Meyer's latest post has my current favorite title -
http://blog.mrmeyer.com/2015/if-math-is-the-aspirin-then-how-do-you-create-the-headache/#comments As usual the comments are worth reading too! Richard |
But Dan thinks that math is the headache, so his title is quite
contradictory. Bob Hansen On 6/18/15, 6:02 AM, "Richard Strausz" <[hidden email]> wrote: >Meyer's latest post has my current favorite title - > >http://blog.mrmeyer.com/2015/if-math-is-the-aspirin-then-how-do-you-create >-the-headache/#comments > >As usual the comments are worth reading too! > >Richard |
In reply to this post by Richard Strausz
Concerning your post #9322 below, aside from your Meyer 'joke', why not play along? Do you buy his motivational premise? If so, what would happen in your classroom to motivate the students?
Richard > But Dan thinks that math is the headache, so his > title is quite contradictory. > > Bob Hansen > > > On 6/18/15, 6:02 AM, "Richard Strausz" > <[hidden email]> wrote: > > >Meyer's latest post has my current favorite title - > > > >http://blog.mrmeyer.com/2015/if-math-is-the-aspirin-t > hen-how-do-you-create > >-the-headache/#comments > > > >As usual the comments are worth reading too! > > > >Richard |
In reply to this post by Richard Strausz
I honestly do not believe it is possible for Robert to even entertain doing what you suggest, Richard, let alone do it. "Playing along" would mean, in his universe, cooperating with a fraud. He has checked and concluded that Dan Meyer is a fraud. Once so branded, all that Mr. Meyer does, says, thinks, writes, advocates, etc. is fraudulent. "Playing along" even for a second would be to deny the absolute nature of the RHJ (Robert Hansen Judgment™).
Instead, despite the black & white evidence to the contrary, Robert must declare what he claims Dan Meyer believes to trump anything and everything else. Who cares what the rest of the world sees or what Meyer actually says, does, believes? An RHJ cannot be superseded. Period. Richard Strausz wrote: > Concerning your post #9322 below, aside from your > Meyer 'joke', why not play along? Do you buy his > motivational premise? If so, what would happen in > your classroom to motivate the students? > > Richard > > > But Dan thinks that math is the headache, so his > > title is quite contradictory. > > > > Bob Hansen > > > > > > On 6/18/15, 6:02 AM, "Richard Strausz" > > <[hidden email]> wrote: > > > > >Meyer's latest post has my current favorite title > - > > > > > > >http://blog.mrmeyer.com/2015/if-math-is-the-aspirin-t > > hen-how-do-you-create > > >-the-headache/#comments > > > > > >As usual the comments are worth reading too! > > > > > >Richard |
In reply to this post by Richard Strausz
I’ll answer this when I get home, but I know my answer won’t have
avoidance in it. Bob Hansen On 6/18/15, 9:19 AM, "Richard Strausz" <[hidden email]> wrote: >Concerning your post #9322 below, aside from your Meyer 'joke', why not >play along? Do you buy his motivational premise? If so, what would happen >in your classroom to motivate the students? |
In reply to this post by Richard Strausz
> I’ll answer this when I get home, but I know my
> answer won’t have > avoidance in it. > > Bob Hansen > > On 6/18/15, 9:19 AM, "Richard Strausz" > <[hidden email]> wrote: > > >Concerning your post #9322 below, aside from your > Meyer 'joke', why not > >play along? Do you buy his motivational premise? If > so, what would happen > >in your classroom to motivate the students? There are now over 70 responses to Meyer's question. #58 duplicated below is one that particularly caught my eye. It definitely could be presented in a low-tech way. ====== #58 Tim Hatman "There are a lot of people commenting on the theoretical side of this post but not a lot (at least in the first half of the comments that I actually read) who are actually taking on your challenge of finding the headache. No offense to those who wrote it, but “math for math’s sake” and “it’s a puzzle” are only going to work as headaches for those that already love math and completely defeat the purpose of the finding a headache – a perplexing problem that makes EVERY students want a shortcut. So here’s my headache. Graph y=(x^2+7x+10)/(x+5) Without factoring, the only way to graph this is to just start plugging in x’s and making a table – that’s a headache! But when you start plotting the points…Whaaaaaaaat?!? It’s a straight line! How did that happen? What’s the equation of that line (why is one point missing) and how can I get there through a shortcut? In my opinion, this works better than solving 0=x^2+7x+10 because students often have other methods of solving this before they get to factoring. Needing one more method to solve a quadratic is not really a headache." ==== Richard |
On Tue, 23 Jun 2015 07:53:54 -0600, Richard Strausz
<[hidden email]> wrote: > So here’s my headache. Graph y=(x^2+7x+10)/(x+5) And why, pray, would one want that graph? Seems to me you've replaced one unmotivated problem with another. - --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver <http://rowdy.msudenver.edu/~talmanl> |
In reply to this post by Richard Strausz
At 06:53 AM 6/23/2015, Richard Strausz wrote:
>There are now over 70 responses to Meyer's >question. #58 duplicated below is one that >particularly caught my eye. It definitely could be presented in a low-tech way. For any student who needs rational polynomial functions, that student also needs a standard mathematics approach to the subject dramatically, not its avoidance. Avoiding the glaringly obvious factoring simplification as the first step is educational malpractice. Wayne >====== >#58 Tim Hatman > >"There are a lot of people commenting on the >theoretical side of this post but not a lot (at >least in the first half of the comments that I >actually read) who are actually taking on your >challenge of finding the headache. No offense to >those who wrote it, but âmath for mathâs >sakeâ and âitâs a puzzleâ are only going >to work as headaches for those that already love >math and completely defeat the purpose of the >finding a headache a perplexing problem that >makes EVERY students want a shortcut. >So hereâs my headache. Graph y=(x^2+7x+10)/(x+5) >Without factoring, the only way to graph this is >to just start plugging in xâs and making a >table thatâs a headache! But when you start >plotting the points Whaaaaaaaat?!? Itâs a >straight line! How did that happen? Whatâs the >equation of that line (why is one point missing) >and how can I get there through a shortcut? >? > >In my opinion, this works better than solving >0=x^2+7x+10 because students often have other >methods of solving this before they get to >factoring. Needing one more method to solve a >quadratic is not really a headache." >==== >Richard |
In reply to this post by Richard Strausz
> On Tue, 23 Jun 2015 07:53:54 -0600, Richard Strausz
> <[hidden email]> wrote: > > > So here’s my headache. Graph y=(x^2+7x+10)/(x+5) > > And why, pray, would one want that graph? > > Seems to me you've replaced one unmotivated problem > with another. > > - --Louis A. Talman > Department of Mathematical and Computer Sciences > Metropolitan State University of Denver > > <http://rowdy.msudenver.edu/~talmanl> What caught my eye - and I think might be a hook for more students than 'hey, gang, let's see how to factor this fun quadratic' - is the surprise element. Very few students will anticipate that it will linear. Richard |
Such students don't then even understand "linear" to be perplexed by it. Tim's is theory (which I have studied before) is silly.
If it weren't, then these teachers would be bragging about and showing us all the factoring their students are now doing, rather than offering us endless excuses for pretending to teach math. Bob Hansen > On Jun 23, 2015, at 12:01 PM, Richard Strausz <[hidden email]> wrote: > > Very few students will anticipate that it will linear. |
In reply to this post by Richard Strausz
> On Jun 18, 2015, at 9:45 AM, Richard Strausz <[hidden email]> wrote: > > Do you buy his motivational premise? No, I don't think you can motivate an art by using purpose. What headache is music the aspirin for? However, if practical procedures intersect with another interest then that is a motivation, but not for the art. For example, an interest in electronics might motivate me to learn and apply formulas, but not necessarily learn how they came to be. The higher you go in math though (half way through algebra) without the art, there is nothing for the rest of it to stick to. > If so, what would happen in your classroom to motivate the students? I would use use cases, both practical and mathematical. Drawing faces in Desmos is neither. Bob Hansen |
In reply to this post by Richard Strausz
> At 06:53 AM 6/23/2015, Richard Strausz wrote:
> > >There are now over 70 responses to Meyer's > >question. #58 duplicated below is one that > >particularly caught my eye. It definitely could be > presented in a low-tech way. > [Wayne replied (without having read the original prompt from Meyer] > For any student who needs rational polynomial > functions, that student also needs a standard > mathematics approach to the subject dramatically, not > its avoidance. > > Avoiding the glaringly obvious factoring > simplification as the first step is educational > malpractice. > > Wayne > When you read Meyer's post you will see that your response doesn't fit. Richard > >====== > >#58 Tim Hatman > > > >"There are a lot of people commenting on the > >theoretical side of this post but not a lot (at > >least in the first half of the comments that I > >actually read) who are actually taking on your > >challenge of finding the headache. No offense to > >those who wrote it, but âmath for mathâs > >sakeâ and âitâs a puzzleâ are only going > >to work as headaches for those that already love > >math and completely defeat the purpose of the > >finding a headache a perplexing problem that > >makes EVERY students want a shortcut. > >So hereâs my headache. Graph y=(x^2+7x+10)/(x+5) > >Without factoring, the only way to graph this is > >to just start plugging in xâs and making a > >table thatâs a headache! But when you start > >plotting the points Whaaaaaaaat?!? Itâs a > >straight line! How did that happen? Whatâs the > >equation of that line (why is one point missing) > >and how can I get there through a shortcut? > >? > > > >In my opinion, this works better than solving > >0=x^2+7x+10 because students often have other > >methods of solving this before they get to > >factoring. Needing one more method to solve a > >quadratic is not really a headache." > >==== > >Richard |
In reply to this post by Richard Strausz
Richard Strausz posted:
http://mathforum.org/kb/message.jspa?messageID=9803205 >> There are now over 70 responses to Meyer's question. #58 duplicated below >> is one that particularly caught my eye. It definitely could be presented >> in a low-tech way. >> ====== >> #58 Tim Hatman >> >> There are a lot of people commenting on the theoretical side of this post >> but not a lot (at least in the first half of the comments that I actually >> read) who are actually taking on your challenge of finding the headache. >> No offense to those who wrote it, but "math for math's sake" and "it's a puzzle" >> are only going to work as headaches for those that already love math and >> completely defeat the purpose of the finding a headache -- a perplexing >> problem that makes EVERY students want a shortcut. >> >> So here's my headache. Graph y=(x^2+7x+10)/(x+5) >> Without factoring, the only way to graph this is to just start plugging >> in x's and making a table -- that’s a headache! But when you start plotting >> the points...Whaaaaaaaat?!? It's a straight line! How did that happen? >> What's the equation of that line (why is one point missing) and how can >> I get there through a shortcut? >> >> In my opinion, this works better than solving 0=x^2+7x+10 because students >> often have other methods of solving this before they get to factoring. >> Needing one more method to solve a quadratic is not really a headache. >> ==== Wayne Bishop wrote: http://mathforum.org/kb/message.jspa?messageID=9803289 > For any student who needs rational polynomial > functions, that student also needs a standard > mathematics approach to the subject dramatically, not its avoidance. > > Avoiding the glaringly obvious factoring > simplification as the first step is educational malpractice. Of course, anyone past the first day of graphing rational functions should as a matter of course discover this before beginning to plot points, since the first step is to identify the relevant stuff such as x-intercepts, y-intercepts, vertical asymptotes, etc. In fact, the first step should be to factor the numerator and denominator (or use the quadratic formula to force out the roots if not "nicely factorable"), which makes the formation of a sign chart straightforward. However, I think this could work well in class beginning to look at graphs of rational functions as "an opener" to the topic, which is essentially what Richard is saying in his reply to Louis Talman (URL just below). http://mathforum.org/kb/message.jspa?messageID=9803309 You can find a more concealed issue like this in most any of the more comprehensive analytic geometry texts published between the late 1800s and the mid 1900s, such as the following example on p. 254 of Osgood/Graustein's "Plane and Solid Analytic Geometry" (1921), which is freely available on the internet at https://archive.org/details/planesolidanalyt00osgoiala The graph of 8x^2 + 24xy + 18y^2 - 14x - 21y + 3 = 0 happens to be a pair of parallel lines. One way to see this is to look carefully at it with your "algebra glasses". First, notice that the non-linear terms would form a perfect square if their coefficients were half of what they are . . . 8x^2 + 24xy + 18y^2 = 2(4x^2 + 12xy + 9y^2) = 2(2x + 3y)^2 And lo and behold (for those with sufficiently developed number sense), we see 2x + 3y pop up elsewhere ... -14x - 21y = -7(2x + 3y). So the equation becomes 2(2x + 3y)^2 - 7(2x + 3y) + 3 = 0, which immediately tells us that the (x,y) solutions take the form of 2x + 3y equal to either of two real constants, equal to exactly one real constant, or no solution. Incidentally, this example isn't all that artificial, as it represents an example of a degenerate conic situation. Also, such examples are easy to create, since all you have to do is expand the product of a couple of random linear factors, such as (3x - y + 2)(2x + y - 3) = 0 Dave L. Renfro |
In reply to this post by Richard Strausz
Bob, concerning your post #9335 below, it would be helpful to a skeptic like me if you would give *one* specific example that you would use to motivate a typical 8th or 9th grade student to learn the topic.
Richard > > > On Jun 18, 2015, at 9:45 AM, Richard Strausz > <[hidden email]> wrote: > > > > Do you buy his motivational premise? > > No, I don't think you can motivate an art by using > purpose. What headache is music the aspirin for? > > However, if practical procedures intersect with > another interest then that is a motivation, but not > for the art. For example, an interest in electronics > might motivate me to learn and apply formulas, but > not necessarily learn how they came to be. The higher > you go in math though (half way through algebra) > without the art, there is nothing for the rest of it > to stick to. > > > > If so, what would happen in your classroom to > motivate the students? > > I would use use cases, both practical and > mathematical. > > Drawing faces in Desmos is neither. > > Bob Hansen |
In reply to this post by Richard Strausz
Dave L. Renfro wrote (in part):
http://mathforum.org/kb/message.jspa?messageID=9803389 > Incidentally, this example isn't all that artificial, as it represents > an example of a degenerate conic situation. Also, such examples are > easy to create, since all you have to do is expand the product of a > couple of random linear factors, such as > > (3x - y + 2)(2x + y - 3) = 0 Oops ... if we want it to actually represent a degenerate conic, we need the homogeneous linear stuff in each factor to be the same, such as (3x - y + 2)(3x - y - 3) = 0 or (2x + y + 2)(2x + y - 3) = 0 Also, I meant to preface all this with something like "since conics has been a recent topic here ..." and forgot. (See [1] and the posts below it in the same thread.) However, I doubt that "math coach" has done much of what used to pass for conics. [1] http://mathforum.org/kb/message.jspa?messageID=9797540 Dave L. Renfro |
In reply to this post by Dave L. Renfro
And no part of that math brain of yours ever wonders when does the "opener" finally end and the "topic" finally begin?
I don't think that is what Richard is saying to Lou, or we would have seen the topic, at least 10 years ago. This isn't math avoidance by matter of conjecture. It is math avoidance by matter of fact. Who shows so many openers and no topic? Maybe he will show you the topic. None of us have been able to get it from him. Bob Hansen > On Jun 23, 2015, at 1:33 PM, Dave L. Renfro <[hidden email]> wrote: > > However, I think this could work well in class beginning to look at graphs > of rational functions as "an opener" to the topic, which is essentially > what Richard is saying in his reply to Louis Talman (URL just below). |
In reply to this post by Richard Strausz
> On Jun 23, 2015, at 2:15 PM, Richard Strausz <[hidden email]> wrote: > > Bob, concerning your post #9335 below, it would be helpful to a skeptic like me if you would give *one* specific example that you would use to motivate a typical 8th or 9th grade student to learn the topic. The quadratic rational expression thingy isn't a topic, it is a facet, and the only way the student is going to experience this interesting facet is if they are prepared. Thus, either - A. They are prepared and we jump right into this new (to them) and interesting dimension of expressions, which might include a graph or two or even three. But the only thing that makes it interesting is WHY and that means algebra and in this example that means polynomial arithmetic, which includes factoring. Without the algebra, it isn't interesting at all. In that context, even I would rather be drawing faces. B. They are not prepared and we start at the beginning. Everything else is fraud. Bob Hansen |
In reply to this post by Richard Strausz
Bob, concerning your post #9337 below, there are now 2 things you should avoid if you ever would apply for a teaching job.
1. How you made your son cry. 2. This answer to the question of motivation. Richard > > On Jun 23, 2015, at 2:15 PM, Richard Strausz > <[hidden email]> wrote: > > > > Bob, concerning your post #9335 below, it would be > helpful to a skeptic like me if you would give *one* > specific example that you would use to motivate a > typical 8th or 9th grade student to learn the topic. > [Bob's reply] > The quadratic rational expression thingy isn't a > topic, it is a facet, and the only way the student is > going to experience this interesting facet is if they > are prepared. Thus, either - > > A. They are prepared and we jump right into this new > (to them) and interesting dimension of expressions, > which might include a graph or two or even three. But > the only thing that makes it interesting is WHY and > that means algebra and in this example that means > polynomial arithmetic, which includes factoring. > Without the algebra, it isn't interesting at all. In > that context, even I would rather be drawing faces. > > B. They are not prepared and we start at the > beginning. > > Everything else is fraud. > > Bob Hansen Richard |
On 6/23/15, 4:14 PM, "[hidden email] on behalf of Richard
Strausz" <[hidden email] on behalf of [hidden email]> wrote: >Bob, concerning your post #9337 below, there are now 2 things you should >avoid if you ever would apply for a teaching job. >1. How you made your son cry. >2. This answer to the question of motivation. As I said earlier, regarding #1, there has never been an issue with that story (and I was crying to). With regard to #2, that is what teaching mathematics is about and that is exactly how it is done in legitimate classrooms. And when they teach music, hold on to yourself, they play real songs, written by geniuses. I will talk about this later, but all you are bringing to this list thus far are examples of teachers trying to avoid their situation. None of these examples are blossoming into mathematics, so I asked myself (years ago) what is the point then? It is one thing to talk about openers, but when that is all there is and all there ever is, then the appeal can’t be mathematics, because you would get to that rather quickly, and never leave. I know openers. In fact, that quadratic/rational (lol pun) expression is an opener all by itself. Just like the opening notes of a memorable composition, but you have to be prepared to see it. These teachers are both misunderstanding and misusing it because they don’t understand what they are doing (like the gym coach) and/or their students are so misplaced that they can’t do anything resembling genuine mathematics, even if they do understand it. I don’t think it is too much to ask that we connect these activities to genuine results. Otherwise, it all looks like the next weight loos or quitting smoking gimmick. Bob Hansen |
In reply to this post by Richard Strausz
Bob, you are like a chess neophyte who wants to know good openings. However, you need to know how to checkmate your opponent when he just has a lone king. An experienced chess player likes good openings too, but she takes the checkmate for granted. All veterans know those checkmates.
There is nothing wrong with being a rookie, but it is wrong when you tell veterans that they don't know how to play because they don't teach you the basics. Richard > On 6/23/15, 4:14 PM, "[hidden email] > on behalf of Richard > Strausz" <[hidden email] on behalf of > [hidden email]> wrote: > > >Bob, concerning your post #9337 below, there are now > 2 things you should > >avoid if you ever would apply for a teaching job. > >1. How you made your son cry. > >2. This answer to the question of motivation. > > > As I said earlier, regarding #1, there has never been > an issue with that > story (and I was crying to). > > With regard to #2, that is what teaching mathematics > is about and that is > exactly how it is done in legitimate classrooms. And > when they teach > music, hold on to yourself, they play real songs, > written by geniuses. I > will talk about this later, but all you are bringing > to this list thus far > are examples of teachers trying to avoid their > situation. None of these > examples are blossoming into mathematics, so I asked > myself (years ago) > what is the point then? It is one thing to talk about > openers, but when > that is all there is and all there ever is, then the > appeal can’t be > mathematics, because you would get to that rather > quickly, and never leave. > > I know openers. In fact, that quadratic/rational (lol > pun) expression is > an opener all by itself. Just like the opening notes > of a memorable > composition, but you have to be prepared to see it. > These teachers are > both misunderstanding and misusing it because they > don’t understand what > they are doing (like the gym coach) and/or their > students are so misplaced > that they can’t do anything resembling genuine > mathematics, even if they > do understand it. > > I don’t think it is too much to ask that we connect > these activities to > genuine results. Otherwise, it all looks like the > next weight loos or > quitting smoking gimmick. > > Bob Hansen |
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