Publications
Development of Linear and Exponential Concepts CoRDThe MIP publishes peer-reviewed resources designed by Oklahoma faculty author teams to support student learning in entry-level college mathematics courses through inquiry.
Collaborative Research and Development (CoRD) teams produce a collection of resources to be used throughout a course to support development of critical concepts and skills through inquiry.
Activity Revision Collaboration (ARC) teams revise a single existing activity to improve student learning through inquiry.
Quantitative Reasoning
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Jayne Ann Harder, Oral Roberts University |
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 |
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 |
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. |
Functions and Modeling
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Development of Linear and Exponential Concepts (CoRD) Ashley Berger, University of Oklahoma |
Our CoRD materials address modeling and quantitative reasoning within the context of a Functions & Modeling course. There are eight activities, which can be divided into two units of four activities. The first unit focuses on developing understandings of various aspects of linear functions, while the second unit focuses on exponential functions. The activities are presented in a specific order, if an instructor wished to utilize them all. However, the activities can be used individually as instructors see fit. Within the instructor materials, there are guided questions and commentary to help instructors implement the activity with the intended targeted understandings in mind, as well as optional extensions for the activities. |
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Exploring Average Rate of Change Given by Tables (ARC) Christi Hook, Northern Oklahoma College
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In Exploring AROC Given by Tables, Functions & Modeling instructors are provided with problems involving analyzing rates of change given in tables. A large group activity is provided where the entire classroom discusses, calculates, interprets, and applies rates of change with population values. Students then use rates of change to estimate and predict future population values. An alternative small group activity includes a shorter full-class activity with four small group tasks. With this option, students will consider increasing, decreasing, and constant rates of change with similar explorations. Each option allows students to determine if a limiting value exists for the population data provided in the table. |
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Systems of Linear Equations Exploration (ARC) Cecil Phibbs, Northern Oklahoma College |
In this systems of linear equations exploration for a Functions & Modeling course, students work with tables, graphs, and algebra to investigate the definition of a solution to a linear equation and apply that definition to a solution of a system of linear equations. In part one, students explore the definition through making tables of values in a scenario involving money. In part two, students transition to equations and graphs to see the visual representation of a solution and how it applies to a patio scenario. In part three, students find a solution using algebra and check the answer with graphing in a brunch item scenario. |
College Algebra and Precalculus
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Quantitative Reasoning about Rates of Change (CoRD) John Paul Cook, Oklahoma State University |
The four activities in this module are intended to be used throughout a College Algebra or Precalculus course to develop and reinforce students’ quantitative reasoning about rates of change. They first reinforce thinking about changes in quantities then encourage comparing those changes for two covarying quantities. The activities then focus on working with constant rates as a constant ratio between changes in two covarying quantities. |
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The Quadratic River Application with Area and Perimeter (ARC) Narges Dehdashti, Rose State College |
In both parts of the College Algebra Quadratic River Application activity, students will work with applying a quadratic function to a scenario. In part one, students will initially access prior knowledge of area and perimeter of rectangles to engage with the material with tables and GeoGebra. Through the structure of the activity, students will then transition to making algebraic representations of area and perimeter given particular constraints of the scenario. Lastly, students will find the length and width that will maximize an area. In part two, students will complete a similar task to reinforce the idea that the vertex of the quadratic provides maximum area. |
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Discovering Absolute Value (ARC) Dee Cooper, Northern Oklahoma College |
In An Absolute Value Discovery, Algebra for STEM instructors are provided with problems that introduce students to the concept of absolute value as a distance. The discovery will lead students to further understand absolute value as a distance measured from zero, and that both positive and negative values can have the same absolute value. Students can model these concept on number lines leading to formal equations which they can solve realizing the possibility of more than one solution or no solutions. This Activity can be used as a whole class discovery, in smaller groups or individually by students. |
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Michael Fulkerson, University of Central Oklahoma
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This lesson serves as an introduction to the number e and the application of continuously compounded interest. Students begin by exploring the expression %5En "\left(1+\frac{1}{n}\right)^n") for large values of n, and they discover that the expression approaches a number (2.71828…) as n approaches infinity. For college algebra students, this also serves as an introduction to the idea of a “limit.” Students then explore the relationship between compound interest and continuously compounded interest. |
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Tray Folding Activity: Polynomials and Optimization (ARC) Deborah Moore-Russo, University of Oklahoma
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This collaborative activity involving scaffolded contextual optimization is appropriate for algebra or applied algebra students. It is also a good activity for calculus students to introduce optimization with differentiation, but no differentiation is required to complete the activity. The lesson helps facilitate students’ conceptual development reinforcing their quantitative and covariational reasoning as they identify the relevant quantities, namely the dimensions and volume of the tray, with the appropriate units and algebraic expressions for each. This is done in a geometric context so that students can see how a change in one quantity (the height of a tray) affects its volume. |
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Michael Fulkerson, University of Central Oklahoma |
This lesson explores the Rule of 70, a financial mathematics concept that estimates the time it takes for an investment to double at a given annual interest rate, compounded continuously. Students will use both algebraic methods and an interactive Desmos activity to understand and apply the rule, enhancing their grasp of logarithms, exponential growth, and financial literacy. |
Calculus I
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Liz Lane-Harvard, University of Central Oklahoma
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This ARC provides a pair of activities designed to help students develop an intuitive understanding of the Mean Value Theorem that is grounded in understanding its key foundational ideas (e.g., continuity, average rate of change, instantaneous rate of change). The activities provide opportunities for student engagement with mathematics while also allowing opportunities for collaboration. Active student engagement is promoted through a contextual situation as well as meaningful scaffolding that builds on previous student experience. |
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Michael Oehrtman, Oklahoma State University |
These resources are designed to be used through a first-semester calculus course to help students develop a rigorous and productive understanding of limits, derivatives, and integrals. The activities engage students in problem-solving about approximating unknown quantities using appropriate function values, difference quotients, or Reimann sums. While these ideas reflect the underlying structure of formal ε-δ definitions and proofs, they are framed in more accessible language and ideas of errors, error bounds, and reasoning to achieve any desired degree of accuracy. Representing their reasoning in consistent ways across multiple representations helps students link these situation-specific ideas to the underlying mathematical principals in a coherent way. Then engaging in similar tasks across different contexts supports attention to the general mathematical structure of limits, derivatives, and definite integrals that can support subsequent modeling and interpretation. |
Academic Success Skills
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Productive Struggle, Persistence, and Perseverance (CoRD) Lucas Foster, Northeastern State University |
Learning mathematics can be a struggle. Sometimes, a student will experience multiple failures before enjoying a success. The idea of productive struggle is that the student persists throughout the process with creativity and determination until a solution presents itself. When students face problems that they don’t know how to solve right away, math educators do not want them to stop trying, but to continue with effort and think creatively to achieve a solution. If productive struggle is a central part of the learning environment, student success can be more evident and prevalent in math classrooms. In this study, investigators introduce the REACT framework, clarify how the framework reinforces the learning pillars of the Math Inquiry Project, and explore the effect that productive struggle has on student learning in an entry level college mathematics course. |
Other Resources
This work is licensed under CC BY-NC-SA 4.0
