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Thanks for the extremely interesting thread. I have a question, and maybe KarenAnne and all who have children who learn like this can help me.

As some of you know, I teach physics at a university, and reading your descriptions makes me suspect that I may have the occasional student who thinks "differently".

With the insight you have into your children's learning process, is there any advice you could give a college instructor how to work with this kind of student?

For exampls: many test problems are very linear, and we expect our students to not just write an answer, but document the whole solution process, following a certain sequence of steps (which is very beneficial to the TYPICAL student and, in addition, can earn the student partial credit if the result is incorrect.) From what you explained, it sounds as if this is not possible for some students? How could I go about evaluating whether they understand the specific parts of problems and all concepts that are involved, if a student can not break down the problem into parts and can not document his thought process? (I am sure similar problems arise in mathematics).

I had the occasional student who just would not write down his solution. What do you suggest a professor do in this situation? (The ideal solution, oral exams, is not feasible)

It is a question I have been wrestling with or several years; on the one hand, "seeing" a solution is very valuable - on the other hand, learning a systematic procedure to arriv at a non-intuitive solution is equally important.

Thanks for any advice. I apologize if this is too off topic.

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That's a really great question, Regentrude; and I don't think I'm the best one to try to answer it -- Jackie, for one, can probably be much more helpful.

 

I can tell you that I worked really hard to get dd to understand WHY it was helpful to show her steps in algebra problems. She would jump immediately to the answer. The issue is, of course, that when something gets messed up, neither of us knows what it is or where it happened.

 

Dd would actually rather go back and redo the problem in whatever intuitive method she has than write out the steps.

 

I have gotten her to write them out, but so far, I can't see honestly what has been gained for HER, although naturally there's more clarity for ME, who thinks in the write-it-out-step-by-step way. I can see, however, what has been lost for her; it's engagement, and confidence in her own way of figuring things out (which was actually almost always right, and when it wasn't, involved transposing signs or mis-adding rather than anything else).

 

In geometry this year, dd chose a book that used a flow-chart type diagram for writing proofs, which she claimed to understand MUCH better than the two-column version I learned, or a couple of other possibilities we looked at. But she will still often work partly backwards and partly forwards when constructing a proof.

 

Don't know whether or not that is helpful to you, but it's what I see at this point.

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Hi Regentrude,

 

I have a student that is like the ones being described in the other thread, except he is now an adult and not a child. He is an intelligent Aspie with incredibly low processing speeds (in the 1st% for both auditory and visual which translates to an IQ equivalence of approx 56 for processing issues.) He doesn't learn like other students.

 

At the risk of being blasted (b/c I have been before), I strongly disagree with the contention that advanced education should be altered to fit him. He has to function in the world. Learning how to adapt and cope is exactly where he is weakest. Those are the areas where accepting the way that he functions is debilitating in the long term. In order to hold a job, learn to interact with employers and other employees, adaptation to normal expectations is where he needs to be pushed.

 

So, if it were my student, I would want you to comply with the standard university procedures......extra time, laptop for writing issues, and sitting in the front of the class. What my student really needs is a professor to detail exact expectations. Generalities and inferences leave him hanging b/c he cannot infer. So, if he came to your office to ask a question that might seem dumb and obvious, take the question seriously and answer it literally. Literal is good. :)

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What a fantastic question!

 

I have a couple of ideas. Of course oral exams would be great. In lieu of this allowing more time for a student to process questions and perhaps having office hours so that they can discuss these ideas with you before they attempt to get their ideas on paper would help some of these students.

 

My child may be different from the others but he has been able to overcome difficulties in getting his thoughts down on paper, especially in areas where his passion lies. However, it is helpful for him to be able to talk things through before he writes them down and he almost always takes a long time to organize his thoughts in a way that other people might understand his process.

 

Writing down one's thoughts is a bit different from learning a systematic procedure to arrive at a non intuitive solution though. I very much see the value in the first. And while I do see why it might be important to be able to understand systematic procedures, I am not sure it is as important that all students use these to find their path. Of course I don't have the physics background to really judge what might be important to a physicist. However I have an intuitive feeling that nontraditional thinking might have its place. I'd be interested to hear your thoughts on this though.

 

I think 8fill is right, our kids do need to learn to manage. Still there is a difference between accommodating and enabling. When a child can't see you give them glasses but you don't read everything for them. Sometimes doing a bit extra for alternative learners (or special needs kids) is like giving them glasses but it is possible to go overboard and never give them the tools that they need to manage on their own. I find it a bit of a balancing act. I am sure at times I err in one direction or the other. But I think she would probably agree since she had a list of appropriate accommodations handy.

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It occurs to me that one thing I started doing with dd was having her show me that she was able to write out steps in the standard way, and then do a set of problems her own way. If she continued to do what she did, which was to get about 97% of them correct, then she only had to show her work on a couple of problems at a time -- and she could choose which ones. Showing her work was an accommodation she made FOR ME, because it's the way I think, rather than the other way around.

 

I don't know whether this type of thing would work in a university setting or not. But perhaps it's an idea to play with.

 

There is a difference between this kind of internal, mental jumping over intermediate steps, and the kinds of processing issues which call for extra time, or a need for explicit instructions. Kids with different wiring are also wired differently from each other. My dd, for instance, doesn't need extra time on tests or any of the standard university accommodations. You'll probably get a variety of ways in which kids think differently. Makes everything very complicated. At least I only have to deal with one!

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Regentrude I have no experience in this at all, but what comes to mind is that if you allow some students to only show the answer, some who are so inclined might take advantage of that and put the answer as it appears on the test next to them without having any idea what they're doing. I would think that you could avoid that by speaking with the few students who you suspect might have a problem with the linear approach, and offering them the alternative of putting the answer, and then writing a few sentences on their thought processes which helped them to arrive at that answer, I think it would become obvious if they truly understand, or if they just copied the correct answer. If it's only a couple of students per course, maybe it would be possible for them to be given the opportunity to meet with you and explain how they arrived at the solutions. Of course this would be best done right after the test was given, so scheduling might be a problem.

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There is a difference between this kind of internal, mental jumping over intermediate steps, and the kinds of processing issues which call for extra time, or a need for explicit instructions. Kids with different wiring are also wired differently from each other. My dd, for instance, doesn't need extra time on tests or any of the standard university accommodations. You'll probably get a variety of ways in which kids think differently. Makes everything very complicated. At least I only have to deal with one!

 

FWIW, I didn't describe how my ds learns b/c my pt was explicitly that it doesn't matter at the collegiate level.

 

The accommodations I listed are the ones that are standard and offered by most universities w/proof of disability (not that VSL is disability; however it seems that VSL and inability to output "traditionally" are being intertwined (another pt that I don't necessarily agree with)).

 

My ds does not use any of the listed accommodations w/the exception of extra time. He has also had professors deny him extra time b/c he had the highest grade in the class. So, they can be denied by the professor at the professor's discretion.

 

If a professor was expected to accommodate every student's learning style and strengths/weaknesses, I think it would be next to impossible to establish a standard for grading. It is why disability depts exist at the collegiate level vs. the professor. It takes the onus off the professor for "allowing" a student something that other students do not receive.

 

But, my perspective is very different than some of the other posters. My ds is not a child. He is not being taught at home. He is almost 20, going to college, and has to function b/c one day he needs a job in order to become independent. It is not a hypothetical scenario.

 

There needs to be some standard for which to assess students against expectations.

 

ETA: Regentrude......basically, I guess my main pt is that typically proof is required before any accommodations are allowed.....and the proof has to be documented testing less than 2 or 3 yrs old (I can't remember off the top of my head) along with a psy's recommendations to the university as to what accommodations they recommend (the uni may alter those). I think it would be very difficult for an individual teacher to assess the situation realistically w/in the parameters of a single class. Perhaps if the student had documented VSL testing w/disabilities demonstrated elsewhere, accommodations could be pursued from the disability dept at that school and professors could work with that dept on how to help the individual.

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For exampls: many test problems are very linear, and we expect our students to not just write an answer, but document the whole solution process, following a certain sequence of steps (which is very beneficial to the TYPICAL student and, in addition, can earn the student partial credit if the result is incorrect.) From what you explained, it sounds as if this is not possible for some students? How could I go about evaluating whether they understand the specific parts of problems and all concepts that are involved, if a student can not break down the problem into parts and can not document his thought process? (I am sure similar problems arise in mathematics).

I had the occasional student who just would not write down his solution. What do you suggest a professor do in this situation? (The ideal solution, oral exams, is not feasible)

I asked DH this question, because I know that for him the answer to a complex problem is often just a sudden "aha" or what he describes as "emergence" — all of the components are sort of floating around and then just kind of congeal into the solution. Sometimes he can then work backwards to fill in the steps, but that takes a long time and perhaps the student wouldn't have time to do that on a test? He said that if the student is consistently getting the answers right, then he would assume that they do understand the process.

 

Also, he asked if the solution would be something the student could draw? He said that when he was in boarding school (UK), he had a biology teacher who would let him draw the answers on exams, and he was always at the top of the class; a few times the teacher even reproduced his diagrams and passed them out to the other students. OTOH, his physics and chemistry teachers wanted everything in writing, didn't care if he got the right answer if he couldn't show how he got there, etc., and he had lousy grades in those classes even though he loves physics.

 

I understand 8's point that some kids just need to learn to deal with the structures and requirements that exist in the real world, but I think there are also some kids who end up being excluded from something they would actually have been very very good at. DH was IQ tested as a child, because his teacher was convinced he was "retarded" — in fact his IQ is 164, and the psychologist said it was probably higher since he had "ceilinged out" on some of the spatial tests. As I mentioned in the other thread, he told me that he thinks in multiple dimensions and in very abstract images, and he "gets" quantum physics in a way I never could, no matter how hard I might try. He reads it for fun, he does thought experiments, he has said that if he could do it over he would love to have been a physicist.

 

He was one of those kids who was always taking things apart and building rockets and messing around with circuits and electronics from the age of 5. School did nothing for him except make him miserable and prevent him from doing all the cool and interesting things he wanted to do. Once he got out of college, he earned two quite prestigious fellowships in the US, which allowed him to do his own research. The guy who nearly flunked chemistry in HS had his original research, conducted at the Smithsonian, published by the American Chemical Society. He was invited to do a PhD at Cambridge after someone saw him present some of his other research at the British Museum.

 

In the process of doing a PhD at Cambridge, he decided he needed to write his own software in order to accomplish what he wanted to do, so he taught himself advanced calculus and several programming languages, wrote a very complex piece of software that does things no one has ever been able to do before, and showed it to his supervisor, who told him to get himself a patent lawyer ASAP. He now has patents granted or pending in 7 countries, he's presented his work at professional conferences where execs from places like Sony and Disney and Hitachi were literally throwing business cards at him from across the table, he's designing and building customized stereo/3D camera systems, he's working on new projects with medical applications — and he still daydreams about becoming a physicist when he "retires" from computer science.

 

Would it be "fair" to let a student like him draw his answers or just provide the solution, if he doesn't arrive at the solution in a step-by-step way? Is it "fair" that educational institutions are designed almost entirely by and for one particular type of thinker? Would it make sense to flunk a profoundly gifted student with a passion for physics because he doesn't think the "normal" way? Those are (IMHO) very complicated questions.

 

Jackie

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Sometimes he can then work backwards to fill in the steps, but that takes a long time and perhaps the student wouldn't have time to do that on a test? He said that if the student is consistently getting the answers right, then he would assume that they do understand the process.

 

 

This is exactly what dd does: works backwards or from both ends to middle in proofs or certain kinds of math problems, while in literature she prefers to read the spin-off or spoof or later adaptation first, then trace back to the origins. I'm also glad that what he says confirms my approach in letting dd only show work in a couple of problems as long as she does consistently get things right. Sometimes she can explain how, and sometimes not. But I feel a lot better knowing that someone who thinks like this can explain it and validate what I decided to do out of desperation rather than certainty it was the right thing for dd. Thanks for asking him and posting this, Jackie.

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FWIW, I didn't describe how my ds learns b/c my pt was explicitly that it doesn't matter at the collegiate level.

 

The accommodations I listed are the ones that are standard and offered by most universities w/proof of disability (not that VSL is disability; however it seems that VSL and inability to output "traditionally" are being intertwined (another pt that I don't necessarily agree with)).

 

My ds does not use any of the listed accommodations w/the exception of extra time. He has also had professors deny him extra time b/c he had the highest grade in the class. So, they can be denied by the professor at the professor's discretion.

 

If a professor was expected to accommodate every student's learning style and strengths/weaknesses, I think it would be next to impossible to establish a standard for grading. It is why disability depts exist at the collegiate level vs. the professor. It takes the onus off the professor for "allowing" a student something that other students do not receive.

 

But, my perspective is very different than some of the other posters. My ds is not a child. He is not being taught at home. He is almost 20, going to college, and has to function b/c one day he needs a job in order to become independent. It is not a hypothetical scenario.

 

There needs to be some standard for which to assess students against expectations.

 

 

I don't think this is a hypothetical situation for any of us who are participating on this thread. I for one am talking about a kid who is soon to be an adult, going to college, working in the real world. I don't see homeschooling as her permanent situation.

 

What I find interesting is how very specific and, to me, narrow, the realm of what constitutes acceptable "accommodation" actually is. Why should extra time or a separate room for testing be any more legitimate than someone sketching an answer to a science problem, using a flow chart, or otherwise using visual diagrams -- assuming the final answer is correct? I think that the whole point Jackie and I are making is that indeed this is not really an accommodation in the conventional sense; it's a recognition of the fact that there are multiple ways to represent how one arrives at an answer to a given problem -- or even of the fact that showing all sequential steps may not always, under all circumstances, for every problem, for every class, be a necessary component of assessment.

 

Is the point of the assessment, the standard by which students are graded, getting the correct answer, or demonstrating mastery of one specific method to get to that answer? In some cases, there are perfectly valid reasons for expecting all students to do the latter; in others, not so much. This is a very different kind of question than whether professors should be expected to accommodate all possible learning style variations or student strengths and weaknesses.

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And while I do see why it might be important to be able to understand systematic procedures, I am not sure it is as important that all students use these to find their path. Of course I don't have the physics background to really judge what might be important to a physicist. However I have an intuitive feeling that nontraditional thinking might have its place. I'd be interested to hear your thoughts on this though.

 

That is a very good point, and I have given this a lot of thought over the years - because even for typical students, the question arises all the time: WHY should they be expected to follow certain procedures.

I see two goals for my students: the mastery of the subject material, AND the ability to communicate the thought process which leads to the results.

The most brilliant scientific achievement is worthless if the brilliant thinker can not communicate his ideas to other people. So, to stay with the simple example of a physics problem: I want to teach my students not just to come up with an answer, but to communicate with a person of same expertise, but no knowledge of the particular problem: to draw a figure that visualizes the problem in such a way that the other person can see what is going on, and to write out his solution in such a way that the other person is able to follow the thinking. This is AS important a learning objective as coming up with the answer - because that is what scientists and engineers will have to do during their careers.

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ETA: Regentrude......basically, I guess my main pt is that typically proof is required before any accommodations are allowed.....and the proof has to be documented testing less than 2 or 3 yrs old (I can't remember off the top of my head) along with a psy's recommendations to the university as to what accommodations they recommend (the uni may alter those). I think it would be very difficult for an individual teacher to assess the situation realistically w/in the parameters of a single class. Perhaps if the student had documented VSL testing w/disabilities demonstrated elsewhere, accommodations could be pursued from the disability dept at that school and professors could work with that dept on how to help the individual.

 

Thanks. Our disabilities department does a good job working with students, and I have no problem granting them the accommodations which are typically extra time, quite testing and the like. It would be nice if I could understand what the accommodations are supposed to accomplish, but I realize that privacy rules prevents me from obtaining this information unless the student volunteers to share with me.

Nevertheless, I find it very helpful if a student approaches me to discuss his specific needs (aside from handing me the paper from the disabilities office) - often there are things I can do in addition to the stated accommodations if I know it helps the student. This may, of course, be easier for students with a very specific and easy to discuss disability - but I think even for students with different learning and processing styles it would be beneficial if they could just talk to their instructors. I may not necessarily modify the requirements for the course -but I could use my knowledge in the evaluation of the student's work.

And let's be honest: even in subjects with seemingly objective evaluation criteria, there can be some subjectivity (which may not be conscious at all), so knowing whether a student just does not WANT to do xyz or whether he just has a lot of trouble doing xyz because of processing issues may make a difference - even if the instructor is not aware of any bias.

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What my student really needs is a professor to detail exact expectations. Generalities and inferences leave him hanging b/c he cannot infer. So, if he came to your office to ask a question that might seem dumb and obvious, take the question seriously and answer it literally. Literal is good. :)

 

Thanks, that is helpful. Actually, I think detailed and exact expectations are beneficial to ALL students. I'd much rather have them ask questions to clarify things beforehand than make worng assumptions.

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Jackie,

thanks for sharing your DH's story.

 

I asked DH this question, because I know that for him the answer to a complex problem is often just a sudden "aha" or what he describes as "emergence" — all of the components are sort of floating around and then just kind of congeal into the solution. Sometimes he can then work backwards to fill in the steps, but that takes a long time and perhaps the student wouldn't have time to do that on a test? He said that if the student is consistently getting the answers right, then he would assume that they do understand the process.

 

Also, he asked if the solution would be something the student could draw?

To a certain extent, yes - drawing a diagram IS part of the required process for all students. Even the ones who don't "think in pictures" have to learn how to do that, because, as I explained in another answer, learning to communicate about a problem is also a learning objective.

 

Would it be "fair" to let a student like him draw his answers or just provide the solution, if he doesn't arrive at the solution in a step-by-step way? Is it "fair" that educational institutions are designed almost entirely by and for one particular type of thinker? Would it make sense to flunk a profoundly gifted student with a passion for physics because he doesn't think the "normal" way? Those are (IMHO) very complicated questions.

Yes, these are complicated questions.

As I explained in the other answer: the goal of a physics course is not just to understand the material, but also to learn how to communicate about physics. "Seeing" an answer is not very useful unless the thinker can explain to somebody else what his brilliant idea is - if a physicist can not publish his results for others, they are pretty much lost.

In a well designed course, this is not an ability the students are expected to just possess, but something that is taught. This may come easier to some students, but it is a skill that can be acquired, and a course should give the student the opportunity to practice this skill.

So, I think it would be unfair to expect students to just HAVE a certain ability - but if students are given help to DEVELOP a skill, it is a learning objective like any other and I do not quite understand why a non-traditional thinker should not be able to just learn it - even if that means he has to go "backwards" when he already sees the result. Does that make sense?

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Regentrude,

 

I think the problem you face as a college professor is very difficult. You have adults and you are preparing them for working in a field in which certain "rules" must be followed.no.exceptions. You might find a creative way to grade their work, but at the end of the day, if the employer needs the documentation to be x.y.z., then the adult must produce x.y.z.

 

I think it is something that needs to be taken care of at a younger age so that habits do not become ingrained.

 

My second boy, third child, is an "out-of-box" thinker and does a HUGE amount of mental math quite successfully. He did not want to write down his processes at all. Just. never. Answers only and no solutions. So, what I did, when my exasperation level had hit the top by 6th grade, was to explain to him that math and science are all about discovery and documenting your discoveries. If you can't properly show the steps of your discovery, then anyone coming after you, other mathematicians and scientists, can't "see" how to reproduce your work. A scientist cannot get published in a journal, get credit for research, etc. unless he has detailed, organized lab notes that will allow other scientists to verify his work. I told him that while he would make a great rocket scientist, no one would want to fly one of his rockets because they would not be able to read his schematics or check his math to make sure his rocket wasn't dangerous. I then did give him the option of showing his solutions the way he solved them in his head instead of the way the standard format.

 

All I can say is if I assigned him a d=rt, two part story problem, I received a flow chart type thing. Not a neat, vertically aligned typical math process. There would even be arrows drawn from one side of the paper to the other to show what step came next....I do not know how to describe the way this kid thinks mathematically except to say it's kind of, uhmmm, horizontal???? But, once I could read the flow chart and usually he could do a wonderful job of orally explaining it, I was then able to teach him how each step of his problem should be represented in "mathese" and slowly, slowly, he began to, with lots of patient coaching, convert to standard solutions. I don't believe his thinking has changed. I really do not...I still believe he quickly arrives at his solution with his rather none standard thinking process, but he can now translate that into a mathematical formula on the page and show organized steps vertically, no more flow charts.

 

But, and this is a huge but, I think this is something that needs to be tackled at a much younger age. I cannot imagine how you could, as a college professor, take a young adult already stuck in this pattern, and retrain him/her. The reality is that anyone in a STEM field may work in a job related in some way to public safety. That means that others must be able to quickly evaluate their work and that means they must be able to produce it in standard format and they absolutely must show their work, their steps, and their details according to industry accepted standards. So, I don't think you should feel it necessary to accomodate other methods of documentation or other procedures for showing work. The adult needs to adjust and willingly do so, or he/she needs to find a different major.

 

Faith

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Jackie,

As I explained in the other answer: the goal of a physics course is not just to understand the material, but also to learn how to communicate about physics. "Seeing" an answer is not very useful unless the thinker can explain to somebody else what his brilliant idea is - if a physicist can not publish his results for others, they are pretty much lost.

In a well designed course, this is not an ability the students are expected to just possess, but something that is taught. This may come easier to some students, but it is a skill that can be acquired, and a course should give the student the opportunity to practice this skill.

So, I think it would be unfair to expect students to just HAVE a certain ability - but if students are given help to DEVELOP a skill, it is a learning objective like any other and I do not quite understand why a non-traditional thinker should not be able to just learn it - even if that means he has to go "backwards" when he already sees the result. Does that make sense?

 

I think most students can learn to communicate their solutions in a more standard way (though as I stated in the other thread, maybe not all students). As a non-linear systems analyst, I have to do it often.

 

But consider that in a test situation, it will take them longer because they've spent their time solving the problem in their own way and now they have to spend additional time translating to a linear format. Possibly a compromise would be that students have to communicate their work for labs (even if it's after the fact) and other assignments and then only on a few(not all) test problems?

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I have gotten her to write them out, but so far, I can't see honestly what has been gained for HER, although naturally there's more clarity for ME, who thinks in the write-it-out-step-by-step way. I can see, however, what has been lost for her; it's engagement, and confidence in her own way of figuring things out

 

I wonder if a more long-term gain for her would be relational and future academic and professional satisfaction, even if she can't see that right now? If she can successfully communicate to others what is going on in her mind, if she feels "heard" even if she has to "work" at that communication that doesn't come naturally, wouldn't that be a gain for her?

 

I can see that you work very hard to help others understand your daughter and others like her. Likewise, people who don't think like her must also work hard at making themselves understood. Yes, the real adult world is not strictly linear, because humans are all so diverse. But we must still work at understanding each other, and learning possibly uncomfortable ways of expressing ourselves, so that we can be understood in personal/academic/professional settings. I have to work very hard here on the boards to get my words down in a way that I hope communicates well with others who don't think the way I do, and it's painful at times! :lol: (poking fun at myself here, not anyone else) It's frustrating for me, but I keep making the effort because, well, it's just part of adult living and very, very diverse humanity.

 

In reference to the OP, :iagree: with FaithManor. And I find DebbS's comments interesting, as someone who thinks one way, yet has to constantly "translate."

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So, I think it would be unfair to expect students to just HAVE a certain ability - but if students are given help to DEVELOP a skill, it is a learning objective like any other and I do not quite understand why a non-traditional thinker should not be able to just learn it - even if that means he has to go "backwards" when he already sees the result. Does that make sense?

 

Yes it makes sense..I think the trouble comes when you have a nonlinear or whole-to-parts thinker who isn't actually going backwards - he's unzipping and sometimes when he unzips he finds he doesn't remember the little steps that he mastered long ago.

 

How could I go about evaluating whether they understand the specific parts of problems and all concepts that are involved, if a student can not break down the problem into parts and can not document his thought process??

 

It's rather like asking an older student who can read fluently to go back and explain how to use phonics to decode. He can't because he can't remember all the phonemes involved without a lot of effort - these steps have been automated in his brain. If the student is in the course though and hasn't tested out, he really has no choice but to dust off the 'obvious' labels and write solutions as if he was teaching the course. When I was in college, it was not necessary that the steps be linear (unless the problem was very narrow) but it was necesary that the parts or cases be shown. Showing algebra steps was completely unnecessary if one wrote a sentence such as "gathering like terms and solving for the variable, then.." . I can remember statics tests driving people to tears because they wanted linearity and obvious steps and those tests made you think. It was impossible to discuss the test with these kids because they were so linear...discussing it with nonlinear thinkers..who could grab different parts, talk about it ,and then go grab another part was very very easy.

 

If the student can't break a problem in to parts, perhaps you could ask for the answers to each of the parts.

 

What do your colleagues say to this question?

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I can remember statics tests driving people to tears because they wanted linearity and obvious steps and those tests made you think.

 

 

You can actually have both - and I try to design my course this way: teach the students a procedure they can use to unravel any problem with any number of components - but make the questions sufficiently different so they have to THINK about how to apply the procedure. Both parts, the procedure AND the thinking, need to be in place.

 

If the student can't break a problem in to parts, perhaps you could ask for the answers to each of the parts.

 

 

You have no idea to what trouble I go to hunt down partly correct statements on pags full of rather random gibberish.. we DO try very hard to find answers to parts. Which can be very frustrating.

 

What do your colleagues say to your question?

 

The ones I talked to see the same issues: brilliant results are nothing without the ability to communicate. We try to teach our students along both lines: develop the conceptual thinking and "intuition" - and give them a "cooking recipe" they can use to train themselves to approach a problem in a systematic way.

All agree, however, that for instance a clearly labeled diagram is an essential part of a solution and that students are reuired to produce this, whether they need itfor themselves or not - it is part of what they have to learn.

 

Btw, it seems to be extremely rare to have the conceptual genius who can't write out a compete solution. All our exams consist of both open ended, fully worked problems and conceptual multiple choice questions. I never have students who ace the conceptual part and blow the problems - usually, it works the other way: half-way decently done problems which earn partial credit, but quite a few missed conceptual questions.

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But consider that in a test situation, it will take them longer because they've spent their time solving the problem in their own way and now they have to spend additional time translating to a linear format. Possibly a compromise would be that students have to communicate their work for labs (even if it's after the fact) and other assignments and then only on a few(not all) test problems?

 

And how would you go about deciding who gets this special treatment?

 

I am very grateful that we have a disabilities office who takes care of evaluating students' special needs and tells me what accommodations to give - if they determine a student gets extra time, I give extra time. I do not consider myself qualified to make these decision, this is outside my area of expertise.

 

One thing the students value is an appearance of "fairness" (I say appearance, because of course there is no absolute fairness). To manage a large class, rules and clearly stated expectations are essential - I honestly have no idea how one would implement your suggestion to waive requirements on tests for SOME students without opening a Pandaora's box.

I'd much rather have a qualified person make the decision that this student has to be compensated for his specific learning style by getting additional time on exams.

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You have no idea to what trouble I go to hunt down partly correct statements on pags full of rather random gibberish.. we DO try very hard to find answers to parts. Which can be very frustrating..

 

Oh, I do. I had roommates that were apparently taught in their high schools to fill the page with formulas if they had no clue, then hope for partial credit.

 

The ones I talked to see the same issues: brilliant results are nothing without the ability to communicate. We try to teach our students along both lines: develop the conceptual thinking and "intuition" - and give them a "cooking recipe" they can use to train themselves to approach a problem in a systematic way.

All agree, however, that for instance a clearly labeled diagram is an essential part of a solution and that students are reuired to produce this, whether they need itfor themselves or not - it is part of what they have to learn.

 

Btw, it seems to be extremely rare to have the conceptual genius who can't write out a compete solution. All our exams consist of both open ended, fully worked problems and conceptual multiple choice questions. I never have students who ace the conceptual part and blow the problems - usually, it works the other way: half-way decently done problems which earn partial credit, but quite a few missed conceptual questions.

 

That says to me that the problem is study skills, not divergent thinking.

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As a person who learned that way, I would ask that you really explain those steps and tell me why. I got lost without why. Even if it takes a long time, and you are going over it again and again. It's why I failed Algebras with less talented teachers. They couldn't play with their medium. When I finally hit a teacher that could toss those equations up in the air and spin them around, THAT's when it all started to click.

 

As an adult, knowing the steps has given me the ability to play with my medium more completely. Now, as an adult, I really value the steps, the logical progression. As a student my brain couldn't have been bothered and it was excruciating to do, but I STILL remember teachers trying to teach me the steps. It adds more to the well of reference.

 

My son is the same way. He can't tell you HOW he got the answer, but, the world, bosses, teachers, require the steps and they need to be taught how to accomplish that.

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And how would you go about deciding who gets this special treatment?

 

I was thinking that it wouldn't be special treatment but a requirement for everybody. On labs and assignments, the VSL students will probably take more time because they'll have to translate their work every time. On tests, most linear students will show their work on all of their solutions because it's how they think. It's low overhead for them with the advantage that they can receive partial credit. But, if you only require it on some test problems, then the time factor involved for the VSL student would be that much less of an issue. Of course, the VSLs can not receive partial credit when they don't show their work.

 

It's commendable that you desire to adjust your teaching so that all students have the opportunity to learn. But even in doing so, you can't insure that test results will directly reflect their abilities. Life is not fair. Sometimes you just have to get over it.

 

I do feel empathy for people who are so far to the outer ends that they cannot work on both sides of the spectrum. But, for these people, there are other paths in life. We don't all have to take the same route. Maybe the bigger problem is that we over value the institution and believe that grades are a direct reflection of how successful our children will be in life. This just isn't so. The VSL, of all people, ought to know that there's more than one way from point A to point B.

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Regentrude you may already been familiar with their work and this paper, but I just found it and found it very interesting. Here's the link:

 

http://www.google.com/search?q=visual+sequential+learners&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

 

Go to the first link and go to Learning and Teaching Styles in Engineering Education - it's a pdf file so I don't know how to link that directly.

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You have adults and you are preparing them for working in a field in which certain "rules" must be followed.no.exceptions. You might find a creative way to grade their work, but at the end of the day, if the employer needs the documentation to be x.y.z., then the adult must produce x.y.z.

Faith

 

Or else they may find themselves kicked out of university and working in the patent office?:tongue_smilie:

 

OK so I may not be the mother of Einstein but still I would think that in some fields rule breaking could be a helpful skill.

 

I am a music teacher and in my field I find grades somewhat counterproductive to the learning process. I am not saying at all that a professor should make exceptions or fail to make students accountable. But grades are grades. Good teaching is more than providing a good and fair evaluation of your students' skills. It seemed that way too much of my college teachers time and energy went into weeding out and evaluating students (in my first degree, my music teachers did a fine job). College is expensive! I am always very encouraged to see professors who are more interested in the process of education than the process of evaluation. I am not saying that evaluation doesn't have it's place, I just think that it should be subordinate to the learning process and not the ultimate goal.

 

Back to the question at hand. How do you deal with a student who seems to have the knowledge but can't communicate the information. I have a suggestion. What if you spend a small amount of your class time helping students with this skill. It is an undegrad class right? I would think this could be tremendously helpful for your students and it might save you some headache. Show the students examples of what a well written answer looks like and show them examples of what a poorly written answer looks like. Make the writing expectations clear. Also let students know that you are willing to help them in your office hours. This way a student who is motivated and needs a little extra help has an opportunity to work on this skill.

 

Really, I agree with the other posters. A child should have these skills prior to college. However, I am able to see instances where a child might not have had the opportunity to learn the great art of communicating in writing. Certainly it is their job and responsibility to learn this but as a teacher I find it an almost sacred responsibility to help my students on their path to success. So I think it is terrific that you are thinking about this. I hope you find something that works for both your students and you.

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That is a very good point, and I have given this a lot of thought over the years - because even for typical students, the question arises all the time: WHY should they be expected to follow certain procedures.

I see two goals for my students: the mastery of the subject material, AND the ability to communicate the thought process which leads to the results.

The most brilliant scientific achievement is worthless if the brilliant thinker can not communicate his ideas to other people. So, to stay with the simple example of a physics problem: I want to teach my students not just to come up with an answer, but to communicate with a person of same expertise, but no knowledge of the particular problem: to draw a figure that visualizes the problem in such a way that the other person can see what is going on, and to write out his solution in such a way that the other person is able to follow the thinking. This is AS important a learning objective as coming up with the answer - because that is what scientists and engineers will have to do during their careers.

 

That sounds perfectly reasonable to me in terms of overall aims. But my question is: does it therefore necessarily follow that a student must do both these things you mention (draw and write a step-by-step process) every single time, for every single problem, to accomplish your aims? Must the step-by-step process take only one particular form, or are there a variety of possible ways to show how they got there? I don't know physics; it's the single class I dropped as an undergrad because I simply couldn't understand it, so I'm asking out of total ignorance here, not a desire to criticize what you're doing in any way, shape, or form.

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The ones I talked to see the same issues: brilliant results are nothing without the ability to communicate. We try to teach our students along both lines: develop the conceptual thinking and "intuition" - and give them a "cooking recipe" they can use to train themselves to approach a problem in a systematic way.

All agree, however, that for instance a clearly labeled diagram is an essential part of a solution and that students are reuired to produce this, whether they need itfor themselves or not - it is part of what they have to learn.

 

I was knitting today. I just learned how a few years ago at age 39 or so, because my Mom sat down and showed me. Once she showed me (the visual learner), and I tried a few rows of knits and purls, and then went backwards in the process to learn how to cast on, I was on my way. My Mom was visiting me when she showed me, and she lives far away so she can't come over whenever I want to figure out how to make a new item. So, I've depended on books to learn more from. In a way, books are visual to me, but to follow text in a "how-to" book is not an easy task for me. Sometimes pictures help, but only if they are really step by step pictures, and I don't come across many books like that (they are probably out there, I just don't have the time to track them down). But I've decided that sometimes my desire to learn how to make, say, the panels for a stuffed ball for my sister's new babies, overrides my frustration in trying to follow text. I saw a picture of this ball in knitting book a few weeks ago, I examined the panels, and decided by the look that they were something I wanted to learn. So I sat last night and this morning with this book, my glasses, and another knitting book (that better explained some of the terms), going line by line through each instruction. I made mistake after mistake and had to keep unravelling, because even a word missing makes it all the harder for me to "process", no, translate, what I am seeing in the picture, into inferring from the text what my hands and needle are supposed to be doing to make it LOOK like the picture that I like. Believe me, I cherish a well-written, clear, step-by-step set of instructions for doing a knitting project, esp. when pictures for me to imitate are scarce. If a visual person can learn how to communicate in words what they see in pictures, they bridge communication gaps that others can cross. And vice versa - if linear person can figure out how to turn their words into pictures to explain something to someone else, the gap gets bridged. To me, it's win-win for people to apply themselves to learn how to make these bridges.

 

So anyway, as I was knitting (finally successfully, though there is still a bulge that I don't think belongs there...), I was thinking. Someone made up this panel for this ball. How did they do that? Knitting has probably been around for thousands of years. People probably took sticks and string and played around with them (visually, three-dimensionally), and found they could make useful stuff. And then I imagine they showed each other their creations. Well now we have scads of knitting instruction books on the market, and someone somewhere had to take someone's ball panel and break it down in to step by step instructions in words. I suppose it's so they could sell their books and make money from their patterns. Motivation was there to sell the patterns and books, so they made the ball panel accessible to more than just visual people. (as an aside, I also recently discovered a great craft book series that has mostly step-by-step pictures - it's very appealing to me and I've figured out how to do some things mostly by studying the series' of pictures - I can't look at just one picture and figure out how to knit something - too many details are hidden from me inside the weaving)

 

In relation to the OP here, I am thinking that if a student is in a college physics class, he/she is usually there because he *wants* to be or because he is fulfilling a requirement in a bigger picture that he wants to achieve. Also most of these students are young adults, not approx. 5-12 year olds who are all over the place in terms of reading/math/grammar/writing abilities. I would think by the time someone goes to college or university, the student does take on more of the learning responsibility himself. So if he wants to succeed in a physics class, then I would think he would apply himself to learning (if required for the class) in a fashion that may be difficult, but would yield helpful mental results in the long run. If a student cannot fulfill, for whatever reason, what is required in that class, should the student be there in the first place?

 

When I was in grade 11, I started pre-cal class, after taking Algebra I, Geometry, and Algebra II, because I was on the college-prep track and wanted to fulfill as many pre-reqs as possible. Well, I stayed after school for two hours every single day for a whole month that fall, getting extra help from the teacher. He was a good teacher, and had lots of patience with me. But in the end, nothing was making sense, and looking back I blame lack of good grounding in the previous math classes. There was no accommodation this pre-cal teacher could have made for me - if I wanted to take pre-cal, I would have had to go back and start all over again with the previous maths, and I was already in grade 11. So I dropped out and felt like such a failure. So now math scares me. I don't know if it's because I don't "think mathematically" (and yet I've learned here on the boards that math can be very visual - I had no clue!), or if it's because I wasn't taught well. I am pretty sure, though, that if I really wanted to apply myself, I could conquer math bit by bit. I sometimes think about going to nursing school when I'm done homeschooling - yet I know I'd have to face the math monster first. I just think that by the time we are young adults, we should be willing and equipped to take on whatever requirements are presented to us in things that we want to achieve, even if they are difficult and go against our wiring. For my kids, I consciously try to shore up difficulties as well as play up their strengths.

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That sounds perfectly reasonable to me in terms of overall aims. But my question is: does it therefore necessarily follow that a student must do both these things you mention (draw and write a step-by-step process) every single time, for every single problem, to accomplish your aims?

 

I can't speak for physics but it is certainly true for math. If you say "I have this great proof but I can't fit it in the margins", the validity of your proof might be called into question. I think the question is not if a student should be expected to communicate their thinking in detail every time, but when we should expect them to do this. Clearly, as in my mathematical example, even world famous mathematicians don't always write out their thoughts. But I think this falls into the "nobody's perfect" category. Clear communication is something we should be striving for. That said, I know I have to adjust my expectations for the reality of my child (That umm thingamabober, you know...nevermind type kid.)

 

I think the key word is student. Students are by definition learners and not final products. The goal is clear communication every time but students by definition have something to learn and as you stretch your mind to increasingly challenging concepts, communication becomes proportionately more challenging. And, as many of us know, some kids are able to tease out their thoughts and articulate them more easily than others.

 

I keep answering questions that are not directed at me. Sorry about that. I am just loving this discussion and I think I am missing my child who is away at math camp.

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I have not read through the other responses, so, apologies if this is a repeat! irst, how awesome you would even consider trying to work with these students! Would it be possible to allow one (or all) of the following -- if you were, in advance, able to give detailed examples in class of what you would want and what is acceptable AND it is an acceptable option for all students in the class:

 

- detailed flow chart

- list of key words/concepts rather than complete sentences

- draw/illustrate with detailed captions

- mind map

(here is HOW to mind map; sadly, you must sit through an ad at the start; here is a how-to article and a video)

- a form of visual notetaking

(see this blog, and this video, embedded in the website)

 

 

Also, what about encouraging these students to seek out the university's special needs department, where they can hire a notetaker or a test taker -- some students might be able to *dictate* the steps to the problem, when, due to a "short circuit" in the brain, writing out the steps is almost impossible for them. In these cases, the guidelines for using a test taker (someone who writes out your answers for you) is carefully laid out and the process is monitored by the university special needs dept.

 

Warmest regards, Lori D.

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I can't speak for physics but it is certainly true for math...

 

I think the key word is student. Students are by definition learners and not final products. The goal is clear communication every time but students by definition have something to learn and as you stretch your mind to increasingly challenging concepts, communication becomes proportionately more challenging.

 

So would you then insist that a student of any age, at any stage of learning, should be expected to write down a step-by-step working out of a problem (I'm thinking of algebra here), every single time? I decided not to require this of dd as long as she could show me in a couple of problems of her choice that she could do it if need be, and as long as her final answers were correct, which they usually were. I'm not alone in this; I'm so insecure sometimes that I search like a madwoman all over the internet and in the heaps of books on cognition and learning I've got at home to see whether someone else has a solution that fits for dd or if anyone else has come to use the approach I'm thinking about with other kids.

 

With geometry, she wrote proofs out (flow-chart style) if required; a few times I'd find solutions worked in (some) explicit steps; for other problems there would just be the answer or final diagram sitting there on the page, and I would ask her to tell me what she did. Sometimes she could explain it, sometimes not. But by golly, it was almost always correct.

 

It sounds as though you're saying there is no point at which this kind of thing would work, for you as a teacher, and that "communicating" or proving an answer for both you and regentrude must take a particular specified form, each and every time, in every grade level? Please read my tone here as entirely neutral; I'm just wondering.

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Hello Regentrude,

 

First, thanks so much for sharing your ideas. My son made an unexpected switch between high school and college when he decided to pursue a STEM major. I send him links to many of your posts. He's making a successful transition, but it's a lot of work...as in harder and more time consuming than he expected. ;)

 

Getting this child to document his work was a struggle in high school, but with a lot of work he was able to learn how to do so. I'm mystified at why you'd be seeing students who don't seem to be motivated by the possibility of partial credit. Were these students not previously required to show work? After seeing some of the exchanges in the original thread, I don't want to get mired in quarreling about adjusting teaching styles to learning styles, though.

 

My take as a former instructor (but not in a STEM field) is that you might ask students if they know how to document their thinking processes, but are failing to do so. If that's the case perhaps you explain the importance of being able to communicate their thought processes with others and give them a few examples of what you expect. If they have never been taught or find the process difficult perhaps they need to make more use of the tutoring center?

 

There are several people in my extended family who were blessed with keen intellects but who are unable or unwilling to get past their unique ways of processing information and often fail at some level to communicate with others. That can be very isolating. I'll apologize in advance if this comes across as overly harsh, but IMO, most people are capable of learning to adjust their work in a way that facilitates interacting with others. Many are unwilling to make the effort. For those who simply cannot, the outcomes I've seen over the years tend to fall into two groups; I've know people who become increasingly frustrated, alienated, and isolated and I've know a few who manage to find a niche in which they can function effectively. Either way, it's a difficult, often lonely path.

 

I'm not against nurturing and celebrating "neurodiversity", just musing about the implications. YMMV.

 

Martha

 

ETA: My son is one of those people who finds in necessary to translate his way of thinking into a more typical format, and as a pp has noted that does take time. He benefits from classes where there is no strict time limit on exams, and he doesn't need a lot of extra time usually an extra 20-30 minutes. During his high school days I'd compare his standardized test scores when allowing him to work an extra 10 minutes vs. cutting work off at an arbitrary time limit. It made a huge difference. He's capable of doing excellent work, but what is difficult is doing it within strictly timed parameters.

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Sometimes she could explain it, sometimes not. But by golly, it was almost always correct.

 

"Correct" is good and important - how important to you is her learning to communicate the process so that others receive her communication in a way that makes her understood? Do you want her to be understood by others who aren't wired the same way?

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My experience comes from teaching post-secondary mathematics.

 

High school math teachers might insist on students documenting a thought process in a particular way, but college level math is another thing entirely. Students must conform to standard notation--but it is the notation which is liberating for non-linear thinkers.

 

College students are often obsessed with fairness. They want to be judged by the same rubric as their classmates which is why some students who are allowed accommodation choose not to use it.

 

One of the methods that I used for evaluating students in courses like Calculus or Differential Eqns was to give "choice" sections on tests with an assortment of problems that would appeal to different kinds of thinkers. This would include something visual, something theoretical, application problems for the pragmatic. Granted, students had to choose 2 of 3 problems, but they were empowered with options for demonstrating to me that they had understood the material.

 

I love pictures and cannot teach mathematics without them. I encourage my students to sketch, to give a flowchart, to make marginal notatations---anything to demonstrate their ideas.

 

Now the Off Topic Editorial:

It is easy for many students not to show work in Algebra I. The problem comes later. It is very difficult for the average Calculus student to succeed without showing work within the layers of their multistep problems. I believe that learning to write mathematics well is a skill many highschoolers today do not learn, especially in this era of standardized testing.

 

Frankly many people who do math well think "differently". It is actually a pretty good field for out of the box thinkers.

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My take as a former instructor (but not in a STEM field) is that you might ask students if they know how to document their thinking processes, but are failing to do so. If that's the case perhaps you explain the importance of being able to communicate their thought processes with others and give them a few examples of what you expect. If they have never been taught or find the process difficult perhaps they need to make more use of the tutoring center?

I think for some people the problem isn't that they haven't been taught to write properly, but that there is an inherent difficulty in documenting a thought process that looks like a cloud of fuzzy concepts that suddenly forms into a whole, complete answer, often in a way that is not even accessible to the conscious mind. It's really not the same thing at all as a child who thinks sequentially but is perhaps not good at describing those steps in words. How can a student "document the steps" in his thought process if there were no steps? Often the best they can do is start from the answer and try to work backwards, which can be very time-consuming. Drawing the answer and then trying to describe the drawing or diagram in words is another approach, but for a non-sequential person, understanding what order to put the steps in can be problematic because for them the solution was simultaneous.

 

Jackie

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"Correct" is good and important - how important to you is her learning to communicate the process so that others receive her communication in a way that makes her understood? Do you want her to be understood by others who aren't wired the same way?

How often do you include algebra steps or geometry proofs in your letters, emails, and conversations?

 

If writing it out is not necessary for Karen's DD to understand it; if she has written steps/proofs and therefore demonstrated that she's not incapable of it; if she's not in an institutional situation where she needs to show her work in order to earn "partial credit;" then how does not writing out every step for every algebra problem interfere with her learning to communicate with others?

 

Jackie

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So would you then insist that a student of any age, at any stage of learning, should be expected to write down a step-by-step working out of a problem (I'm thinking of algebra here), every single time?

 

Absolutely not. As a matter of fact I was saying quite the contrary, that even master mathematicians sometimes goof up and don't write things down in detail. However as you get more advanced, I think it becomes more important.

 

My son does not write down each step of an algebra problem BTW. Or at least he doesn't write down someone else's version of what the steps are. I think he does write down enough that someone can follow his logic. But whether or not a student develops this skill at the algebra level is unimportant. I just think they should develop this skill....eventually.

 

It sounds as though you're saying there is no point at which this kind of thing would work, for you as a teacher, and that "communicating" or proving an answer for both you and regentrude must take a particular specified form, each and every time, in every grade level? Please read my tone here as entirely neutral; I'm just wondering.

 

Again, I think you misunderstood. I am 100% with you. At least in the early years.

 

When my son was a totling we did math almost exclusively on walks. Putting anything on paper was excruciatingly difficult. I was not going to limit him by making him write things down when clearly he loved doing it in his head and on paper it was misery.

 

Getting him to write down just answers was huge. Forget about the steps, sheesh.

 

Even just getting him to articulate his thought process verbally is a challenge (still). We go on walks and I ask him questions. He wants me to understand his thinking so he has motivation, but it takes effort on his part and on mine. It's a work in process. We talk and he learns how to tell someone what he is thinking.

 

What really worked for him, as far as writing goes, was AOPS. He took just one class but it was a lightbulb for him. He all of a sudden was motivated to communicate his thoughts on paper. His mathematical writing is not mature but he is excited about showing his work and his steps in a way that he would have NEVER been had I forced it along the way.

 

Interestingly enough skill in math writing translated to increase writing skills in all content areas. Weird but true.

 

I am not saying that their is a magic grade or a magic math program that will miraculously help your child communicate. I am also not saying that this is the only goal. As a matter of fact there was a long time where I put off helping my son develop this skill because in my opinion he wasn't ready yet. I think forcing this inappropriately would indeed have harmed his soul or however it was put before. But in spite of this I still think that communication is a handy tool to have in your box, so I like to help him with this as I can and when he is ready.

 

I think I see why you misunderstood. I said "the goal is clear communication every time." by this I meant the ultimate goal. I am talking about long term objectives. Even with these objectives in mind I am not convinced that students always have to be working towards them. I suppose I should be working towards that goal too.:lol:

 

I am a music teacher so in my classes communication is everything. I am not going to have a student draw a picture of their interpretation of a Mozart concerto, that would just be silly. University physics is kind of out of my realm. I do have a math background and in university math it's all about proof which is a very formulaic method of getting your thoughts explicitly on paper. But it is WAY different than writing steps to an algebra problem. There are always different ways of going about a proof but some of these ways are considered better than others. It is it's own weird little language cult and it has it's own rules. Do we need to indoctrinate our children into this? I would say it depends on what their goals are (and perhaps your goals for your child). Certainly not every child needs to be able to write mathematical proofs. But if they are going to be a mathematician that might be a good thing to work on.

 

I hope I was a bit less unclear this time. I am having a jumbled day.

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If writing it out is not necessary for Karen's DD to understand it; if she has written some proofs and therefore demonstrated that she's not incapable of it; if she's not in an institutional situation where she needs to show her work in order to earn "partial credit;" then how does not writing out every proof for every algebra problem interfere with her learning to communicate with others?

Jackie

 

I don't see any reason to make students write out all their work in algebra.

 

Writing proofs though is a different process. It's the art of making an argument. It's not documenting your thoughts really it is using theorems to prove that something is correct. It's more like what a lawyer does. It is a cool thing to be able to do. I don't think it is essential that everyone learn this skill but it is not necessarily a skill that sequential thinkers are better at. As a matter of fact I think most really great mathematicians are non sequential thinkers. So I wouldn't encourage a kid to not get into heavy math just because they are not good at showing their work in algebra and I don't necessarily think algebra is the best platform to teach mathematical writing. It's more something you would need in logic or geometry. I wouldn't worry about a kid not showing work in an algebra class.

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Now the Off Topic Editorial:

It is easy for many students not to show work in Algebra I. The problem comes later. It is very difficult for the average Calculus student to succeed without showing work within the layers of their multistep problems. I believe that learning to write mathematics well is a skill many highschoolers today do not learn, especially in this era of standardized testing.

 

Frankly many people who do math well think "differently". It is actually a pretty good field for out of the box thinkers.

 

YES.

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How often do you include algebra proofs in your letters, emails, and conversations?

 

If writing it out is not necessary for Karen's DD to understand it; if she has written some proofs and therefore demonstrated that she's not incapable of it; if she's not in an institutional situation where she needs to show her work in order to earn "partial credit;" then how does not writing out every proof for every algebra problem interfere with her learning to communicate with others?

 

Jackie

 

Hold on--Are you suggesting by your first question that if one does not use things in everyday life, they are not valuable?

 

I will argue with your use of the word "proof" in your response. Most high school algebra courses have little in the way of proof. There are usually lists of problems in which students practice technique and apply knowledge. If a student has mastered the material, it probably is unnecessary to do every single problem. But here is the challenge: mathematics builds. So let's say that a student factors cubic equations in his head. In Calculus, it is one thing to take a derivative, it is another thing to find the critical points of a function. Suppose the student correctly takes the derivative, then incorrectly factors the resulting cubic (for example). All subsequent work is incorrect. If I know the nature of a student's mistake (algebraic), I am inclined to give some partial credit for the Calculus work performed. But if it looks like the numbers came out of thin air, the student has failed to communicate.

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Hold on--Are you suggesting by your first question that if one does not use things in everyday life, they are not valuable?

No, no, not at all! Colleen replied to Karen's post about not making her daughter write out all the steps of algebra problems by asking Karen if she wants her DD to be able to communicate with others and "to be understood by others who aren't wired the same way?" The point I was trying to make is that not making her write out all the steps for every algebra problem is not going to impair her ability to communicate with others in real life. Karen's DD is actually extremely verbally gifted; she is an excellent writer. I have no doubt that she can write letters and emails and essays just fine whether she's been forced to write out the steps to every algebra problem or not.

 

I will argue with your use of the word "proof" in your response. Most high school algebra courses have little in the way of proof.
I don't see any reason to make students write out all their work in algebra.

Writing proofs though is a different process...

My mistake... Karen was talking about algebra steps and geometry proofs and I was typing quickly in an uncaffeinated state, while kids were begging to go rock climbing, and I mushed them together. I'll correct that.

 

Jackie

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One of the methods that I used for evaluating students in courses like Calculus or Differential Eqns was to give "choice" sections on tests with an assortment of problems that would appeal to different kinds of thinkers. This would include something visual, something theoretical, application problems for the pragmatic. Granted, students had to choose 2 of 3 problems, but they were empowered with options for demonstrating to me that they had understood the material.

I think this is brilliant, and could be applied to many different subjects.

 

Jackie

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I think this is brilliant, and could be applied to many different subjects.

 

Jackie

 

Thank you. Truly, I am not the hardliner that I am sometimes painted to be. I want the best for my students--not sure that I was able to implement the best for my son given my own limitations. Nonetheless, he carries on admirably well.

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Sometimes she could explain it, sometimes not. But by golly, it was almost always correct.

 

"Correct" is good and important - how important to you is her learning to communicate the process so that others receive her communication in a way that makes her understood? Do you want her to be understood by others who aren't wired the same way?

 

How often do you include algebra steps or geometry proofs in your letters, emails, and conversations?

 

Hold on--Are you suggesting by your first question that if one does not use things in everyday life, they are not valuable?

 

No, no, not at all! Colleen replied to Karen's post about not making her daughter write out all the steps of algebra problems by asking Karen if she wants her DD to be able to communicate with others and "to be understood by others who aren't wired the same way?" The point I was trying to make is that not making her write out all the steps for every algebra problem is not going to impair her ability to communicate with others in real life.

 

And my point was not about writing out every step for every math problem. I never said that. In my comment, I was setting aside math for the moment, to look at a bigger picture of communication (as well as asking for some clarification again - I'm still having a hard time understanding KarenAnne's points, and feeling quite dense because of it). My point was, correct answer aside, is it a concern that though dd gets a correct answer, that she sometimes cannot explain it. I ask because to me, being able to explain your (for example, math) answer translates over into other areas. Of course I don't write out math problems in letters, etc.. But the same skill of thinking-then-communicating-to-a-differently-wired-person is highly transferable. I could even play the devil's advocate and say that it's more important than being useful for that higher level Calculus Jane was talking about! :D But she might clunk me over the head. :D

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My point was, correct answer aside, is it a concern that though dd gets a correct answer, that she sometimes cannot explain it. I ask because to me, being able to explain your (for example, math) answer translates over into other areas. Of course I don't write out math problems in letters, etc.. But the same skill of thinking-then-communicating-to-a-differently-wired-person is highly transferable.

Many VSLs arrive at math solutions in a sort of instantaneous way, without going through the steps that other people do. So making them write it out in steps — which is not how they solved the problem — isn't really teaching them to "communicate their thoughts to others." It's basically teaching them to reconstruct something that didn't happen, for the benefit of someone else. Karen's DD is verbally gifted, and an excellent writer; the fact that she can't easily describe steps she never took doesn't mean she isn't able to communicate normally with other humans.

 

Jackie

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Many VSLs arrive at math solutions in a sort of instantaneous way, without going through the steps that other people do. So making them write it out in steps — which is not how they solved the problem — isn't really teaching them to "communicate their thoughts to others." It's basically teaching them to reconstruct something that didn't happen, for the benefit of someone else.

 

This sounds sort of miraculous or something. Will you explain with words (notice I'm not asking for "steps"), since it's hard to draw pictures here, and since many humans communicate via words, how this happens? I'm wondering if this will help regentrude with the problem she described in her OP. But I'm also thinking that if it can't be explained, she won't be able to help those students.

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Many VSLs arrive at math solutions in a sort of instantaneous way, without going through the steps that other people do. So making them write it out in steps — which is not how they solved the problem — isn't really teaching them to "communicate their thoughts to others." It's basically teaching them to reconstruct something that didn't happen, for the benefit of someone else. Karen's DD is verbally gifted, and an excellent writer; the fact that she can't easily describe steps she never took doesn't mean she isn't able to communicate normally with other humans.

 

Jackie

 

As an extension of what you're saying, Jackie: There are a whole lot of VSL thinkers out there, in families, workplaces, schools. Do logical-sequential thinkers/communicators have ANY kind of reciprocal responsibility to learn how to "communicate their thoughts to others" in a way that those others -- for instance, VSLs -- can comprehend? If not, why not?

 

And note, with dd I'm not concerned that she can't perform in the standard way if required to do so; I've SAID she can do it, and does so regularly -- just not with every problem.

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There are a whole lot of VSL thinkers out there, in families, workplaces, schools. Do logical-sequential thinkers/communicators have ANY kind of reciprocal responsibility to learn how to "communicate their thoughts to others" in a way that those others -- for instance, VSLs -- can comprehend?

 

YES! I believe all humans are responsible to do our best with communicating so that others can understand! It won't always work perfectly, but I believe we should try with those we interact with. I believe this because I think humanity is all about relationships. It's just that there are, in some situations that cannot be easily changed (I'm thinking of regentrude's dilemma in her OP as an example), sometimes adaptations have to be made. For another example, there are people groups around the world who communicate in a whole different way I sure do not understand (I'm thinking of...can't remember what they are called....a people group in Africa, who communicate through mouth clicks). Yet if I wanted to go live and work among them, I'd have to adapt. Yikes! :D

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This sounds sort of miraculous or something. Will you explain with words (notice I'm not asking for "steps"), since it's hard to draw pictures here, and since many humans communicate via words, how this happens? I'm wondering if this will help regentrude with the problem she described in her OP. But I'm also thinking that if it can't be explained, she won't be able to help those students.

 

You're floating in the pool, watching the swallows in their evening dogfight, and out of left field, the answer is there in your head.

 

Yup, it's magic. I'm not being sarcastic.

 

You have to learn to trust your intuition enough to let it work. You turn the problem over and over in your head like a mixed up rubic's cube, you toss it around, you look at it from each angle, you let your brain show you the possibilities, and then, you let it go. You stop thinking about it, so your subconscious can do its magic. Then a few minutes, days, weeks, months later, there it is, the answer, fully formed in your head.

 

I think all of us have the possibility of those moments (I'm assuming we all do?). I think VSLs breathe the process.

 

Which is why you can't write it out. You have nothing but air to write out. BUT, I think learning to write it out is an extremely valuable process, and one that we owe the public. Because someone, from that point, can pick it up and take it forward. Can expound on it. Can use it in a way the originator wasn't thinking of, aware of, and apply it to a different problem.

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