<p>I’d like to hear your thoughts on my 3rd-grade son’s math assignments. He is constantly being asked to do things like complete several multiplication problems and then write a story about them. Today he brought home a paper that was scored below grade level, with an attached rubric so that I can see exactly why his math skills have been judged deficient. </p>
<p>The paper has a list of 7 schools, each with an associated 4-digit number that represents the number of cans collected for a food drive. The problem is to list the 1st, 2nd, and 3rd place schools. The students are asked to write down the three names, and then to explain how the problem was solved. There are about 10 lines for the explanation. My son wrote one sentence, “I looked at the thousands and the hundreds.” That seems like a perfectly adequate explanation to me. </p>
<p>According to the rubric, this explanation is unsatisfactory. To get the highest rating (3; my son got a 2), a very detailed explanation is required. This is the example they gave of an explanation that meets the objectives:</p>
<p>“I put all the numbers in order from the biggest to the smallest. First I looked at the thousands place. Then I looked at the hundreds place. I found out that Barnhart was first and Washington was second. Then I looked at the tens place and the ones place. I saw that Campbell was third.”</p>
<p>First, the top three schools can be determined by looking only at the thousands and hundreds places, so the model explanation is actually wrong. Second, I think the whole idea of having to write a long explanation of how a trivial problem has been solved is dumb. This problem is trivial for my son, who is according to the teacher the top math student in the class. I suppose the answer is that writing the explanation may be useful for a child who is having difficulty with the concept. </p>
<p>Oh God – this brings back memories! My son, who is outstanding in math (800 on the SAT I) HATED this type of stuff. He just absolutely KNEW the answer right away and couldn’t fathom why he had to explain it. I genuinely think this exercise is designed to help kids grow their “logic” capabilities. To kids who are already extraordinarily logical and math-y, it’s a total insult.</p>
<p>My son really enjoyed his summer at CTY when he took “Reasoning, Logic, and Formal Proof.” MUCH more advanced!</p>
<p>For a 3rd-grade student…yes, the elongated explanation is unnecessary. If it was an 8th grade problem that was more complex, I don’t see a problem.</p>
<p>But in your situation…the simple answer your child gave should be sufficient. Do they really expect a 3rd grader to be able to write what the example says? At that age they don’t think through things that thoroughly–that develops over time, and a trivial math problem isn’t the time for it.</p>
<p>I think that this is also supposed train kids to show their work in words, step by step. You could never have gotten my kid to do this. He also never showed his work until 10th grade. He lost so much credit b/c of his refusal to comply. He never was able to get partial credit, and nobody knew where he errored b/c he would never break down a problem. He is quite strong in math, but did not have the patience required for these exercises.</p>
<p>Well, I hate to come off sounding as if I support this crap, but I can see one positive outcome. If a child is forced to supply a detailed verbal explanation for solving a math problem, it might (might) help the child explain the solution to someone who doesn’t get it. Maybe. So in an overcrowded and inadequately staffed classroom, children who can help other children are an asset.
However, if this were my child, I’d find another school/class/teacher. Altruism can take you just so far.</p>
<p>My S used to provide the kind of explanations Nymomof2’s S gave. Now he is in college as a math major doing proof-based math, and his besetting weakness is insufficient explanation. By the standards of my S’s college math, “I looked at the thousands and hundreds” is an incomplete explanation. I now wish we had insisted on his giving fuller explanations when he was in k-12. They would likely be just as trivial as what NYmom’s S encountered, but it would have accustomed him to be less terse.</p>
<p>I’m with Marite on this one. My S also has a tendency to give the Cliff Notes version of his thought process. He now has a math class that is unrelenting in asking for “professional” write-ups of one problem a week, and showing steps on ALL problems every week. </p>
<p>On the other hand, it might be a good idea to give a third-grader a harder underlying problem than arranging in order numbers up to four digits long in decimal notation. Perhaps a harder problem would elicit more thinking about what to do, and thus more words about what the process was. Some kids like challenging problems more than easy exercises.</p>
<p>first, dont blame the teachers. blame the state tests. </p>
<p>open-ended questions like the one presented now comprise a good portion of state assessments… and with nclb percentages increasing, teachers dont have much choice but to make sure their students are prepared.</p>
<p>of course, that doesnt actually address the issue of whether such problems are educationally beneficial. for the gifted student, they often arent. but for the average student… the one who tends to have difficulty connecting numerical exercises with real applications, forcing a justification (and application) of the learned ‘steps’ is essential.</p>
<p>btw, the ‘explanation’ in the initial post is indeed unsatisfactory.</p>
<p>The average male students that have come across while in elementary school would simply not put in the “effort” to do the assignment the way it is supposed to be completed.</p>
<p>Actually, from a neurological standpoint, it is counterproductive to encourage students to resolve quantitative comparison problems with sequential reasoning strategies. If the kid were asked to calculate the numbers, that would be one thing – but making a value judgment as to which numbers are larger and rank them in order relies on different brain functions (i.e., spatial reasoning rather than linguistic processes). In short, you are asking the child to solve a right-brained problem with a left-brained strategy. See: “MIT, French researchers find different kinds of math use different parts of the brain” -
<a href=“http://web.mit.edu/newsoffice/1999/brainmath.html[/url]”>http://web.mit.edu/newsoffice/1999/brainmath.html</a></p>
<p>So ideally, a school math program should accept any explanation that adequately expressed the strategy used – recognizing that spatial reasoning can be better for certain kinds of math. </p>
<p>As to the problem Marite brings up – it is very common for students who have very strong conceptual math skills to have weaker language skills. If anything, these elementary level programs probably are incorporated to give the less mathematically inclined, more verbal students a chance to boost their math skills. You can see how the verbal child who has difficulty with the concepts would be more likely to take a slower approach and verbalize their thought processes – that kid would get a 3 on the rubric, but essentially that “3” is the equivalent of rewarding the kid who counts on his fingers and punishing the kid who has memorized his multiplication tables. The skills that Marite talks about could be built up with a focus on symbolic logic rather than forcing the nonverbal child to write out words & sentences – a good way to do that with young kids is through computer programming type tasks, where leaving out a step will cause the program to fail. </p>
<p>Taking a long time to explain something doesn’t make the answer better or right – in many cases it can increase confusion. Sometimes good problem solving strategies means getting right to the heart of the problem, and learning how to dispense with irrelevant or unnecessary information. The kid who has to think about and explain about looking at thousands, hundreds, and tens to know that the number 4865 is bigger than 92 may be functioning at grade level for a 3rd grader<em>, but for most kids that is about as useful as explaining what sound each letter of each word makes in deciphering the meaning of a sentence. It’s absolute beginner stuff, and at some point in cognitive development it should shift from a conscious thought process to an subconscious, intuitive process. I don’t think any program that punishes the kid who is developmentally ahead of the pack is very useful. (</em>I actually don’t know where typical 3rd graders would be - my kids certainly would have been way ahead of that – but I do remember once spending some time with a 4th grade buddy of my daughter’s who really was struggling with that concept. However, I don’t know if she was typical or lagging behind - she just happened to be a kid who needed my help with homework).</p>
<p>Our 3rd grader has also run into a bit of trouble for not explaining her answers in enough detail. Haven’t seen any problems quite like the one you mention, though.
Am still trying to figure out the report card/progress report that arrived today. It seems they change the format every year. Twelve categories with four subsets each, yet only two short sentences in the teacher comment section. I would like them to explain THEIR answers in more detail Oh well, guess that’s what conferences are for–</p>
<p>Calmom’s explanation does not apply to my S or, most likely, to Tokenadult’s S. It was not the lack of oral or written skills that my S lacked, but lack of willingness to describe his thought processes. We had the same incredulous reaction as NYmomof2’s. And now, I regret it.
I do agree with Tokenadult that giving a child a more challenging math problem would elicit fuller explanations. My S tackled a problem that was given as a “bonus problem” in 4th grade. He wrote out a full explanation of why that problem could have 96 different solutions–and listed them all. By and large, however, too many problems were not sufficiently challenging—they were more exercises than problems–, and allowed him to cultivate the bad habit of providing insufficient explanations, a habit which we did too little to counteract.</p>
<p>Thank you for all your comments. I do realize, erica, that the standardized test are behind this. This is part of the problem; the school needs the brighter kids to get top scores on the tests, and this means forcing my son to do something that makes no sense educationally for him.</p>
<p>I think that what bothers me the most is that the problem is far too easy for my son, as are all the other math problems he gets. I have been struggling with the school system for years with my older son, who is now in 8th grade (but going to the HS for math and science). He is now asked to provide derivations and proofs, and he does them willingly. I agree that it is important to learn to do this, but at age 8?</p>
<p>I’d like to add a note that when you see these sorts of grade, the real problem is usually a teacher who doesn’t understand math. And elementary school teachers with weak math skills tend to be very common – no matter whether the school adopts the current PC fuzzy curriculum or a standard traditional approach. Either way, the kid will end up being penalized as soon as he presents a solution not found in the book. In other words, if the book says that the way to multiply 49 x 51 is to write it out and add the results of 9x51 to 40x51 – then woe be to the kid who multiples 50 by 50 and subtracts 1… even though the latter is the strategy more likely to be used by the budding Einstein. Kids who are strong in math see patterns and quickly recognize ways to restate the problems to make them easier. Math-challenged teachers don’t have a clue as to how to recognize an alternate strategy. </p>
<p>I think the saving grace for me was that I sent my kids to an elementary school where the children were not graded… and then we could shrug this sort of thing off. My son used to get geography papers marked wrong for things like identifying a country on the map as “UK” when the answer sheet said it was supposed to be “Great Britain”. </p>
<p>Also, it often turned out that some of the worst stuff came up when someone other than the teacher was doing the grading – such as a parent volunteer or teacher’s aide – or sometimes (as they got older) a student aid. This problem, unfortunately, does not go away – my daughter has run into some issues with TA’s grading homework in college - in her case, through comparing notes with others in her study group, it turned out the exact same answers to the same problems would be graded very differently.</p>
<p>Calmom, Thank you for your thoughtful comments. You are, of course, correct that this problem involved only comparing numbers, and not solving a problem. So it is silly to ask for a detailed explanation of the process. </p>
<p>My son does not lack verbal skills. He considered his explanation adequate, and was miffed at getting the score he got. </p>
<p>He is having a bad year. Until now, he’s had one wonderful teacher after another. Now he has a brand new, inexperienced teacher who has no understanding of children. For example, she sent a note home earlier this year - the first discipline problem my son has ever had. His crime? “Hopping on one foot on his way back from the water fountain.” He was 7 at the time.</p>
<p>I think that your son’s underlying problem is not really the explanations. It’s the too-easy math. If he had more challenging math, he would have to struggle though it, and by struggling through it, he would have to explain it to himself and to others. Perhaps you can pose him challenging problems at home and ask him to explain his solutions to you.</p>
<p>Have you read Sarah Flannery’s In Code? Very worth reading for parents of math-gifted children. And as Tokenadult wrote in another thread, Liping Ma’s Knowing and Teaching Elementary Mathematics is a real eye-opener.</p>
<p>About the inexperienced third-grade teacher: My Ss both had inexperienced teachers in k-8. Don’t let the inexperienced teacher bother you or overwhelm him. Life will indeed go on.</p>
Oh well, guess that’s what conferences are for–</p>