[VERY ot] WEB sources of middle school MATH word problems

Why post here?
  1. If you weren't good at restating and solving you wouldn't be here ;)
  2. Many are parent/grand-parent/....
  3. I'm an >60 bachelor needing help whose mother threatened him with
                      "kids JUST like him" :)

I'm attempting to tutor a 15 yro ADHD male who has TOO GOOD A MEMORY.
[ He remembers _answers_ teacher got when solving homework for class.
   He _DOES NOT_ remember process. ]

I've done some *PRELIMINARY* Google searches.

[ And just in case someone else is going in this direction, I like
       http://mathforum.org/dr.math/faq/faq.age.problems.html
       http://www.leeric.lsu.edu/bgbb/7/ecep/math/math.htm
       http://mathforum.org/mathworld/
       http://www.jimloy.com/algebra/word4.htm
and for general info
       http://mathforum.org/
]

Suggestions anyone?
TIA

"Richard Owlett" <rowlett@atlascomm.net> wrote in message 
news:12jl0erp1thda92@corp.supernews.com...
> Why post here?
>  1. If you weren't good at restating and solving you wouldn't be here ;)
>  2. Many are parent/grand-parent/....
>  3. I'm an >60 bachelor needing help whose mother threatened him with
>                      "kids JUST like him" :)
>
> I'm attempting to tutor a 15 yro ADHD male who has TOO GOOD A MEMORY.
> [ He remembers _answers_ teacher got when solving homework for class.
>   He _DOES NOT_ remember process. ]
>
> I've done some *PRELIMINARY* Google searches.
>
> [ And just in case someone else is going in this direction, I like
>       http://mathforum.org/dr.math/faq/faq.age.problems.html
>       http://www.leeric.lsu.edu/bgbb/7/ecep/math/math.htm
>       http://mathforum.org/mathworld/
>       http://www.jimloy.com/algebra/word4.htm
> and for general info
>       http://mathforum.org/
> ]
>
> Suggestions anyone?
> TIA

Richard,

Assuming that simple processes can be retained:

Yeah....  I've long held that math is much more about *language* than 
anything else.
Try this:
- Walk into a classroom of English-speaking kids where there are students 
who just "don't get it" (math).
- Greet them with "Buenos dias".  How many answer you or understand?  Ask 
them.  Ask them how they know that.  Ask them when they learned that.  Ask 
them if it's somehow mysterious now....
- Ask them what is the sum of all the integers from 1 to 6.  Explain what 
you mean by integer if you need to.  Get the answer from them.
- Write on the board: sigma over i from 1 to 6.  Ask them what it means. 
Tell them it means the same thing as the sum of all the integers from 1 to 
6.
Only the language and/or symbols have changed.
So, if they understood the first question then they can learn to "read" the 
other form.  There is nothing new except language.

I hope this will take away some of the mystery of math.  Goodness knows 
there is too much mystery associated with it.

I find some of those websites filled with jargon and what may be new 
concepts to an entry-level student.  So, no wonder there's confusion!  Too 
much to swallow at once if there is difficulty.

Here are my own suggestions for process:

0) Patience is a virtue.  Don't try to "jump" ahead to an answer.  Be 
deliberate.  Patience is rewarded here.  Being pedantic is good.

1) Write down what you know / what is given.
Take a look at it.
Be aware that usually you will need all of what is given to solve the 
problem.  But, sometimes not.
So, don't get too hung up on what is there as you deal with finding a 
solution.
It might be good to label this section: "Given"
I assume that "given" is not unfamiliar jargon at this stage.

2) Write down what is wanted as a solution.
Take a look at it.
It might be good to label this section: "Required"
I assume that "required" is not unfamiliar jargon at this stage.

3) Draw a picture or write some words that help you relate what is given 
("known") to what is needed/required ("unknown").  There - I've added some 
jargon.  So there's a little vocabulary lesson here.
Go back and add "known" after "given"
Go back and add "unknown" after "required"

4) If you can, write some expressions that relate the knowns and the 
unknowns.
At first, these should be such that simple arithmetic is all that's needed 
to find the unknowns.

***At this stage the idea of worded problems should be much less daunting.

5) After some practice with examples using simple arithmetic you might use 
the same examples with the idea that you will use very fundamental algebra.
The first step is the idea of assigning names (i.e. letters) to the 
unknowns.
So, go back and assign letters to each of the unknowns.
Now, add those letters to the pictures or words that you've written.
No solutions yet.  Just the assignment of letters.
Patience is a virtue.

***Now you shift gears.

6) Now that you have algebraic expressions the task changes from one of 
identifying things and relating them to one of using algebra for getting to 
solutions.
I imagine that an iterative process of doing lots of exercises with simple 
constructs and then moving to more complex constructs is the way to go.
Learn how to generate a solution at each stage.  This builds confidence.

I would leave the situation of simultaneous equations to a much later point 
where these real basics are comfortable to the student.

There are a variety of "forms" of worded problems:
Sums and differences
Muliples, sums and differences.
Ratios.
So, you want to  practice dealing with all of these at the simplest level.

************************

Also, algebraic manipulation should be practiced without any worded 
problems.
I think it's important to practice dealing with simple equations at this 
stage in parallel with the worded problems:

x - 5 = 12
we want "x" to be alone so
add 5 to both sides
x= 12 + 5 = 17;

x + 5 = 12
we want "x" be be alone so
subtract 5 from both sides
x = 12 - 5 = 7

3x = 12
we want "x" to be alone so
divide both sides by 3
x = 4

etc...... doing this builds confidence in doing the algebra and should help 
in being able to formulate the worded problems.
This practice should be followed by worded problems that result in the same 
forms as those being practiced.

Then different forms and different worded problems can be dealt with.

*************************

I find that "dimensional analysis" is extremely helpful when dealing with 
ratios.

Let's say that I want to compute speed in miles per hour ... or: miles/hour

Here is a problem:
Given:
A man walks 3 miles in 2 hours.
The man walks 3 miles.
He walks it in 2 hours.

Required:
How fast does the man walk in miles per hour?

Possibilities:
(3 miles) - (2 hours) = 1 what?  this doesn't work because the dimensions 
don't agree.
(2 hours) - (3 miles) = -1 what?  same issue here.
(2 hours / 3 miles = 0.6667 hours/mile  this is better but hours/mile isn't 
what we need.
(3 miles) / (2 hours) = 1.5 miles/hour ... the dimensions suggest this is 
what we want.

Solution:
(3 miles) / (2 hours) = 1.5 miles/hour

Written more graphically:

(3) (miles)
__________    = 1.5 _(miles)__  = 1.5 miles/hour
(2) (hours)          (hour)

thus - dimensional analysis helps me know if I'm on the right track.  Just 
doing the multiplying and dividing of the names of the dimensions and 
canceling out any like words from numerator and denominator help a lot!

(fps) miles lbs
___________________ = miles/second  because lbs cancel and feet cancel.
lbs feet

******************************************

I hope this helps.

Fred

Fred Marshall wrote:
> "Richard Owlett" <rowlett@atlascomm.net> wrote in message
> news:12jl0erp1thda92@corp.supernews.com...
> > Why post here?
> >  1. If you weren't good at restating and solving you wouldn't be here ;)
> >  2. Many are parent/grand-parent/....
> >  3. I'm an >60 bachelor needing help whose mother threatened him with
> >                      "kids JUST like him" :)
> >
> > I'm attempting to tutor a 15 yro ADHD male who has TOO GOOD A MEMORY.
> > [ He remembers _answers_ teacher got when solving homework for class.
> >   He _DOES NOT_ remember process. ]
> >
> > I've done some *PRELIMINARY* Google searches.
> >
> > [ And just in case someone else is going in this direction, I like
> >       http://mathforum.org/dr.math/faq/faq.age.problems.html
> >       http://www.leeric.lsu.edu/bgbb/7/ecep/math/math.htm
> >       http://mathforum.org/mathworld/
> >       http://www.jimloy.com/algebra/word4.htm
> > and for general info
> >       http://mathforum.org/
> > ]
> >
> > Suggestions anyone?
> > TIA
>
> Richard,
>
> Assuming that simple processes can be retained:
>
> Yeah....  I've long held that math is much more about *language* than
> anything else.
> Try this:
> - Walk into a classroom of English-speaking kids where there are students
> who just "don't get it" (math).
> - Greet them with "Buenos dias".  How many answer you or understand?  Ask
> them.  Ask them how they know that.  Ask them when they learned that.  Ask
> them if it's somehow mysterious now....
> - Ask them what is the sum of all the integers from 1 to 6.  Explain what
> you mean by integer if you need to.  Get the answer from them.
> - Write on the board: sigma over i from 1 to 6.  Ask them what it means.
> Tell them it means the same thing as the sum of all the integers from 1 to
> 6.
> Only the language and/or symbols have changed.
> So, if they understood the first question then they can learn to "read" the
> other form.  There is nothing new except language.
>
> I hope this will take away some of the mystery of math.  Goodness knows
> there is too much mystery associated with it.
>
> I find some of those websites filled with jargon and what may be new
> concepts to an entry-level student.  So, no wonder there's confusion!  Too
> much to swallow at once if there is difficulty.
>
> Here are my own suggestions for process:
>
> 0) Patience is a virtue.  Don't try to "jump" ahead to an answer.  Be
> deliberate.  Patience is rewarded here.  Being pedantic is good.
>
> 1) Write down what you know / what is given.
> Take a look at it.
> Be aware that usually you will need all of what is given to solve the
> problem.  But, sometimes not.
> So, don't get too hung up on what is there as you deal with finding a
> solution.
> It might be good to label this section: "Given"
> I assume that "given" is not unfamiliar jargon at this stage.
>
> 2) Write down what is wanted as a solution.
> Take a look at it.
> It might be good to label this section: "Required"
> I assume that "required" is not unfamiliar jargon at this stage.
>
> 3) Draw a picture or write some words that help you relate what is given
> ("known") to what is needed/required ("unknown").  There - I've added some
> jargon.  So there's a little vocabulary lesson here.
> Go back and add "known" after "given"
> Go back and add "unknown" after "required"
>
> 4) If you can, write some expressions that relate the knowns and the
> unknowns.
> At first, these should be such that simple arithmetic is all that's needed
> to find the unknowns.
>
> ***At this stage the idea of worded problems should be much less daunting.
>
> 5) After some practice with examples using simple arithmetic you might use
> the same examples with the idea that you will use very fundamental algebra.
> The first step is the idea of assigning names (i.e. letters) to the
> unknowns.
> So, go back and assign letters to each of the unknowns.
> Now, add those letters to the pictures or words that you've written.
> No solutions yet.  Just the assignment of letters.
> Patience is a virtue.
>
> ***Now you shift gears.
>
> 6) Now that you have algebraic expressions the task changes from one of
> identifying things and relating them to one of using algebra for getting to
> solutions.
> I imagine that an iterative process of doing lots of exercises with simple
> constructs and then moving to more complex constructs is the way to go.
> Learn how to generate a solution at each stage.  This builds confidence.
>
> I would leave the situation of simultaneous equations to a much later point
> where these real basics are comfortable to the student.
>
> There are a variety of "forms" of worded problems:
> Sums and differences
> Muliples, sums and differences.
> Ratios.
> So, you want to  practice dealing with all of these at the simplest level.
>
> ************************
>
> Also, algebraic manipulation should be practiced without any worded
> problems.
> I think it's important to practice dealing with simple equations at this
> stage in parallel with the worded problems:
>
> x - 5 = 12
> we want "x" to be alone so
> add 5 to both sides
> x= 12 + 5 = 17;
>
> x + 5 = 12
> we want "x" be be alone so
> subtract 5 from both sides
> x = 12 - 5 = 7
>
> 3x = 12
> we want "x" to be alone so
> divide both sides by 3
> x = 4
>
> etc...... doing this builds confidence in doing the algebra and should help
> in being able to formulate the worded problems.
> This practice should be followed by worded problems that result in the same
> forms as those being practiced.
>
> Then different forms and different worded problems can be dealt with.
>
> *************************
>
> I find that "dimensional analysis" is extremely helpful when dealing with
> ratios.
>
> Let's say that I want to compute speed in miles per hour ... or: miles/hour
>
> Here is a problem:
> Given:
> A man walks 3 miles in 2 hours.
> The man walks 3 miles.
> He walks it in 2 hours.
>
> Required:
> How fast does the man walk in miles per hour?
>
> Possibilities:
> (3 miles) - (2 hours) = 1 what?  this doesn't work because the dimensions
> don't agree.
> (2 hours) - (3 miles) = -1 what?  same issue here.
> (2 hours / 3 miles = 0.6667 hours/mile  this is better but hours/mile isn't
> what we need.
> (3 miles) / (2 hours) = 1.5 miles/hour ... the dimensions suggest this is
> what we want.
>
> Solution:
> (3 miles) / (2 hours) = 1.5 miles/hour
>
> Written more graphically:
>
> (3) (miles)
> __________    = 1.5 _(miles)__  = 1.5 miles/hour
> (2) (hours)          (hour)
>
> thus - dimensional analysis helps me know if I'm on the right track.  Just
> doing the multiplying and dividing of the names of the dimensions and
> canceling out any like words from numerator and denominator help a lot!
>
> (fps) miles lbs
> ___________________ = miles/second  because lbs cancel and feet cancel.
> lbs feet
>
> ******************************************
>
> I hope this helps.
>
> Fred

Though kind of OT but Fred! i really enjoyed reading as much as you had
enjoyed posting these interesting thoughts. 

ali

Richard Owlett wrote:
> Why post here?
>  1. If you weren't good at restating and solving you wouldn't be here ;)
>  2. Many are parent/grand-parent/....
>  3. I'm an >60 bachelor needing help whose mother threatened him with
>                      "kids JUST like him" :)
> 
> I'm attempting to tutor a 15 yro ADHD male who has TOO GOOD A MEMORY.
> [ He remembers _answers_ teacher got when solving homework for class.
>   He _DOES NOT_ remember process. ]
> 
> I've done some *PRELIMINARY* Google searches.
> 
> [ And just in case someone else is going in this direction, I like
>       http://mathforum.org/dr.math/faq/faq.age.problems.html
>       http://www.leeric.lsu.edu/bgbb/7/ecep/math/math.htm
>       http://mathforum.org/mathworld/
>       http://www.jimloy.com/algebra/word4.htm
> and for general info
>       http://mathforum.org/
> ]
> 
> Suggestions anyone?
> TIA
> 
One thing I learned from tutoring is that everyone has a different way 
of learning, and everyone has different roadblocks.

So when you're starting out don't just use one favorite method -- try as 
many different ways of thinking about the problem as you can, and 
present them all until one clicks.  After a while you'll figure out 
which one works best for that kid -- but the next one will be different.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

Fred Marshall wrote:
> "Richard Owlett" <rowlett@atlascomm.net> wrote in message 
> news:12jl0erp1thda92@corp.supernews.com...
> 
>>Why post here?
>> 1. If you weren't good at restating and solving you wouldn't be here ;)
>> 2. Many are parent/grand-parent/....
>> 3. I'm an >60 bachelor needing help whose mother threatened him with
>>                     "kids JUST like him" :)
>>
>>I'm attempting to tutor a 15 yro ADHD male who has TOO GOOD A MEMORY.
>>[ He remembers _answers_ teacher got when solving homework for class.
>>  He _DOES NOT_ remember process. ]
>>
>>I've done some *PRELIMINARY* Google searches.
>>
>>[ And just in case someone else is going in this direction, I like
>>      http://mathforum.org/dr.math/faq/faq.age.problems.html
>>      http://www.leeric.lsu.edu/bgbb/7/ecep/math/math.htm
>>      http://mathforum.org/mathworld/
>>      http://www.jimloy.com/algebra/word4.htm
>>and for general info
>>      http://mathforum.org/
>>]
>>
>>Suggestions anyone?
>>TIA
> 
> 
> Richard,
> 
> Assuming that simple processes can be retained:

I don't think there is a general problem there. When he was getting 
interested in polishing rocks, he gave a good description of the 
process. Language skills is something else.

> 
> Yeah....  I've long held that math is much more about *language* than 
> anything else.
> Try this:
> - Walk into a classroom of English-speaking kids where there are students 
> who just "don't get it" (math).
> - Greet them with "Buenos dias".  How many answer you or understand?  Ask 
> them.  Ask them how they know that.  Ask them when they learned that.  Ask 
> them if it's somehow mysterious now....
> - Ask them what is the sum of all the integers from 1 to 6.  Explain what 
> you mean by integer if you need to.  Get the answer from them.
> - Write on the board: sigma over i from 1 to 6.  Ask them what it means. 
> Tell them it means the same thing as the sum of all the integers from 1 to 
> 6.
> Only the language and/or symbols have changed.
> So, if they understood the first question then they can learn to "read" the 
> other form.  There is nothing new except language.
> 
> I hope this will take away some of the mystery of math.  Goodness knows 
> there is too much mystery associated with it.

I think I'll try that. Although he reads near grade level (if slowly), I 
wonder if he has internalized the concept that "you read in order to 
gain information".


> 
> I find some of those websites filled with jargon and what may be new 
> concepts to an entry-level student.  So, no wonder there's confusion!  Too 
> much to swallow at once if there is difficulty.
> 

My primary use for them was to gather sample problems he had never seen. 
  One of them I thought had explanations that I thought would be 
informative for his custodial grandfather. Definitely not for Ryan ;)


> Here are my own suggestions for process:
> 
> 0) Patience is a virtue.  Don't try to "jump" ahead to an answer.

"Jumping ahead" is one of his major problems.

> Be deliberate.  Patience is rewarded here.  Being pedantic is good.
> 
> 1) Write down what you know / what is given.
> Take a look at it.
> Be aware that usually you will need all of what is given to solve the 
> problem.  But, sometimes not.
> So, don't get too hung up on what is there as you deal with finding a 
> solution.
> It might be good to label this section: "Given"
> I assume that "given" is not unfamiliar jargon at this stage.
> 
> 2) Write down what is wanted as a solution.
> Take a look at it.
> It might be good to label this section: "Required"
> I assume that "required" is not unfamiliar jargon at this stage.
> 
> 3) Draw a picture or write some words that help you relate what is given 
> ("known") to what is needed/required ("unknown").  There - I've added some 
> jargon.  So there's a little vocabulary lesson here.
> Go back and add "known" after "given"
> Go back and add "unknown" after "required"
> 
> 4) If you can, write some expressions that relate the knowns and the 
> unknowns.
> At first, these should be such that simple arithmetic is all that's needed 
> to find the unknowns.
> 
> ***At this stage the idea of worded problems should be much less daunting.

That's the stage his textbook is at. His teacher's version of "show all 
work" includes writing all that down. The arithmetic is trivial -- on or 
of "if 3 apples cost 99 cents, how much doe one apple cost?"


> 
> 5) After some practice with examples using simple arithmetic you might use 
> the same examples with the idea that you will use very fundamental algebra.

I know that he has had some contact with the concept "algebra". And last 
year when I was working with him on something else I answered an OT 
question with an equation and he got the idea immediately. But now to 
use it ????? ;)

> The first step is the idea of assigning names (i.e. letters) to the 
> unknowns.
> So, go back and assign letters to each of the unknowns.
> Now, add those letters to the pictures or words that you've written.
> No solutions yet.  Just the assignment of letters.
> Patience is a virtue.
> 
> ***Now you shift gears.
> 
> 6) Now that you have algebraic expressions the task changes from one of 
> identifying things and relating them to one of using algebra for getting to 
> solutions.
> I imagine that an iterative process of doing lots of exercises with simple 
> constructs and then moving to more complex constructs is the way to go.
> Learn how to generate a solution at each stage.  This builds confidence.
> 
> I would leave the situation of simultaneous equations to a much later point 
> where these real basics are comfortable to the student.
> 
> There are a variety of "forms" of worded problems:
> Sums and differences
> Muliples, sums and differences.
> Ratios.
> So, you want to  practice dealing with all of these at the simplest level.
> 
> ************************

Of necessity one prong of my approach has to be attempting to keep him 
current with his assignments. The other prong is to use his difficulties 
as an opening to drill him of fundamentals where he is weak.

A major success will be to get him to *WANT* to do rote memorization of 
multiplication tables. For historic reasons I have to tread lightly there.

> 
> Also, algebraic manipulation should be practiced without any worded 
> problems.
> I think it's important to practice dealing with simple equations at this 
> stage in parallel with the worded problems:
> 
> x - 5 = 12
> we want "x" to be alone so
> add 5 to both sides
> x= 12 + 5 = 17;
> 
> x + 5 = 12
> we want "x" be be alone so
> subtract 5 from both sides
> x = 12 - 5 = 7
> 
> 3x = 12
> we want "x" to be alone so
> divide both sides by 3
> x = 4
> 
> etc...... doing this builds confidence in doing the algebra and should help 
> in being able to formulate the worded problems.
> This practice should be followed by worded problems that result in the same 
> forms as those being practiced.
> 
> Then different forms and different worded problems can be dealt with.
> 
> *************************
> 
> I find that "dimensional analysis" is extremely helpful when dealing with 
> ratios.

That's far beyond where his text is at currently. I found "dimensional 
analysis" extremely enlightening when I was introduced to it in college.

> 
> Let's say that I want to compute speed in miles per hour ... or: miles/hour
> 
> Here is a problem:
> Given:
> A man walks 3 miles in 2 hours.
> The man walks 3 miles.
> He walks it in 2 hours.
> 
> Required:
> How fast does the man walk in miles per hour?
> 
> Possibilities:
> (3 miles) - (2 hours) = 1 what?  this doesn't work because the dimensions 
> don't agree.
> (2 hours) - (3 miles) = -1 what?  same issue here.
> (2 hours / 3 miles = 0.6667 hours/mile  this is better but hours/mile isn't 
> what we need.
> (3 miles) / (2 hours) = 1.5 miles/hour ... the dimensions suggest this is 
> what we want.
> 
> Solution:
> (3 miles) / (2 hours) = 1.5 miles/hour
> 
> Written more graphically:
> 
> (3) (miles)
> __________    = 1.5 _(miles)__  = 1.5 miles/hour
> (2) (hours)          (hour)
> 
> thus - dimensional analysis helps me know if I'm on the right track.  Just 
> doing the multiplying and dividing of the names of the dimensions and 
> canceling out any like words from numerator and denominator help a lot!
> 
> (fps) miles lbs
> ___________________ = miles/second  because lbs cancel and feet cancel.
> lbs feet
> 
> ******************************************
> 
> I hope this helps.

*YES* Thank you.

> 
> Fred
> 

Fred Marshall skrev:

> Yeah....  I've long held that math is much more about *language* than
> anything else.

My first job was a summer internship at a metal-producing plant.
The product was FerroSilicone, FeSi, which is an alloy between
silicone and iron. The main raw material is quartz, SiO_2, and
carbon in various forms. The chemistry is simple: The O's in the
quartz react with the C's from the carbon to form CO and CO_2,
leaving the Si for the alloy.

One of the metallurgists asked us to keep track of the "yield"
of the process: Each ton of quartz fed into the furnace ought to
result in x tons of FeSi twelve hours later. Any deviation in the
yield might indicate something about the status of the process,
higher yield might indicate that we were draining accumulated
stores of metal, lower yields might indicate accumulation taking
place or loss of Si to the smoke stack filters.

One of the regulars was very confused about the metallurgist's
request. "What does that number x mean? Why not subtract the
molecular fraction of 2xO from the quartz tonnage, and scale
by the iron fraction in the alloy? Wouldn't that be simpler?"

My attempts to explain to the guy that if you did that, one would
find that the result was always the same and equivalent to scaling
the quartz tonnage by the very factor x, were never successful.

You never know what people understand and what they do not.

Rune

Richard Owlett <rowlett@atlascomm.net> writes:
> [...]
> Suggestions anyone?

Richard,

Here's my $0.02, for what it's worth. Some of this may be stating
the obvious, so caveat reader.

I have believed for a long time that becoming "good" at math is as
much a matter of confidence as it is intelligence. In fact, while I
won't quite say that ANYONE can be good at math, I belive the truth is
not far from this.

We also know math is also a layered subject: you need to know a in order
to understand b in order to understand c, ... . 

So I would think that helping a person in math consists of an iteration
of the following two basic procedures:

  1. Learn and build confidence in the fundamentals.
  2. Proceed to the next level

How do you help someone build confidence? I think that you start out at
the level they are comfortable with. Then make them work. This is perhaps
the hardest part - many folks (myself included) are lazy and don't want
to put in the work required. BUT THE LEVEL AT WHICH THEY ARE WORKING 
SHOULD NEVER BE BEYOND THEIR MEANS - in this manner they build confidence
as they work. 

Things that I believe impede confidence-building:

  1. Anger.
  2. Trivializing.
  3. 
  3. Turning off the person with some personality problem or physical
  problem (body odor?).

Anyway, these seem to me to be basic, but that's exactly where learning
occurs.

I may have told this story here before, but it may be helpful to repeat
it. I think one of the pivotal points in my childhood development towards
math came in the sixth grade where I was taught by a lady who had none
of the bad traits above and all of the good points. She was practical
(not an "ivory-tower academic"), likable, and "ad-hominem" - she never
gave me the feeling that she was looking down her nose at me (or any
of the rest of the class) but rather was holding our hands through a
journey she herself had to take at one time. Perhaps that makes all the
difference in the world.
-- 
%  Randy Yates                  % "I met someone who looks alot like you,
%% Fuquay-Varina, NC            %             she does the things you do, 
%%% 919-577-9882                %                     but she is an IBM."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://home.earthlink.net/~yatescr

Randy Yates <yates@ieee.org> writes:

> Things that I believe impede confidence-building:
>
>   1. Anger.
>   2. Trivializing.
>   3. 
>   3. Turning off the person with some personality problem or physical
>   problem (body odor?).

Sorry, I hit send before I finished an edit to this list. 

  1. Anger.
  2. Trivializing. "That's easy!" If the student says that, great,
  but the teacher never should.
  3. Demeaning or patronizing, looking down one's nose at someone.
  4. Turning off the person with some personality problem or physical
  problem (body odor?).
-- 
%  Randy Yates                  % "Midnight, on the water... 
%% Fuquay-Varina, NC            %  I saw...  the ocean's daughter." 
%%% 919-577-9882                % 'Can't Get It Out Of My Head' 
%%%% <yates@ieee.org>           % *El Dorado*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

Randy Yates wrote:
> Randy Yates <yates@ieee.org> writes:
> 
> 
>>Things that I believe impede confidence-building:
>>
>>  1. Anger.
>>  2. Trivializing.
>>  3. 
>>  3. Turning off the person with some personality problem or physical
>>  problem (body odor?).
> 
> 
> Sorry, I hit send before I finished an edit to this list. 
> 
>   1. Anger.
>   2. Trivializing. "That's easy!" If the student says that, great,
>   but the teacher never should.
>   3. Demeaning or patronizing, looking down one's nose at someone.
>   4. Turning off the person with some personality problem or physical
>   problem (body odor?).


Well, I taught post high-school and I met an incredibly wide range of 
people. The places I taught were private tech schools, where the 
students were, in general:

a. Highschool grads who failed to make it to college and wanted to learn
b. Highschool grads who failed to make it to college and were told by 
their parents to learn something
c. Older students who hadn't been to college but wanted to learn 
something new

I had students who ranged in age from 17 to 50.

When faced with that, one uses all the tools available. One I found 
incredibly useful was basic profiling (in it's best sense) - figure out 
how the student thinks and then match the teaching style to it.

I personally like the guidance of 'Type Talk' (available as a book - 
maybe online) that follows the MBTI, and some other resources based on 
the same ideas - Please understand me (available on the web, Kersey 
et.al.) is a closely related set of ideas.

Without going into whether it's appropriate or not, such profiling is an 
enormous assistance when teaching someone who may not even wish to learn 
(see b above). It worked for me, far more often than not.

As other noted, there's no one way to teach - and teaching is *not* 
about imparting information - it's about getting the student to learn 
*how to learn* first - the information part comes afterward.

Cheers

PeteS

Rune Allnor wrote:
> Fred Marshall skrev:
> 
> 
>>Yeah....  I've long held that math is much more about *language* than
>>anything else.
> 
> 
> My first job was a summer internship at a metal-producing plant.
> The product was FerroSilicone, FeSi, which is an alloy between
> silicone and iron. The main raw material is quartz, SiO_2, and
> carbon in various forms. The chemistry is simple: The O's in the
> quartz react with the C's from the carbon to form CO and CO_2,
> leaving the Si for the alloy.
> 
> One of the metallurgists asked us to keep track of the "yield"
> of the process: Each ton of quartz fed into the furnace ought to
> result in x tons of FeSi twelve hours later. Any deviation in the
> yield might indicate something about the status of the process,
> higher yield might indicate that we were draining accumulated
> stores of metal, lower yields might indicate accumulation taking
> place or loss of Si to the smoke stack filters.
> 
> One of the regulars was very confused about the metallurgist's
> request. "What does that number x mean? Why not subtract the
> molecular fraction of 2xO from the quartz tonnage, and scale
> by the iron fraction in the alloy? Wouldn't that be simpler?"
> 
> My attempts to explain to the guy that if you did that, one would
> find that the result was always the same and equivalent to scaling
> the quartz tonnage by the very factor x, were never successful.
> 
> You never know what people understand and what they do not.
> 
> Rune
> 

Or if they ever think first.
Once worked for a manufacturer of sequence of events recorders. 
[Monitored switch operations throughout a power plant or entire 
distribution system.] Systems I worked on could be up to 2000 points. 
Some might be "grouped" others not. My job was to create the wire lists 
between the input terminal cabinet and our hardware. I had a job with 
two similar units -- almost identical but for Unit 1 monitoring some 
points that related to plant as a whole rather than one generator. 
Someone had done their homework so that the interconnections were very 
regular - so I wrote a program to generate the lists. All was well and 
Unit 1 shipped and was operational. Order for Unit 2 (the smaller unit)
came in. I generated wire list and sent it to Project Engineer before 
submission to production. It received his "blessing" snicker snicker LOL

A couple of weeks later the customer submitted a change order affecting 
less than 10% of the points. I modified wire list and submitted it for 
*his* approval. since he had had no problem with original wire list he 
gave it to his brand new engineering aide. Not only was aide new to 
project, *she* was new to the company. So, not being yet up to speed on 
project, she started her assignment working from original 
_specification_ , NOT my original wire list THANKFULLY ;)

Seems my original had generated wiring for _hundreds_ of nonexistent 
points.

POSTMORTEM: Company had used two different styles of wire lists. I 
didn't know which this particular engineer preferred -- as it was 
essentially *ZERO* effort, I gave him the original lists in BOTH formats.

He had compared the two lists and found them identical.
Never referring to original specification.

I actually overheard him saying,

"It came from a computer. IT HAD TO BE RIGHT!"

Rune, *THANK YOU* !!!!!!!!!!!!!!!
I've been looking for an excuse to tell this story ;)