Business Calculus

Business Calculus

CSU Instructor Open Textbook Adoption Portrait

Abstract: This open textbook is being utilized in a mathematics course for undergraduate students by Abigail Higgins, Ph.D., at California State University Maritime Academy. The open textbook provides a survey of calculus with business applications. The main motivation to adopt this open textbook was it seemed to be the most coherent business calculus textbook available via MERLOT. Most students access the open textbook as a PDF from our Learning Management System.

About the Textbook

Business Calculus:

Description:

Business Calculus by Dale Hoffman, Shana Calloway, and David Lippman is a derivative work based on Dale Hoffman’s Contemporary Calculus. The course covers one semester of Business Calculus for college students and assumes students have had College Algebra. Students will learn to apply calculus in economic and business settings, like maximizing profit or minimizing average cost, finding the elasticity of demand, or finding the present value of a continuous income stream.

Chapter 0 Introduction and Preliminaries gives a brief introduction to calculus in general and this course in particular.
Chapter 1 Review contains review material that you should recall before we begin calculus.
Chapter 2 The Derivative builds on the precalculus idea of the slope of a line to let us find and use rates of change in many situations.
Chapter 3 The Integral builds on the precalculus idea of the area of a rectangle to let us find accumulated change in more complicated and interesting settings.
Chapter 4 Functions of Two Variables extends the calculus ideas of chapter 2 to functions of more than one variable.

Authors:

Shana Calaway - Shoreline Community College
Dale Hoffman - Bellevue College
David Lippman - Pierce College

Formats:

This textbook is only available as a PDF. Students can download it from my course management system.

Cost savings:

I previously used Calculus for Business, Economics, Life Sciences, and Social Sciences, by Barnett, Ziegler, and Byleen, which retails for $189 on Amazon. Since I usually teach this class to about 50 students each year, the potential savings for students is $9450.

License:

Business Calculus is licensed under a Creative Commons Attribution 3.0 United States License. This means you are free to Share (copy and redistribute the material in any medium or format) and Adapt (remix, transform, and build upon the material) for any purpose, even commercially. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

About the Course

MTH 205: Calculus for Business

Description: Focuses on basics of calculus and the application of this topic to business decision-making and problem-solving. Students will concentrate on formulae that will be performed on Excel later in the curriculum. The course will present math theory and math models. Exercises in critical thinking and model building will be introduced, along with the application of these two tools to the quantitative analysis of business problems.

This course is required for students majoring in International Business and Logistics. In this course, students learn the theory behind calculus and some applications of calculus to business situations.

Prerequisites: MTH 100 with a C- or higher

GE credit: 3 units, degree applicability

Learning outcomes:

Apply mathematical techniques and reasoning to solve problems in mathematics.
Create mathematical expressions from word or application problems and analyze those expressions applying mathematical principles.
Understand practical aspects of mathematics problems.
Understand the benefits and limitations of applying mathematical techniques to problems in mathematics.
Use deductive reasoning and critical thinking to solve problems.
Understand essential properties of limits, continuity, derivatives, and integrals.
Apply basic rules of differentiation, differentials, and derivatives to solve problems in business and economics.
Comprehend the interplay between graphical, numerical and algebraic concepts and solve practical problems that require various differentiation techniques (e.g. product rule, quotient rules, chain rule).
Graph functions and solve optimization problems using first and second derivative properties.
Understand the concepts behind indefinite and definite integrals and their application to practical problems.
Apply anti-differentiation techniques to problems that require integration.

Curricular changes:

I used a number of supplementary materials

Teaching and learning impacts:

Collaborate more with other faculties: Yes
Use a wider range of teaching materials: Yes
Student learning improved: Unsure
Student retention improved: Unsure
Any unexpected results: No

This experience helped expand the resources available to me as an instructor. It forced me to ask my colleagues for help and advice and consequently opened my eyes to more options for instructional materials in the classroom.

I’m not stuck with the book! I can use any supplementary materials I want.

Sample assignment and syllabus:

Assignment
This is an example of an assignment I used for this class.

Syllabus
This is the syllabus I used for the Fall 2017 class.

OER/Textbook Adoption

OER Adoption Process

This seemed to be the most coherent business calculus textbook available via MERLOT.

Explain any external materials that you used to supplement the textbook. These can be found at the links below.

I found several errors in the textbook. I was also unhappy with the flow of content in the textbook and the selection of exercises.

Honestly, this was not a good textbook for this course and I would not use it again. I have not found a good open-source business calculus textbook yet. If I had to teach this course again, I think I would try to do it completely without a textbook. Maybe someday I’ll have enough time to write my own text.

Student access:

Students only access the textbook by the PDF I put in our Learning Management system.

Student feedback or participation:

Students were very happy to not have to lug around a heavy textbook. They also were pleased that they would not have to spend money on a textbook.

Elasticity of Demand
This is a supplement I developed when we covered elasticity

Optimization
This is a reading I developed regarding Optimization.

Surplus
This is a reading I developed regarding consumer and producer surplus.

Marginal Analysis
This is a supplement I developed on Marginal Analysis

Related Rates
This is a supplement I developed on Related Rates.

This is a reading I developed on the Derivative

Abigail Higgins, Ph.D.

I am a mathematics professor at the California State University Maritime Academy. I teach a variety of mathematics courses.

When I began teaching in graduate school, I was certain that I knew the best way to teach. I was confident and sure of myself. I intentionally modeled my teaching after the lecture-only instruction I received in my undergraduate career. After all, this must have worked well for me; I made it to graduate school. It did not take much time for me to realize the flaws in my design. In short, my teaching philosophy has evolved to include the following tenets: Learning happens by doing; not just watching. Students need opportunities to “do” in class and receive feedback. A focus on conceptual understanding rather than procedural understanding is more valuable for my students. Listening to my students is my most important day-to-day practice

My Learning Perspective

My learning perspective is rooted in Lave & Wenger’s (1991) Community of Practice approach. They conceive of learning as a process of apprenticeship. Watching, listening, imitating are important components of this process. But legitimately participating in the practice is the most important part. This perspective highlights the importance of guidance and respect from experts for novices within the community. I see a parallel between this perspective and the learning of mathematics. My classroom is its own community of practice and I am explicitly positioned as the expert. It is my job to model practices of mathematics for my students, but it also my job to create opportunities for my students to legitimately engage with mathematics in the classroom. This means that my students must have the chance to practice procedures and concepts in the classroom and receive feedback from me and from their peers. Each class I teach incorporates opportunities for students to solve problems on their own during instruction, work with their peers on material from previous classes, and discuss questions among themselves (both conceptual and procedural. It is my hope that as students engage with mathematics, they will see the beauty and the relevance of this field. I hope that the opportunities I create for student engagement will continue to develop as I learn more from my students.

Conceptual Understanding vs. Procedural Knowledge

It is of utmost importance to me as an educator that my students develop conceptual understanding. Many students see mathematics as a means to an end. To counteract this, I connect mathematics to the real world as much as I can. While I encourage my students to be skeptical and wonder why they are learning a particular topic, I also emphasize the value of critical thinking and problem-solving skills. A conceptual understanding of a mathematical topic equips an individual with problem-solving tools that can be applied in any context. On the other hand, procedural knowledge is specific. To best serve my students and their changing needs as they transition from college to the workplace, I emphasize conceptual understanding in all my classes.

Listening

Since I began teaching nine years ago, my teaching has evolved immensely. This is almost entirely the result of listening to my students. My experiences with mathematics are drastically different than most of my students’. I cannot understand and attend to my students without understanding their experiences. My students’ unique experiences have shaped how they understand the world and how they learn. In order to serve them to the best of my ability, I must listen to them and understand who they are. As I continue to age, my students’ experiences will be farther and farther away from my own. The world is a dynamic place and it is my duty to learn from students and learn from those different than I. My most important day-to-day and class-to-class objective is to listen to and value my students. This practice prevents my teaching methods from stagnating and will help me keep up with a dynamic student population.

Conclusion

My goals as a teacher are ultimately to serve my students as best I can. I believe my best service is a result of listening to my students and reflecting on their experiences. I believe student learning happens through practice and feedback. Because of this, I intentionally provide my students with a number of ways to actively engage during class. My content focus is conceptual-based. While we, of course, practice procedures, I strive to highlight the importance of concepts throughout a class. Great teaching does not just happen; it takes work, constant thoughtful reflection, and respect. I hope to never assume I have achieved greatness in teaching; I want to constantly be listening to my students and striving to perfect my practice.

My research interests lie in the field of mathematics education. I focus on student issues of equity, access, agency, motivation, and learning.