Introductory statistics (in college or as high school AP statistics) typically has algebra 2 as a prerequisite. More in-depth statistics courses are calculus-based.
Very few colleges in the US of any kind require or expect entering frosh to have had calculus while in high school (though math through precalculus is more often expected). The few colleges appear to be:
- (all majors) Caltech, Harvey Mudd
- (engineering only) Cornell, WUStL, Stevens
- (engineering and business only) Penn
Note: MIT says “We recommend (please note that these are not 'requirements) … Math, through calculus”.
Math is not just for studying bachelor’s degree subjects in college.
Suppose you are a carpenter who wants to build an A-frame with specific angles and base width. What lengths of wood do you need to use to build that A-frame?
Suppose you want to align two linear objects so that they are at a right angle from each other. You do not have any right angle objects around, but you do have a tape measure. How would you do that?
Hacker’s point is that the carpenter and a lot of other people need arithmetic but not trig or calculus and not much algebra if any. I see both sides of this one. I loved math as a kid. I took calculus in my junior year of high school and that’s the last time I ever used it. I’ve long since forgotten calculus and trig but I’ve always assumed that the fact that I once knew it sharpened my brain and helped me learn other subjects. Hacker says there’s no empirical evidence that this is true.
I have a child who really struggles with math. One reason is she has very poor spatial perception; graphs are like hieroglyphics to her. It’s also possible that she hasn’t received the best math instruction. Regardless, her grades in pre-calc and calc have tanked her GPA and that will likely keep her out of a good college. She is already applying test-optional due to a huge gap between her math and verbal SAT and ACT scores. Also, we now have to be very careful about the core requirements at the schools to which she chooses to apply. She was able to muddle through at the lower levels, but the material in those two classes was too much for her brain to grasp. Regrettably, due to math dept. policies and graduation requirements, there was no other option available to her. So at the moment math is her enemy!
I was PBK and won awards from 4 different departments in college, but was not great at math either. Fortunately, my college allowed us to take logic to fulfill the math requirement. Had they made me pass calculus, who knows if I could have done it and might have failed to even graduate! I loved that logic class and found it to have been the most helpful class I ever took as far as teaching me to think. So I think we can still train brains without higher math. But we do need to teach logical reasoning somehow.
I think this is the wrong way to tell people why math is important. Practically, the only correct answer to “how would you do that” is that “I’d go find a right angle object because being creative in construction is a recipe for disaster even if I think my unusual solution will work.” Maybe it would work, but it’s more likely that if you do something unusual, you will make a mistake or fail to account for an insight that the “standard accepted way of doing things” has accounted for.
The real importance of math is in its ability to understand the underlying structure of things. Why do population sizes explode and why do investments accumulate? Exponential growth. Why can you make predictions from data? Statistics. Why are those statistical methods justified? The underlying probability theory. Why does a right angle even matter for construction? Geometrical arguments on stress/strain properties. This is what math is really for, not for some unusual and unlikely scenarios where you try to substitute “tricks” for proper practice.
Math is of course done mostly by computers because they make fewer mistakes. But if you don’t understand what the computer is doing or why, you will really limit what you are capable of doing.
I don’t think we teach Algebra in the best ways for many students.
The course I’d really drop, however, is geometry. It was by far my favorite math class in high school, but other than in physics and some engineering classes, I never used it again. I think it would be much more helpful for students to take statistics.
The same people who think math is not that important also seem to oppose tracking students. This is odd to me because letting your student take less math is the ultimate form of tracking. You have already virtually eliminated the possibility of a STEM career for them.
Instead of dumbing down the curriculum, we should invest in non-university-track high schools/trade schools, where higher math isn’t required. Like they do in the rest of the world. (Although I’m pretty sure algebra isn’t considered higher math anywhere, lol.)
I would argue just the opposite. Math helps teach the critical thinking skills that one needs to ‘lead a productive life.’
But the real problem with dropping all those pesky (and ‘difficult’?) math courses, is that the result is that a matriculating college student is precluded from nearly half of the colleges’ offerings. And, inhibits students from going into good paying STEM jobs.
The carpenter’s problem described in #22 is a trigonometry problem.
This was actually a real world situation that I encountered. It was not construction or a situation where precision of 90 degrees versus 89.5 degrees was especially important.
We need to stop standardizing curricula so much, and instead teach math in different ways. St John’s, for example, teaches advanced mathematics in ways which are very easy for visual-spatial students to grasp, as VS students tend to fill in the blanks through what is given. We need to stop putting emphasis on route memorization and facilitate creativity backed up by facts.
But see, that’s the problem. Most kids don’t have good visual-spatial skills. 
Big mistake. Its one of the few classes in HS that teaches/requires visual-spatial thinking. Perhaps such reasoning came easy to you; Geom was my favorite class too. But for most, visual spatial learning takes awhile to absorb.
Despite the BSCE, Masters (math), and Phd (physics), I’ve never taken geometry. I think it would have helped a lot at various points along the education path.
Rather than stop requiring advanced math, we should be researching what exactly is making it so tough for some otherwise bright students who are capable of complex thinking, and address those math “hurdles” with better instruction or strategies.
THIS is the problem. People need to understand that math is the study of relationships, not just a bunch of funny looking numbers. Trig is the relationship of angles and lines, using triangles. If people were more conversant in math, you would know that carpenters are usually the best people in trig. They need to precisely figure out lengths based on angles of their dimensions (not everything is a ninety-degree angle - and even know that part requires some basic knowledge). You know who else are good with angles and geometry? Quilters. Seamstresses . Plumbers. Landscapers.
At first I thought so, but then I realized that geometry simply focused on the correct subject in a bad way. Geometric knowledge is important because it crops up everywhere (engineering, physics, calculus, even in real analysis and advanced probability theory). But it’s very hard to care about being able to prove that a line that is a perpendicular bisector of a triangle has this and that property. Perhaps if it made a better effort to have more effective ways of teaching proofs?
But it’s not something you would learn math for. I could think of at least a handful of problems with measuring that way (real objects don’t have 1D thickness and there is a margin of error associated with that) and there are quite a few ways you could solve that without using trigonometry.
The so called “advanced math” is not all that advanced. They are basic math taught all over the world. Some of the reasons students have tough time with math may be that they weren’t taught fundamental quantitative understanding in elementary grades.
It seems to me that the author wants us to be more creative with mathematics and learn how to apply it and use it more actively in our lives.
It is very difficult to be fully functional in the modern, data driven world without being mathematically literate. Without statistical literacy you cannot decipher the assumptions behind the claims made for products, services and by politicians. Bad decisions are made every second because people mistakenly or deliberately misinterpret data for their own ends. Look at climate change, Apple cryptography, both left and right wing economics, and health care coverage as recent examples. “Freakanomics” is full of examples of this.
How can anyone possible interpret the conclusions of research without understanding how their models were developed?
The real issue IMO is that we, as a nation, have far too little understanding of mathematics and are innocents subject to charlatans because we refused to educate ourselves.