Education 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.

Numeracy Tasks: Inspiring Transfer Between Concrete And Abstract Thinking Spaces, Taras Gula, Miroslav Lovric

Numeracy

In our paper we build a case for conceptualizing numeracy tasks as distinct from mathematical tasks (or at least as a special type of mathematical task), and for abstraction and interpretation as a set of key activities necessary for designating a numeracy task as being high-quality. We start with an attempt to tame the fuzziness of numeracy and its family members (including quantitative reasoning, quantitative literacy, mathematical literacy, and the word problem cousins) by outlining six areas of consensus gleaned from literature. These provide the foundation for a core mandate of numeracy. We then build our case for the distinctness …

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 …

Instructional Decision Making In A Gateway Quantitative Reasoning Course, Deependra Budhathoki, Gregory D. Foley, Stephen Shadik

Numeracy

Many educators and professional organizations recommend Quantitative Reasoning as the best entry-level postsecondary mathematics course for non-STEM majors. However, novice and veteran instructors who have no prior experience in teaching a QR course often express their ignorance of the content to choose for this course, the instruction to offer students, and the assessments to measure student learning. We conducted a case study to investigate the initial implementation of an entry-level university quantitative reasoning course during fall semester, 2018. The participants were the course instructor and students. We examined the instructor’s motives and actions and the students’ responses to the course. …

Threshold Concepts In Quantitative Reasoning, Judith Canner, Jennifer E. Clinkenbeard

Numeracy

The idea of “threshold concepts” has been used to identify discipline-based concepts that are critical to that academic area. Threshold concepts are often difficult for students to assimilate in a meaningful way but, once done, can be powerful for the learner. In general, threshold concepts are 1) transformative to learner thinking; 2) bounded by the discipline; 3) integrative with other concepts; and 4) irreversible once understood (Meyer and Land 2003). This paper presents five threshold concepts in quantitative reasoning (QR) developed by transdisciplinary faculty workgroups that may be applicable for non-mathematics disciplines as well. They are as follows: 1) QR …

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.

Covid Learning Loss: A Call To Action, Nathan D. Grawe

Numeracy

The COVID-19 pandemic and policy responses designed to mitigate transmission have caused deep and persistent mathematics learning loss among K–12 students. While initial data might have been read optimistically as a blip that would reverse once schools returned to normal, 2023 data from the National Assessment of Educational Progress (NAEP) show that losses persist. While the NAEP does not directly measure quantitative reasoning (QR), the data present a disturbing picture for QR instruction and call for new lines of research that inform QR pedagogical response.

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 …

The Development, Validation, And Standardization Of A New Tool: The Dyscalculia Test, Stella Eteng-Uket

Numeracy

This paper describes a study that focused on developing, validating and standardizing a dyscalculia test, henceforth called the Dyscalculia Test. Out of the 4,758,800 students in Nigeria's upper primary and junior secondary schools, l randomly drew a sample of 2340 students, using a multistage sampling procedure that applied various sampling techniques. For data collection, I used the Test of General Reasoning Ability and Paper 1 of the Mathematics Achievement Test section of the 2021 National Common Entrance Examination, as well as the Dyscalculia Test introduced in this paper, which was developed and standardized in stages. My analysis shows that the …

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 …

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 …

Focused On Pedagogy: Qr Grading Rubrics For Written Arguments, Ruby Daniels, Kathryn Appenzeller Knowles, Emily Naasz, Amanda Lindner

Numeracy

Institutional assessments of quantitative literacy/reasoning (QL/QR) have been extensively tested and reported in the literature. While appropriate for measuring student learning at the programmatic or institutional level, such instruments were not designed for classroom grading. After modifying a widely accepted institutional rubric designed to assess QR in written arguments, the current mixed method study tested the reliability of two QR analytic grading rubrics for written arguments and explored students’ reactions to the grading tools. Undergraduate students enrolled in a business course (N = 59) participated. A total of 415 QR artifacts from 40 students were assessed; an additional 19 …

Exploring The Relationship Between Quantitative Reasoning Skills And News Habits, Bennett Attaway, John Voiklis, Jena Barchas-Lichtenstein, Eric Hochberg, Jim Hammerman, Uduak Grace Thomas, Nicole Lamarca, Laura Santhanam, Patti Parson

Numeracy

Because people are constantly confronted with numbers and mathematical concepts in the news, we have embarked on a project to create journalism that can support news users’ number skills. But doing so requires understanding (1) journalists’ ability to reason with numbers, (2) other adults’ ability to do so, and (3) the attributes and affordances of news. In this paper, we focus on the relationship between adults’ news habits and their quantitative reasoning skills. We collected data from a sample of 1,200 US adults, testing their ability to interpret statistical results and asking them to report their news habits. The assessment …

College Students’ Numeracy Events In Discussing Public Issues, Samuel L. Tunstall

Numeracy

An important consideration in the design and development of numeracy-focused coursework is ensuring that one meets students where they are with respect to both their mathematics background and their existing numeracy practices in relation to public issues. The latter consideration is especially important, given that students already think about such issues in their daily lives, long before we use them as a means for motivating quantitative exploration in the classroom. In this article, I report on a qualitative study of eight college students’ numeracy events—that is, events mediated in some way by quantification–when reasoning in focus groups with three distinct …

What Can We Learn From The Different Understandings Of Mathematical Literacy?, Svein Arne Sikko

Numeracy

Mathematical literacy, quantitative literacy, numeracy, matheracy, disciplinary literacy, and content-area literacy are among a plethora of terms used to link mathematics and literacy. In addition to this abundance of terms, the content of the terms is not precise, and in some cases the terms are used interchangeably. I delve into this landscape and dissect the meaning of each of them. From such an analysis of mathematical literacy, numeracy, and quantitative literacy, we learn about the importance of quantitative practices and elementary mathematics in society, including both how mathematics is necessary for everyday life but also how it can be used …

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 …

Let All Voices Be Heard: Creating An Engaging And Inclusive Asynchronous Qr Classroom, Ruby A. Daniels, Kathryn Appenzeller Knowles

Numeracy

With the shift to remote teaching, many instructors used Zoom for synchronous work. However, this presented issues (fatigue, turning cameras off, inequitable technical hurdles) that motivated quantitative reasoning (QR) instructors to look for asynchronous alternatives. A common technique has been text-based online discussions, which can be difficult for students to find engaging. This mixed method study (N = 41) describes an inclusive video alternative, specifically for teaching QR and quantitative fluency skills, which was piloted in two asynchronous sections and one hybrid section of the same course. Students posted their video responses, watched their classmates’ videos, and wrote short …

A Tale Of Success: Embedding Remediation And Curricular Design, Joseph P. Mccollum, William Adamczak, James R. Nolan

Numeracy

This paper reports how high failure rates in the first quantitative course that college business majors take were significantly reduced by implementing course-embedded remediation. More specifically, this paper details our process for identifying students at risk, placing them in special sections of the first quantitative course, and adding an additional hour of application of course concepts which resulted in a statistically significant increase in pass rates. The study focused on the learning environment, the attitude of the student, the utility of the material and the role of the professor for this special course. We feel this research is timely, as …

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 …

Covid-19: A Developing Crisis For Quantitative Reasoning, Nathan D. Grawe

Numeracy

Assessment data show substantial learning losses resulting from pandemic-era teaching and learning. While all learning domains have been affected, mathematics performance shows particularly large losses among elementary and secondary school students. Advocates for quantitative reasoning in high schools and colleges should anticipate weaker levels of basic numeracy among entering cohorts for a decade to come. As a consequence, the urgency to reform curricula and student support has never been greater.

Building A Social And Academic Online Bridge To Quantitatively-Rich College Coursework, Melissa Eblen-Zayas, Lin Winton

Numeracy

We describe the online summer portion of a quantitative skills bridge program focused on helping students prepare socially and academically for the transition to college. College students are increasingly asked to employ quantitative skills across the curriculum, but students arrive at college with varied preparation. Further, those with the least preparation often encounter other challenges to social belongingness and navigating their institution. In response to these needs, our institution developed a bridge program aimed at students with a broad range of interests -- not just STEM, and the program has a significant focus on community-building as well as strengthening quantitative …

Surveying The Landscape Of Numbers In U.S. News, John Voiklis, Jena Barchas-Lichtenstein, Bennett Attaway, Uduak G. Thomas, Shivani Ishwar, Patti Parson, Laura Santhanam, Isabella Isaacs-Thomas

Numeracy

The news arguably serves to inform the quantitative reasoning (QR) of news audiences. Before one can contemplate how well the news serves this function, we first need to determine how much QR typical news stories require from readers. This paper assesses the amount of quantitative content present in a wide array of media sources, and the types of QR required for audiences to make sense of the information presented. We build a corpus of 230 US news reports across four topic areas (health, science, economy, and politics) in February 2020. After classifying reports for QR required at both the conceptual …

Quantitative Literacy And Guns, William Briggs

Numeracy

Briggs, William. 2017. How America Got Its Guns: A History of the Gun Violence Crisis; (Albuquerque, University of New Mexico Press). 352 pp. Paperback: ISBN 978-0-8263-5813-4. E-book ISBN 978-0-8263-5814-1.

Quantitative literacy and statistics are just two of many disciplines required to understand the problem of gun violence in America. However, it’s also useful to appreciate their limitations in an issue that is so complex.

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 …

Lessons From The Pandemic, Nathan D. Grawe

Numeracy

The COVID-19 pandemic highlights the importance of quantitative literacy--for policy makers and the public at large. While all aspects of numeracy have been shown relevant to the past year, our need for broader statistical literacy appear particularly pressing. Pandemic experiences may motivate greater interest in developing numeracy skills.

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 …

Investigating Alignment In A Quantitative Literacy Course For Social Sciences Students, Vera Frith, Pam Lloyd

Numeracy

The Numeracy Centre at the University of Cape Town has taught a one-semester quantitative literacy course for social sciences students since 1999. This study aims to provide an example for how the design of such a course can be assessed for alignment with quantitative reasoning goals. We propose a framework of learning outcomes for the course and use that framework to analyse the assessments and student performance on them. We find that just under half of the overall mark for the course was devoted to the interpretation and communication of quantitative information (our “main” outcomes), and about a quarter was …

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.

Simplified But Not The Same: Tracing Numeracy Events Through Manually Simplified Newsela Articles, Ellen C. Agnello

Numeracy

New York-based education startup Newsela has quickly gained popularity with K-12 educators in the six years since its launch. Its website boasts that it serves 90% of schools in the United States including the 1.5 million teachers they employ and their 20 million students. But what makes it so popular? Teachers are drawn to its Common Core-aligned informational texts which facilitate content-area connections while exposing students to important current events. Likely the most appealing aspect of the platform is its compatibility with differentiation, as it makes available five iterations of each article at varying levels of complexity or Lexile which …