Our S was at the tail end of an Everyday Math based class. It drove him crazy. In the end we advised him to take a pass at solving the way his teachers wanted and then checking his answers on the side using the basics that he had learned years earlier. So on each math test or assignment he basically solved each problem twice. To this day he rants about the way that the math that he loved was “butchered”.
I was taught these arithmetic recipes when I was a kid, too: long division, borrowing for subtraction. But these recipes, taught as they were with no understanding, are not mathematics. They’re just not mathematics at all. I thought I hated math. Turns out, I love math and am good at it, but I hated going through boring, tedious, error-prone recipes.
People who were facile at the recipes, and who, unlike me, didn’t make errors, somehow have nostalgia for them. But why? They’re just recipes. If your idea of math is recipes, you don’t understand math. If you teach a kid a recipe, you haven’t taught them any math, and you might just as well have taught them the easier recipe of using a calculator.
I agree that basic addition and multiplication are just that - basic building blocks. However, properly taught they do introduce basic concepts of base 10 math appropriate for for the age of the student. The problem is that many teachers do not go beyond teaching the mechanics. A failure in teaching.
Even though I got 790 in SAT math, I realized I wasn’t good in math when my friend who went to MIT finished his SAT math in 10 minutes and then spent next 10 minutes to double check to make sure his answers were correct. I still remember what he told me: “The difference between you and me is that even if they made SAT math twice harder, I would still get 800.” He wasn’t being an a***le; he was just being matter of fact. That’s when I realized SAT math doesn’t really test kids’ ability in math. If you are really good in math, you should only miss SAT math problem due to not understanding the problem correctly, which is reading comprehension ability issue, not math ability issue.
I also remember what he told me of his MIT (he basically got accepted to Harvard, MIT, Yale, Princeton all early long time ago) experience. He told me he was for sure among top 20% students in that with a decent amount of time spent of studying, he got almost all As. But he told me there were some kids at MIT who literally did not study and still managed to get As in classes, and they spent most of their non-sleeping hours working on some projects. He told me he is not on their level, and he was a kid who regularly placed in top 5 in state math competitions. He also graduated top 5% from a prestigious law school which he attended while working but he never ended up practicing law because he felt it was just paper pushing. lol There is no question in my mind he would have made at least $500K per year as a patent lawyer at a top law firm, but instead he has his own small business where he does some consulting work several days per week and makes around $200K per year. I asked him once why he didn’t try to make more money, and he told me that as long as he makes enough to live comfortably, it doesn’t really matter to him. By the way, he’s also a very good poker player.
@websensation Your story just illustrated one of my statements to @Tanbiko: That the best and the brightest of American math students often DON’T go into typically math-oriented fields such as engineering. Your MIT friend went to law school, then started his own business. This is why we have so many foreign-born engineers and IT personnel. Because Americans often take their math talents elsewhere.
Properly taught. Which they almost never are, because they are taught by elementary school teachers who are afraid of mathematics and don’t understand it.
You have a very high standard of “good in math.” I would say you were good in math.
“The difference between you and me is that even if they made SAT math twice harder, I would still get 800.”
“But he told me there were some kids at MIT who literally did not study and still managed to get As in classes…He told me he is not on their level”
That’s a good example of the limits of US standardized testing - there simply isn’t enough of a long tail to find the most gifted kids, and in math that long tail is very long indeed.
These subtraction examples make my head hurt. The goal of teaching math in early grades shouldn’t be giving kids one recipe for every subtraction problem they ever see, it should be to develop number sense so they use the appropriate method for every problem and feel comfortable doing this in their heads.
Hard “agree” on that!
It’s ok to be challenged by linear algebra or calculus. It is not ok for an elementary educator to be challenged by arithmetic. If you can’t do arithmetic functions in multiple ways, and learn new ways to do them, you should not be teaching children.
It should not be ok for elementary teachers to think or say or accept from students “I’m not good at math” when talking about basic arithmetic. Just like it’s not ok for elementary teachers to proclaim they can’t learn the basic rules of english grammar, or figure out where Florida or New Mexico are on the map.
How do you solve subtraction and long division problems?
---- But he told me there were some kids at MIT who literally did not study and still managed to get As in classes, and they spent most of their non-sleeping hours working on some projects. He told me he is not on their level, and he was a kid who regularly placed in top 5 in state math competitions. ----
An agreed upon illustration that it isn’t all instruction or interest. Ability varies, on a sliding scale.
How is scrubbing the male, Western civilization component out of math instruction going to level up those without the innate ability? And, will it get the oppressed to the point they literally don’t have to study?
Unfortunately, that is correct. When I looked up the numbers awhile ago, future teachers had the second lowest SAT math score, only beating Parks & Rec prospies. (Back in the old days, CB would ask applicants what their planned career was.) Few elementary (K-6) teachers got close to Calculus in college.
“The best and the brightest of American math students often DON’T go into typically math-oriented fields”
The US does have a level of respect for public intellectuals, but mostly in arts subjects. There are only rare exceptions in the sciences and math (eg Richard Feynman). I can’t imagine a comparable development to the situation in France where a famous mathematician (Fields Medal winner), Cedric Villani, is using that as the basis of a serious run for Mayor of Paris.
From today’s WSJ (https://www.wsj.com/articles/lady-gaga-of-math-splits-macrons-party-by-running-for-mayor-of-paris-11572429603):
“Cédric Villani calls himself the “Lady Gaga of mathematics” because he is both a star in his domain—a winner of the Fields Medal, math’s highest honor—and an unconventional dresser, pairing 19th-century cravats with dazzling spider-shaped brooches. He also has Lady Gaga’s flair for provocation. Mr. Villani’s campaign to become the next mayor of Paris is roiling French politics…”
I guess that’s one way to use math to help the oppressed 
^This illustrates the cultural problem we have in this country. Math, and sciences, are held in higher esteem in many other cultures.
I have been teaching/tutoring K-12 math for 20+ years, and doing SAT/ACT prep for 15 years. Students I see in test prep tend to be either top students aiming for scholarships/elite admissions or below average students who got around a 17 or 18 ACT who need a 20 or 21 for State U. Many on CC are thinking of that gifted or well-above-average group of math students, who pick up on abstract concepts easily. Math ability is, like many other abilities (artistic, athletic, musical, etc.) innate. Some are talented. Others can only go from failing to below average with years of practice. (Thinking of my own musical ability here…)
For most average to below average students, math is procedural. See this, do this. The biggest problem I have seen with high school students is that they don’t know their times tables. I wish I were joking. No mental math at all. They are using calculators for single digit addition, etc. , which is so slow. Either that, or they think they know arithmetic facts and consistently guess wrong–but close. (And they will often congratulate themselves for being close!) They may know how to solve the problems, but get the wrong answer almost every time due to simple arithmetic errors. (Again, these are the average to below average math students–real world, not CC world.) IMO, there is not enough drill in elementary school arithmetic. Now they have kids wasting time writing a paragraph on how they solved a problem. They do fewer problems and have less practice. There is a reason some teachers/tutors prefer older math textbooks. In the old days, kids drilled until they knew the basic facts backwards, forwards, inside out, upside down, sideways, standing on their heads, in their sleep, etc.–and they never forgot them. No amount of teaching kids to “believe they can be good at math because someone who looked like them was good at math” is going to help them pass Algebra if they don’t know their times tables. I agree that there is something wrong with how math is taught. Let the gifted kids take off to the highest levels. But let those with little aptitude stop after basic Algebra/geometry. Teach consumer math/financial literacy that they will actually use. There is no point pushing most people into Algebra II and beyond.
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Consumer math and financial literacy would include selected more advanced topics, such as exponential functions for interest rates, or enough algebra 2 stuff to understand basic statistics, even if the student did not have to take the full algebra 2 or higher course.
@atomom when I raised the same concern about the lack of drilling in times tables, etc. I got the reply that kids just don’t need those skills anymore since they can use calculators. Made steam come out of my head. So I had to spend time at home drilling my kids.
Maybe some of these folks were working on the Boeing 787-800 Max. Hey, we held a group meeting and felt good about our group answer - it was close. Grrrrr.
Seriously, if you need a calculator to tell you how much 3 items costing $5.99 each are going to cost you when you get to the register (and don’t have the ability to calculate (3X6)-3) life is going to be hard. Not all the old ways were good - the corollary to this is - not all the old ways were bad.