The foundation of math is number sense, which is not developed by learning rote recipes, but is developed by such topics as estimating and data collection.
In our experience, there is an issue with way estimating was taught (and it drove our math literate kids crazy) - the problems used were just too simple. While the teacher was looking for an answer like “somewhere between 5 and 6” our kids wondered why an exact answer like “5.25” would be considered incorrect. The teaching methods need to be complex enough that they underscore the importance of estimating. How many ping-pong are required to fill up a 2ft x 2ft x 2ft box? That would be more interesting.
Yes, and “how much water/sand would it take to fill up this irregular object (toy truck, sock, handbag…)?” And then after everyone works on the problem for a while, proposes answers, considers everyone else’s answers, you pour in the water or the sand to find out.
Asked 3rd grade grandson if they were working on their times tables. He looked at me like I had 3 heads…and asked, “What’s that?”
I’ll also second a million times that many elementary and high school non-math teachers hated math, and they appear completely willing to give a pass to students “who don’t like math.” I have many teacher friends, and I hear this all the time.
Save the oppression and paragraphs of explanation for humanities. Our kids need to know basic math facts!
Is that because they weren’t drilling math facts, or because nobody uses the term “times tables” nowadays?
“how much water/sand would it take to fill up this irregular object”
Isn’t that usually part of a science lesson on the density of different materials?
The beauty of math is that it’s abstract. Trying to force it into real world applications may make it superficially more “relevant” and might avoid turning off kids who don’t like and don’t have any desire to learn basic math, but potentially has the opposite effect on talented math kids. Recognizing beauty in patterns (eg Pascal’s triangle) is a better way to experience the joy of numbers. The problem is that it may not work for everyone.
Math is about abstraction and deduction, not memorization or guesstimation. A student doesn’t really understand the concept if s/he doesn’t know where it came from and how it came about.
Not if you want to know how many cups of sand fit in this handbag or sock, no. The density would be irrelevant. You’d want to estimate the volume of the sock or bag.
I was pretty impressed with my daughters old math curriculum. She was doing simultaneous equations in first or second grade (just iterative approach). They were often doing problems that I was not exposed to until much older. They used much simpler techniques than the way I learned to solve the problems. When they learn the more sophisticated techniques they should have a better understanding of the basic principles than I did.
Last year we moved to a public school that by most measures is great. Their math curriculum however seems to be written by people who do not to really understand math. I don’t think it would have stood out to me if I had not been exposed to her old curriculum.
Incidentally, DS and I won cool prizes twice when playing a game of “guess the number of things in this jar” (first time it was tangerines, second M&M’s). I believe we were the only ones who actually tried to estimate the numbers instead of just guessing. Talk about practical applications of math!
Wife is an educator (average at math at best) and most of her friends are educators. All K-5. As a group, they are terrible at math so I’m not sure who is teaching what. Very sad. To a person they would argue that drilling is not fun, kids don’t learn that way, etc.
Well, I learned that way and not everything is suppsoed to be fun. Getting problems right is fun. getting in to a good college and getting a good job is fun. Worth a little drilling don’t you think?
Perhaps true, but what they ignore is that one needs automaticity in the basics to be able to perform the next level math. And I have no idea how one gets automaticity without memorizing times tables (aka drill and kill) and other basic rules such as for right triangles and circles.
If it’s true, as the teachers assert, that kids don’t learn from drilling, then they won’t gain the automaticity you desire from drilling because they don’t learn from drilling.
Which was kinda my point. Alternatively, besides drill-and-kill memorization, how do such educators expect students to gain automaticity in the basics? What other ways can they teach it in an efficient, effective & timely manner? (I suspect none, since we’ve had new math, new-new math, hand-holding math, manipulative math, touchy-feely math (ok, I made that last one up) and all other kinds of math revisions, but none of them appear to be more effective than good old memorization.
My son has trouble memorizing. We taught him his multiplication facts with dice. He’d throw two ten-sided dice and announce their product. He did it for speed: how many could he get in a minute. He’s competitive. He got very fast.
^^excellent. Whatever works.
“Not if you want to know how many cups of sand fit in this handbag or sock, no. The density would be irrelevant. You’d want to estimate the volume of the sock or bag.”
Yes I understand that. My point is that playing with sand and water is your typical elementary school science lesson. But to me enjoying math really comes from an interest (where possible a fascination) with numbers which can begin at a very early age (though whether teachers are able to convey it is another matter).
I grew up loving number tricks and games (solving simultaneous equations, figuring out Pythagorian triples, that the sum of 1 to n is n(n+1)/2, etc.). I still enjoy doing math puzzles (like Putnam questions) for fun on occasion.
I agree that knowing basic facts like times tables automatically is critical. My kids school did (and hopefully still does) challenge tests of who could complete a grid of 100 random single digit multiplication calculations the fastest.
Taken to an extreme it leads to this sort of thing (the Hardy-Ramanujan number https://en.m.wikipedia.org/wiki/1729_(number)), a story which every math PhD I know just loves:
“I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”
Brain research confirms what we already know - that it’s easier to memorize things if they’re not standalone facts but are related to other memories. It’s easier to remember practical phrases in a foreign language when you’re using them than try to memorize separate words. It’s easier to remember math facts when you’re using them in some meaningful or cool way.
I have a client, 1st generation Korean-American, who told both her kids they WILL be engineers. The daughter is a civil engineer and the son is in college studying electrical engineering. She finds it interesting that I am letting my D20 pick her college major (public policy and/or business).
Do her kids actually like civil and electrical engineering, and are they good at those subjects? If not, seems like a way to cause lifelong resentment.