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Math OER
Classroom Library

There are no problems, just pauses between ideas.

- David Morrell

The High Five

What does it mean to be math literate?

Someone who is computer literate has not memorized every detail of the software programs they use, but knows how to find those details when they need to do something new.

Someone who is economically literate is not completely fluent with every financial theory, but knows the basics of the important financial theories and how to read about finance when he or she wants to learn more.

Someone who is math literate similarly needs to know about certain foundational ideas and where to find sources to learn more.

Much of traditional upper division college mathematics is trapped in the past. Its content was established after World War II, when the topics of math literacy were chosen because electrical engineering and rocketry were the exciting and promising careers for that generation that appeared to show a new direction for math in society. Those jobs involve trigonometry, calculus, and imaginary numbers. So those topics dominate traditional upper division mathematics.

Today math literacy needs different topics. The five most important for our generation are:

• reading and presenting data, and how people's brains handle data
• algorithmic thinking, how people make decisions, and how to give machines instructions
• behavioral economics, and how math is being used to shape society
• finance and health numeracy, and how wealth and health differ in the present and future
• why nature's language is mathematics, and how that creates science

Fortunately, for each of these five topics an exemplary book stands high above the crowd.

Factfulness

Factfulness by Hans Rosling and his family is currently one of the most important books in the world.

First, a bit of history. Hans Rosling presented two TED talks in 2010 about global population growth and global demographics. In 2014 he returned and presented about how most people are incredibly ignorant about what the world is really like and how it is changing, especially about population growth. He founded a website named GapMinder to work on correcting misconceptions based on outdated stereotypes..

The book Factfulness is his inspiring and enlightening finale. It has two parts.

First, it talks about many examples of how people and the planet are doing much better than most people realize. It uses charts and statistics but is quick to read and not burdened down by the math.

Second, and most relevant to our class, is the book's discussions about why most people are ignorant about those issues. There are Ten Rules of Thumb about how our brains naturally latch onto dramatic information instead of accurate information. Thus Factfulness is also guidebook for learning to use math to see the world more clearly, with better habits.

The first chapter of Factfulness is available freely online, from Bill Gates or this website.

Algorithms to Live By

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian and Tom Griffiths is a book about happiness through already solved problems.

The study of Computer Science has expanded far from its orginial scope of electronic calculations and simple computations. It now studies general issues about how to solve problems when you do not know all the information, when information is fuzzy, when there is random chance involved, or when new options appear as the problem develops.

Those are real-life issues too. In many fascinating ways computer scientists have mathematically solved all sorts of common problems. The answers they found can apply to the real-life issues everyone faces. The book shares these issues and answers in a very readable way, and might help reduce your stress when you recognize already answered solutions to common everyday situations.

Freakonomics

Freakonomics (Revised and Expanded Edition) by Steven D. Levitt and Stephen J. Dubner has become the classic introduction to behavioral economics.

The phrase "behavioral economics" was invented because of two trends. It is a response to classical economics, which ignores how most shopping behavior is based upon loyalty to a store, brand, or habit instead of a fully-reasearched pursuit of the best deal. It also extends economics by looking at non-economic behaviors using classical ways to measure and discuss incentives, options risks, and equilibria.

Freakonomics is fun to read, and also helpful for learning to use math to see the world more clearly.

The authors host a main podcast and a question of the day podcast to continue sharing their favorite examples of behavioral economics.

A Random Walk Down Wall Street

A Random Walk Down Wall Street (12th Edition) by Burton G. Malkiel has become the classic introduction to investing.

Although most students in a community college math class are not themselves doing much investing, a lot of them do talk with parents or grandparents about investing—or they know they should be having those conversations but do not yet feel ready.

This book explains why anyone can invest as well as the experts. It explains how to think about risk. It describes how your age, income, and personality should affect your investing strategy.

The Character of Physical Law

The Character of Physical Law by Richard P. Feynman is a book about why mathematics is the language of nature, and how this turns into science.

This book is the transcription of a set of lectures, whose video is here for people who prefer watching and listening over reading a book.

Other Books

Aha! Insight

The best math book to sound smart at parties (and feel smart all the time) is Aha! Insight.

The author, Martin Gardener, was a magician and puzzle connoisseur. This book contains his favorite puzzles from when he wrote the "Mathematical Games" column in Scientific American for twenty-five years. There are logic puzzles, number puzzles, language puzzles, and more.

The illustrations are adorable. The puzzles and their explanations are elegant. Someone you know will love this book—probably you!

Naked Statistics

The best introduction to statistics that I know of is Naked Statistics by Charles Wheelan. This book calls itself a textbook but is easy to read.

Our class does a lot with the most foundational and basic statistics. The books above about behavioral economics do a little more with basic statistics.

But statistics can be interesting, helpful, and even awesome in its own right. It is not only a nice part of math because of our class topics and behavioral economics. This book shares how statistics can generally be useful and fun, and part of learning to use math to see the world more clearly.

Most statistics textbooks have a lot of math. There is a tradititonal set of stuff they teach, which involves many formulas, some of which are tricky. This is not that kind of book. The author purposefully avoids formulas to focus on the intuition that is developed by people who study statistics.

Mathematician's Delight

Mathematician's Delight by W. W. Sawyer is the only math textbook in our classroom library. It was written in 1943.

This book describes all sorts of mathematical concepts, from the definition of a rectangle to imaginary numbers, with an unusually welcoming approach.

Surely You're Joking, Mr. Feynman!

"Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character by Richard P. Feynman is a book about happiness through problem solving.

Many our classroom library books are "business books" of one kind or another. This book is not. It is purely about using math to see the world more clearly.

Richard Feynman was not the smartest mathematician or physicist at Los Alamos. But he was the most fun. His stories share his approach to life. He balanced practical jokes with gentle kindness, faking it to get ahead with up-front honesty, and most importantly focusing on problems as something fun to analyze and scrutinize whether or not getting a final answer was important or even possible.

Feynman approached personal decisions with behavorial economics, and he did it decades before that topic had been formally invented. No other math book has such fun stories about moving ants, cracking top-secret safes, or picking up women at bars.

Grasp

Sanjay Sarma is a leader in open education. In Grasp he writes about all levels of learning: neurological, cognitive, pedagogical, social, and historical.

This book explains what makes learning effective. It explains why certain kinds of math classes do not work for many students.

This is an important book for current and future teachers to read, no matter the age of your students.

Moneyball

One of the most popular books about economics is Moneyball by Michael Lewis.

This book will be an obvious choice if you love sports. But it is not a book about playing a sport. It is about the business of owning and managing a sports team

With just the right amount of math it tells the story of when conventional wisdom was wrong, and using math to see the world more clearly not only turbocharged the Oakland A's but revolutionized that industry.

Priced to Influence, Sell & Satisfy

Priced to Influence, Sell & Satisfy by Utpal Dholakia is a great introduction to pricing issues.

A specific kind of behavioral economics is how to pick prices for retail or menu items. Everyone has heard about how a price of $4.99 appears to be a better deal than $5 despite a mere one cent difference. There are actually dozens of behavior issues about pricing. This book is very readable as an introduction to the topic. It remains clear, yet goes into many issues quite deeply.

During class we will learn the basics of markup, discount, and menu pricing. This book goes much further. It might also be more fun.

The Complete Idiot's Guide to Game Theory

The Complete Idiot's Guide to Game Theory by Edward C. Rosenthal is the best introduction to its topic.

A deeper layer of behavioral economics is considering how your competitors are doing business. Not only will good decisions about pricing depend on your customers, they also depend on your competition.

The study of competitive decision-making is called game theory. Finding an easy to read book about game theory can be tricky. Most dive into complicated math right away. Yet this book is great. It teaches enough to be of practical help in business decisions, without burdensome math. Every topic is accessible, even if you skip certain extra-complicated parts at the end of a few chapters.

This book is not as fun to read as the books above, but might make a big difference in how profitably you run a business.

Markup & Profit: A Contractor's Guide, Revisited

Markup & Profit: A Contractor's Guide, Revisited by Michael C. Stone is a specialized introduction to pricing for contractors.

A contractor's bid is like a small business plan. All pricing must consider materials and labor. But for contractors these can quickly get complicated in ways specific to the trade.

This book has a very specific target audience. If you are part of that specific target audience, doing a book report with this book might be your most valued part of the class.

How to Read a Paper: The Basics of Evidence-based Medicine and Healthcare

How to Read a Paper: The Basics of Evidence-based Medicine and Healthcare by Trisha Greenhalgh is a specialized book useful for nursing students.

Sometimes using math to see the world more clearly involves many specialized issues. This book goes deeply into which issues apply to reading medical papers. It is the most advanced textbook in our classroom library. Yet it could be worth the more difficult read by helping jump-start a nursing career.

It is is another book with a very specific target audience.

A Billion Wicked Thoughts

A Billion Wicked Thoughts by Ogi Ogas and Sai Gaddam is the world's most salacious book about data mining.

In 2010 two researchers decided that all academic research about human sexual behavior was stupid. It all depended upon surveys, and everyone knows that people lie like crazy on surveys, especially when talking about sex.

If someone wanted actual information about human sexual behavior they would need to look where people were honest. So Ogi Ogas and Sai Gaddam looked at anonymous data from internet searches (on search engines, dating websites, and porn websites). This vast amount of data is the "billion wicked thoughts". Then they did it again looking at sexy romance novels. What would their data analysis tools tell them about that type of titillation?

Unfortunately, in an effort to make their book as readable as possible, they spend very little time talking about the actual data mining. How did they dig through that immense amount of data to get their charts and rates? How did they deal with signal-to-noise? Which of the issues they discuss are most appropriate for data mined answers? Which questions have they answered definitively, and which are a stretch to try to answer using data mining?

So for this topic we need two books. Sifting through data is an important topic. How to use data about sales can help a person run any small business.

The best companion book I know of is Data Smart by John W. Foreman. This book is a guidebook. Each chapter leads the reader step-by-step through a spreadsheet. It really demonstrates how small business data can be used to answer useful questions.

I hesitate to recommend this pair of books. I worry that A Billion Wicked Thoughts is long and full of numbers without enough actual math, and will waste time being entertaining and distracting. I worry that Data Smart will take many more hours to get through than a book you only have to read. However, a student who has a lot of time might have a lot of fun and learn great lessons about how to run a business from these books. But please heed my warning that one of these books is barely a math book, and the other is actually a small math course.

Videos

	The website Khan Academy is the most famous website for math videos.
	The website Hawkes Learning also has nice math videos.
	The website Learners TV also has nice math videos.
	YouTube has some great playlists or channels for math videos. Below is a list of student favorites.

• The Video Math Tutor
• Pat McKeague
• Math Antics
• Mathispower4u
• The Organic Chemistry Tutor
• BittingerBasicMath
• Gregg Learning
• Parvin Taraz
• Plettski Productions
• OCL Phase2
• Morgan Kenneth

E-Books

LCC students can use their LCC e-mail and L# to log into the State Library of Oregon's downloadable math e-books.

There are some interesting titles, such as Practical Math Success in 20 Minutes a Day and Express Review Guides: Math Word Problems, that try to be interesting and efficient as they explain math fundamentals with their own voice.

That website has many other math resources. Look under three different "centers" at the upper menu. The centers named School Center, College Students, and Adult Core Skills all have different math resources appropriate to our topics.

Podcasts

	As mentioned above, the authors of Freakonomics host a main podcast and a question of the day podcast to continue sharing their favorite examples of behavioral economics.
	The Skeptoid podcast examines popular myths, using just enough math and history to clear up confusions.
	The Breaking Math podcast highlights interesting math news and applications without getting too deep into the math.
	The podcast This Week in Virology is timely and full of math.
	The podcast Brains On! does not always use math, but has some nicely mathy episodes.
	The popular Netflix show Adam Ruins Everything has a few old podcast episodes that involve math.
	The Adam who ruins everything has a second podcast named Factually! that so far involves little math, but might still be appropriate for our assignments.
	A group of teachers reflect in the podcast Math Before Breakfast.
	For seven years Jason Marshall had a fun podcast named Quick and Dirty Tips with short episodes (most only 7-8 minutes) about math tricks and techniques.
	The Math Ed Podcast interviews researchers in mathematics education.

Apps

	Bedtime Math for fun challenges ranging from trivial to tricky
	Socratic for general help with math (or many subjects) but not solving specific problems
	Photomath for arithmetic and algebra steps
	Microsoft Math for arithmetic and algebra steps
	Mathway for paid help with pre-algebra

OERs

Many textbooks are Open Educational Resources, which means that anyone can use them. They can be printed inexpensively, or used for free online. Some grant permission for instructors to modify them to best fit their classes.

Below are links to three OER textbooks that teach similar math topics to our first three topics. Seeing the same concepts explained in different ways can be very helpful!

Prealgebra Textbook by College of the Redwoods is a pretty standard textbook. It has a consistent attitude of "here is a technique" rather than exploring concepts. The homework has answers for odd numbered problems. The first three chapters are a bit heavy on the "new math" of the 1960s rather than explaining with diagrams or arrays. Each chapter is a PDF file with a convenient table of contents on the third page.

Prealgebra by Santa Ana College uses the nice CNX OpenStax website. It is a the friendliest of these OER textbooks, with very elaborate inclusion of Math 10 concepts. It has a good use of warm-up problems for each section. It helpfully explains the "language of algebra" before it discusses more advanced ideas such as simplifying terms. Note that the proportion topic (6.5) is hidden at the end of Percents chapter. Beware the awkward numbering of example and try-it problems.

Arithmetic for College Students by the Monterey Institute for Technology and Education is decent, and also has a very elaborate inclusion of Math 10 concepts. Unfortunately, it is formatted as one huge PDF file and its table of contents lacks links. Neither example problems nor self-check problems are numbered well. This book likes to use parenthesis to show multiplication, as well as a grouping structure. Beware how it models the bad habit of neglecting to label with words the rates in proportions. Unfortunately, it uses the equal sign 905 times to mean "the next step in a process" before finally showing an equation as an equation.

Note that the § symbol means "section".

After opening the link, you might need to use CTRL-F to search for the section number. That will let you jump to the right place.

If searching with CTRL-F for the section number is not working well, try adding a space afterwards. That sometimes jumps to a section, rather than an example problem that happens to include a similar decimal value.

Shapeshifting

Mad Science

Justice