I was recently asked to answer a series of questions about Math for Life, so I’ve posted the Q&A set below. For additional information about the book, please see the Math for Life web site.
1. How is “math for life” different than the math we learned in school?
A: There’s math involved in virtually everything we do in modern life, from personal finance to choosing a health care plan to deciding how best to deal with national issues such as the federal budget, energy, and climate change. But the traditional school curriculum focuses only on one very narrow aspect of this math, which is the arithmetic and algebra used in calculations. As an analogy, the way we teach math today is rather like teaching literature by focusing only on the mechanics of reading and writing.
2. Why do you think so many people feel they’re “bad at math”? What are the implications of that on a personal and global scale?
A: Few people would ever announce that they can’t read very well or are unable to think logically, yet it’s considered socially acceptable to say that you’re “bad at math.” But given how important math is to virtually everything we do in modern life, being “bad at math” is really just another way of saying that you don’t understand how to function in the modern world — and we see this playing out in the way poor mathematical thinking has led to global problems like the recent financial crisis and personal problems like people spending money on scams or gambling.
3. What piqued your interest in quantitative reasoning?
A: I’ve been teaching since I was a teenager, and it didn’t take me long to realize that our schools not only do a poor job of teaching mathematical skills but almost entirely skip teaching the broader range of “math for life” reasoning ideas. I therefore started including quantitative reasoning in my own curriculum materials as far back as in a math and science summer school that I first ran when I was 18, and later incorporated similar ideas into materials for my college courses in astronomy. So when the University of Colorado asked me to help develop their quantitative reasoning curriculum (in 1987), I jumped at the opportunity.
4. What does math have to do with talking on your cell phone while driving?
A: The only way to make an intelligent decision about whether it is safe to use your cell phone while driving is by looking at the safety statistics (which is math because it deals with numbers) and the effects of cell phone use on brain function (which is math because it involves complex imaging and analysis). Both of these show that use of a cell phone while driving is extremely dangerous — just talking on a cell phone (even hands-free) can make you as dangerous as a drunk driver, and texting can be much worse because your eyes leave the road. If people understood this equation, I think they’d be less likely to use a cell phone while driving and more likely to support laws restricting such use, and many lives would be saved as a result.
5. How could the housing bubble have been prevented? The recent recession?
A: At the risk of oversimplifying, the recession was caused by the bursting of the housing bubble, the bubble was caused by housing prices rising faster than was sustainable, and the fuel that allowed prices to rise so fast was the fact that many people obtained mortgages with payments that they could not actually afford. Ultimately, then, the two causes of the recession were: (1) too many people believing that housing prices could continue to rise at a rate that a bit of mathematical thinking showed to be clearly unsustainable; and (2) creditors offering loans (and individuals accepting these loans) that a bit of financial analysis quickly showed to have payment terms beyond the budgetary means of the people taking the loans. In other words, the problems all come down to ignoring simple math, which is why I believe the bubble and the recession could have been avoided if we as a society paid more attention to math.
6. What do Americans need to know about the 2014 federal budget?
A: What Americans need to know is how the budget actually works, and it’s really very simple. The federal budget consists of revenue, which is almost entirely from taxes, and spending, which is divided broadly between three main categories: (1) spending that is “mandated” by past promises, of which the largest chunks go to Social Security, Medicare and Medicaid, and interest on the federal debt; (2) national defense and homeland security; and (3) everything else, including education, food stamps, transportation, scientific research, the space program, and much more. Only once you know these things can you legitimately begin discussions about how to improve the budgetary picture. Unfortunately, on both sides of the political divide, most of the people speaking loudly about the budget seem to ignore at least some aspects of these simple budget basics.
7. Do you see any realistic solutions to the federal deficit?
A: Mathematically, the solution is very simple. The deficit exists because spending is higher than revenue, so if you want to eliminate the deficit you must either raise revenue, cut spending, or some combination of both. Numerous bipartisan commissions, including Simpson-Bowles, have looked at this issue and have all reached the same conclusion: You can’t realistically eliminate the deficit with revenue increases alone or spending cuts alone, so it will take a combination of both. The only question is the precise nature of the combination, but even on this question there is remarkable agreement between conservatives and liberals who are honest about it. For example, on the spending side there’s no getting around the need to make cuts to the largest government spending programs, which are Social Security and Medicare; and on the revenue side, there’s no getting around the fact that current tax revenues as a percentage of GDP are very low compared to their historical average, and therefore should be increased toward their historical norm. So if we could just get Congress to pay a little attention to basic budget math, the long-term deficit problem could be solved almost immediately.
8. What changes would you propose to our tax system?
A: When you look at the mathematics of our tax system, it is so incredibly complex and convoluted that I don’t think anyone would say that it is either fair or efficient. So from a mathematical point of view, the obviously needed changes are to make to our tax system simpler and more efficient. Beyond that, we delve into the realm of opinion, and since you asked, mine is that I place a higher value on fairness than on debatable calculations of economic impacts. For example, the idea that capital gains get taxed at a lower rate than earned income may have some economic justification to it, but it also leads to the clearly unfair situation in which a person living off an inheritance can pay much less tax than a hard-working person with the same annual income. Similarly, tax deductions have the same budgetary effect as government spending, and when considered in that light have the perverse effect of meaning the government actually spends more helping the wealthy than the poor. Therefore, my personal suggestions would be to eliminate the distinction between different types of income (such as wages and capital gains), eliminate all deductions, and base tax brackets on the total tax paid by individuals rather than breaking it by category into FICA and income tax. These changes would not only make our tax system simpler and fairer, but they’d also allow us to lower current tax rates significantly while still eliminating the deficit.
9. What do you mean by “truth, truthiness, and statistics”?
A: The famous line “lies, damned lies, and statistics” focuses only on the fact that statistics can be abused in dishonest ways, but with thanks to Stephen Colbert for the middle term, the reality is much better expressed by “truth, truthiness, and statistics.” Our obvious goal is to search for truth, and we can do that either by going with our gut, as in Colbert’s idea of “truthiness,” or by actually looking at facts such as those we can collect through the science of statistics. Clearly, the latter is a better way to reach our goal of learning the truth.
10. What are the most important steps to take in managing personal finances?
A: Basic budgeting is easy to understand — it’s just a matter of keeping track of how much you earn and how much you spend — so the more important issues generally surround how we make financial and budgetary decisions. If I were to give only one piece of advice, it would be to focus on the long-term picture. For example, when choosing a health care plan, be sure to consider how you’d be affected if you suffered an unforeseen medical emergency. Similarly, when deciding whether to go to college and what to study, keep in mind that over a typical career, the average college graduate earns over $1 million more than a high school graduate, and that those who major in more technical fields and those who get better grades tend to earn even more than the average.
11. What is your opinion on the Common Core State Standards for math education?
A: I really like what I see in the new standards. As I discuss in Math for Life, big problems with mathematics education include not only a lack of emphasis on quantitative reasoning but a poor job in teaching the mechanics of arithmetic and algebra. Both of these problems are addressed in the new standards. Of course, the key to success will be in how well the vision of the standards is turned into reality in the classroom, and that’s the truly difficult part. So while I like the standards a lot, I remain very concerned that they won’t be implemented successfully unless we put a lot more effort into getting high-quality teachers and combatting the social acceptability of people saying they are “bad at math.”
12. To ensure our kids are “good at math,” how can we improve the way math is taught in the classroom? How can we improve math education on a policy level?
A: As I explain in more detail in Math for Life, I would focus primarily on four ideas: (1) If we want kids to learn math, we need to be sure they have plenty of study time, and in general, I think study time is too short today; (2) We need to set high expectations for all students, but also allow them to move along at a pace that makes sense for each individual; (3) We need to make sure math is taught in context with other subjects, rather than only during “math time”; (4) We need to expect all teachers to be good at math and to convey positive attitudes toward math — for example, just as we wouldn’t hire an elementary teacher who can’t read at 9th grade level, we should not hire an elementary teacher who can’t do 9th grade algebra. And personally, I think that any teacher who ever says “I’m not good at math” to his or her students should be immediately fired, or at least required to undergo some retraining.
13. How does math play a role in political polarization?
A: As many news analysts have explained, it’s easy to trace much of our current political polarization to effects of the way Congressional and legislative districts are drawn, which is the process known as “redistricting.” But I’ve found that even though this is easy to say, very few people actually understand how redistricting works or why it can have such political effects. In fact, as I explain with examples in Math for Life, redistricting can in principle make a state that is equally divided between Democrats and Republican voters end up with a set of representatives heavily tilted toward one side or other. I think that if people understood how this process is being abused politically, we could come up with solutions that would lead to much less polarization and much more getting done.
14. What mathematical ideas should people consider/be thinking of when voting?
A: Everything! When we vote, we are choosing representatives who will make decisions on a wide range of issues that are important to us as individuals and as citizens, and I can’t really think of even a single such issue that does not require some level of mathematical understanding. So unless you know how to reason quantitatively, you will be voting from the gut (Stephen Colbert’s “truthiness”) rather than based on reality.
15. What are the problems we face in maintaining our energy economy?
A: Finding enough and dealing with the costs. That’s really the entire story, and it explains why math is so important to energy policy: If you want to find enough energy, you have to understand how energy is measured and how much potential there is from various sources, and if you want to know the true costs of energy use, you need to know not only the production costs but also the consequence costs — such as health effects of pollution — of each different energy source.
16. Do you see any potential solutions to our energy crisis?
A: There are many potential solutions, but to find them you have to understand the true costs of energy, and unfortunately, we currently ignore the long-term costs entirely and focus only on the direct production costs. Once you factor in the long-term costs — especially those of pollution, militarily protecting the energy supply, and global warming — it becomes clear that fossil fuels cannot solve our energy problems, and indeed are the main cause of many of them. Therefore, the solutions must come from some combination of other sources, such as nuclear, solar, and wind. I’m particularly interested in some potentially game-changing solutions, such as advanced biofuels, solar energy from space, or nuclear fusion.
17. How long can the world sustain population growth at its current rate?
A: Not long at all. In fact, the consensus projection that population will increase by 2 to 3 billion people by 2050 is already based on the assumption that the growth rate will decrease significantly by that time; the growth would be much higher at the current rate. Indeed, if the current rate were maintained, population would double to 14 billion by about 2070, double again to 28 billion by 2130, and reach 56 billion by 2190. I don’t think anyone can seriously imagine that such numbers could actually be reached without a complete collapse of our civilization, so it is very clear that population growth will stop long before it reaches that point. The only question is how it will stop: Will it stop because of conscious family planning choices that we all make, or will it stop because we push nature beyond its limits and suffer catastrophe?
18. What are some other issues that can be helped or solved through applying quantitative thinking?
A: I think the easier question is what are the issues that cannot be helped or solved through applying quantitative thinking — and I can’t think of any. That’s why “math for life” is so important, because you really can’t live an informed life unless you develop your skills of quantitative reasoning.