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 …

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 …

Facilitating Effective Mathematical Teaching Practices In Preschool, Funda Gonulates, Jasook Gilbert

Journal of Global Education and Research

Initial seeds for mathematics literacy are planted during early childhood. Children benefit when they are exposed to and provided with opportunities for math experiences that emphasize their holistic development and not just mathematics proficiency in isolation. This way of viewing and presenting mathematics to young children requires teachers who are equipped with strong mathematics teaching skills. This study examined a 21-hour professional development series for public school preschool teachers on early numeracy, geometry, mathematical reasoning, and teaching pedagogies. This professional development series aimed to help preschool teachers incorporate effective mathematical practices and increase their comfort level in teaching mathematics. Participants …

Catalyzing Change For Equitable Participation, Liza Bondurant, Seema Rivera

Journal of Practitioner Research

This manuscript discusses the Plan, Do, Study, Act (PDSA) cycles designed to help math teacher-researchers (TRs) create more equitable discourse patterns in their classrooms. Before the first cycle, TRs were asked to complete gender and race implicit assessment tests (IATs). Then, TRs planned and recorded a video of themselves facilitating a math discussion. Next, math teacher educators (MTEs) used the Equity QUantified In Participation (EQUIP) classroom observation instrument to code and analyze the discussion. Subsequently, TRs had an opportunity to reflect on the EQUIP and IAT results and set goals for making their teaching practices more equitable. MTEs provided guidance …

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.

Teaching Mathematics To All Learners By Tapping Into Indigenous Legends: A Pathway Towards Inclusive Education, Nahid Golafshani

Journal of Global Education and Research

This study explored the use of Indigenous storytelling in the planning and teaching of mathematical content. In collaboration with Indigenous and non-Indigenous educators, a culturally inclusive mathematical lesson was developed, implemented, and reviewed in an elementary school in Northern Ontario. This study used a culturally authentic approach to address the current educational issue of diversity within the Ontario curriculum and education system. The results of this study suggested that utilizing Indigenous storytelling for teaching mathematical curricular expectations could benefit both Indigenous and non-Indigenous students. Storytelling can allow students to relate abstract mathematical concepts to their own lived experiences, to be …

Approach To Problem Solving And Use Of Intuition By Engineering Technology Students, Meher R. Taleyarkhan, Anne M. Lucietto, Natalie L. F. Hobson, Therese M. Azevedo

Journal of Global Education and Research

Engineering technology students often forgo a methodical approach of solving or answering questions on assignments or exams in favor of an intuition-based approach, emphasizing educated guessing (Broberg et al., 2008). Faculty observations have noted these student solutions often provide explanations, usually sans calculations, to support answers the students believe to be reasonable when in reality deviated from the correct answer. An extensive study was developed to assess several distinctions between student intuition and use of cognition in problem solving, as related to a generalized student population. The study was comprised of a survey and interview. The survey utilized two instruments, …

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 …

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser

Journal of Practitioner Research

Whole group math talks, or number talks, are a common practice to get students talking about their own understanding of mathematical concepts. The purpose of this study was to implement math talks in small group settings to see what would happen, specifically to students’ conceptual understanding as well their general perceptions of math talks. This study took place in a fourth-grade math classroom, and math talks were implemented with the whole class for a week and then moved to small groups for the remaining three weeks of the study. During the study, a pre-and post-assessment was given, field notes were …

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.

Advances In Global Education And Research: Volume 4, Waynne B. James, Cihan Cobanoglu, Muhittin Cavusoglu

University of South Florida (USF) M3 Publishing

This is the fourth volume of the Advances in Global Education and Research Book Series. This volume has the following parts:

• Part 1: Adult Education
• Part 2: Curriculum and Instruction Development
• Part 3: Educational Technology
• Part 4: Education in Other Specialties
• Part 5: English as a Second Language
• Part 6: Global Competence
• Part 7: Higher Education and Educational Leadership
• Part 8: Inclusive Education
• Part 9: International Education
• Part 10: PreK-12
• Part 11: Research Methods in Education

ISBN: 978-1-955833-04-2

Adult Education

• Teaching for knowledge transfer: Best practices from a graduate-level educational psychology distance learning program
  • Bobby Hoffman
• A study on the …

The Attributes Of Mathematics Learning Which Ghanaian Senior High School Students Value, Ernest Kofi Davis, Wee Tiong Seah, Nathaniel Howard, Eric Magnus Wilmot

Journal of Global Education and Research

Valuing constitutes an important aspect of mathematics pedagogy and hence student learning outcomes. This study surveyed 416 students from Cape Coast, Ghana to explore what senior high school students in this country in West Africa valued in their study of mathematics. The data collected were analyzed using principal component analysis. The results suggest that Ghanaian senior high school students found connections, understanding, fluency, learning technologies, feedback, instructional materials, open-endedness and problem-solving important in their mathematics learning. Implications of the findings for curriculum delivery in mathematics and future research opportunities are also discussed.

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 …

Equitable Mathematics Classroom Discourse, Liza Bondurant

Journal of Practitioner Research

In this article the author shares a self-study investigation into how the quality of talk and opportunities to participate are distributed across individual students based on race and gender in her college math class. Readers will learn how to conduct a similar investigation in their classroom. A discussion of ways to use the information gathered from equitable mathematics classroom discourse investigations will follow.

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 …

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 …