<p>Does this student know WHEN she needs to do long division? Can she use the correct numbers and do this with a calculator? If not, perhaps this is an issue. If she knows when to use the operation and how to set it up, and how to use a calculator to get the right answer, maybe not a problem.</p>
<p>I just now caught the very clever play on words in sg12909’s post #7:
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<p>OP here – She probably has some grasp on when to divide, but the math and physics grades have been principally in the C range through high school, so the higher-order thinking about math (as opposed to just doing arithmetic by hand) may be weak, as well. I question the lack of number sense – even if the steps taught in fifth grade seemed rote at the time, and you don’t remember how to do the steps by rote, it still seems that by 12th grade, you should have some general number sense. According to my friend, her daughter couldn’t see that if 19 (a divisor) is practically 20, and if it’s being divided into 211, which is practically 200, then the answer should be somewhere around 10. This, to me, is more concerning than maybe fumbling through the steps with a pencil. </p>
<p>The young lady hopes to study comp sci in college. She sort of avoids the humanities because she does not like to write. One teacher is concerned that her math fluency and skills set is not going to be enough to support this.</p>
<p>I guess the only way to remedy this, if she’s determined to pursue a technical field, would be to find the gaps in her knowledge – find where the bricks are missing in the foundation – and have her work independently, or with a tutor, to fill in those gaps. My intuitive sense of it is that this is a kid who needs to make better friends with math, on her own initiative, or think about some other career goals. Any feedback from you guys?</p>
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<p>Perhaps it should be called standard level to take pre-calc/trig in 12th grade. It’s well within the “normal range” to take some sort of Calc by 12th grade nowadays in many “good” districts all over the country. Though in most districts (I’m told this is changing in some though - where Algebra starts in 8th grade and Calc in 12th) it is considered “standard” and “on track” to do pre-calc/trig in 12th grade. </p>
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<p>A math instructor I had told the class a story from back when they used to tutor (or TA - don’t recall) a “Math Education” class, a class about how to teach math to elementary school kids. This was for people who were specializing in math education. There was one student who simply could not grasp the concept of fractions. </p>
<p>It’s amazing how math ignorant some people can be when they think certain specific things are unimportant. </p>
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<p>You’d probably be able to reason though it. Chances are you remember the concept. </p>
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<p>If she’s willing to work on this issue, I suggest she try to find optimal solutions to linear programming problems. Not algorithmically, but just by intuition and guess and check. Using a calculator is fine but not a solver. I have no idea if this would do anything, but it would be my guess that this should help her build stronger math intuition. Chances are if she has such a lacking in understanding now the first several she tries will be pretty difficult for her but I think it will help her build intuition about how different variables relate to each other, which I think is the critical bit in gaining better math intuition. </p>
<p>Here’s a page with some very simple problems that would be a good place to start. It might take her a while (think 30 min+) to do each problem right now though: [Linear</a> Programming Sample Problems](<a href=“http://www.sonoma.edu/users/w/wilsonst/courses/math_131/lp/]Linear”>http://www.sonoma.edu/users/w/wilsonst/courses/math_131/lp/)</p>
<p>There are solutions but they show how to get the answer algorithmically, which is useless for building intuition. Tell her to just try and guess the answers until she can figure it out.</p>
<p>I do division with 2- and 3-digit numbers in my head all the time. I would indeed find it worrisome that she can’t do it with pencil and paper. Her extremely low math SAT would seem to indicate a major lack of understanding of basic arithmetic. (The fact that she may share this inability with many others is not reassuring, to me.)</p>
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<p>Ya think? :rolleyes:</p>
<p>I think your friend is completely correct: her total lack of number sense–not knowing that 19 is close to 20, enabling her to perform a reasonable estimate–is disturbing. I’m not sure what to do about it, though. It is almost like being illiterate, except that teaching an adult to read has a fairly established protocol, if I am not mistaken. Is there one for innumeracy?</p>
<p>I’m sort of appalled that so many adults can’t remember how to do it. But I’m more worried that students have little experience of it in grade school. Apparently in our town it’s assumed they can use calculators starting very young.</p>
<p>Teaching bio, my H is dismayed how little his HS students understand and can do basic math, which shows up when they don’t realize when an answer is wrong, let alone absurd, because they don’t have any deeper grasp of what the numbers and operations mean.</p>
<p>Many undergrad/grad school classmates and colleagues are amazed I can still do long division by hand as they’ve haven’t had to do it for a while. While “drill to kill” tends to be heavily panned by many edu school theorists I’ve read about, I do believe it’s useful to provide a foundation upon which to learn the how and why of arithmetic/basic math later on. </p>
<p>If there’s a way for math educators to retain positive aspects of “drill to kill” while also teaching for understanding and eliciting interest in the early grades, that would be one possible ideal solution for the math education controversy I’ve been reading/hearing about from friends who teach K-12 math. </p>
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<p>I believe this is a big mistake. Calculators should only be introduced AFTER the basic arithmetic/math concepts are taught and solidified. IMHO…not until late middle school or HS at the earliest. </p>
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<p>Unless she seriously does her utmost to improve her math proficiency, she’s very likely to end up as one of the weeded out students due to underpreparation from what I’ve seen in the intro-level CS courses for CS majors I took. In the words of one CS major friend, CS is mathematics infused with electricity. </p>
<p>She may have less issues if she goes into MIS or IT, but she may still run into some obstacles as her math SAT and level of math she’s undertaking up to now is very low in relation to most folks I’ve known who did MIS/IT majors.</p>
<p>Integrated Math created similar issues for my two Ds. Neither of them were ever taught traditional long division until I taught them at home. Beginning in first grade, every school they attended (and there were quite a few - we moved around a lot) taught Integrated Math. In early elementary school, it was great. They would come home with a little understanding of geometry one week, fractions the next. But when it came time to make more complicated calculations, they were lost. I think by third or fourth grade, the connection needs to be made between Integrated thinking and rote calculations.</p>
<p>My younger D is very good at the approximations. She gets it that 19 is close to 20 and can make estimates in her head. That’s great when approximating is good enough, but when the multiple choice answers were close, she didn’t know how to arrive at the precise answer. My older D is very precise and rules driven. Drill a series of steps with her and she’ll repeat it correctly every time, but estimating completely flabbergasts her.</p>
<p>This drove me nuts all through middle and high schools!</p>
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<p>That is probably the biggest issue for the general public with respect to very low math ability – to fail to notice when a numerical result is “obviously” incorrect.</p>
<p>Not saying this girl isn’t just missing some of her math facts, because she may be, but I have dyscalculia and have very little number sense… I know 19 is close to 20, however I have to estimate percentages at work all the time for numbers in the millions to determine if they are within 10% of each other… say 3,200,000 and 2,800,000-- I would need a calculator to be absolutely certain that is within 10%, because all I see is that 400,000 is a big number and so it seems like a big difference. I also end up swapping the two numbers a lot and think a person’s home is under insured when really it’s over insured and vice versa, I always have to triple check to make sure I didn’t reverse the numbers. I can memorize “steps” really well but one way or the other I get lost in a blur somewhere in the middle and can’t execute the steps correctly. Usually there are mistakes in arithmetic due to poor number sense or transposition of numbers or signs. Interestingly, I was really good at algebra if I could use a basic calculator for the arithmetic-- otherwise I failed it several years in a row. I can do the hard part, just not the “easy” parts.</p>
<p>In trying to help her, researching strategies for coping with dyscalculia might be helpful-- people who work with people like me are really attuned to these huge “gaps” in math education which boggle the minds of average people. I think I scored in something like the 12th percentile in math on the ACT and high 90’s everything else. It was kind of a bummer so far as college admissions were concerned, but it all ended up working out really well for me in the end. I have learned to muddle through well enough.</p>
<p>I’m concerned about this student–it seems unlikely that she can make it in CS.
She needs practice. </p>
<p>I’m teaching Algebra I and SAT prep this semester. (I also tutor middle school math.) On the 1st day I gave the Algebra class (and myself) a speed test on a mixture of single digit addition/subtraction/multiplication/division problems. No one got 100%, (except me) and all took at least twice as long as I did. Today, a student was doing a problem on the board and asked, “Six times eight is forty-two, right?” Biggest source of mistakes comes from not knowing times tables. Had a long division problem with decimals on the first test–it was the most commonly missed problem.<br>
They really should have had all this down cold, years ago.
There just isn’t enough drill. Now, with the latest curriculum adjustments for common core, my own third grader is coming home with math problems that require explaining, in complete sentences, why or how she got an answer. This drives me NUTS! There is enough writing in English class. (Nothing against English. I also teach English, and it is my first subject.) Time would be better spent doing more problems. I remember sitting for HOURS in fourth grade doing PAGES and pages of long division. (Thank you, Mrs. Moore. I’ve never forgotten it.) IMO, a lot of math, beyond memorizing the basic facts is knowing the procedures. “I see this, I do that.” See this, do that. Over and over. More DOing the math, and less talking about it is what I’d like to see.</p>
<p>When I was in fourth grade I asked my father why we had to do so many long division problems every night over and over and he said, “Because someday you’re going to be doing a presentation in front of a big group of people and someone is going to ask a question that you can answer only by doing long division so you need to know how to do it.” Well, that made sense and I did learn it and can do it to this very day. But he didn’t tell me they would invent calculators and I never did have to do long division in front of a group of people.</p>
<p>If she can’t do long division with numbers she’s going to have an interesting time when polynomials are involved.</p>
<p>atomom, D had the same “write in complete sentences how you got the answer” questions. She would often get C,D, or F on this portion because of misspellings and quite frankly she had no clue how to answer “how did you know 8*4=32?” So instead of being an A student because she knew her math and got the answer right she often got C’s in math. Sadly, I also had no idea what to write and I was a math major; my husband also had no clue and he earned a PhD in math. We all loathed these questions.</p>
<p>That was when we pulled our daughter from the public elementary school and back into Montessori where she was happily getting problems in third grade like (3+7)^2=? She knew the answer was 100 but the point was to multiply out the entire equation, add the components and get 100. This was for ordinary students. Also in Montessori, it was very common for kids to write out a random long division problem on their own like 987654/234 and then solve it.</p>
<p>The idea behind all this was twofold. the first was to practice basic arithmetic, the second was to become comfortable manipulating numbers. It became fun so math wasn’t about “hard” operations, instead it was just playing with numbers just as a writer plays or works with words.</p>
<p>" But he didn’t tell me they would invent calculators and I never did have to do long division in front of a group of people."</p>
<p>I spent six weeks, every day, with the slide rule. The next year pocket calculators came out.</p>
<p>I’m thinking of doing an essay on 40 things you can do with an old sliderule.</p>
<p>I used a slide rule in high school chemistry - 1970 I think. Haven’t used one since.</p>
<p>They used to require that we learn the long way to do square roots. That was really useful…</p>
<p>I never did get the hang of the slide rule: mine was very sticky and tight, and despite putting graphite on it and whatever, it was almost impossible to get it to the right numbers. So by the time I did the rest of the class had moved on. Why I didn’t just get another one I do not know. You would think maybe the teacher would notice me pounding the end of it on the desk. Or I could have mentioned it to my father the chemical engineer, who used one all the time. :rolleyes:</p>
<p>MIni – I had a vision of you doing six weeks of work every day with the <em>bleeping</em> slide rule. </p>
<p>I never did figure out the slide rule – because calculators took over!</p>
<p>atomom and SlackerMomMD: I can really sympathize with you and your children (third-grader and older D) in terms of the “explain how you got this” math assignments. My spouse refers to these as “social compliance math.” I think the heart of the problem is that different sorts of problems are just completely obvious to different students. I don’t think many students are compelled to write out how they know that 1 + 1 = 2. But for a math-inclined student, some of the “show how you got your answer” assignments are essentially equivalent to explaining how you know that 1 + 1 = 2.</p>
<p>It is a useful skill to be able to work through math problems in words, even if only to explain to others how your reasoning worked, in a form that they can understand. But for students who are naturally math-inclined, it would be much, much better to have questions where <em>they</em> need a multi-step approach, and can then explain it, rather than questions where they know the answer already and just need to work out some phony explanation of how they got it. The latter is burdensome at best.</p>
<p>With regard to the OP’s daughter’s issue: CS sounds like a really, really bad choice of major. Near us, there is a Mathnasium. They seem to be a national chain. From what I’ve read, I think they might be able to help the OP’s daughter to acquire sufficient number sense to succeed in some of the business fields (communications, marketing, human resources?) or in another area that is neither writing-intensive nor math-intensive.</p>