Science and Mathematics Education Commons^™

Faculty Viewpoints On Teaching Quantway®, Heather Howington, Thomas Hartfield, Cinnamon Hillyard

Numeracy

Quantway is a quantitative reasoning-based pathway for developmental math that has been developed as an alternative to the traditional remedial algebra sequence. To explore the experiences of faculty involved with Quantway, we interviewed eight individuals who have taught the course in the past year to survey their attitudes and opinions about students in their classes, the materials and pedagogies in use, and the collegial interaction of networked faculty. Faculty were selected with the intention of gathering a broad set of opinions resulting from differences of location, experience, and other factors. In this paper, we summarize those interviews by identifying common …

Improving University Students' Perception Of Mathematics And Mathematics Ability, Shelly L. Wismath, Alyson Worrall

Numeracy

Although mathematical and quantitative reasoning skills are an essential part of adult life in our society, many students arrive at post-secondary education without such skills. Taking a standard mathematics course such as calculus may do little to improve those skills. Using a modification of the Tapia & Marsh questionnaire, we surveyed 62 students taking a broad quantitative reasoning course designed to develop quantitative skills, with respect to two broad attitudinal areas: students’ perception of their own ability, confidence and anxiety, and their perception of the value of mathematics in their studies and their lives. Pre- to post-course comparisons were done …

Quantitative Literacy And Co-Construction In A High School Math Course, Mark Russo

Numeracy

This article reports some of the key findings from a practitioner-action research study that analyzed the impact of co-construction on students’ quantitative literacy (QL) and attitudes towards mathematics. Co-construction is a process where students work alongside their teachers to plan units, lessons, and assessments, and this approach was chosen because of its potential to help students advocate for the specific mathematical contexts that would best develop their QL. This yearlong study took place in a public high school, with forty-five students in two different classes participating. Students formally contributed to the development of the course by completing written questionnaires and …

Assessing Numeracy In The Upper Elementary And Middle School Years, Carol Ann Gittens

Numeracy

Numeracy is the ability or tendency to reason critically about quantitative information. The preponderance of published research on numeracy examines this construct among either pre-K or early elementary samples, students with developmental challenges, or is focused on post-secondary and adult cohorts. The numeracy skills of upper-elementary and middle school students is less documented and understood, most notably because of the lack of valid instruments that are developmentally appropriate for the age range. A numeracy scale for use among upper-elementary and middle school students is introduced in this paper. Scale validation was performed using a gender-balanced, racially / ethnically diverse sample …

Parts Of The Whole: Strategies For The Spread Of Quantitative Literacy: What Models Can Tell Us, Dorothy Wallace

Numeracy

Two conceptual frameworks, one from graph theory and one from dynamical systems, have been offered as explanations for complex phenomena in biology and also as possible models for the spread of ideas. The two models are based on different assumptions and thus predict quite different outcomes for the fate of either biological species or ideas. We argue that, depending on the culture in which they exist, one can identify which model is more likely to reflect the survival of two competing ideas. Based on this argument we suggest how two strategies for embedding and normalizing quantitative literacy in a given …

Quantitative Reasoning Learning Progression: The Matrix, Robert L. Mayes, Jennifer Forrester, Jennifer Schuttlefield Christus, Franziska Peterson, Rachel Walker

Numeracy

The NSF Pathways Project studied the development of environmental literacy in students from grades six through high school. Learning progressions for environmental literacy were developed to explicate the trajectory of learning. The Pathways QR research team supported this effort by studying the role of quantitative reasoning (QR) as a support or barrier to developing environmental literacy. An iterative research methodology was employed which included targeted student interviews to establish QR learning progression progress variables and elements comprising those progress variables, development of a QR learning progression framework, and closed-form QR assessments to verify the progression. In this paper the focus …

History Of Numeracy Education And Training For Print Journalists In England, Steven Harrison

Numeracy

If the history of journalism education has been a footnote to accounts of the profession’s development, then the history of numeracy training for journalists must be considered a footnote to a footnote. Despite the universally acknowledged centrality of numbers to a clear understanding of the world, many journalism students and entrants are proudly number-phobic; it is even suggested that an aversion to maths is a key reason why some choose journalism as a career. This study traces the development of numeracy education for journalists in England. It is only with the incipient professionalisation of journalism from the mid-19th century that …

Looking At The Multiple Meanings Of Numeracy, Quantitative Literacy, And Quantitative Reasoning, H. L. Vacher

Numeracy

The subject of this journal goes by a variety of names: numeracy, quantitative literacy, and quantitative reasoning. Some authors use the terms interchangeably. Others see distinctions between them. Study of psycholinguistic and ontological concepts laid out in the literature of WordNet and familiarity with the papers in this journal suggests a vocabulary matrix consisting of four rows (word senses) and three columns (word forms, namely numeracy, QL, and QR). The four word senses correspond to four sets of synonyms: {numeracy}, {numeracy, QL}, {QL, QR}, and {numeracy, QL, QR}. Each of the word forms is polysemous: “numeracy” points to the first, …

Parts Of The Whole: Only Connect, Dorothy Wallace

Numeracy

This is the first of several columns that will focus on the mechanisms by which new ideas become accepted by a culture, offering some familiar examples, deriving basic principles from these examples, and applying them to the problem of promoting quantitative literacy in an educational system. In this essay we describe how new concepts become embedded in a culture through their connections to existing ideas, and use this principle to suggest strategies of discourse about numeracy that promote it among various constituencies in the culture.

The Language Of Comparisons: Communicating About Percentages, Jessica Polito

Numeracy

While comparisons between percentages or rates appear frequently in journalism and advertising, and are an essential component of quantitative writing, many students fail to understand precisely what percentages mean, and lack fluency with the language used for comparisons. After reviewing evidence demonstrating this weakness, this experience-based perspective lays out a framework for teaching the language of comparisons in a structured way, and illustrates it with several authentic examples that exemplify mistaken or misleading uses of such numbers. The framework includes three common types of erroneous or misleading quantitative writing: the missing comparison, where a key number is omitted; the apples-to-pineapples …

Sixth Graders Benefit From Educational Software When Learning About Fractions: A Controlled Classroom Study, Susanne Scharnagl, Petra Evanschitzky, Judith Streb, Manfred Spitzer, Katrin Hille

Numeracy

This study analyses the effectiveness of an educational web-based software package for teaching mathematics in schools. In all, 864 sixth graders and their teachers took part in the controlled study. Students learned the addition and subtraction of fractions with (intervention group; n = 469) or without (control group; n = 395) the support of the educational software. Compared to the controls, students who used the software showed better results in the post-test. Gains were dose dependent and particularly marked in high-ability students and students with lower scores of math anxiety.

Teaching Quantitative Reasoning: A Better Context For Algebra, Eric Gaze

Numeracy

This editorial questions the preeminence of algebra in our mathematics curriculum. The GATC (Geometry, Algebra, Trigonometry, Calculus) sequence abandons the fundamental middle school math topics necessary for quantitative literacy, while the standard super-abundance of algebra taught in the abstract fosters math phobia and supports a culturally acceptable stance that math is not relevant to everyday life. Although GATC is seen as a pipeline to STEM (Science, Technology, Engineering, Mathematics), it is a mistake to think that the objective of producing quantitatively literate citizens is at odds with creating more scientists and engineers. The goal must be to create a curriculum …

Parts Of The Whole: The Educational Sieve, Dorothy Wallace

Numeracy

This essay argues that the structure of course prerequisites affects retention of students in a course of study. The same argument suggests that the structure of degree requirements, including quantitative reasoning courses, affects retention in college. In particular, the same set of courses required in a rigid sequence will cause more students to exit the program early than if the same courses were offered in a flexible order.

Parts Of The Whole: When Variation Is The Goal, Dorothy Wallace

Numeracy

The goals of higher education are a population of extreme variability in expertise, a diffusion of specialized knowledge across disciplinary boundaries, and production of strong K-12 teachers. Promoting these three goals has implications at all granularities, from the pedagogy of an individual college professor to the incentives and policies that shape systemic change.

Quantitative Reasoning Learning Progressions For Environmental Science: Developing A Framework, Robert L. Mayes, Franziska Peterson, Rachel Bonilla

Numeracy

Quantitative reasoning is a complex concept with many definitions and a diverse account in the literature. The purpose of this article is to establish a working definition of quantitative reasoning within the context of science, construct a quantitative reasoning framework, and summarize research on key components in that framework. Context underlies all quantitative reasoning; for this review, environmental science serves as the context.In the framework, we identify four components of quantitative reasoning: the quantification act, quantitative literacy, quantitative interpretation of a model, and quantitative modeling. Within each of these components, the framework provides elements that comprise the four components. The …

Personal Financial Behavior: The Influence Of Quantitative Literacy And Material Values, Pete Nye, Cinnamon Hillyard

Numeracy

Some consumers finance discretionary spending at extremely high interest rates. Many carry substantial balances on their credit cards at effective annual rates as high as 36 percent, and some pay annual rates on “pay day” loans as high as 400 percent. High interest debt can rapidly cascade into an overwhelming financial burden, threatening the consumer’s credit and long-term financial health.

This survey study investigates how quantitative literacy may promote forward-looking financial decisions, decisions that recognize the long-term consequences of current choices and may favor the future over the present. In addition, we examine the consumer’s confidence in their quantitative skills. …

Parts Of The Whole: The Virtue Of Books, Dorothy Wallace

Numeracy

This column argues that the majority of commercial textbooks do not serve students well. Strategies for change include clearly distinguishing the textbook requirements of different priority subjects and assembling writers who can address, in addition to content development, the cognitive level of the children as well as writing in an age-appropriate way. A discussion of the forces that produce current texts leads to the recommendation that textbooks be a focus of research and improvement rather than the byproduct of an individual’s lecture notes.

Introducing Geoscience Students To Numerical Modeling Of Volcanic Hazards: The Example Of Tephra2 On Vhub.Org, Leah M. Courtland, Charles Connor, Laura Connor, Costanza Bonadonna

Numeracy

The Tephra2 numerical model for tephra fallout from explosive volcanic eruptions is specifically designed to enable students to probe ideas in model literacy, including code validation and verification, the role of simplifying assumptions, and the concepts of uncertainty and forecasting. This numerical model is implemented on the VHub.org website, a venture in cyberinfrastructure that brings together volcanological models and educational materials. The VHub.org resource provides students with the ability to explore and execute sophisticated numerical models like Tephra2. We present a strategy for using this model to introduce university students to key concepts in the use and evaluation of Tephra2 …

Spreadsheets Across The Curriculum, 4: Evidence Of Student Learning And Attitudes About Spreadsheets In A Physical Geology Course, Heather L. Lehto, H. L. Vacher

Numeracy

Spreadsheets have been used in education for teaching math concepts for years. However, when faculty at the University of South Florida began using a new set of spreadsheet-based modules to help teach students math and geology concepts the students were not receptive. The complaint most often heard was that students spent more time learning how to use Excel than they did learning the concepts presented in the modules. We began to wonder if the learning curve for Excel was so great that it prevented our students from attaining the level of learning for the math and geology concepts that we …

Number Sense: The Underpinning Understanding For Early Quantitative Literacy, Effie Maclellan

Numeracy

The fundamental meaning of Quantitative Literacy (QL) as the application of quantitative knowledge or reasoning in new/unfamiliar contexts is problematic because how we acquire knowledge, and transfer it to new situations, is not straightforward. This article argues that in the early development of QL, there is a specific corpus of numerical knowledge which learners need to integrate into their thinking, and to which teachers should attend. The paper is a rebuttal to historically prevalent (and simplistic) views that the terrain of early numerical understanding is little more than simple counting devoid of cognitive complexity. Rather, the knowledge upon which early …

Quantitative Reasoning And Sustainability, Corrine H. Taylor

Numeracy

Quantitative Reasoning and Sustainability have much in common. Both are complex, nuanced concepts with rather long definitions that have evolved over time. Both subjects are “everybody’s business” on college campuses, and must be approached in courses across the curriculum, not merely in one course on QR or in one course on Sustainability. The growing, wider presence of both QR and Sustainability on college campuses is due to their applicability in individuals’ personal, professional, and public lives. Moreover, QR and Sustainability support and enhance each other in and out of the classroom. Sustainability is an important, authentic, relevant context for lessons …

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 …

Parts Of The Whole: Learn More, Learn Better, Dorothy Wallace

Numeracy

Building on previous columns in Numeracy, this column analyzes various teaching techniques in terms of their ability to build cognitive schema, extend existing schema, reinforce learning, move mean understanding of a group of students, and reduce variance in understanding of a group. We offer a pedagogical cycle as an example of how to address multiple learning goals using common teaching methods.

If Only Math Majors Could Write..., Bernard L. Madison

Numeracy

This text of the opening plenary address to the 2011 Summit of the Appalachian College Association and the meeting of the National Numeracy Network makes an argument that quantitative reasoning and writing should be taught together. The argument is set up by noting that humanists have historically banished quantitative issues from their study of the liberal arts and that science, engineering, and mathematics education suffers from lack of approaches to learning that promote complex, deeper understanding, most notably integrative and reflective learning. Therefore, everyone would profit from combining writing and quantitative reasoning. Five more specific reasons are discussed, drawing evidence …

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 …

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Numeracy

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students.

Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

Quantitative Literacy Interventions At University Of Cape Town: Effects Of Separation From Academic Disciplines, Vera Frith

Numeracy

The aim of the Numeracy Centre at the University of Cape Town is to develop students’ quantitative literacy (QL) in a manner consistent with their programmes of study and intended roles in the community. Our theoretical perspective on the nature of QL is in line with that of the New Literacies Studies and sees academic QL as practices in different academic disciplinary contexts. This means that for us the ideal curriculum structure for developing QL would fully integrate it into the teaching of the disciplines. This is in practice not achievable in most cases, especially since many students do not …

Numeracy, Financial Literacy, And Financial Decision-Making, Annamaria Lusardi

Numeracy

Financial decisions, be they related to asset building or debt management, require the capacity to do calculations, including some complex ones. But how numerate are individuals, in particular when it comes to calculations related to financial decisions? Studies and surveys implemented in both the United States and in other countries that are described in this paper show the level of numeracy among the population to be very low. Moreover, lack of numeracy is not only widespread but is particularly severe among some demographic groups, such as women, the elderly, and those with low educational attainment. This has potential consequences for …

The Joy Of Quantitative Reasoning, Caren Diefenderfer

Numeracy

One of the advantages of focusing on quantitative reasoning is that it spans a wide variety of topics. As incoming president of the National Numeracy Network, I would like to take the opportunity of this editorial to tell my story of intellectual reward from finding common purpose in quantitative reasoning with colleagues from disciplines outside of mathematics. The story starts with an NSF-funded faculty development project (DUE-9952807) to further a QR across-the-curriculum program and the finding from that program that merging authentic context with mathematics brings interaction and collaboration. That joy in learning from and working with colleagues in other …

Parts Of The Whole: An Algebra Lesson, Dorothy Wallace

Numeracy

This column draws on research of Eon Harper to demonstrate how an understanding of his proposed stages of algebra acquisition would inform a systemic overhaul of algebra education. Harper's stages also explain why students may pass a series of algebra courses yet still be unable to make sense of calculus, as well as offering insight on what aspects of algebra support quantitative literacy.