<p>We were purchasing a car this week, and, on the bill of sale form, the numbers just did not makes sense. Using mental math was enough to bring me to the conclusion that something was just not quite right, but we broke out the calculators to figure out where the mistake was. </p>
<p>I teach elementary school, and I do worry about the curriculum, particularly in math and science. It seems to me, in the push to be more competitive in these areas, we are actually going in the wrong direction. We (teachers) talk frequently about how we cannot teach to mastery, because we simply have to move along to the next thing in the curriculum. We have to teach, even if it’s only in an introductory fashion, all of the concepts that will be on the standardized tests at the end of the year, and that they will be expected to be familiar with in the next grade level. The math book we are required to use is confusing and flies through important concepts, or makes huge assumptions about the student’s background knowledge. In one lesson the book may have students “learning” several different methods to find an answer. There is nothing wrong with demonstrating that there is more than one way to do something, but it confuses the kids when you try to show them too much at once, but, because we don’t know exactly what will be tested, or which methods will be emphasized, we are reluctant to skip as much as we’d really like.</p>
<p>^^^ This remind me of my son showing me a math problem in 4th grade that required him to multiply something and I watched him draw this odd looking matrix to multiply two double digit numbers…it was weird and took a long drawn out time to come up with the correct answer, which it did but when I showed him how to just multiple two double digit numbers the old fashioned way (you know what I mean), he was flabberghasted that they didn’t teach him that in 3rd grade and he’s been taking all this time to do it an alternate way. When I asked the school about this, they said they teach multiple ways and the children will gravitate to the one that like best. My son said he must have been absent the day they taught my way because he certainly would have selected that over the “lattice” method. That was a long time ago and did well in school with a 750 SAT math score but not because they overtaught but because he ended up in the accelerated and honors classes where they narrowed the focus instead of broadening it.</p>
<p>I’ve yet to come across an SAT math question that required a calculator. And I’ve seen several hundred of them. I can probably do 80% of them mentally. But the kids I work with, especially those with AP calc and other advanced math coursework tend to be the ones reaching for the calc to divide 360 by 4. The actual arithmetic on SAT math is very basic.</p>
<p>Well…in both instances when I took the SATs, the place where I took them in 1994 and 95 specifically instructed us that calculators weren’t allowed.</p>
<p>I talked with my very math-y college son today. (He’s an engineering major, but he co-found a campus math club “for fun”). He says he can was taught to do traditional “by hand” long division. But… now that he does elementary school math coaching he has started to teach a different newer method that is more logically converted to “in your head” division. I’ve asked for a demo at Thanksgiving break.</p>
<p>I think many people forget how to do divisions by hand. However, it is very important to estimate the answer.</p>
<p>Can the OP’s girl make a quick estimation? Does she have a feeling for numbers (For example, 858/5 shall be more than 100 but less than 200). If she can do it - I’ll relax, everything is fine with the girl.</p>
<p>^ As an aside, I remember by 3rd grader indignantly showing us her grade for a homework.
[mom] Your teacher marked it wrong because you were supposed to estimate the answer
[DD] Why would I put down a wrong answer when I can work it out in my head??</p>
<p>The next year she got into the advanced math taught by the Principal who had a math PhD. In that she learned all kinds of shortcuts and tricks to check calculations.</p>
<p>Was advanced math the only place that required right answers?<br>
This must work in English too–spelling is “close enough”, some “ballpark” History (bad example since they change that all the time anyways).
My kid got marked wrong on such questions as “If you have 10 marbles and give your brother some, how many do you have left?” Right answer: 5
My kid’s answer: 9 ( Why? I only gave him one!) Obviously, there was no reason to share halfsies with a brother…
I dreaded anything to do with word problems–I only know the people writing them weren’t the brightest crayon in the box. I was pretty sure that the textbook was a plot to undermine the education of our youth and the sanity of their parents.</p>
<p>When my son was in 3rd and 4th grade, he was struggling learning his division facts but he loved long division. He insisted that I write big numbers with big divisors - divisors had to be at least 3 digits and never 1 digit. I didn’t know why until I realized that long division is merely a series of multiplication and subtraction operations. He didn’t need to know division facts for long division involving big numbers. It was also very easy for him to check his answers - more multiplication!</p>
<p>Now, in 5th grade, we’re doing some practice on the distributive law and solving for x. I need to throw in some fractions.</p>
<p>Niquii–like I said, a plot of some kind…but I’m not kidding about the “some” language. It ranged throughout the book. The amazing thing is that nobody at the school seemed to think it was wrong to word problems that way. Today, I would tell them that I’ll make sure they get “some” of their paycheck…</p>
<p>In defense of the author of the textbook or worksheet with the question
</p>
<p>It seems to me that it is possible that the author of the text/worksheet intended that the correct answer should be “between 0 and 9, inclusive,” or “between 1 and 9, inclusive,” or “between 0 and 8, inclusive,” or “between 1 and 8, inclusive.” The “right” answer of 5 might have been supplied by the teacher, who didn’t get the intent of the text/worksheet author.</p>
<p>I prefer the first answer, “between 0 and 9, inclusive,” on mathematical grounds. However, I could see someone arguing that if you give your brother all the marbles, you wouldn’t describe that as “some.” I can also see arguing that if you give your brother a single marble, you wouldn’t describe that as “some,” either.</p>
<p>Of course, the teacher may have been the author of the worksheet. If so, this makes me imagine the scenario at her house, on a birthday: “Would you like some birthday cake?” A guest answers “Yes,” and gets served half of the cake.</p>
<p>A gazillion years ago, when I went to school, we didn’t have calculators. In whatever grade one learned division then, I was sent to the principal’s office for cheating on a math test. I couldn’t seem to explain why I thought it was silly to divide by 25 when you could multiply by 4, but afterwards my father advised me to just suck it up and show the division work. Okay, but I still know most of the useful reciprocals and use them all the time.</p>
<p>This was precisely my reaction. “Some” implies that the number of marbles given was between 2 and 9. Actually, I think it <em>really</em> implies between 2 and 4 or 6, because a good writer would say “half” if the number given was 5, and “most” if it were between 7 and 9. 6 is in a gray area. :D</p>
<p>I was always driven crazy by estimating problems where the quantities were too small and the precise answer was too obvious. I will proudly say that when my S was in K I won the parents’ night estimating contest of jelly beans in a jar, because I estimated the number on one level and multiplied by an estimate of the number of levels in the jar. I’m not competitve or anything. :D</p>
<p>Only if this theoretical good writer had that much information at his or her disposal. This writer may have mad writing skills, but very little information about the number of marbles given. Then some would be the correct word to use.</p>
<p>“I think many people forget how to do divisions by hand.” - Wow, surprised by that. Admittedly I’ve forgotten how to derive a square root by hand. But even though I often use calculator, I still do remember how to divide. </p>
<p>Per calculating tips, I’ve seen many diners (men and women) pull out a calculator or laminated cheat-sheet. That boggles my mind. I assume all can determine 10%. Then if they can’t divide that by 2 and add those numbers together to get 15%… they could easily double for a generous tip Tipping is not an exact science - you usually round up or down anyway.</p>
<p>I will say that when I grew up we got into “new math”…as if math needed changing in the few thousand years it had been in existence. That was like 4th grade. I can only say that my dad saved me at that point. He taught me math almost through HS up until Calculus when I hit another “old school” teacher. My dad was straightforward–calculations, write your work down, get the answer.
I had some great other math teachers along the way but they tended to ignore texts and just teach what they knew we needed to know.</p>
Tipping is not an exact science - you usually round up or down anyway.</p>