Science and Mathematics Education Commons^™

Mathematics Anxiety: Understanding Its Concept, Impact On Secondary Students’ Academic Performance And Career Prospects, And Effective Intervention Strategies, Sabiruddin Molla, Safwana Rashid, Saba Sultana

Numeracy

This study investigates the influence of mathematics anxiety on secondary school students’ academic performance and career pathway selection. Mathematics, often perceived as abstract and challenging, can evoke high levels of anxiety that affect both learning outcomes and career-related decisions. Data were collected from 106 students across two urban secondary schools in Kolkata. Findings revealed that students possessed a significant understanding of the concept of mathematics anxiety (t (105) = 8.48, p < .001, d = 0.82). A strong positive correlation was observed between mathematics anxiety and academic performance (r = .686, p < .001), indicating that elevated anxiety levels correspond with lower achievement. Additionally, a significant positive correlation (r = .475, p < .001) showed that mathematics anxiety influences students’ career pathway selection, with higher anxiety leading to avoidance of mathematics-related careers. The study highlights that negative attitudes toward mathematics often stem from perception rather than actual difficulty. Overall, the findings emphasize the need for innovative teaching strategies and targeted interventions to reduce mathematics anxiety and enhance students’ academic and career outcomes.

Analysing Numeracy Demands In Alberta Curriculum: A Focus On High School Mathematics, Asia Majeed, Kwesi Yaro

Numeracy

In recent years, numeracy has been recognized as a key educational priority across the curriculum in many international jurisdictions, including almost all Canadian provinces. In Alberta province, Canada, for example, the Teaching Quality Standard (TQS) #3 explicitly states that all teachers are responsible for fostering literacy and numeracy skills, regardless of the specific subject areas they teach. This expanded focus reflects a broader understanding of numeracy not merely as a subset of mathematical skills, but as a fundamental competency that supports informed participation in civic, economic, and personal life. This paper applies the 21st Century Numeracy Model (Goos et al., …

Improving Quantitative Support Across An Institution Using An Ecosystem Framework, Laura Muller, Melissa Eblen-Zayas

Numeracy

In our keynote address at the 2025 National Numeracy Network Annual Meeting, we introduced the framework we developed for considering four domains of an institution’s quantitative skills/reasoning support ecosystem that includes bridge programs with a quantitative component, approaches to assessing readiness, curricular on-ramps, and supplementary support. We believe this ecosystem framework has the potential to help campus leaders coordinate institutional efforts around student success in areas connected to students’ quantitative preparation. This keynote highlighted the idea that coordination of stakeholders and their engagement with domains of the ecosystem fall along a spectrum. We provide approaches for using this framework to …

Quantitative Reasoning In Calculus Iii: Advancing Student Engagement, Confidence, And Aspirations At An Hsi, Tanvir Prince

Numeracy

This study examines the impact of integrating Quantitative Reasoning (QR) into a Calculus III course at a Hispanic-Serving Institution (HSI) on student engagement, confidence, and aspirations. The course is offered at Hostos Community College in the South Bronx. It incorporated QR-focused projects on economic inequality, environmental pollution, and access to healthcare. These projects allowed students to apply advanced calculus concepts to real-world social issues. A pre- and post-survey design was employed to assess changes in students’ mathematical confidence, perceptions of relevance, and career and educational goals. Results showed statistically significant gains in confidence and in the belief that advanced math …

Toward Fairer And More Equitable Numeracy Measurement: Improvements To The Quantitative Reasoning For College Science Assessment, Vonna L. Hemmler, Isaac Rosenthal, Kate Follette, Catherine Sarosi, Erin Galyen, Sanlyn Buxner, Jackson Carter, Samantha Maynard, Sarah Bunnell

Numeracy

Numeracy has become an increasingly important 21st-century skill that, due to the relationship between math and science, is often formally developed at the college level in general education science courses. These courses serve a diverse group of students, many of whom have historically experienced science teaching, curriculum, and assessment on the margins. The well-documented biases of assessments in particular against Individuals of Color (IoC) have inspired us to approach numeracy for social justice in our work from this angle, and in this paper, we detail our efforts to revise our validated numeracy assessment to ensure it more fairly and equitably …

Unskilled But Aware Of It: Understanding Self-Assessment By Estimating Guessing From Cognitive-Metacognitive Paired Measures, Edward Nuhfer, Steven Fleisher

Numeracy

We utilize concepts of numeracy including number sense, reading and interpreting graphs, basic probability and statistics, and reasoning to estimate guessing and verify our earlier findings on human self-assessment as replicable. Our field study employed a low-stakes paired measures assessment (11,229 scores from the validated Science Literacy Concept Inventory and postdicted global self-assessment ratings generated upon completion of the Inventory) in conjunction with a five-category taxonomy of self-assessment proficiency. We also simulated 11,229 random guessing responses, to model responses that disengaged, purely random-guessing participants should produce. At least 90% of participants sincerely engaged with the instruments of measure, self-assessed imperfectly …

High Ability, Hidden Gaps: Building Quantitative Reasoning Amongst Singapore’S Mathematically Literate, Rebecca M. Nichols

Numeracy

In Singapore, where primary and secondary students routinely top standardized worldwide mathematics examinations, a paradox emerges: when reaching university, many struggle to apply their skills critically in real-world contexts. This commentary examines the challenges and strategies involved in teaching quantitative reasoning (QR) to mathematically literate students in a top-ranking Singaporean university. While these students arrive well-trained in computation and procedural problem-solving, they often lack confidence and flexibility in ambiguous, data-driven decision-making. This article argues that fostering QR education is crucial not only for Singapore but for education globally, as QR skills underpin evidence-based reasoning within and across disciplines. Such an …

An Argument For Expanding Research On Quantitative Pedagogical Content Knowledge, Randall E. Groth

Numeracy

Pedagogical content knowledge (PCK) traditionally has been used in research concerning prospective and practicing classroom teachers. This essay argues that PCK is also relevant to other professions including those advancing quantitative reasoning (QR). To illustrate, the case of PCK for teaching QR is considered. Those in fields such as public health, journalism, meteorology, and government increasingly find themselves responsible for helping the public understand an ever-growing amount of quantitative information that has a bearing on societal well-being. Several examples illustrate how such professionals’ responsibilities require knowing prevalent QR patterns in society, strategies for fostering sound reasoning, and the general nature …

Examination Of The Delphi Method For Establishing A Quantitative Literacy Framework In Undergraduate Mathematics Course, Emily Elrod, Joo Young Park

Numeracy

The increased relevancy and importance of quantitative literacy (QL) have called for educational reform in undergraduate mathematics course offerings. However, lack of clear guidelines has led to wide variability in the content and outcomes of math courses meant to address QL. Therefore, having an expert consensus regarding content and outcomes for an undergraduate mathematics course focusing on QL would advance the quantitative literacy initiative in higher education. The authors propose the Delphi Method to aid in developing a framework based on expert opinions. The authors explain the Method and suggest the result of this process should yield a research-based framework …

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 …

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 …

A Tale Of Success: Embedding Remediation And Curricular Design, Joseph P. Mccollum, William Adamczak, James R. Nolan

Numeracy

This paper reports how high failure rates in the first quantitative course that college business majors take were significantly reduced by implementing course-embedded remediation. More specifically, this paper details our process for identifying students at risk, placing them in special sections of the first quantitative course, and adding an additional hour of application of course concepts which resulted in a statistically significant increase in pass rates. The study focused on the learning environment, the attitude of the student, the utility of the material and the role of the professor for this special course. We feel this research is timely, as …

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.

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 …

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 …

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 …

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 …

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.

Effects Of Quantitative Literacy On Healthcare Decision-Making: An Aural Context, Robert G. Root, Sonia Bhala

Numeracy

We propose a relationship between sensory modality, numerical formatting, and performance on a survey simulating healthcare decision-making. We examine the current literature on aural health literacy, and specifically aural literacy coupled with health numeracy. We then create a survey instrument called the Bhala test for this purpose and demonstrate that it is moderately internally consistent and provides results that correlate with the NUMi assessment, a widely accepted measure of health numeracy. The quantitative information provided in the Bhala test has two treatments, percentage and natural frequency formats, in an effort to determine which format is easier for subjects to use …

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 …