Okay, if you knew the distances involved, and then knew you had to figure out the square root, and your calculator had the little square root symbol on it, and you pushed it, and you came up with 318 feet (or whatever), you would know that was wrong. I knew it was wrong. The kid figured it was right. After all, that was what the calculator said.
Obviously, it has to be shorter than the distance if you ran the bases. After I explained that, he seemed to get it.
So as a double check of sorts I asked him how far it would be if we drilled straight through the center of the earth to the other side, supposing that the circumference of the earth is 24,000 miles. Again, he knew the procedure. Again–and this time without a calculator–he came up with a preposterous result. I mean obviously preposterous although this time with the decimal in the wrong place so it was 70,000 miles (or something like that). (Of course we have to add one extra mile since we live in Denver.)
“So, Kid, if you go around it’s 24,000 miles, if you go halfway around it’s 12,000 miles, and if you go straight through it’s 70,000 miles. Right?”
Kid gets perplexed look. Whatever the calculator says.
Depending on how fast the grounder got to the fielder and whether it was taken first by the shortstop and flipped to the third baseman for a force or fielded by the third baseman who then ran to tag the bag, approximately 127 feet. Of course, if you only need one out or the ball came too slowly to get the double play the distance is 0 feet as the ball gets tossed somewhere else, maybe the pitcher or another infielder. You’d love to be able to go to second for a double play but the runners were probably in motion and thus it’s something like 6-5-3 or 5-3 if you’re lucky and the batter is somewhat slow.
So what you’re saying is that you intuitively know what the ballpark answer of a question like this should be, but you don’t remember the particular formula to determine the exact answer?
I think you can be a lot more helpful than you think you can be. You can show him how to visualize problems. You can re-learn the basic math stuff – it will come back. Hey, if you can just get him to plug in the right formula into the calculator, you don’t even need to do that.
He thinks of “doing math” as “following procedure”. He needs to UNDERSTAND things conceptually. The whole point of a mathematical education is to learn clear, objective, logical thinking; to understand why, not the how. This is particularly important to learn before High School.
I am not sure tutoring is the right way to get this across, as most tutoring services focus on test prep, i.e., drillwork, which doesn’t seem to be the problem here. It’s an attitude thing towards learning in general, and math in particular. Not “attitude” as in “effort”, as in a kid who needs pushing to do his homework, but an appreciation for why it’s important to be able to reason things out from first principles.
In other words, time to get Socratic on him (I guess you could find a Socratic tutor). Ask him leading questions and make him give you the answers, do not feed them to him, until he develops a desire to anticipate the next question with an answer ready in mind that is both testable and reasonable.
Unlimited tutoring for $99.99 a month, but I’m pretty sure it’s limited to phone calls and internet. No house calls at those rates:
My experience as a math student and as a parent tells me that practice is by far the most important thing. Much more important than understanding, IMHO. I’d buy as many books as possible from the following link and just make him practice as much as possible:
I think you’re right. If he knew the concept, he’d be able to estimate, and to figure out without my prompting that the answer is wrong.
But I think he needs to be able to do long division, too. The first math problem I mentioned he got the wrong answer via calculator; but the second time he was doing the figuring by hand.
You don’t. If you just tagged third then that means there had to be a runner at first and second, otherwise it’s not a force out. So you throw to second for the double play, unless the runner had a good jump and you don’t think you can get the throw in time. If you have to throw to first it’s probably about 120-125 feet, because you are moving towards first as you scoop up the ball and fire to the first baseman. This assumes that there was not a player at third and or no play at the plate.
The problem with that question is there’s really no good way to go straight through the center of the earth, as proven by the late Jules Verne. You’re going to take a circuitous path, fraught with peril, monsters, villians and what not.
Okay. The first problem was the base thing. The answer was messed up, I don’t know why. He was looking for the square root of something or another, but the answer was so far off that obviously he wasn’t paying attention. Or something.
So the next problem was drilling through the center of the earth, and this time, no calculator, because I wanted to see if he knew the math. And he didn’t. And still wasn’t paying attention. (This time off by a decimal point. But he knows what pi is and theoretically how to find the measurement we were after.)
Other tests followed. Dividing by a three-digit number–failed. Dividing by a two-digit number–failed. Dividing by a one-digit number–that one he knows.
What age are seventh-graders, that they don’t know about the square on the hypotenuse? I must’ve known the rule by the time I was eleven, though I sure didn’t know the proof (even though it’s easy).
The problem is not long division. Most people nowdays rarely use long division. Using a calculator for it is fine. The problem is that your son can’t visualize the problems he’s working on. Either you or a tutor need to teach your son how to visualize the problems he works on (and one of you also needs to find out why he’s misusing the calculator to get these wrong answers).
I have been told that the Chicago Math thing is less of a problem if you either (a) get the school to give you the Parent’s Guide (which they will apparently not do unless you demand it because it obviously costs them money) or (b) get a teacher that understands that there is more to life than teaching 4 different ways to achieve the answers without the child learning any one consistent method. Luckily, my 14 year old daughter got one of those teachers this year and she went from failing math last year back to an A grade this year.
In my opinion, Chicago math really sucks for everyone involved - except perhaps for the Chicago Math teachers who have perpetual job security. I say that because once you start the cycle, you can not easily have kids come in late or go back to a traditional math sequence because they only learn “slices” of each of the topics that are traditionally taught in order.
I’ve been thinking of getting a tutor for my son too…not because I can’t handle his fifth-grade math, but because he gets so frustrated he starts crying and yelling. Obviously he can do that with his family members, but if he was dealing with a stranger he’d suck it up and maybe learn something.
