quantitative reasoning in mathematics and science education

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Quantitative Reasoning in Mathematics and Science Education (Mathematics Education in the Digital Era, 21) 1st ed. 2022 Edition

This book focuses on quantitative reasoning as an orienting framework to analyse learning, teaching and curriculum in mathematics and science education. Quantitative reasoning plays a vital role in learning concepts foundational to arithmetic, algebra, calculus, geometry, trigonometry and other ideas in STEM. The book draws upon the importance of quantitative reasoning and its crucial role in education. It particularly delves into quantitative reasoning related to the learning and teaching diverse mathematics and science concepts, conceptual analysis of mathematical and scientific ideas and analysis of school mathematics (K-16) curricula in different contexts. We believe that it can be considered as a reference book to be used by researchers, teacher educators, curriculum developers and pre- and in-service teachers.

• ISBN-10 3031145526
• ISBN-13 978-3031145520
• Edition 1st ed. 2022
• Publisher Springer
• Publication date January 2, 2023
• Language English
• Dimensions 6.25 x 1 x 9.25 inches
• Print length 350 pages
• See all details

Editorial Reviews

From the back cover, about the author.

Graduating (1993-1996) from the Department of Mathematics Education in Middle East Technical University, Turkey, Gülseren Karagöz Akar earned her master’s degree in 2001 and PhD in December 2006 in Mathematics Education at the Pennsylvania State University where she continued her post-doctoral studies and worked as a full-time instructor between January 2007 and July 2008. In 2010, she started working at Boğaziçi University, Turkey, as a full time professor where she worked as the head of the Department of Mathematics and Science Education from 2018 to 2021. She was involved in the development of Turkish National Mathematics Program for Gifted (K-12) in 2018 and served as an International Advisory Board member for Journal for Research in Mathematics Education (JRME) between July 2018 and July 2021. Her research involves development of mathematical concepts and the nature of mathematics teacher knowledge.

Product details

• Publisher ‏ : ‎ Springer; 1st ed. 2022 edition (January 2, 2023)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 350 pages
• ISBN-10 ‏ : ‎ 3031145526
• ISBN-13 ‏ : ‎ 978-3031145520
• Item Weight ‏ : ‎ 1.6 pounds
• Dimensions ‏ : ‎ 6.25 x 1 x 9.25 inches
• #2,408 in Science for Kids
• #5,933 in Education Research (Books)
• #6,634 in Math Teaching Materials

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Quantitative Reasoning, Edition 1 (2021)

Quantitative Reasoning was designed to align with the objectives of the Virginia Community College System course MTH 154 Quantitative Reasoning.

Table of Contents include:

Chapter 1: Ratio and Proportional Reasoning Chapter 2: Mathematical Modeling Chapter 3: Personal Finance Chapter 4: Validity Studies

A PDF file of, Quantitative Reasoning, Edition 1 (2021), is attached. This textbook is remixed from Math in Society, by David Lippman (CC-BY-SA, 2017), Precalculus: An Investigation of Functions, by David Lippman and Melonie Rasmussen (CC-BY-SA 2011), and other open resources, along with new content by Jason Lachniet, Jennifer Polm, and Libby Watts, with support from the VIVA Open and Affordable Course Content Program. The remixed book is licensed under a Creative Commons Attribution-ShareAlike License (CC-BY-SA, 2021).

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Quantitative Reasoning

Mathematics is one of the great achievements of the human mind, and applications of mathematics pervade today’s society. A mathematical way of thinking, more broadly referred to here as “quantitative reasoning,” is widely used, for example, to justify data-based decisions, encode and protect information, manage the treatment of disease, provide a unified understanding of the forces of nature, and formulate government and international policies. As such, it represents several distinct modes of thinking, which can broadly be classified as analysis, logic, probability and statistics, and modeling. From each of these derive techniques that are applicable to specific classes of problems. Often, a combination of different quantitative techniques is necessary to approach specific situations.

Students completing courses that satisfy the quantitative reasoning requirement should have been exposed to multiple aspects of quantitative reasoning. For example, they should learn how to use deductive reasoning in problem-solving, apply the inductive process to draw conclusions through quantitative analysis, evaluate data and think probabilistically, assess the strength of numerical evidence, and mathematically model processes or systems to be able to predict (or change) their outcomes. In short, the main goal of courses that satisfy the quantitative reasoning requirement is for students to engage in multiple mathematical ways of thinking that will enhance their ability to make informed decisions as citizens and as potential leaders.

Learning Goals

The quantitative reasoning requirement recognizes that the ability to understand and analyze measured quantities is not the only aspect of mathematical reasoning that is important. Another fundamental mode of reasoning involves the ability to think in the abstract and to switch reasoning and analysis from the abstract to concrete, from the cognitive model to the experienced reality.

The quantitative reasoning requirement thus includes two distinct, but complementary components, quantitative analysis/inductive reasoning and deductive/formal reasoning . Courses meeting the majority of the learning goals for either component would satisfy the quantitative reasoning requirement, as described below. The rationale and learning objectives for these two components are as follows.

Quantitative analysis/Induction

Applications of mathematical analysis pervade today’s culture. We live in an era with vast amounts of quantitative information that can be easily accessed. Big data analyses have become indispensable in the operations of business, education, health, and other settings. Policymakers and ordinary citizens increasingly confront issues in science and technology that can be approached using mathematical techniques. For example, quantitative methods are used to analyze personal finances, formulate government policy, justify data-based decisions, encode and protect information, provide a unified understanding of the forces of nature, and manage the treatment of disease. Understanding the scope and power of mathematical analysis and how to draw conclusions from it enables graduates to better make informed decisions as citizens and as potential leaders of the country and of the world.

Goals and Perspectives

The main goal of the quantitative analysis component of the requirement is to provide students with experience in the use of mathematical and statistical methods in the analysis of real-world problems.

• Students will be able to set and solve numerical or geometric problems in a variety of contexts.
• Students will be able to analyze data with appropriate tools, think probabilistically, interpret results, and assess the reliability and uncertainty of conclusions.
• Students will develop the skills to mathematically model processes or systems so as to be able to predict or change their outcomes. Students will gain an appreciation that models only approximate real-world situations and are therefore imperfect, and will develop the skills to quantify these imperfections.

Formal reasoning/Deduction

The ability to abstract symbolic representations of arguments or problems and to utilize formal logic in the analysis of their structure is a distinct form of reasoning that empowers the human intellect, enhances critical thinking, and facilitates rational decision-making. Representing ideas in a symbolic manner and analyzing arguments with the help of logic are, first and foremost, mathematical exercises, but also occur in many other contexts. Many disciplines, such as the physical sciences, computer science, cognitive science, linguistics, and even music theory rely on the principles and rules of logic to classify, predict, and analyze.

The main goal of the formal reasoning component of the requirement is to provide students with experience in the mathematical way of thinking, especially insofar as this way of thinking fosters the development of disciplined habits of the mind and enhances the power of the intellect.

• Students will learn deductive reasoning in problem-solving through problems in which the system of formal reasoning is itself the object of study.
• Students will learn how mathematics and statistics can be used to abstract key features of our world and reason about these features in a general context.
• Students will be engaged with problems whose goal is to follow a rigorous path of deducing conclusions from simple basic assumptions.

A course recognized as meeting the requirements for quantitative reasoning is one that provides a rigorous basis in logical or analytical thought. In terms of learning goals, a course that meets any three of the six goals from either Inductive or Deductive reasoning would be considered a quantitative reasoning course. Rigorous courses in formal logic, statistics, computer programming, and calculus are expected to qualify for this designation, as are, for example, mathematically intensive courses in specific disciplines, where quantitative methods are applied to analyze and model observational data. Courses based on discipline-specific applications of formal logic may also qualify, given the level of formal logic employed. In all cases, it is expected that a substantial focus on the understanding and the application of mathematical ideas, as defined above, should form the core syllabus of a quantitative reasoning course.

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Quantitative Reasoning, Mathematics, and Other Disciplines

Differences between Mathematics and Quantitative Reasoning (QR)

The differences between mathematics and QR create a strong complementarity between the two disciplines. For example, QR emphasizes specific context while mathematics wrestles with generalizable abstractions. QR includes finding, interpreting, and using "dirty," real-world data--data which may include missing values, may not match theoretical constructs, may be dominated by outliers, or may be of questionable reliability. From these imperfect data, quantitatively literate students often use inductive reasoning (sometimes through formal statistics) to better understand the problem of interest. By contrast, mathematics generally begins with "clean" postulates and then uses deductive reasoning to generate conclusions.

A student who masters both of these disciplines will likely be better in applying both mathematics and QR than has she who has mastered one alone. For instance, we would surely like QR-equipped students to be able to pair their data exploration with formal modeling which may in turn involve significant mathematical abstraction. As we revise courses to support student QR, we would expect students to exercise their mathematical skills at the same time. Ultimately, the best quantitative thinking flows from a cycle between the abstract approach of mathematics and the context-rich skills of QR.

QR across the Curriculum

The contextual nature of QR does, however, suggest that QR needs to be taken up across the curriculum and not just in mathematics courses.

In Achieving Quantitative Literacy (an excellent introduction to QR and its interaction with mathematics), Lynn Steen writes,

"If quantitative literacy remains the responsibility solely of mathematics departments--especially if it is caged into a single course such as 'Math for Liberal Arts'--students will continue to see it as something that happens only in the mathematics classroom" (2004 p. 18).

And that outcome would fundamentally undermine the entire point of the QR movement. If we want to train students in the tricky work of transference, teaching them to apply their quantitative understanding to varied and distinct contexts, then we need to teach them in an equally wide range of fields.

While the most explored applications of QR may be found in the social and natural sciences, recent work in the digital humanities highlights the relevance of QR to these disciplines as well. Even in the arts, QR has a role. For one example, see Chris Jordan's collection Running the Numbers , which uses digital tools to represent our society through quantities. In all of these applications, the key point is that QR is authentically relevant to the discipline--not tacked on as a contrived exercise.

Support for Integrating QR in the Curriculum

The complementarity between math and applied disciplines in teaching QR is reflected in the coordinated work by three supporting organizations which seek to advance QR instruction:

• The Mathematical Association of America (MAA)'s special interest group for quantitative literacy ( SIGMAA-QL ), provides support specific to mathematics.
• Project Kaleidoscope ( PKAL ( This site may be offline. ) ), provides support specific to science.
• and the National Numeracy Network ( NNN ), provides support for faculty from all disciplines including the arts, literature, and the humanities.

Read more about supporting organizations

Resources for Teaching QR

A number disciplines have taken up this challenge of weaving QR in a natural way into their subject matter. Below are links to these disciplinary (and interdisciplinary) assignment collections. If your discipline is not represented, take heart. Most users of the collections revise assignments to the particulars of their own course context even when they find an assignment originally designed for their discipline. So, go ahead and browse a collection from a neighboring field and look for assignments can can be altered to meet your own needs.

Interdisciplinary

• Numeracy Infusion Course for Higher Education : NICHE is a project of the City University of New York (CUNY) Quantitative Reasoning (QR) Alliance to foster the infusion of QR instruction and assessment into undergraduate courses in a broad range of disciplines. The NICHE site includes many tips, videos, and online resources to support curriculum revision.
• The Math You Need, When You Need It : Math You Need is designed to give students the quantitative knowledge that they need, just before they need to use it in their concurrent geoscience course. This program includes pre- and post-testing and self-paced modules.
• Teaching Quantitative Skills in the Geosciences : This site provides resources for faculty that include pedagogic methods, teaching resources, supporting materials for students and a discussion of the issues.
• Kéyah Math : The Kéyah Math Project has developed a series of versatile online activities in mathematical geoscience, using the natural and cultural landscapes of the Southwest United States as context and setting.
• Using Data in the Classroom : This site provides information and resources mainly for science faculty to incorporate collecting, manipulating, and aggregating data in their classes.

Social Science

• Data Counts! : Data Counts! is an interactive website designed to help integrate social statistics into the classroom setting and provides access to an archive of datasets and teaching modules created for SSDAN's Census in the Classroom project.
• Starting Point: Teaching and Learning about Economics : This project provides teaching resources for two-year college economics faculty and also runs workshops and webinars to help two-year college faculty connect with each other and stay current on important topics in economics and teaching.
• Resources for Teaching Introductory Statistics : This module provides information for teaching several topics in statistics.
• Mathematics and Statistics Models : This module provides information and resources for using statistical models in the sciences.

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What is Quantitative Reasoning?

• Author: Noreen Niazi
• Last Updated on: January 14, 2024

Quantitative reasoning is understanding and working with numbers and data to solve problems. It is an essential skill today, where data-driven decisions are increasingly important. In this ultimate guide, I’ll help you understand  what is quantitative reasoning, why it’s important, how it’s used in different fields, and how to improve your quantitative reasoning skills.

Introduction to Quantitative Reasoning

Quantitative reasoning uses mathematical and statistical methods to analyze and solve real-world problems. It involves understanding the relationship between numbers, data, and other variables and using that understanding to make informed decisions. Quantitative reasoning is used in various fields, from finance and business to science and engineering.

Quantitative reasoning is a broad term that encompasses many different skills and abilities. At its core, it involves understanding, analyzing, and working with numbers and data. This can include everything from basic arithmetic and algebra to more advanced statistical analysis and modeling.

Why is Quantitative Reasoning Important?

Quantitative reasoning is important for several reasons. First, it allows us to make informed decisions based on data and evidence rather than relying on intuition or guesswork. This is especially important in finance and business, where decisions can have significant consequences.

Second, quantitative reasoning is essential for scientific research and discovery. Scientists use quantitative reasoning to analyze data and test hypotheses , allowing them to make new discoveries and advance our understanding of the world.

Finally, quantitative reasoning is a valuable skill in everyday life. It can help you make better financial decisions, understand news reports that involve data, and even improve your health by tracking your diet and exercise habits.

The Role of Quantitative Reasoning in Different Fields

Quantitative reasoning plays an important role in many different fields. In finance and business, it is used to analyze market trends, forecast future sales, and make investment decisions. In science and engineering, it is used to analyze data from experiments and simulations and to design new products and technologies.

In healthcare, quantitative reasoning is used to analyze patient data and develop new treatments and therapies. In education, it is used to evaluate student performance and develop effective teaching strategies. And in government and public policy, it is used to analyze social and economic trends and develop policies that address important issues like poverty, healthcare, and education.

Different Types of Quantitative Reasoning

There are many different types of quantitative reasoning, each with its own set of skills and applications. Some of the most common types include:

• Basic arithmetic and algebra: This includes skills like addition, subtraction, multiplication, and division, as well as solving equations and inequalities.
• Descriptive statistics: This involves analyzing and summarizing data using mean, median, and mode measures.
• Inferential statistics involves using data to make predictions or draw conclusions about a larger population.
• Probability: This involves understanding the likelihood of different outcomes based on data and assumptions.
• Data visualization involves presenting data in a visual format, such as graphs or charts, to help people understand and interpret it.

How to Improve Your Quantitative Reasoning Skills

If you want to improve your quantitative reasoning skills, there are several things you can do:

• Practice: The more you work with numbers and data, the more comfortable you will become with quantitative reasoning.
• Take courses: Many online courses and tutorials can help you learn new quantitative reasoning skills.
• Read books: There are many books on quantitative reasoning and related topics that can help you develop your skills and understanding.
• Seek feedback: Ask for feedback on your work from others knowledgeable about quantitative reasoning, and use that feedback to improve.

Common Tools Used in Quantitative Reasoning

There are many tools and technologies used in quantitative reasoning. Some of the most common include:

• Spreadsheets: Programs like Microsoft Excel are commonly used for data analysis and modeling.
• Statistical software: Programs like R and SPSS are used for advanced statistical analysis and modeling.
• Calculators: Basic and scientific calculators perform calculations and solve equations.
• Data visualization tools: Programs like Tableau and Power BI are used for creating visual representations of data.

Examples of Quantitative Reasoning in Real Life

Quantitative reasoning is used in a wide range of real-life situations . Some examples include:

• Budgeting: Using quantitative reasoning to create and manage a household budget.
• Investing: Using quantitative reasoning to make informed investment decisions based on market trends and other data.
• Healthcare: Using quantitative reasoning to analyze patient data and develop new treatments and therapies.
• Sports: Using quantitative reasoning to analyze player and team performance data to make strategic decisions.

Careers in Quantitative Reasoning

Many different careers require strong quantitative reasoning skills . Some examples include:

• Data analyst: Analyzing and interpreting data to help organizations make better decisions.
• Actuary: Analyzing and managing risk for insurance companies and other organizations.
• Financial analyst: Analyzing financial data to help organizations make investment decisions.
• Scientist or engineer: Using quantitative reasoning to analyze data and develop new products and technologies.

Conclusion and Final Thoughts

Quantitative reasoning is an essential skill in today’s world. It allows us to make informed decisions based on data and evidence, and it is used in a wide range of fields, from finance and business to science and engineering. By understanding quantitative reasoning, why it’s important, and how to improve your skills, you can become a more effective problem solver and decision-maker in your personal and professional life.

Quantitative Reasoning is all about using logic and critical thinking to make sense of numbers. It’s not just about being good at math (although that certainly helps), it’s about being able to apply mathematical concepts to real-world situations. Imagine being able to look at a chart or graph and immediately understanding what the data is telling you. That’s Quantitative Reasoning in action!

The great thing about Quantitative Reasoning is that it’s a skill that can be learned and developed over time. You don’t have to be born with a natural talent for it – you just need to be willing to put in the effort to learn. And trust me, it’s worth it! Having strong Quantitative Reasoning skills can open up all sorts of doors in your academic and professional life. It can help you excel in fields like finance, engineering, or data analysis.

So, in conclusion, if you’re looking for a way to level up your problem-solving skills and gain a deeper understanding of the world around you, then Quantitative Reasoning is definitely worth exploring. Don’t be intimidated by the numbers – embrace them! With practice and dedication, you too can become a master of this powerful tool.

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The Role of Students’ Quantitative Reasoning in Solving Mathematical Problems Based on Cognitive Style

• August 2021
• VYGOTSKY 3(2):87
• CC BY-NC-SA 4.0

• Universitas Cokroaminoto Palopo

• Institut Agama Islam As'adiyah Sengkang
• This person is not on ResearchGate, or hasn't claimed this research yet.

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Quantitative Reasoning as a Framework to Analyze Mathematics Textbooks

• First Online: 02 January 2023

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• Gülseren Karagöz Akar 22 ,
• Tad Watanabe 23 &
• Nurdan Turan 24  

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 21))

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We consider quantitative reasoning as a possible venue to analyze textbooks in order to identify the kind of reasoning students are likely to be engaged in learning mathematics. In this chapter we attempt to extend previous research by using quantitative reasoning as a framework to provide a cross-national textbook analysis. We analyzed how quantitative reasoning is embedded within Japanese curricular materials. We did this in the context of the elementary school curriculum, especially in introducing and developing whole number multiplication and division between Grades 2 to 4. In our analysis, we identified tasks, problem situations and representations likely to trigger students’ quantitative reasoning. We also investigated the kind of questions students are asked to think about regarding quantities and quantitative relations. Results pointed that in the Japanese curricular materials quantitative reasoning has been given a great place for the concepts of multiplication and division. Particularly, taking students’ attention to the quantities and their relationships in the problem situations, an understanding of multiplication multiplicatively and division as relative size seem to be the focal points in these curriculum materials.

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Gülseren Karagöz Akar

Kennesaw State University, Kennesaw, GA, USA

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Trabzon University, Trabzon, Turkey

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Arizona State University, Tempe, AZ, USA

Patrick W. Thompson

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Karagöz Akar, G., Watanabe, T., Turan, N. (2022). Quantitative Reasoning as a Framework to Analyze Mathematics Textbooks. In: Karagöz Akar, G., Zembat, İ.Ö., Arslan, S., Thompson, P.W. (eds) Quantitative Reasoning in Mathematics and Science Education. Mathematics Education in the Digital Era, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-031-14553-7_5

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