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 …

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.

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 …

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 …

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 …

Course Design And Academic Outcomes In Quantitative Literacy After Eliminating Required Remediation, Jennifer E. Clinkenbeard

Numeracy

In Fall 2018, remedial mathematics courses were eliminated from the 23-campus California State University system under Executive Order 1110. Incoming first-year students were placed into college credit-bearing mathematics courses with options for corequisite support. This study examines the academic outcomes for students at California State University Monterey Bay in a college credit level quantitative literacy (QL) mathematics course with optional corequisite support during the 2018-2019 academic year. Taken together, the results of this study suggest that required remediation is not necessary for success in college-level QL. The corequisite support model also has potential to support more equitable outcomes for all …

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.

Measuring Numeracy: Validity And The Programme For The International Assessment Of Adult Competencies (Piaac), Samuel L. Tunstall

Numeracy

A tension raised in recent scholarship is that between numeracy as a social practice and numeracy as a functional skill set. Such frameworks for conceptualizing numeracy pose a challenge to assessment because what individuals do with numeracy is not the same as what individuals can do (or express) in an assessment setting. This study builds on work related to numeracy assessment through a validity examination of a portion of a well-known assessment: the OECD’s Programme for the International Assessment of Adult Competencies (PIAAC). In following a path set out by standards for assessment, I ask: What does the PIAAC numeracy …

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 …

Parts Of The Whole: The Having Of Wonderful Ideas: Eleanor Duckworth Introduces Us To Piaget, Dorothy Wallace

Numeracy

The small book of essays by Eleanor Duckworth has been a staple of teacher education for decades, serving as a bridge between Piaget’s observations of infants and the needs of the classroom. As her examples tend to be of young children, we consider more general ideas in the context of older grades and higher education. Several of her insights are discussed with an eye to application in the field of quantitative education, highlighting the need to integrate issues of pedagogy with those of content.

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. …

Embedded Remediation Is Not Necessarily A Pathway For Equitable Access To Quantitative Literacy And College Algebra: Results From A Pilot Study, Rebecca L. Matz, Samuel L. Tunstall

Numeracy

Courses in developmental and introductory mathematics are changing. Because nearly all students need mathematics coursework to graduate from a postsecondary institution, yet institutions consistently struggle to ensure that students of all demographics succeed in credit-bearing mathematics courses, student success in such courses may be viewed as an issue of social justice. In particular, there is a need for institutions to provide pathways through college-level mathematics courses that meet the needs of students with a wide array of incoming mathematical knowledge and skills. In light of questions about pedagogy, pass rates, and effects on degree completion time, some institutions have moved …

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 …

The World In Your Pocket: Digital Media As Invitations For Transdisciplinary Inquiry In Mathematics Classrooms, Lynette Deaun Guzmán, Jeffrey Craig

Occasional Paper Series

Building a curriculum from online digital media may provide opportunities for students to draw on their funds of knowledge, deconstruct dominant narratives, and engage with complex multimodal artifacts. We focus on an example of how we have used a digital infographic, The World as 100 People, to unpack global and local issues in mathematics classrooms. Using digital media as invitations for critical mathematical inquiry, we call for mathematics educators to push back on (1) the way mathematics should be formally taught in schools, and (2) a common practice of social media restrictions in schools.

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.

The Gini Index: A Lens For Analyzing Inequality In An Interdisciplinary College Classroom, Jared Warner, Vivian Lim

Numeracy

The Gini index is one of the most commonly used indicators of income inequality, and its computation and interpretation require a thorough understanding of various quantitative literacy concepts. In this article, we describe a unit for an interdisciplinary quantitative literacy course at a community college that treats concepts of ratio and proportion, percentages, and mathematical modeling through an exploration of income inequality and the Gini index. The broader theme of the interdisciplinary course is immigration, so the unit also invites students to explore connections between the Gini index and immigration. Employing in-class simulations, interactive online applets, and real-world data sets, …

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 …

The Connection Between Financial Literacy And Numeracy: A Case Study From India, J.D Jayaraman, Saigeetha Jambunathan, Kenneth Counselman

Numeracy

Making financial decisions involves mathematical calculations, both simple and complex. It is a well-documented fact that financial literacy levels among young people all over the world are quite low and that these low levels contribute to various undesirable outcomes with respect to personal financial well-being and the economy as a whole. This study explores the relationship between financial literacy and numeracy by measuring and modeling the relationship between financial literacy and numeracy levels among high school students (N = 586) in India. The results show a strong relationship between numeracy and financial literacy skills. Low numeracy is associated with …

Six Propositions Of A Social Theory Of Numeracy: Interpreting An Influential Theory Of Literacy, Jeffrey Craig, Lynette Guzmán

Numeracy

We share our experiences comprehending social theory as it applies to numeracy scholarship. We build on existing arguments that social theory—explicitly acknowledging the presence and influence of histories, power, and purposes—offers something important to scholars who study and discuss numeracy. In this article, we translate the six propositions of one particular social theory of literacy into propositions about numeracy, then we explore the meaning of each proposition, its connections to existing scholarship, and its implications. This article emerges from two literature reviews: one on social theories (especially their application to and development in literacy) and one on numeracy. We bring …

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 …

Models As Weapons: Review Of Weapons Of Math Destruction: How Big Data Increases Inequality And Threatens Democracy By Cathy O’Neil (2016), Samuel L. Tunstall

Numeracy

Cathy O’Neil. 2016. Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy (New York, NY: Crown) 272 pp. ISBN 978-0553418811.

Accessible to a wide readership, Cathy O’Neil’s Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy provides a lucid yet alarming account of the extensive reach of mathematical models in influencing all of our lives. With a particular eye towards social justice, O’Neil not only warns modelers to be cognizant of the effects of their work on real people—especially vulnerable groups who have less power to fight back—but also encourages laypersons to take initiative …

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 …

Learning To Think Slower: Review Of Thinking, Fast And Slow By Daniel Kahneman (2011), Samuel L. Tunstall, Patrick N. Beymer

Numeracy

Daniel Kahneman. Thinking, Fast and Slow (New York, NY: Farrar, Straus and Giroux) 499 pp. ISBN 978-0374275631.

As an expansive review of Kahneman and others' work over the past half-century in understanding human decision-making, Thinking, Fast and Slow provides Numeracy readers much to consider for both pedagogy and research. In this review, we outline Kahneman's core argument—that humans use both rash (emotional) System 1 thinking and slow (logical) System 2 thinking—then discuss how such systems might be addressed in a quantitative literacy classroom.

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

Numeracy

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added …

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.

A Quantitative Reasoning Approach To Algebra Using Inquiry-Based Learning, Victor I. Piercey

Numeracy

In this paper, I share a hybrid quantitative reasoning/algebra two-course sequence that challenges the common assumption that quantitative literacy and reasoning are less rigorous mathematics alternatives to algebra and illustrates that a quantitative reasoning framework can be used to teach traditional algebra. The presentation is made in two parts. In the first part, which is somewhat philosophical and theoretical, I explain my personal perspective of what I mean by “algebra” and “doing algebra.” I contend that algebra is a form of communication whose value is precision, which allows us to perform algebraic manipulations in the form of simplification and solving …