Science and Mathematics Education Commons^™

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 …

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 …

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 …

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.

National Numeracy Network Officers And Board Of Directors, Milo Schield

Numeracy

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

Parts Of The Whole: The Last Column: Freire's Pedagogy Of Liberation, Dorothy Wallace

Numeracy

The educational theory of Paolo Freire is briefly summarized for instructors of quantitative reasoning, with a focus on what it means to give students “agency.” Some examples are given of how to implement his basic ideas.

A Comparison Of Students’ Quantitative Reasoning Skills In Stem And Non-Stem Math Pathways, Emily Elrod, Joo Young Park

Numeracy

Quantitative Reasoning (QR) is essential for today’s students, yet most higher education institutions have not effectively addressed this issue. This study investigates students’ quantitative reasoning in STEM and Non-STEM math pathways using a non-proprietary, NSF grant-funded instrument, the Quantitative Literacy & Reasoning Assessment (QLRA). Participants were students enrolled in at least one college-level math pathway course at a large public institution in the southeastern US. The results showed a significant difference between STEM and Non-STEM students’ QLRA scores, with STEM students (n = 244, M = 27%, SD = 16.21%) scoring, on average, about 6% higher than Non-STEM students …

Parts Of The Whole: Logical Categories Of Learning: Why Teaching Qr Is Hard, Dorothy Wallace

Numeracy

This column introduces the reader to an essay by anthropologist Gregory Bateson on the nature of learning. In that essay, he stratifies the learning process into categories based on what aspect of the student’s understanding is required to change in order to accomplish a given learning task. A discussion of the first three categories is followed here by examples from quantitative reasoning tasks and a further example from the ongoing discussion in the community of what numeracy entails. Bateson’s classification of learning into “logical categories” sheds light on what the goals of numeracy ask of both student and teacher, as …

The Numbers We Need: Review Of Shifting Contexts, Stable Core: Advancing Quantitative Literacy In Higher Education, Edited By Luke Tunstall, Gizem Karaali, And Victor Piercey (2019), John Macinnes

Numeracy

Luke Tunstall, Gizem Karaali, and Victor Piercey, eds. 2019. Shifting Contexts, 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.

Mine is a rather UK-centric view. The ability to understand numbers is increasingly vital for citizenship in a world where almost every argument, no matter how bogus, comes with numbers attached. Maths and stats, however, are too important to leave to the mathematicians and statisticians alone. There are as many varieties of application as there are disciplines and interests. Maths faculty are not there to …

Introducing Maa Notes #88: Shifting Contexts, Stable Core: Advancing Quantitative Literacy In Higher Education, Samuel L. Tunstall, Gizem Karaali, Victor Piercey

Numeracy

Tunstall, Samuel, Gizem Karaali, and Victor Piercey, eds. 2019. Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education (Washington, DC: Mathematical Association of America) 258 pp. ISBN 978-1614443247.

This brief essay introduces readers to Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education, a new edited volume published by the Mathematical Association of America. We begin by describing the story behind the volume, and then outline its four major parts: "A Bird’s Eye View," "Curriculum for Quantitative Literacy," "Quantitative Literacy in an Institutional Context," and "Perspectives from the Quantitative Literacy Community." We end with an excerpt from …

Alignment Between Learning Objectives And Assessments In A Quantitative Literacy Course, Younggon Bae, Samuel L. Tunstall, Kathryn S. Knowles, Rebecca L. Matz

Numeracy

In this analysis, we examine how course assessment items were aligned with learning objectives in a quantitative literacy course at Michigan State University. The alignment analysis consisted of mapping assessment items to a list of operationalized learning objectives from the course. Our analysis shows how often the learning objectives are represented in assessment items, how often they are paired with other learning objectives, and how influential they are in contributing to a student’s course grade. In addition, through comparisons across four assessment types (e.g., exams and homework), we show how each learning objective was assessed differently within each assessment type. …

The Ultimatum Game: An Introduction To Quantitative Literacy In A Social Justice Context, Robert G. Root

Numeracy

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation offer nuanced views of the nature and importance of quantitative literacy. Its use in a writing seminar connecting quantitative literacy and social justice is described.

Roots And Seeds: Finding Our Place In The Social Practice Nexus That Is Quantitative Literacy, H. L. Vacher, Nathan D. Grawe

Numeracy

The purpose of our new Roots and Seeds feature is to provide an open-access space to archive first-hand accounts of QL activities that have preceded our journal (2008). The first two contributions in the collection appeared last issue: Linda Sons on the making of what has come to be known as the 1994 Sons Report (Mathematics Association of America), and Dorothy Wallace on her path to the Quantitative Literacy Design Team for Mathematics and Democracy (2001), and the questions that bedeviled them then – and us now. In this issue, we get Rick Gillman’s account of how the committee that …

Investigating Levels Of Graphical Comprehension Using The Locus Assessments, Charlotte A. Bolch, Tim Jacobbe

Numeracy

Statistical literacy refers to two interrelated components: people’s ability to interpret and critically evaluate statistical information, and their ability to discuss or communicate their reactions to statistical information. The ability to read and interpret graphical displays is part of statistical literacy because much of the statistical information people encounter in their everyday lives are graphical displays or tables of data. The purpose of this study was to investigate college-level students’ graphical comprehension. Students’ graphical comprehension was assessed using items from the Levels of Conceptual Understanding in Statistics (LOCUS) assessments. Much can be learned about students’ graphical comprehension based on this …

The Second Decade Of Numeracy: Entering The Seas Of Literacy, H. L. Vacher

Numeracy

This multipurpose editorial explores and tries to count the many types of literacy that are referred to by name in Wikipedia and Numeracy. Wikipedia’s Category:Literacy page identifies 44 kinds of literacy that are the subject of articles, ranging from numeracy and graphicacy to braille literacy and diaspora literacy. In addition, searching Google finds more than 30 adjective-literacy or noun-literacy collocations, including quantitative literacy, adult literacy, and document literacy, that do not have Wikipedia pages of their own but are mentioned on other Wikipedia pages. The sum puts this modest literacy count in line with the more than 70 bodies …

Numeracy And Social Justice: A Wide, Deep, And Longstanding Intersection, Kira Hamman, Victor Piercey, Samuel L. Tunstall

Numeracy

We discuss the connection between the numeracy and social justice movements both in historical context and in its modern incarnation. The intersection between numeracy and social justice encompasses a wide variety of disciplines and quantitative topics, but within that variety there are important commonalities. We examine the importance of sound quantitative measures for understanding social issues and the necessity of interdisciplinary collaboration in this work. Particular reference is made to the papers in the first part of the Numeracy special collection on social justice, which appear in this issue.

Review Of Towards Equity And Justice In Mathematics Education, Edited By Tonya Gau Bartell, Emily Lardner

Numeracy

Tonya Grau Bartell, editor. 2018.Toward Equity and Social Justice in Mathematics Education. (Cham, Switzerland: Springer International Publishing). 341 pp. ISBN 978-3-319-92906-4 (also available as an e-book).

Toward Equity and Social Justice in Mathematics Education is a welcome addition to ongoing conversations about what mathematics should be taught and how it should be taught at both the college and pre-college level. Although the primary audience for the volume will be math educators and researchers, readers of this journal will discover intersecting interests, concerns, and strategies.

An Uncommon Textbook: Review Of Common Sense Mathematics By Ethan Bolker And Maura Mast, Bernard Madison

Numeracy

Ethan D. Bolker and Maura B. Mast. 2016. Common Sense Mathematics.(Washington DC.: Mathematics Association of America) ISBN-13: 978-1-93951-210-9.

Common Sense Mathematics is an integrative quantitative reasoning (QR) textbook that is built around scores of exercises derived from authentic circumstances from public media and other public sources. The exercises elicit responses from students requiring extensive communication and analyses and distinguish the book from ones typically encountered in a mathematics or science course. Responses to exercises often require one-half page or more of writing and can occupy considerable class time in discussion. The book has material for a one- or two-semester …

Quantitative Literacy: Now More Than Ever, Gail O. Mellow

Numeracy

This editorial highlights the eloquent words of Drs. Bernard Madison and Lynn Arthur Steen who, in the inaugural issue of Numeracy, note that quantitative literacy (QL) provides “tools for survival” in a highly competitive world. I discuss how QL is desperately needed at a precarious time for our nation’s democracy and how at LaGuardia Community College, and community colleges across the nation, important and creative work is being undertaken to build students’ math skills. The pivotal role of faculty is discussed and a call is made for colleges to support faculty as they undertake the challenging work of building QL …

Parts Of The Whole: Hands On Statistics, Dorothy Wallace

Numeracy

In this column we describe a hands-on data collection lab for an introductory statistics course. The exercise elicits issues of normality, sampling, and sample mean comparisons. Based on volcanology models of tephra dispersion, this lab leads students to question the accuracy of some assumptions made in the model, particularly regarding the normality of the dispersal of tephra of identical size in a given atmospheric layer.

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 …

Numeracy Across The Curriculum In Australian Schools: Teacher Education Students’ And Practicing Teachers’ Views And Understandings Of Numeracy, Helen J. Forgasz, Gilah Leder, Jennifer Hall

Numeracy

In this article, we confront the challenges to teacher education students and practicing teachers raised by the concept of numeracy and its place in the curriculum. In the Australian Curriculum, there is an expectation that teachers at all grade levels and in all subject areas develop students' numeracy capabilities. At Monash University, a public, research-intensive university, the largest university in Australia, graduate level teacher education students are now required to complete a course entitled Numeracy for Learners and Teachers. We describe the content of this course and, from an online survey, report findings of the impact on students' understandings …

A Twenty-Year Look At “Computational Geology,” An Evolving, In-Discipline Course In Quantitative Literacy At The University Of South Florida, Victor J. Ricchezza, H. L. Vacher

Numeracy

Since 1996, the Geology (GLY) program at the USF has offered “Computational Geology” as part of its commitment to prepare undergraduate majors for the quantitative aspects of their field. The course focuses on geological-mathematical problem solving. Over its twenty years, the course has evolved from a GATC (geometry-algebra-trigonometry-calculus) in-discipline capstone to a quantitative literacy (QL) course taught within a natural science major. With the formation of the new School of Geosciences in 2013, the merging departments re-examined their various curricular programs. An online survey of the Geology Alumni Society found that “express quantitative evidence in support of an argument” was …

The Quantitative Reasoning For College Science (Quarcs) Assessment 2: Demographic, Academic And Attitudinal Variables As Predictors Of Quantitative Ability, Katherine Follette, Sanlyn Buxner, Erin Dokter, Donald Mccarthy, Beau Vezino, Laci Brock, Edward Prather

Numeracy

In this article, we explore the ability of demographic and attitudinal variables to predict student scores on the Quantitative Reasoning for College Science (QuaRCS) Assessment. Variables measured by the assessment include: students' academic choices and plans, attitudes and perceptions regarding mathematics, self-reported effort level, and basic demographics such as age, race/ethnicity, gender and disability status. As in previously published numeracy studies, we find significant score deviations according to gender, race/ethnicity, and disability status; however, the effect size of these correlations pale in comparison to the effect size of affective/attitudinal variables on QuaRCS score. A large number of variables with …

Providing Open-Access Know How For Directors Of Quantitative And Mathematics Support Centers, Michael Schuckers, Mary B. O'Neill, Grace Coulombe

Numeracy

The purpose of this editorial is to introduce the quantitative literacy community to the newly published A Handbook for Directors of Quantitative and Mathematics Centers. QMaSCs (pronounced “Q-masks”) can be broadly defined as centers that have supporting students in quantitative fields of study as part of their mission. Some focus only on calculus or mathematics; others concentrate on numeracy or quantitative literacy, and some do all of that. A QMaSC may be embedded in a mathematics department, or part of a learning commons, or a stand-alone center. There are hundreds of these centers in the U.S. The new handbook, …

Parts Of The Whole: Teaching Quantitative Reasoning In An Exponential Decay Model, Dorothy Wallace

Numeracy

The simple calculus example of exponential decay can be an excellent vehicle for teaching quantitative reasoning in calculus or differential equations. Insect maturation provides a rich context for thinking about the meaning of the rate constant for exponential decay, which is derived in the context of a system at equilibrium but is generally measured using a single cohort of individuals.

Review Of Sustainable Energy -- Without The Hot Air By David Mackay (2009), Kira Hamman

Numeracy

David MacKay. Sustainable Energy: Without the hot air. (Cambridge, England: UIT Cambridge Ltd., 2009). 384 pp. ISBN 978-0954452933 (also available as a free e-book).

Physicist David MacKay transforms what has historically been a debate fraught with skepticism and hysteria into an informed conversation. He does this by providing clear, accurate quantitative information on energy production and consumption in a form that allows comparison and invites thoughtful analysis. By recalibrating power into kilowatt-hours per day per person, he makes the numbers meaningful on an individual level. He then meticulously estimates the productive capacity of various renewable energy sources, explores alternative …

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 …