Quantitative Reasoning
MIP faculty collaborations on the Quantitative Reasoning pathway began with an Initiation Workshop in May, 2021. At this workshop, faculty identified the central concepts and skills critical for success in the Oklahoma Quantitative Reasoning Pathway (OSRHE Common Code MA201, https://www.okhighered.org/transfer-students/2018-19/mathematics.pdf). Participants of the workshop identified seven foundations to guide development, testing, and refinement of inquiry-oriented course materials to support the development of the central concepts and skills in the Quantitative Reasoning pathway.
Information Presentation and Consumption
Responsible citizenship in our modern society is driven by quantitative literacy skills. If a society does not ensure that all are able to think critically when consuming and presenting mathematical ideas, then some will be limited in their social, financial, and employment opportunities. Students with an understanding of various modeling techniques and ways in which information is presented (and mis-presented) are better equipped to be contributing members of society. Being critical consumers of information supports people in analyzing problems and making decisions. Students who are critical consumers of information, and good presenters of information, have healthy skepticism and know when to ask for more information. [Explore the Details]
Spreadsheets are a useful tool for organizing, analyzing, and visualizing data. Moreover, facility with spreadsheets is useful for students in their real lives and careers, as many occupations involve spreadsheet use. Spreadsheets are particularly useful for Quantitative Reasoning because they allow students to work with large, complex data sets and hence retain more of the complexities of real-world contexts. [Explore the Details]
Ratios, Proportions, and Proportional Reasoning
Proportional reasoning “involves maintaining a sense of multiplicative scale in a relationship between quantities” (Gaze, 2019, p. 90). It includes understanding proportion, ratio, percent, and linearity; constant multiple/ratio and scaling; constant multiple/ratio of changes and scaling changes; and multiplicative reasoning. Gaze (2019) suggests “the concept of ratio can provide a common theme to convey the interrelated meanings of fractions, percentages, proportions, decimals, and rates” (p. 91). Proportional reasoning helps students make comparisons in realworld contexts, supports covariational reasoning, and assists students in recognizing reasonable answers to numerical problems. [Explore the Details]
Understanding a quantity as a measurable attribute of an object is foundational for understanding how to work with numbers and making sense of what numbers represent. It also provides the basis for variational, proportional, and covariational reasoning. Students should be able to quantify a given situation, reason with variables that represent quantities, represent changes in quantities, and make estimates. Students should also understand what it means to measure a quantity, which involves envisioning a measurement process that results in a multiplicative comparison between a targeted magnitude and the unit of measure. [Explore the Details]
Critical thinking involves analysis, evaluation, objectivity and reflection that leads to self-corrective reasoning and the ability to reconstruct an idea from different viewpoints in order to understand a situation, solve a problem, or evaluate an outcome. It enables students to make decisions based on relevant information and make sense of a situation. In addition to the computational and procedural fluency that is involved in arriving at a numerical answer, developing students’ critical thinking is essential in a QR course because it involves learning to both ask and answer such questions as “does this make sense?”, “what are the implications?”, “is this meaningful?”, and “what alternative explanations exist?” [Explore the Details]
Modeling is a powerful tool for analyzing real-life phenomena. Modeling is the process of using mathematics to describe, analyze, and gain insight into real life phenomena. It entails identifying and representing quantities and determining relationships among relevant quantities. Modeling requires careful recognition of, and attention to, the relevant quantities involved in the situation. [Explore the Details]
A problem is generally considered to be a mathematical task for which one does not know a solution method in advance. Problem solving therefore generally involves the mental activity in which one must engage to identify, select, perform, and evaluate solution methods. Developing productive problem-solving habits and a disposition for critical thinking are essential components of mathematical proficiency. Problem-solving skills are necessary to aid the critical thinking on which quantitative reasoning relies. A goal of entry-level mathematics instruction is to enhance students’ problem-solving ability while leveraging it as a foundation for their learning of central ideas. [Explore the Details]
Quantitative Reasoning CoRDs and ARCs
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Jayne Ann Harder, Oral Roberts University
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This CoRD provides a peer-reviewed set of activities and assessments designed to enhance students’ conceptual understanding of essential aspects of financial mathematics, including budgeting, interest, savings, and taxes. These topics hold significance beyond a student’s academic journey, as they play a crucial role in their personal, and possibly professional, success. Many of the activities intentionally involve collaborative learning activities to encourage communication. Active student engagement is promoted through meaningful applications relevant to student experience. For example, compound interest, annuity, and loan applications develop deeper students’ conceptual understanding of proportions and percentages. The activities are provided below via hyperlinks (denoted by blue, underlined text). Each activity is provided in a lesson plan format consistent across the activities.
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Michael Fulkerson, University of Central Oklahoma
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This lesson focuses on weighted averages and their applications. This set of materials includes a short lecture, an in-class activity, and an out-of-class activity. Students will practice computing a weighted average in the context of figuring an overall class grade. Students will use a spreadsheet to calculate a weighted average and explore the effects of various changes in the data. They will follow directions on how to enter formulas related to weighted averages based on key pieces of information provided. Students will also generalize their knowledge to the context of financial portfolios as they compute a weighted average return.
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Mean and Median with Spreadsheets (ARC) Michael Fulkerson, University of Central Oklahoma
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This activity involves using spreadsheets to investigate the mean and median of a data set and how those averages change when additional data is provided. Through various scenarios (exam grades, household income, and batting averages) students develop their mathematical reasoning skills and intuition about these averages. In particular, students learn when the median is more appropriate to use than the mean (and vice versa) and how outliers have a greater effect on the mean than the median.
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Financial Math Matters: A Jack and Jill Adventure (ARC) Nathan Drake, Oklahoma Baptist University
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This activity will provide a holistic view of financial math in an interactive story-telling fashion as one moves through the various stages in the life of a fictional family. It provides real-life scenarios that most students themselves will encounter and need to navigate through. The skills developed in this activity will allow students to identify real world ways that their financial decisions could impact their lives.
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Roshini Gallage, University of Oklahoma
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This lesson focuses on representing both qualitative and quantitative data. The set of material includes a slideshow and instructor guide. Students will interpret and create different visual representations for various data types. In particular, students will create a scatter plot and pie chart using google sheets. This lesson requires not only engaging with a real life scenario, but using their mathematical prowess to extract meaning from the different charts provided and to see how some might try to misrepresent the scenario when using graphs that might be construed as being deliberately misleading.
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Joan Brenneman, University of Central Oklahoma
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These activities encourage active learning of statistics through exploration of non-routine problems. By actively learning topics such as sampling, bias, sample means, sampling variability, sampling distributions, and confidence intervals, students engage directly with the core concepts of statistical literacy. This hands-on approach brings awareness to various data-driven statistics that students encounter in their everyday lives. Not only will students be prompted to analyze and reflect upon various interpretations of data to determine their validity, but they will also collect and analyze their own data. Afterwards, they will reflect on the meaning of their results, hence enhancing their statistical literacy.
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Inferring the Central Limit Theorem (ARC) Brett Elliott, Southeastern Oklahoma State University
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This activity begins with consideration of a problem the Central Limit Theorem would help students solve and provide justification for their solution. After some reflection, students realize that they have no method of justifying any answer they provide, which produces a need to be able to describe the sampling distribution for the mean. Construction of that knowledge is facilitated via use of an online simulation tool to generate sampling distributions and identify trends that allow students to infer the Central Limit Theorem. Students then apply what they have learned to determine and justify an answer to the original question.
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Unit Conversions with Spreadsheets (ARC) Brenden Balch, University of Central Oklahoma
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This activity uses spreadsheets to tackle unit conversion problems. Through various scenarios, students will learn to carefully read word problems, extract and organize the given information, and use Microsoft Excel to solve the problems. The lesson is intended to be given after students have already had an introduction to basic unit conversion problems.
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Brenden Balch, University of Central Oklahoma
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This activity uses dice and spreadsheets to investigate empirical data (through dice rolling and data collection, as well as random simulation) as a means to introduce distributions from probabilistic concepts. Through various scenarios (single die, resulting sum of two dice, with an application to games) students strengthen their understanding of the relationship between empirical randomness and theoretical randomness while also encountering histograms/distributions. In particular, students will be exposed to the Law of Large Numbers and expected value through various exercises.
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Dee Cooper, Northern Oklahoma College
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This CoRD provides a set of guided learning activities, backyard layout projects, phases, and final bid proposals for landscape architecture services. It has been created to reinforce students’ cognitive understanding of the geometry concepts: perimeter, circumference, area, volume, and Pythagorean theorem. These real-world applications use acquired knowledge from guided learning activities and will infuse the knowledge through geometric calculations of specific landscape architect projects using professional images provided. Students will then take the computed geometric quantities and calculate the total cost applying real-world cost values. At the end of the activities students will create a final itemized quote statement for the customer’s backyard layout.
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Modeling the World with Least Squares Regression (CoRD) Joan Brenneman, University of Central Oklahoma
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The overarching goal is to increase students’ ability to critically evaluate cause-and-effect claims encountered in daily life. Students begin with an activity to help prevent the formation of biases as they utilize data from various countries. They create and interpret scatterplots to determine the form, direction, and strength of relationships between two quantitative variables. Moreover, they determine when it is appropriate to utilize the correlation coefficient and the least squares regression line by analyzing the covariational relationship of the data observed in the corresponding scatterplot. Lastly, students examine correlation versus causation and the potential role of lurking variables.
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Joan Brenneman, University of Central Oklahoma
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In this activity, students begin by assessing various graphics and classifying whether the graphs depict quantitative or qualitative data. They answer questions regarding what the graphs are saying, as well as determine how changes in a graph may distort the picture. Students generate Excel graphs based on real-world data, including pie charts, bar graphs, and line charts. Critical questions are asked regarding the student-generated graphs to enhance their skill in accurately interpreting graphed information. Lastly, students will continue analyzing misleading graphs, make claims regarding the misrepresentation of the graphs, and communicate their justifications to their peers via a homework assignment.
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This work is licensed under CC BY-NC-SA 4.0
