Education Commons^™

Parts Of The Whole: Quantitative Literacy On A Desert Island, Dorothy Wallace

Numeracy

Some of the specific institutional problems faced by quantitative reasoning courses, programs and requirements arise from the fragile intellectual position of “quantitative reasoning” as an idea, or meme. The process of isolation and reintroduction explains both the proliferation of living species and the way in which some difficult ideas take their place in a culture. Using evolutionary explanations as metaphor and the Copernican revolution as an example of a difficult idea, we draw lessons that can be applied to the “quantitative reasoning” meme, including the function of the National Numeracy Network as an island of protected discourse favoring the growth …

Review Of Case Studies For Quantitative Reasoning: A Casebook Of Media Articles By Bernard L. Madison, Stuart Boersma, Caren L. Diefenderfer, And Shannon W. Dingman, Samuel L. Tunstall

Numeracy

Bernard L. Madison, Stuart Boersma, Caren L. Diefenderfer, and Shannon W. Dingman. Case Studies for Quantitative Reasoning: A Casebook of Media Articles (Pearson Learning Solutions, 2012). 215 pp. ISBN 9781256512875.

Concisely organized and timely to a tee, Case Studies for Quantitative Reasoning contains a wealth of articles and exercises to promote higher-order thinking in any course where quantitative literacy is a goal. The text is a self-contained package complete with just enough mathematics to ensure that all students can join in. It contains a total of twenty-four case studies, each of which highlights how numbers appear in day-to-day media. The …

Promoting Numeracy In An Online College Algebra Course Through Projects And Discussions, Samuel L. Tunstall, Michael J. Bossé

Numeracy

This research stems from efforts to infuse quantitative literacy (QL) in an online version of college algebra. College algebra fulfills a QL requirement at many universities, and it is a terminal course for most who take it. In light of the course’s traditional content and teaching methods, students often leave with little gained in QL. An online platform provides a unique means of engaging students in quantitative discussions and research, yet little research exists on online courses in the context of QL. The course studied included weekly news discussions as well as “messy” projects requiring data analysis. Students in online …

Implementing Quantitative Literacy At Southwestern Community College, North Carolina, Vicki Todd, John Wagaman

Numeracy

There is a time when articulation agreements between universities and community colleges come to an end. When this happened in North Carolina, there was great hope that not only would the mathematics classes that were offered in the North Carolina Community College System be revamped with respect to overlapping content, but also that mathematics classes would be developed that have a clear connection between what is seen in the world and what is taught in the classroom especially for non-STEM (science, technology, engineering, and mathematics-related studies) students. This paper describes how Southwestern Community College (SCC) implemented a quantitative literacy class …

Numeracy Infusion Course For Higher Education (Niche), 2: Development Of Students' Bayesian Reasoning Skill, Frank Wang

Numeracy

Gerd Gigerenzer's technique of frequency representations for solving the medical diagnosis problem, mammography problem, and other Bayesian reasoning problems is summarized in this paper. Such a method has been introduced to community college students in an elementary statistics course. With repeated practice, many community college students can acquire the skill and avoid reported judgment errors that are commonly committed by medical professionals. However, weaknesses in basic skills such as percentage calculations prevent some students from obtaining the correct probability.

Numeracy Infusion Course For Higher Education (Niche), 1: Teaching Faculty How To Improve Students' Quantitative Reasoning Skills Through Cognitive Illusions, Frank Wang, Esther I. Wilder

Numeracy

We describe one of the eight units of a professional development program, the Numeracy Infusion Course for Higher Education (NICHE), which introduces research on cognition, including dual-processing theories, to university faculty. Under the dual-processing framework, System 1 (intuition) quickly proposes intuitive answers to judgment problems as they arise, while System 2 (deliberation) monitors the quality of these proposals, which it may endorse, correct, or override. We present several classic questions that demonstrate the pitfalls of overreliance on intuition without analytical thinking, then describe faculty participants’ responses to these questions and their ideas on how to apply cognitive illusion research to …

The Math You Need, When You Need It (Tmyn): Leveling The Playing Field, Jennifer M. Wenner, Eric M. D. Baer

Numeracy

The Math You Need, When You Need It (TMYN) is a set of online tutorials designed to help students develop and review mathematical skills that are applied in undergraduate geoscience courses. We present results of a three-year study of more than 4000 students in 106 geoscience courses at a variety of post-secondary schools who were assigned TMYN tutorials as supplemental mathematics instruction. Changes in student scores from pre- to post-test suggest that the support provided by programs such as TMYN can begin to reduce the gap between mathematically well-prepared and underprepared students; in essence, TMYN levels the quantitative playing field …

Quantitative Reasoning In Environmental Science: Rasch Measurement To Support Qr Assessment, Robert L. Mayes, Kent Rittschof, Jennifer H. Forrester, Jennifer D. Schuttlefield Christus, Lisa Watson, Franziska Peterson

Numeracy

The ability of middle and high school students to reason quantitatively within the context of environmental science was investigated. A quantitative reasoning (QR) learning progression, with associated QR assessments in the content areas of biodiversity, water, and carbon, was developed based on three QR progress variables: quantification act, quantitative interpretation, and quantitative modeling. Diagnostic instruments were developed specifically for the progress variable quantitative interpretation (QI), each consisting of 96 Likert-scale items. Each content version of the instrument focused on three scale levels (macro scale, micro scale, and landscape scale) and four elements of QI identified in prior research (trend, translation, …

The Levels Of Conceptual Understanding In Statistics (Locus) Project: Results Of The Pilot Study, Douglas Whitaker, Steven Foti, Tim Jacobbe

Numeracy

The Levels of Conceptual Understanding in Statistics (LOCUS) project (NSF DRL-111868) has created assessments that measure conceptual (rather than procedural) understanding of statistics as outlined in GAISE Framework (Franklin et al., 2007, Guidelines for Assessment and Instruction in Statistics Education, American Statistical Association). Here we provide a brief overview of the LOCUS project and present results from multiple-choice items on the pilot administration of the assessments with data collected from over 3400 students in grades 6-12 across six states. These results help illustrate students’ understanding of statistical topics prior to the implementation of the Common Core State Standards. Using the …

The Quantitative Reasoning For College Science (Quarcs) Assessment, 1: Development And Validation, Katherine B. Follette, Donald W. Mccarthy, Erin Dokter, Sanlyn Buxner, Edward Prather

Numeracy

Science is an inherently quantitative endeavor, and general education science courses are taken by a majority of college students. As such, they are a powerful venue for advancing students’ skills and attitudes toward mathematics. This article reports on the development and validation of the Quantitative Reasoning for College Science (QuaRCS) Assessment, a numeracy assessment instrument designed for college-level general education science students. It has been administered to more than four thousand students over eight semesters of refinement. We show that the QuaRCS is able to distinguish varying levels of quantitative literacy and present performance statistics for both individual items and …

What Are You Reading? An Analysis Of 100,000 Numeracy Article Downloads, Nathan D. Grawe

Numeracy

This editorial celebrates the first 100,000 downloads of items published in Numeracy. An analysis of item titles suggests readers prefer titles referencing "numeracy" over "quantitative literacy" and those dealing with mathematics and finance. As we look toward the next 100,000 downloads we aspire to greater diversity in readership that diminishes disciplinary differences.

Parts Of The Whole: Moderating Competition In The World Of Ideas, Dorothy Wallace

Numeracy

In both biological and mathematical dynamical systems, competition may be moderated by the presence of a top predator of both competing species. Applying this principle in memetics sheds light on why some strategies are more likely than others to promote quantitative literacy in various kinds of institutions.

Can We Use Polya’S Method To Improve Students’ Performance In The Statistics Classes?, Indika Wickramasinghe, James Valles

Numeracy

In this study, Polya’s problem-solving method is introduced in a statistics class in an effort to enhance students’ performance. Teaching the method was applied to one of the two introductory-level statistics classes taught by the same instructor, and a comparison was made between the performances in the two classes. The results indicate there was a significant improvement of the students’ performance in the class in which Polya’s method was introduced.

Quantitative Literacy And The Common Core State Standards In Mathematics, Bernard L. Madison

Numeracy

How supportive of quantitative literacy (QL) are the Common Core State Standards in Mathematics (CCSSM)? The answer is tentative and conditional. There are some QL-supportive features including a strong probability and statistics strand in grade 6 through high school; a measurements and data strand in K-5; ratio and proportional reasoning standards in grades 6 and 7; and a comprehensive and coherent approach to algebraic reasoning and logical argument. However, the standards are weak in supporting reasoning and interpretation, and there are indications that the applications in CCSSM – mostly unspecified – will not include many QL contextual situations. Early indicators …

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 …

Assessment For Improvement: Two Models For Assessing A Large Quantitative Reasoning Requirement, Mary C. Wright, Joseph E. Howard

Numeracy

We present two models for assessment of a large and diverse quantitative reasoning (QR) requirement at the University of Michigan. These approaches address two key challenges in assessment: (1) dissemination of findings for curricular improvement and (2) resource constraints associated with measurement of large programs. Approaches we present for data collection include convergent validation of self-report surveys, as well as use of mixed methods and learning analytics. Strategies we present for dissemination of findings include meetings with instructors to share data and best practices, sharing of results through social media, and use of easily accessible dashboards. These assessment approaches may …

Development Of The Quantitative Reasoning Items On The National Survey Of Student Engagement, Amber D. Dumford, Louis M. Rocconi

Numeracy

As society’s needs for quantitative skills become more prevalent, college graduates require quantitative skills regardless of their career choices. Therefore, it is important that institutions assess students’ engagement in quantitative activities during college. This study chronicles the process taken by the National Survey of Student Engagement (NSSE) to develop items that measure students’ participation in quantitative reasoning (QR) activities. On the whole, findings across the quantitative and qualitative analyses suggest good overall properties for the developed QR items. The items show great promise to explore and evaluate the frequency with which college students participate in QR-related activities. Each year, hundreds …

Effects Of Reducing The Cognitive Load Of Mathematics Test Items On Student Performance, Susan C. Gillmor, John Poggio, Susan Embretson

Numeracy

This study explores a new item-writing framework for improving the validity of math assessment items. The authors transfer insights from Cognitive Load Theory (CLT), traditionally used in instructional design, to educational measurement. Fifteen, multiple-choice math assessment items were modified using research-based strategies for reducing extraneous cognitive load. An experimental design with 222 middle-school students tested the effects of the reduced cognitive load items on student performance and anxiety. Significant findings confirm the main research hypothesis that reducing the cognitive load of math assessment items improves student performance. Three load-reducing item modifications are identified as particularly effective for reducing item difficulty: …

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 …

Educational Assessment Is An Enduring Theme Of Numeracy, H. L. Vacher

Numeracy

The Assessment Theme Collection in this issue brings the count of papers on QL assessment to 22 out of the 136 papers (16.2%) in the journal’s first 15 issues. After the first ten issues (our first five years), the counts were 13 and 85 respectively (15.1%). A table in this editorial updates the list of our papers on the subject.