on improving student problem-solving skills and general quantitative literacy skills while reinforcing basic manipulative skills. Most of these goals are gained by expanding the current single-year algebra-one course into two years. The model proposes moving “learning to write proofs” from the traditional geometry course into a separate discrete mathematics course. It requires statistics for every student, and requires a senior-level modeling course for every college-going student. In addition, the proposed model creates opportunities for students to move …

Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman

Numeracy

Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent …

Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison

Numeracy

The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, …

Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk

Numeracy

Advancing Assessment of Quantitative and Scientific Reasoning is a four-year NSF Project (DUE-0618599) in part designed to evaluate the generalizability of quantitative (QR) and scientific reasoning (SR) assessment instruments created at James Madison University to four other four-year institutions with very distinct missions and student demographics. This article describes the methods, results, and findings we obtained in our studies. More specifically, we describe how to conduct content-alignment exercises in which faculty members map each item from a prospective test to the student learning objectives taught at the institution. Our results indicated that 92-100% of the QR and SR items were …

An Activity Promoting The Practice Of Quantitative Literacy For Pre– And In–Service Teachers Of Mathematics And Science, Timothy L. Sorey, Teri Willard, Duane Sholz

Numeracy

The purpose of this article is to describe a hands-on, laboratory activity that provided pre-service teachers in mathematics and science methods courses, and also some in-service mathematics teachers, with the opportunity to exercise quantitative literacy (QL) skills. The focus of the activity is electrical resistance, more particularly the resistance (in ohms) that is painted on small resistors by the use of color-coded bands, one of which is a band for % error. The activity consists of four parts. In the first, student teams familiarize themselves with the code, measure the ohmage of resistors for which the codes are visible, and …

Are Statistics Labs Worth The Effort?--Comparison Of Introductory Statistics Courses Using Different Teaching Methods, Jose H. Guardiola, Nadina Duran-Hutchings, Hassan Elsalloukh

Numeracy

This paper compares the academic performance of students in three similar elementary statistics courses taught by the same instructor, but with the lab component differing among the three. One course is traditionally taught without a lab component; the second with a lab component using scenarios and an extensive use of technology, but without explicit coordination between lab and lecture; and the third using a lab component with an extensive use of technology that carefully coordinates the lab with the lecture. Extensive use of technology means, in this context, using Minitab software in the lab section, doing homework and quizzes using …

Review Of Super Crunchers By Ian Ayers, Eric Gaze

Numeracy

Ayers, I. Super Crunchers: Why Thinking-by-Numbers Is the New Way to be Smart. (Bantam Dell Publishing Group, 2007). 272 pp. Hard cover $25 ISBN 978-0-553-80540-6.

Super Crunchers tells the story of how analyzing data is changing the ways in which decisions are made. We in the National Numeracy Network make a case for the importance of quantitative literacy by referring to how much quantitative information is now available to each of us: “a world awash in numbers.” Ian Ayres zeroes in on the people who are making a living crunching all of these data. From the seemingly innocuous (how …

Measuring Resource Inequality: The Gini Coefficient, Michael T. Catalano, Tanya L. Leise, Thomas J. Pfaff

Numeracy

This paper stems from work done by the authors at the Mathematics for Social Justice Workshop held in June of 2007 at Middlebury College. We provide a description of the Gini coefficient and some discussion of how it can be used to promote quantitative literacy skills in mathematics courses. The Gini Coefficient was introduced in 1921 by Italian statistician Corrado Gini as a measure of inequality. It is defined as twice the area between two curves. One, the Lorenz curve for a given population with respect to a given resource, represents the cumulative percentage of the resource as a function …

Using Local Data To Advance Quantitative Literacy, Stephen Sweet, Susanne Morgan, Danette Ifert Johnson

Numeracy

In this article we consider the application of local data as a means of advancing quantitative literacy. We illustrate the use of three different sources of local data: institutional data, Census data, and the National College Health Assessment survey. Our learning modules are applied in courses in sociology and communication, but the strategy of using local data can be integrated beyond these disciplinary boundaries. We demonstrate how these data can be used to stimulate student interests in class discussion, advance analytic skills, as well as develop capacities in written and verbal communication. We conclude by considering concerns that may influence …