<p>It may be a struggle but it’s a good struggle to overcome sooner rather than later. As an engineer, I document what I do. I keep a log of what I’m doing and sometimes put in explanations of what I’m doing in the log. This log can be used for weekly and monthly status reports or if there’s a problem in an area and an audit is done to try to find the cause. I can look through my notes a year or two later to provide my side of the story and what I did and didn’t do and what I signed off on and any reservations that I had at the time.</p>
<p>Explaining your work can also be good training for becoming a tutor.</p>
<p>Thanks for the insights; they do give me much more of an idea on how to deal with it, instead of just feeling annoyed or helpless. Just to clarify, the assignment was a take-home that would receive credit as a quiz, and they weren’t given restrictions like “you must do this on your own.”</p>
<p>This is the assignment:
“The following assignment is due on 5/13.
Green book January 2011 part I
pages 17 - 20
Set up your paper will 3 columns : 1 - 9, 10 - 18, 19 - 27
omit question # 13.
Under the 3 columns of answers you will neatly organize your
work for each question. No work, no credit.”</p>
<p>The last time I did math at anywhere near this level was for the GRE, 25 years ago, so I feel very much out of my depth here.</p>
<p>Could you describe what is the Green Book? Is it a published book or a school book? If it is a common book, you might be able to acquire the Instructor’s Manual and use that version to refresh your own skills. I have seen references to a Green Book as part of the Regent’s tests. Is that it?</p>
<p>From reading your posts, I think the issue might be that your child was moved on without understanding all the previous material. Do not base yourself on previous grades, but try to identify the holes in the current understanding. The good news is that you have plenty of time to redress the issue as she is a sophomore. The key to Algebra II is a very sound understanding of Algebra I. A patient review of the skills that should have been learned is necessary, as some students pass the courses (even with high grades) without really mastering the subject. And it comes back to haunt you. </p>
<p>The solution could be to go over both this year and last year’s book and work to a lot of the problems over this summer. If feasible, you should also identify next year’s book and material (talk to students in that class before the year is over to copy the book or even get the assignments.) The objective would be to start the year prepared and confident. </p>
<p>PS If you describe the assignments with more details, someone here could identify the pitfalls. Also, check the SAT forum. A couple of great math teachers are offering great advice in that forum.</p>
It might seem like someone who “just gets it right” is the next Einstein, but unfortunately, not the case. Part of math is the process itself. If you don’t “get” the process itself, you don’t “just get it right”. At some point you will reach a dead end (albeit probably not in hs algebra).</p>
<p>Marysidney, I don’t dispute this. I know I frustrate the bejeesus out of students with very strong math intuition. I don’t do it to be contrary, and I don’t do it any more than I think is necessary. (I realize, I can speak only for myself here, and not for all math teachers.) I will let the really intuitive kids take more shortcuts sooner than most of the class. </p>
<p>And usually those highly intuitive kids will understand that I need something of a written record so that I can recover their thought processes–especially if I flatter them a little by saying that what’s obvious to them might be less obvious to me. (This isn’t an issue I’ve had all that often, but it has come up from time to time when I’ve taught students who are innately better mathematicians than I am. Every once in a while, I do get a student who makes me think to myself, “I still know more than you do, but that’s only because I’m older and I got farther in school than you’ve gotten.”)</p>
<p>Also, I agree with sylvan that sometimes the process is the product. Almost every process I teach, I teach using problems that are so elementary that good mathematicians can solve them without the process. Heck, I’m not that good a mathematician, and I can do the problems with way less work than I write down for my students. But there are more complicated problems that can be tackled the same way. It’s just that, if you’re choosing between practicing the process with fairly simple problems and practicing the process with extremely complicated problems, using the fairly simple examples is usually the better pedagogical choice.</p>
<p>If this happens then the question was a bad question. The fact that a kid finds an easier way to solve something because the teacher wasn’t able to give an appropriate question doesn’t mean the kid should lose points.</p>
<p>I don’t know where you teach. I live in a world where kids will tell me, “It came out, ‘x = 0.’ You see, I just divided both sides by 0, and there you go.”</p>
<p>ETA: Crepes, I seem to have had some hand in turning this thread away from your original question. I didn’t mean to do that, and I apologize.</p>
<p>Sylvan, I don’t know, because I am not a math person. My daughter, however, who struggled in math on the elementary/jr high level, really started to swing when she got past the “show your work” stage. She got behind in jr high math because of the “process” mindset (she was still multiplying in her head instead of memorizing the times tables), so that when she decided as a senior that she wanted to take physics she didn’t have the pre-calc req. She took AP physics anyway, concurrently with precalc, and then, as a physics major in college, took the prerequisite math at the same time as the physics course, through junior year when she finally caught up. Which is to say, she just gets math on a level that most kids don’t. I don’t know at what point she will reach a dead end, but she is headed for her PhD in EE, so we’ll find out. But she is exceptional, and I don’t doubt that for most people being made to show your work at every stage is a good idea; my point was just that to some kids it is counterproductive.</p>
<p>Hmmm…is it possible that your daughter is hoping you will think this is the fault of the tutor? A couple of thoughts…first…I agree with others. The tutor should NOT have worked on the take home quiz with your daughter (and it doesn’t matter that the assignment said nothing a out doing it alone…it could count as a quiz! Quizzes are supposed to be solely student work). She needed to do the quiz herself. Second…two sessions is not enough to turn around a semesters worth of work…or more. Third…I’d have a discussion with the school GC about math placement. It sounds like your daughter is in the accelerated math track at her high school. Very often, these tracks move very quickly with little review or time to go over the requisite skills to master the concepts presented. Many of the students in these accelerated tracks don’t need this type of instruction but it sounds like your daughter does. </p>
<p>True story here…we were the FIRST parents in the history of our middle school to refuse the accelerated math track. DH is an engineer, and felt very strongly that a good and strong foundation was more important than acceleration in math. Our daughter was an excellent math student…and believe me…she whined about this decision we made. However, she had OUTSTANDING instruction in her math courses, and felt confident all the way through precalc which she took her senior year. NO she never took high school calculus. She was accepted at her first choice college, graduated with a double major in engineering and biology. She took PLENTY of higher level math in college…and didn’t suffer a bit by not being accelerated in high school.</p>
<p>But back to your question. What would I do? I would ask DD to take the returned quiz to her next tutoring session so the tutor can see where your DD went wrong. The two of them should have some kind of review of the quiz so the tutor can see first hand where the breakdown is.</p>
<p>It is NOT the tutors fault that your daughter got this grade. It is May…she has taken this math course since September. There are some missing skills.</p>
<p>I find it unlikely that d is doing Fourier series in her head, or that her professors would let her get away with trying. More likely, she has overcome those earlier problems and reached a stage where what the professor wants to see in the way of “work” allows for more latitude in leaping the “obvious”.</p>
<p>As an example a lot of problems take the form of “show that Expression X = Expression Y”. Just writing down “it is intuitively obvious that X=Y” without every single step to prove it doesn’t cut it.</p>
<p>I’d also like to jump in. I am a math PhD candidate at Stanford and I am quite confident that none of my classmates does math “intuitively.” Of course we will skim over standard arguments and memorize results that come up a lot. (Why compute 7*9 from scratch each time if i can memorize a multiplication table?) However, we can fill in the missing steps in our arguments if requested. </p>
<p>That seems to be what the brighter K-12 math students are doing as well: they recognize patterns, perform several steps between each line they put on paper and memorize the answers to sub-problems that occur a lot.</p>
<p>That’s quite different from the “guess and check” approach that often gets mislabeled as an “intuitive answer” at the K-12 level. Yes, it’s easy enough to guess that the two solutions to x^2 = x are 0 and 1, but the guess and check approach won’t work for most quadratic equations. If guessing is the only way in which students can solve this problem, they really don’t know what they are doing.</p>
<p>Sylan8798 - maybe I should have explained further- some people ( ie the “new” math teacher) memorize formulas and know only one way to get the answer. Others with talent like my S can look at the problem and approach it creatively. Additionally not everyone needs to list 10 steps to get an answer they can do in 3 ! The teacher he had the second half if the year really understands math and is qualified to teach. The reason S went from the low 80’s high 90’s avg. </p>
<p>But this issue is not about my S’s experience. I explained his situation only to help someone else.</p>
<p>Worry about going forward. Call your GC or the head of the math dept. Ask for the name and # of a junior/senior that excels in math and would like to work with your daughter as a tutor (for pay of course.) You will spend 1/4 of the $ or get 4 times the hours. You’ll get a really bright math kid that has recently taken the course and will be familiar with all of the requirements (like all of the steps in show your work.) They were just there.
I connected with the greatest young man to help my son with the trumpet. He is off to study at a conservatory next year as he is pursuing trumpet as a career. Worked out great and my son liked working with a younger person.</p>
<p>I had one DS who would spend time on the test deriving a formula he should have memorized, or who would get lost in thinking about a problem and not finish the test. A tutor helped him remember what was essential and get to the point in his answers quickly.</p>
<p>Just because there’s a quicker way to solve a given problem doesn’t absolve the student of the requirement to show the work doing the problem the way the teacher wants. The point might be that not all problems can be solved the “easier” way, but the teacher wants them to complete the more difficult process with the proscribed method, so they can see how it works. It’s not that different from proofs, which intuitive students hate.</p>
<p>For the students who do not like to show their work because they just see the answer to the problem, I think it would be very helpful to have more difficult problems of the same general category, so that the stepwise approach makes sense to them. If I have a simple linear or quadratic equation to solve in my research, I just write down the answer.</p>
<p>I recall one of Feynman’s stories, where he was helping an older cousin with a “solve for x” type problem. Feynman saw the answer immediately. The older cousin was having difficulty. He discredited Feynman’s answer on the grounds that Feynman had obtained it by arithmetic, whereas he had to obtain it “by algebra.” That reflects some very confused understanding of what was being taught.</p>
<p>I don’t like this advice. But I will disclose that I may have a bias: I am a math teacher who’s not currently teaching, but is tutoring (and charging a fairly high hourly rate, which I think I’m about to raise).</p>
<p>I think there’s a perfectly good reason why an upperclassman charges 1/4 the price that I charge. He or she may have “just been there,” but I have been there many, many times. I’ve written and graded the tests and quizzes. I’ve seen half a dozen potential ways a student could misunderstand mixture problems, and I’ve already corrected them.</p>
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<p>But a math student is not a mathematician. A mathematician may dismiss as trivial a great many things that a math student should not be allowed to. And, if asked, a mathematician could explain why those trivialities are true. She might be annoyed that you asked, but she could do it. In my experience, most of the kids who aren’t writing down all the steps are quite vague about what they’re omitting. It’s almost as if they think “huge leap of faith” is a mathematical operation.</p>
<p>As I’ve said, I do occasionally encounter a student who is a much smarter mathematician than I am–I’m really a math teacher, and really not a mathematician–and I cut those kids some slack. But that’s happened a few times in my career.</p>
<p>Crepes - first and foremost i want to apologize if my attempt to help took this thread in totally different direction!</p>
<p>MarySidney _ I am in TOTAL agreement with you. My son like your daughter found it difficult to show every step - He does/did most of it in his head. However he does shows his work in larger broader steps. He is in precalc and breezing through it! Everyone one has a different way of learning and we ( schools/ society) need to embrace different learning styles.</p>