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Articles 1 - 24 of 24
Full-Text Articles in Education
Numeracy Tasks: Inspiring Transfer Between Concrete And Abstract Thinking Spaces, Taras Gula, Miroslav Lovric
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 …
Covid Learning Loss: A Call To Action, Nathan D. Grawe
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.
The Development, Validation, And Standardization Of A New Tool: The Dyscalculia Test, Stella Eteng-Uket
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 …
Establishing The Validity And Reliability Of The Locus Assessments, Tim Jacobbe, Bob Delmas, Brad Hartlaub, Jeff Haberstroh, Catherine Case, Steven Foti, Douglas Whitaker
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
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 …
Covid-19: A Developing Crisis For Quantitative Reasoning, Nathan D. Grawe
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.
Probing For Bias: Comparing Populations Using Item Response Curves, Paul J. Walter, Edward Nuhfer, Crisel Suarez
Probing For Bias: Comparing Populations Using Item Response Curves, Paul J. Walter, Edward Nuhfer, Crisel Suarez
Numeracy
We introduce an approach for making a quantitative comparison of the item response curves (IRCs) of any two populations on a multiple-choice test instrument. In this study, we employ simulated and actual data. We apply our approach to a dataset of 12,187 participants on the 25-item Science Literacy Concept Inventory (SLCI), which includes ample demographic data of the participants. Prior comparisons of the IRCs of different populations addressed only two populations and were made by visual inspection. Our approach allows for quickly comparing the IRCs for many pairs of populations to identify those items where substantial differences exist. For each …
Measuring Numeracy: Validity And The Programme For The International Assessment Of Adult Competencies (Piaac), Samuel L. Tunstall
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 …
Alignment Between Learning Objectives And Assessments In A Quantitative Literacy Course, Younggon Bae, Samuel L. Tunstall, Kathryn S. Knowles, Rebecca L. Matz
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. …
Quantitative Literacy In The Core Curriculum Of Hood College: Chapter Ii, Outcomes And Assessment, Betty Mayfield, Ann Stewart
Quantitative Literacy In The Core Curriculum Of Hood College: Chapter Ii, Outcomes And Assessment, Betty Mayfield, Ann Stewart
Numeracy
In a previous article, we described our college’s new core curriculum, which included a Quantitative Literacy (QL) component for the first time. We explained how we defined QL in the college catalog, and how we used that definition to choose courses to satisfy the new requirement. We then discussed our early efforts at assessing the effectiveness of the QL program and described our plans for the future. Here we report on our progress towards those goals, including working with faculty from other departments and with our institutional research office to develop a more sophisticated assessment plan, as well as creating …
Using The Quantitative Literacy And Reasoning Assessment (Qlra) For Early Detection Of Students In Need Of Academic Support In Introductory Courses In A Quantitative Discipline: A Case Study, Nathan D. Grawe, Kristin O'Connell
Using The Quantitative Literacy And Reasoning Assessment (Qlra) For Early Detection Of Students In Need Of Academic Support In Introductory Courses In A Quantitative Discipline: A Case Study, Nathan D. Grawe, Kristin O'Connell
Numeracy
As the number of young people attending college has increased, the diversity of college students’ educational backgrounds has also risen. Some students enter introductory courses with math anxiety or gaps in their quantitative training that impede their ability to master or even grasp relevant disciplinary content. Too often professors learn of these anxieties and gaps only during the post mortem of the first midterm. By that time, a good portion of a student’s grade is determined and successful recovery may be impossible. During the 2016-17 academic year, the Department of Economics at Carleton College ran a pilot project using the …
Preliminary Evaluation Of The Psychometric Quality Of HeightenTm Quantitative Literacy, Katrina C. Roohr, Hyesun Lee, Jun Xu, Ou Lydia Liu, Zhen Wang
Preliminary Evaluation Of The Psychometric Quality Of HeightenTm Quantitative Literacy, Katrina C. Roohr, Hyesun Lee, Jun Xu, Ou Lydia Liu, Zhen Wang
Numeracy
Quantitative literacy has been identified as an important student learning outcome (SLO) by both the higher education and workforce communities. This paper aims to provide preliminary evidence of the psychometric quality of the pilot forms for HEIghten quantitative literacy, a next-generation SLO assessment for students in higher education. We evaluated the psychometric quality of the test items (e.g., item analyses), individual- and group-level reliability, the relationship with student performance and related variables (e.g., grade point average) as well as student perceptions, and differences across college-related and demographic subgroups. Our study used data from a pilot test administered to over 1,500 …
Using Think-Aloud Protocols To Uncover Misconceptions And Improve Developmental Math Instruction: An Exploratory Study, Charles Secolsky, Thomas P. Judd, Eric Magaram, Stephen H. Levy, Bruce Kossar, George Reese
Using Think-Aloud Protocols To Uncover Misconceptions And Improve Developmental Math Instruction: An Exploratory Study, Charles Secolsky, Thomas P. Judd, Eric Magaram, Stephen H. Levy, Bruce Kossar, George Reese
Numeracy
Deficiencies in education continue to escalate around the world. The focus on outcomes assessment has narrowed instructional research and curriculum evaluation to standardized testing in certain subject areas. A prototype for a quantitative literacy assessment instrument was developed with the goal of diagnosing student misconceptions of basic mathematics content and changing instructional practices to undo the misconceptions by applying cognitive psychological theory. Two hundred thirty-eight basic math high school students and 209 remedial community college students in New Jersey and New York were administered the instrument, which had been based on coded data from think-aloud protocols. The instrument asked students …
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 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 …
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
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
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
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 …
Assessment For Improvement: Two Models For Assessing A Large Quantitative Reasoning Requirement, Mary C. Wright, Joseph E. Howard
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 …
Effects Of Reducing The Cognitive Load Of Mathematics Test Items On Student Performance, Susan C. Gillmor, John Poggio, Susan Embretson
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
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
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.
Making College Count: An Examination Of Quantitative Reasoning Activities In Higher Education, Louis M. Rocconi, Amber D. Lambert, Alexander C. Mccormick, Shimon A. Sarraf
Making College Count: An Examination Of Quantitative Reasoning Activities In Higher Education, Louis M. Rocconi, Amber D. Lambert, Alexander C. Mccormick, Shimon A. Sarraf
Numeracy
Findings from national studies along with more frequent calls from those who employ college graduates suggest an urgent need for colleges and universities to increase opportunities for students to develop quantitative reasoning (QR) skills. To address this issue, the current study examines the relationship between the frequency of QR activities during college and student and institutional characteristics, as well as whether students at institutions with an emphasis on QR (at least one QR course requirement for all students) report more QR activity. Results show that gender, race-ethnicity, major, full-time status, first-generation status, age, institutional enrollment size, and institutional control are …
The Problem Of Too Many Statistical Tests: Subgroup Analyses In A Study Comparing The Effectiveness Of Online And Live Lectures, David M. Lane
The Problem Of Too Many Statistical Tests: Subgroup Analyses In A Study Comparing The Effectiveness Of Online And Live Lectures, David M. Lane
Numeracy
The more statistical analyses performed in the analysis of research data, the more likely it is that one or more of the conclusions will be in error. Multiple statistical analyses can occur when the sample contains several subgroups and the researchers perform separate analyses for each subgroup. For example, separate analyses may be done for different ethnic groups, different levels of education, and/or for both genders. Media reports of research frequently omit information on the number of subgroup analyses performed thus leaving the reader with insufficient information to assess the validity of the conclusions. This article discusses the problems with …
Quantitative Reasoning Learning Progressions For Environmental Science: Developing A Framework, Robert L. Mayes, Franziska Peterson, Rachel Bonilla
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 …