Physical Sciences and Mathematics Commons^™

The International Crisis In Numeracy Education, Nathan D. Grawe

Numeracy

The OECD recently released results from the 2022 administration of the Programme for International Student Assessment test. As other studies suggest, pandemic mitigation policies resulted in deep learning loss including in basic mathematics which forms the foundation of numeracy. Perhaps of greater concern, however, in many countries pandemic effects amplify declining performance that dates back a decade or more. Losses of two or more years' worth of mathematics education are not uncommon among developed countries. The editorial makes an urgent call for research that identifies practical steps to reverse these trends.

Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince

Numeracy

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of …

An Introduction To The Algebra Revolution, Art Bardige

Numeracy

Bardige, Art. 2022. The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education; (Bookbaby) 135 pp. UNSPSC 55111505.

The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education argues that Algebra 1 can be eliminated by teaching mathematics through spreadsheets. Such a change would eliminate the greatest roadblock to student achievement.

Bite-Sized Quantitative Reasoning Essays: A Review Of Numbers Don’T Lie: 71 Stories To Help Us Understand The Modern World (2020), By Vaclav Smil, Samuel L. Tunstall

Numeracy

In Numbers Don’t Lie: 71 Stories to Help Us Understand the Modern World (2020), Vaclav Smil draws on his interdisciplinary background in science, public policy, and history to provide readers with 71 short essays that help us better understand aspects of the world–including its people, environment, energy consumption, and present crises (among other things). In most of his essays, Smil utilizes both data and reasoning with data to shed light on diverse topics, with issues ranging from happiness rankings and vaccine payoffs to chicken production and diesel engines. Though the book arguably has some flaws, its easy-to-digest essays–many of which …

Artificial Intelligence, Basic Skills, And Quantitative Literacy, Gizem Karaali

Numeracy

The introduction in November 2022 of ChatGPT, a freely available language-based artificial intelligence, has led to concerns among some educators about the feasibility and benefits of teaching basic writing and critical thinking skills to students in the context of easily accessed, AI-based cheating mechanisms. As of now, ChatGPT can write pretty convincing student-level prose, but it is still not very good at answering quantitatively rich questions. Therefore, for the time being, the preceding concerns may not be shared by a large portion of the numeracy education community. However, as Google and WolframAlpha are definitely capable of answering standard and some …

Beyond Statistical Significance: A Holistic View Of What Makes A Research Finding "Important", Jane E. Miller

Numeracy

Students often believe that statistical significance is the only determinant of whether a quantitative result is “important.” In this paper, I review traditional null hypothesis statistical testing to identify what questions inferential statistics can and cannot answer, including statistical significance, effect size and direction, causality, generalizability, and changeability of the independent variable. I illustrate these issues with examples from an empirical study of the association between how much time teenagers spent playing video games and time spent reading. I describe how study design and context determine each of those aspects of “importance,” and close by summarizing how to provide a …

Establishing The Validity And Reliability Of The Locus Assessments, Tim Jacobbe, Bob Delmas, Brad Hartlaub, Jeff Haberstroh, Catherine Case, Steven Foti, Douglas Whitaker

Numeracy

The development of assessments as part of the funded LOCUS project is described. The assessments measure students’ conceptual understanding of statistics as outlined in the GAISE PreK–12 Framework. Results are reported from a large-scale administration to 3,430 students in grades 6 through 12 in the United States. Items were designed to assess levels of understanding as well as components of the statistical problem solving process as articulated in the GAISE framework. We discuss details of how the model used to develop the LOCUS assessments guided the gathering of evidence for validity and reliability arguments. Three types of validity evidence are …

Talking About Statistical Significance In Numeracy, Nathan D. Grawe, Gizem Karaali

Numeracy

In recent years, much debate has surrounded the potential for audiences to be mislead by several common practices when reporting statistical significance tests. Two editors of Numeracy share the journals perspectives on these questions. As an interdisciplinary journal, we recognize and honor the genre differences represented by our authors and audience members. As a consequence, the journal is open to many practices. Still, we acknowledge the concerns raised by the American Statistical Association and others and encourage authors to write with care and clarity, however results may be represented.

Review Of A Framework For Sustainable Thinking: Is Ql For Citizenship Even Possible?, Nathan D. Grawe

Numeracy

Van Antwerp and Heun's A Framework for Sustainability Thinking offers an extensive collection of data related to sustainability with an emphasis on energy. Intended for a primary audience of undergraduate students, the authors set the data in the context of the IPARX identity which notes that impacts (I) are the product of population (P), affluence (A), resource intensity of economic activity (R), and impact of the resources (X). In addition to being a useful text for seminars focused on sustainability and energy use, the book provides a context for contemplating the roles of expertise vs. general quantitative literacy when addressing …

An Introduction To A Framework For Sustainability Thinking, Jeremy Van Antwerp, Matthew Kuperus Heun

Numeracy

Van Antwerp, Jeremy and Matthew Kuperus Heun. 2022. A Framework for Sustainability Thinking: A Student’s Introduction to Global Sustainability Challenges; (Springer, Cham) 275 pp. ISBN 978-3-0317-9184-0.

A Framework for Sustainability Thinking: A Student’s Introduction to Global Sustainability Challenges presents basic information related to sustainability challenges in the context of a cognitive framework that allows students to evaluate problems and potential solutions from a quantitative perspective. Moreover, numerous end-of-chapter discussion questions and project ideas examine moral, ethical, and worldview aspects of sustainability choices and tradeoffs between different approaches to sustainability.

How The Number Line Can Be Used To Promote Students' Understanding Of The Normal Distribution, Danri H. Delport

Numeracy

A strong foundation in early number concepts is crucial for students’ future success in statistics. Despite its importance in statistics, many first-year students struggle to comprehend the normal distribution due to a lack of basic number sense. Students get confused about the order and magnitude of negative z-scores on a standard normal curve or when problems about normally distributed random variables are presented in word questions which involve phrases that indicate inequalities. As a result, students shade wrong areas on the bell-shaped curve when they have to calculate probabilities for normally distributed variables. Visual representations such as the number …

Computing For Numeracy: Kiyoo Mogi And The Nature Of Volcanoes, Charles Connor

Numeracy

Dramatic volcanic eruptions occurred in the Spring of 2021 in Iceland and St. Vincent. This column explores the use of a numerical model to understand the giant displacements of the Earth's surface that result from such volcanic activity. The model used was development by Japanese geophysicist Kiyoo Mogi to explain a much older eruption, the 1914 eruption of Sakurajima volcano, located in Kyushu, Japan. Mogi's model was so successful, and is still widely used today, because he took a step-by-step approach to solving this complicated problem, making simplifying assumptions where he could, and using data to the maximum extent possible …

Educating Consumers And Producers Of Data: Review Of Making Sense Of Numbers By Jane E. Miller (2022), Andrew J. Miller

Numeracy

Author Jane E. Miller has brought her considerable experience writing and teaching about numerate communication to a new textbook, Making Sense of Numbers. Miller uses clear prose, timely and authentic examples, and thought-provoking exercises to educate the next generation of consumers and producers of data, students in introductory quantitative reasoning, research methods, or data analysis courses. While the textbook does not fit the mold of a "typical" quantitative literacy course, creative instructors may find ways to use it in innovative quantitative literacy, data literacy, or introductory data science courses.

Author’S Reflections On Making Sense Of Numbers: Quantitative Reasoning For Social Research, Jane E. Miller

Numeracy

Miller, Jane E. 2021. Making Sense of Numbers: Quantitative Reasoning for Social Research. (Los Angeles: SAGE Publications) 608 pp. ISBN 978-1544355597.

This article introduces and provides an excerpt from Making Sense of Numbers: Quantitative Reasoning for Social Research, published by Sage. The book explains and illustrates how making sense of numbers involves integrating concepts and skills from mathematics, statistics, study design, and communications, along with information about the specific topic and context under study. It teaches how to avoid making common errors of logic, calculation, and interpretation by introducing a systematic approach and a healthy dose of skepticism …

An Introduction To Calling Bullshit: Learning To Think Outside The Black Box, Jevin D. West, Carl T. Bergstrom

Numeracy

Bergstrom, Carl T. and Jevin D. West. 2020. Calling Bullshit: The Art of Skepticism in a Data-Driven World. (New York: Random House) 336 pp. ISBN 978-0525509202.

While statistical methods receive greater attention, the art of critically evaluating information in everyday life more commonly depends on thinking outside the black box of the algorithm. In this piece we introduce readers to our book and associated online teaching materials—for readers who want to more capably call “bullshit” or to teach their students to do the same.

Be Careful! That Is Probably Bullshit! Review Of Calling Bullshit: The Art Of Skepticism In A Data-Driven World By Carl T. Bergstrom And Jevin D. West, James B. Schreiber

Numeracy

Bergstrom, C. T., & West, J. D. 2021. Calling Bullshit: The Art of Skepticism in a Data-Driven World. NY: Random House. 336 pp. ISBN 978-0525509189

The authors provide a journey through the numerical bullshit that surrounds our daily lives. Each chapter has multiple examples of specific types of bullshit that each of us experience on any given day. Most importantly, information on how to identify bullshit and refute it are provided so that reader finishes the book with a set of skills to be a more engaged and critical interpreter of information. The writing has a quick and lively …

Confidence Intervals Of Covid-19 Vaccine Efficacy Rates, Frank Wang

Numeracy

This tutorial uses publicly available data from drug makers and the Food and Drug Administration to guide learners to estimate the confidence intervals of COVID-19 vaccine efficacy rates with a Bayesian framework. Under the classical approach, there is no probability associated with a parameter, and the meaning of confidence intervals can be misconstrued by inexperienced students. With Bayesian statistics, one can find the posterior probability distribution of an unknown parameter, and state the probability of vaccine efficacy rate, which makes the communication of uncertainty more flexible. We use a hypothetical example and a real baseball example to guide readers to …

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Looking Back At Quantitative Reasoning, William Briggs

Numeracy

A teacher looks back on three decades of teaching, pondering, and writing about quantitative reasoning (QR) and shares a few lessons learned. The skills that we teach in QR courses are more important than ever in providing students with a sense of civic virtue: the ability to be engaged and informed citizens in an increasingly complex and quantitative world.

National Numeracy Network Officers And Board Of Directors, Milo Schield

Numeracy

National Numeracy Network Officers and Board of Directors in the year 2020.

Computing For Numeracy: How Safe Is Your Covid-19 Social Bubble?, Charles Connor

Numeracy

The COVID-19 pandemic has led many people to form social bubbles. These social bubbles are small groups of people who interact with one another but restrict interactions with the outside world. The assumption in forming social bubbles is that risk of infection and severe outcomes, like hospitalization, are reduced. How effective are social bubbles? A Bayesian event tree is developed to calculate the probabilities of specific outcomes, like hospitalization, using example rates of infection in the greater community and example prior functions describing the effectiveness of isolation by members of the social bubble. The probabilities are solved for two contrasting …

Review Of Social Workers Count: Numbers And Social Issues By Michael Anthony Lewis, Michael T. Catalano

Numeracy

Lewis, Michael Anthony. 2017. Social Workers Count: Numbers and Social Issues. 2019. New York: Oxford University Press. 223 pp. ISBN 978-019046713-5

The numeracy movement, although largely birthed within the mathematics community, is an outside-the-box endeavor which has always sought to break down or at least transgress traditional disciplinary boundaries. Michael Anthony Lewis’s book is a testament that this effort is succeeding. Lewis is a social worker and sociologist with an impressive resume, author of Economics for Social Workers, co-editor of The Ethics and Economics of the Basic Income Guarantee, and member of the faculty at the Silberman School …

Using Covid-19 Vaccine Efficacy Data To Teach One-Sample Hypothesis Testing, Frank Wang

Numeracy

In late November 2020, there was a flurry of media coverage of two companies’ claims of 95% efficacy rates of newly developed COVID-19 vaccines, but information about the confidence interval was not reported. This paper presents a way of teaching the concept of hypothesis testing and the construction of confidence intervals using numbers announced by the drug makers Pfizer and Moderna publicized by the media. Instead of a two-sample test or more complicated statistical models, we use the elementary one-proportion z-test to analyze the data. The method is designed to be accessible for students who have only taken a …

Covid-19 And Quantitative Literacy: Focusing On Probability, Michael A. Lewis

Numeracy

The COVID-19 pandemic is arguably the worst crisis the world has faced, so far, in this new century. We haven’t seen a pandemic like this since the 1918 Flu at the beginning of the last century, and, as of this writing, there appears to be no end in sight. What those of us who’re focused on quantitative methods have noticed, in addition to the many people dying, becoming ill, and losing their livelihoods, is the importance of quantitative literacy to an understanding of what’s going on. That’s what this article is about. Specifically, it’s about how the COVID-19 pandemic is …

Development And Assessment Of A Continuing Education Unit In Quantitative Literacy For High School Stem Teachers, Craig P. Mcclure

Numeracy

Influencing the teaching of quantitative literacy at all levels of education can be difficult due to the many demands placed on educators. In a continuing education course, public high school science teachers participated in a pilot study of a program on quantitative literacy, involving defining quantitative literacy, how it is beneficial to students, examples of quantitative literacy education, and how it may be supported in the science classroom. Surveys administered before and after the unit indicate an improvement in the teachers’ understanding of quantitative literacy, and a follow-up survey indicates that the unit impacted classroom practice. Results support the conclusion …

Art, Artfulness, Or Artifice?: A Review Of The Art Of Statistics: How To Learn From Data, By David Spiegelhalter, Jason Makansi

Numeracy

David Spiegelhalter. 2019. The Art of Statistics: How to Learn From Data. (London: The Penguin Group). 444 pp. ISBN 978-1541618510

The author successfully eases the reader away from the rigor of statistical methods and calculations and into the realm of statistical thinking. Despite an engaging style and attention-grabbing examples, the reader of The Art of Statistics will need more than a casual grounding in statistics to get what Spiegelhalter, I believe, intends from his book. It should be viewed as a companion to a more rigorous textbook on statistical methods but not necessarily a book that makes statistics any …

The Author’S Reflections On No B.S. (Bad Stats): Black People Need People Who Believe In Black People Enough Not To Believe Every Bad Thing They Hear About Black People, Ivory A. Toldson

Numeracy

Toldson, Ivory. A. 2019. No BS (Bad Stats): Black People Need People Who Believe in Black People Enough Not to Believe Every Bad Thing They Hear About Black People (Boston, MA: Brill-Sense) 194 pp. ISBN 978-9004397026.

This essay provides an introduction to No BS (Bad Stats): Black People Need People Who Believe in Black People Enough Not to Believe Every Bad Thing They Hear About Black People. In the essay, the author discusses how cynical views about the educational potential of Black children motivated him to write a book that challenges negative statistics. The essay also outlines the harmful …

Effects Of Quantitative Literacy On Healthcare Decision-Making: An Aural Context, Robert G. Root, Sonia Bhala

Numeracy

We propose a relationship between sensory modality, numerical formatting, and performance on a survey simulating healthcare decision-making. We examine the current literature on aural health literacy, and specifically aural literacy coupled with health numeracy. We then create a survey instrument called the Bhala test for this purpose and demonstrate that it is moderately internally consistent and provides results that correlate with the NUMi assessment, a widely accepted measure of health numeracy. The quantitative information provided in the Bhala test has two treatments, percentage and natural frequency formats, in an effort to determine which format is easier for subjects to use …

Are We At A Watershed Moment For The Quantitative Literacy Movement?: Review Of Shifting Context, Stable Core: Advancing Quantitative Literacy In Higher Education, By Luke Tunstall, Gizem Karaali, And Victor Piercey, Eds., Maura Mast

Numeracy

Luke Tunstall, Gizem Karaali, and Victor Piercey, eds. 2019. Shifting Concepts, Stable Core: Advancing Quantitative Literacy in Higher Education. Math Notes 88. (Mathematics Association of America, MAA Press). Print ISBN 978-0-88385-198-2. Electronic ISBN 978-1-61444-324-7.

The thematic approach of the edited MAA Notes volume Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education is that the “construct” of quantitative literacy is now fairly stable, but the contexts in which quantitative literacy is taught (and practiced) continue to change. Several chapters give the reader much to consider regarding what constitutes the foundation of this stable core and, relatedly, how quantitative …

Graphicacy For Numeracy: Review Of Fundamentals Of Data Visualization: A Primer On Making Informative And Compelling Figures By Claus O. Wilke (2019), Christy M. Bebeau

Numeracy

Wilke, Claus O. 2019. Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures. (Sebastopol, CA: O’Reilly Media, Inc.). 390 pp. ISBN 978-1-492-03108-6. First edition. First release: 03-15-2019.

Claus O. Wilke has authored an excellent reference about producing and understanding static figures, figures used online, in print, and for presentations. His book is neither a statistics nor programming text, but familiarity with basic statistical concepts is helpful. Written in three parts, the book presents both the math and artistic design aspects of telling a story through figures. Wilke makes extensive use of examples, labels them good, bad, …