The Power of Mathematics Workbook with Notes
Edition: 2
Copyright: 2025
Edition: 2
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The Power of Mathematics is designed for use in a general education mathematics course for college students with diverse majors and various levels of mathematical preparation. It is written from the perspective that our students are accomplished learners who can (and hopefully will) enjoy mathematics. The focus is on engaging students in authentic mathematical practice through problem solving.
The course content is organized in four modules:
M. The Power of Mathematizing: Students reengage with arithmetic and measurement at a deep level, encouraging productive links between arithmetic and algebraic representations. No gimmicky mnemonic techniques are used; instead, students build a mathematical foundation and language for the rest of the book
P. The Power of Proportional Thinking: Innovative approaches using multiple representations help develop the proportional reasoning skills needed to function successfully as a college student and critically as a productive citizen in the society.
D. The Decision-Making Power of Mathematics: Students learn to interpret visual and quantitative information using key concepts and tools in probability and statistics such assimilations, center, and variability. Avoiding black-box approaches, students make use of previous content to explore relevant financial mathematics with problems from loans, mortgages, and savings.
S. The Societal Power of Mathematics: Students use their newly developed mathematical understandings as a tool for identifying, understanding, and solving societal issues. Explorations of topics like voting theory and gerrymandering promote students’ active and well-informed engagement as citizens
The Power of Mathematics workbook includes the content that students actually use:
- notes
- activity work sheets
- homework sets.
- short answers to selected questions
Instructors are provided with:
- Power Point slides and solutions to Activity and Homework tasks through the Kendall Hunt website.
- Power Points include In-Class (IC) questions which may be used with learner engagement polling systems such as iClicker to create an interactive environment.
- Solutions to IC tasks and notes to instructors can be found in the Notes panel of PowerPoint.
- Pedagogical notes are embedded in the Homework and Activity solutions, many of which describe multiple solution strategies and ways to address common student struggles.
The Power of Mathematics supports student learning in virtually any format: large lectures, large lectures with breakout activity sessions, small lectures, and small active learning environments.
M.THE POWER OF MATHEMATIZING
0. Introduction
Activity
Homework
Selected Homework Answers
1. Operations
Notes
Activity
Homework
Selected Homework Answers
2. Generalized Arithmetic
Notes
Activity
Homework
Selected Homework Answers
3. Fractions
Notes
Activity
Homework
Selected Homework Answers
4. Simple and Compounded Interests
Notes
Activity
Homework
Selected Homework Answers
4. Visual Patterns
Notes
Activity
Homework
Selected Homework Answers
5. Measurements
Notes
Activity
Homework
Selected Homework Answers
P. THE POWER OF PROPORTIONAL THINKING
1. Proportional Thinking
Notes
Activity
Homework
Selected Homework Answers
2. Percentage
Notes
Activity
Homework
Selected Homework Answers
3. Inflation
Notes
Activity
Homework
Selected Homework Answers
4. Weighted Average
Notes
Activity
Homework
Selected Homework Answers
D. THE DECISION-MAKING POWER OF MATHEMATICS
1. Probability
Notes
Activity
Homework
Selected Homework Answers
2. Simulation and Data Visualization
Notes
Activity
Homework
Selected Homework Answers
3. Center and Variability
Notes
Activity
Homework
Selected Homework Answers
4. Simple and Compounded Interests
Notes
Activity
Homework
Selected Homework Answers
5. Savings for Future Goals
Notes
Activity
Homework
Selected Homework Answers
6. Borrowing
Notes
Activity
Homework
Selected Homework Answers
S. THE SOCIETAL POWER OF MATHEMATICS
1. Voting Theory
Notes
Activity
Homework
Selected Homework Answers
2. Gerrymandering
Notes
Activity
Homework
Selected Homework Answers
APPENDIX
Success Logs for Study Groups
Success Logs for Student Hours
Success Logs for Tutoring
Success Logs for Exam Review and Exam Corrections
Jen-Mei Chang is a Professor of Mathematics at California State University, Long Beach (CSULB) where she has been the Coordinator of the Early Start Mathematics Program since 2017 and the course coordinator of the entry-level quantitative reasoning course since 2018. Jen-Mei spent her first 18 years in Taiwan before moving to the United States in 1996 as a high school exchange student. Jen-Mei received her B.A. in Mathematics at California State University, Sacramento and her Master's and Ph.D. in Mathematics at Colorado State University. Her research interests include the scholarship of teaching and learning, mathematical analysis of human placenta and its connections to autism, computational and geometric methods for analyzing large data sets, machine learning and digital image processing. Jen-Mei is a red'08 dot in the Mathematical Association of America's Project NExT. She received CSULB's Distinguished Faculty Teaching Award in 2015 and the Faculty Award for Excellence in 2013 in the College of Natural Sciences and Mathematics. Jen-Mei is the Principal Investigator for the National Science Foundation DUE Award #1833753: Mentored Excellence Toward Research and Industry Careers. Her lifelong passions are to inspire, educate, and empower college students to reach beyond their imaginable potentials.
Josh Chesler is a professor in the Department of Mathematics & Statistics at California State University, Long Beach. His research interests are in mathematics education, particularly in the preparation of mathematics teachers. He serves on the curriculum development team for the Mathematical Reasoning with Connections (MRWC) 12th grade mathematics course in California. Prior to completing a Ph.D. in Mathematics, he earned a B.A. in Anthropology, worked in the finance industry, and did some software development. Josh believes that an important power of mathematics is the joy it can bring when sense making and problem solving are emphasized.
“The Power of Mathematics is not your average math book. It's unique in the way that you don't have to memorize formulas or concepts that won't entirely be necessary to your future. Mostly everything you learn in this book can be applied to real life. The contents in this book helped me see the world from a different lens. I've become much better at visualizing math and I don't need to rely on my calculator all the time anymore. It's taught me that I don't always have to look for technology to give me the quickest answer, but that my brain can produce a quick response as well. Concepts may seem difficult when you first learn it; but the more you practice it, the more it gets easier. If I didn't have my struggles with the materials, I wouldn't have learned as much because this is truly one of the best math experiences one can have. It's eye-opening if you really put in the effort!”
Sanjesh Singh, CSULB freshman in Journalism
“The Power of Mathematics is different than any of my previous mathematics experiences because it applies to real life situations. When learning in previous mathematics courses I often thought, “Why do I need to know this? I’m never going to use this again.” Through the duration of the The Power of Mathematics, I never once asked myself this question. As a college student, all topics in the publication are clearly tied to real life situations that you may encounter in the present or the future.
The Power of Mathematics has helped me grow into a well-rounded college student, citizen of society, and person. I now have a solid foundation of knowledge to make educated decisions on important everyday topics such as interest rates and loans. As a person, it helped me develop better interpersonal communication skills.
At the beginning of this course, I thought to myself, “What did I get myself into?” By the end of this course I thought to myself, “Wow, I actually learned skills that I will apply for the rest of my life.” Some topics are challenging and abstract at first, but with guidance and practice, they become much easier. The challenge of this course yields a great reward.”
Lauran Rand, CSULB senior in Liberal Studies
“As a Theatre major I thought having to take math was dumb. But after taking the class I realized that the information I learned was something that every individual should know. It’s valuable information that one should be aware of in case you want to make certain decisions in life such as what discounted item to buy. Reading this may sound ridiculous now but honestly when you realize you could have saved money buying something else then it won't be.”
Priscilla Ortega, CSULB freshmen in Theater Performing Arts
“The main difference between The Power of Mathematics and other publications I’ve used is the emphasis on multiple approaches in solving problems.
As a learner, I was taught to apply a specific procedure to a specific type of problem. In this book, there is a problem that involves finding out what one needs to score in the next bowling game to maintain a desired average. My initial approach was to assign a variable to the unknown quantity, apply the formula to find the average, and solve for the unknown quantity. However, I was unsuccessful in teaching my students this procedure. Instead, my students appreciated more and understood better when I helped them through the process of reasoning with the idea of how many points one is short from the average so they would need to make up those points in the next bowling game.
As a teacher, the content – and the way it was delivered – helped me realize my role as a teacher, which is to facilitate student learning. It is more effective to let the students take more control of the learning process and take part in helping each other learn.
The content will most likely be very different from what your students, and perhaps you, have seen before. To most of my students, what they learned in math courses are disconnected from their everyday life. Context is very important to the students; it is encouraged that you let the students come up with the context as well. I had students initiate long and interesting conversations with me about credit cards debt, mortgage, and student loan after learning about loan and saving.”
Bao Vu, Master's student in applied statistics at CSULB, Activity Instructor for The Power of Mathematics course at CSULB
“The Power of Mathematics provides a gateway to the realm of Mathematics. It is accessible but not trivial.
One of the things that helped me most in delivering the content was keeping a growth mindset as an instructor. Often, we find ourselves looking at a student's performance from a deficit view, but I found it to be much more productive to appreciate the growth students make. Psychologically, students should be ready to be crushed with early material, and may surprise themselves as they rise to the challenge. It is challenging to balance between covering the materials and making sure students are actually learning and understanding the materials.”
Robert Nakano, Master's student in applied statistics at CSULB, Activity Instructor
September 26, 2019 article in LAist
Cal State Scrapped 'Remedial' Math, And So Far Students Are Getting Along Fine
September 25, 2019 article on 89.3 KPCC
A Look At How Cal State Reformed Its 'Remedial' Math And English Classes