It’s always amusing to see how few younger people can do arithmetic in their heads. In my current business, we use a lot of basic arithmetic. It cracks me up when I sit in a meeting when the calculators get pulled out for a simple growth or difference calculation. My wife and I used to drill our kids in simple math by making them compete to calculate addition, subtraction, multiplication and division questions in their heads. Our favorite when they were young and still took baths together was to give them rapid fire problems with the loser getting squirted with a squirt gun. It was fun, and they got good pretty quickly!
Are these kids hopelessly innumerate, and nothing can be done to make them numerate? Is it impossible to teach them to connect what looks like an abstract problem to something concrete they can understand?
Is it really true that 60-year-olds are better at mental arithmetic than 25-year-olds, or is it just that you’re looking at a different subset of 60-year-olds than 25-year-olds?
Also can we please separate arithmetic, which is rote and boring but necessary, from math, which is not rote?
I’m glad that I’m not the only one who did math drills and work books with our D (which thankfully she enjoyed and would often do on her own).
The math curriculum switched when she was between 3rd and 4th grade. She had speed tests through 3rd grade so had a bit of it at school.
We were also fortunate that her HS believed in no calculators most of the time. She also had AMAZING female math teachers, especially at the HS level.
@BKSquared Ha! We did the same thing. Added in simple problems to complete in thier heads as we drove to and from school each day. We added in tic-tac-toe as well. Later, as our son became proficient at chess he would work tactical problems in his head and eventually could play games without a board. I do think all these mental exercises were beneficial as well as fun.
Very interesting discussion and as my posts in the thread suggest, I’m a proponent of “old school” math. You just need to know certain things and basic / intermediate math is one of them. Things like understanding the relationship between fractions and percentages are important for even the least math friendly human so they understand interest rates and other financial items.
That said, and as someone upstream posted, some kids are just naturally better at math than others. I have two kids. S is a math rock star and will use it alot professionally and personally. D is an artist and connects with the musical relationship ( beats and notes) to math but that’s about it. She’s a very smart kid, but actually takes quite a bit of time to do mental math beyond the very basic and frequently gets it wrong. I think more drilling would have helped her become better than average. She actually gets the algebraic concepts but has a hard time with the arithmatic wihtout a calculator.
Doing anything that takes away from sharpening basic skills is a terrible idea (IMO).
An aside - our school system stopped teaching cursive writing many years ago. They claimed it was a waste of time, not a necessary skill, and nowhere near as important as the other material needed for local standardized tests. My wife taught our kids on the side. Certainly hope traditional math doesn’t get that treatment.
How come immigrants from former British colonies are generally so good at mathematics? They faced similar hurdles as African Americans and native Americans? No?
The problem with having k-6 “math” consist largely of tedious recipes and drilling is that it makes students who actually would like math think they hate it. It would be like having K-6 “soccer” entirely consist of passing drills, and never letting anyone play the game. Everyone would think they hated soccer, when in fact lots of kids who actually play soccer like soccer.
Kids have to learn arithmetic, but we should also give them a chance at math.
“Liking” math is not the same thing as being able to do math accurately at a high level. Gaining the basic skills in anything requires a lot of work. Once a person has the skills, it becomes easier and more enjoyable. Kids like being good at something.
Some kids in club sports are practicing 15-20+ hours a week. I guarantee that includes a lot of boring drill–work, not fun–all for the benefit of being the best/winning competitions.
Without the basic foundational skills of arithmetic, kids are frustrated and failing in higher math. I’m not saying gifted kids need 6 years of drill. They should move on after they’ve mastered the basics. Mastery of the basics doesn’t seem to be a priority in a lot of schools these days, though. I’m wondering what “doing real math” means for K-6 kids?
Fibonacci numbers come to mind. Binary and hexadecimal numbers. Logic puzzles. Mobius strip. There’s a lot of exciting stuff accessible to K-6 kids.
Solving real problems. Probability, which lends itself to all sorts of games and fun. Open-ended problems. Puzzles. Easy game theory. Estimation. Logic.
The point is to give the kids something where it’s not immediately obvious what recipe to apply, because in the real world, it’s not immediately obvious.
Agree.
Collect data and analyze it.
Real math for K-6 kids:
Can I remember from Family Math and math themed birthday parties?
Ways of estimating
Simple probability and combinations (two dice for example)
How many ways to make change sort of puzzles
Mobius strips are great
Four color map problem
Cutting up an index card so you can climb through it
Sierpinski Triangle and other simple fractals
Tangams
The infinite hotel paradox
Programming for kids like Scratch
Topology (why is a donut the same as a coffee mug?)
Factorials
I did a ton of set theory as part of fifth grade “New Math”
These immigrants are often selected by the immigration system which prefers skilled workers and PhD students, rather than outgroups who have been educationally suppressed for generations.
“Real math for K-6 kids“
At the older end of that age range, I’d add simultaneous equations. My kids loved working out the price of apples and oranges when it’s $4 for 2 apples and 3 oranges and $1.50 for 1 apple and 1 orange.
Re #113 - I never had any of that stuff (and need to look up what some of it means) but it sounds cool. I had arithmetic drills, which I was too bored about to do well. My parents pushed me into the “advanced” math stream, which the school (appropriately) said I wasn’t ready for, and therefore math was always a struggle. I had an algebra epiphany, fortunately right before the Regents exam, which moved my Algebra I grade from a C- to an A- (your final grade was whatever you got on the test!). I think that with any math teaching, never mind good teaching, I’d have liked math even if I turned out not to be a natural at it.
In a parallel move, my early art experiences were similarly awful and to this day I think I can’t draw anything.
You don’t have to be an immigrant to realize that math in the USA isn’t being taught to the standard the US needs to compete in the future. Crazy curriculums and crazy thinking eventually drove us to very expensive private schools where our kids are light years ahead of their peers vs. being in a public school rated one of the best in the country. My kids are American and are often the only kids with parents not from outside the US ( in math competitions, science and other STEM related activities). Parents need to wake up. If kids cannot do math, they will not be able to do many jobs. And not all of those jobs are STEM jobs either.
It’s so sad how some people place a (racist, sexist, whatever" lens on everything they see.
A house can’t be built without a foundation. The same is true with math. Building a foundation may be boring and tedious, but necessary. There’s a reason math is taught the way it is. Math also requires the ability to think abstractly. These “new” methods will fail because they neither help build a solid foundation for the student nor help develop a student’s ability to think abstractly, just as prior such attempts have all failed.
In K-6, that reason is that teachers are innumerate and afraid of math.