I have to develop a curriculum for a (non-credit) high-school STEM class.

I'm trying to decide how much hand-holding is appropriate vs. "unaided
discovery".

For example, one approach is to introduce a subject/problem space, let
them explore it and help them develop solutions. Then, challenge those
solutions with different problems known (by me) to be poorly addressed
by their previously developed solutions.

Lather, rinse, repeat.

In this case, any "testing" would simply be regurgitating one of the
many scenarios explored during the class to see how well it is recognized
and whether or not the "correct" solution is forthcoming.

A *different* approach is to present the new challenges as *test* material
to see if they: recognize that their solution(s) don't work; why; and
see if they can adapt new solutions, on-the-fly.

This seems like it would lead to a more lasting impression and reinforce
"how to learn" (instead of "how to remember what you've been taught").
But, I'm afraid it may be overly harsh on too many students given the
conditions typically encountered for testing.

ISTR the latter being how much of my later education was based -- though
the earlier years were more "regurgitation".

When does one expect kids to be able to "think for themselves"?

On 3/1/2022 11:02 PM, Don Y wrote:
> I have to develop a curriculum for a (non-credit) high-school STEM class.
>
> I'm trying to decide how much hand-holding is appropriate vs. "unaided
> discovery".
>
> For example, one approach is to introduce a subject/problem space, let
> them explore it and help them develop solutions.  Then, challenge those
> solutions with different problems known (by me) to be poorly addressed
> by their previously developed solutions.
>
> Lather, rinse, repeat.
>
> In this case, any "testing" would simply be regurgitating one of the
> many scenarios explored during the class to see how well it is recognized
> and whether or not the "correct" solution is forthcoming.
>
> A *different* approach is to present the new challenges as *test* material
> to see if they:  recognize that their solution(s) don't work; why; and
> see if they can adapt new solutions, on-the-fly.
>
> This seems like it would lead to a more lasting impression and reinforce
> "how to learn" (instead of "how to remember what you've been taught").
> But, I'm afraid it may be overly harsh on too many students given the
> conditions typically encountered for testing.
>
> ISTR the latter being how much of my later education was based -- though
> the earlier years were more "regurgitation".
>
> When does one expect kids to be able to "think for themselves"?
I would always encourage critical thinking as long as they have the
proper tools to accomplish. When would one expect kids to be able to
think for themselves? As far as I am concerned; at birth.

On 3/1/2022 9:30 PM, Tom Biasi wrote:
>> When does one expect kids to be able to "think for themselves"?

> I would always encourage critical thinking as long as they have the proper
> tools to accomplish. When would one expect kids to be able to think for
> themselves? As far as I am concerned; at birth.

I think a lot depends on "motivation".

E.g., I'd give good odds that a *toddler* could figure out how
to get into the "cookie jar". OTOH, put a bar of SOAP (for
"bath time") there and it will likely remain unchallenged!

If thinking for themselves was so commonplace, one would
expect all students to do well in all fields -- as there
is an incentive ("good grades") to doing so.

So, I see a big part of the problem as being one of generating
"buzz"... motivation to make them WANT to figure out the problems
laid out for them. Putting *cookies* in the jar instead of
bars of soap! The flip side is avoiding confrontations
that they might see as "discouraging".

I.e., "tests" -- with "grades" -- will likely do more harm than
good. So, need to be designed to reinforce their grasp of the
material and not try to trip them up (even if that's only just a
perception).

As this is not-for-credit, they have to *want* to return.

On 02/03/2022 04:02, Don Y wrote:
> I have to develop a curriculum for a (non-credit) high-school STEM class.
>
> I'm trying to decide how much hand-holding is appropriate vs. "unaided
> discovery".

You might want to take a look at the UK's Nuffield syllabus which went
down this road in the mid 1970's. My experience of it was that in
Chemistry at least it was positively dangerous bordering on lethal.

If you are good at the subject it really doesn't make much difference
but if you are not too bright discovery quickly becomes "accident".

The scariest one was when halide and halate salts were the subject and
one non-too-bright student combined nearly 10g of sodium chlorate with
conc sulphuric acid in a test tube. I still recall white hot pieces of
the stuff flying out of the tube as he turned round with it. It was
supposed to have been 1g of NaCl and a few drops of conc sulphuric.

It was suicidal to have both reagents out on the bench at once with
beginners around.

I got to make PCl3/PCl5 on the open lab bench in the same course from
white phosphorus. The other team doing that had their kit explode in the
fume cupboard releasing noxious vapours that were only just contained!

There was another even more lethal practical on eutectic solvent
mixtures that could sometimes form an explosive organic peroxide if left
in sunshine over a weekend part way through. It would then detonate when
the practical resumed on the Monday morning.

Nuffield syllabus is still going and the survivors of that early
experiment are now teachers, lecturers and engineers. I expect by now
all the truly dangerous experiments have been weeded out.

https://www.stem.org.uk/elibrary/collection/3237
>
> For example, one approach is to introduce a subject/problem space, let
> them explore it and help them develop solutions.  Then, challenge those
> solutions with different problems known (by me) to be poorly addressed
> by their previously developed solutions.
>
> Lather, rinse, repeat.
>
> In this case, any "testing" would simply be regurgitating one of the
> many scenarios explored during the class to see how well it is recognized
> and whether or not the "correct" solution is forthcoming.

A quick one that will find the very brightest is draw an ellipse using
only a piece of string and two pins. For physics and engineering things
involving pendulums are not a bad choice with little scope for damage.

> A *different* approach is to present the new challenges as *test* material
> to see if they:  recognize that their solution(s) don't work; why; and
> see if they can adapt new solutions, on-the-fly.
>
> This seems like it would lead to a more lasting impression and reinforce
> "how to learn" (instead of "how to remember what you've been taught").
> But, I'm afraid it may be overly harsh on too many students given the
> conditions typically encountered for testing.
>
> ISTR the latter being how much of my later education was based -- though
> the earlier years were more "regurgitation".

The transition between learning by just remembering stuff and having to
really think out the right answer is quite a tricky one. I know one
genius class individual at school who failed to make the transition to
university successfully. I still don't understand why. She was in
addition a gifted musician as well as being (very) good at the sciences.

There was a BBC Horizon? programme "Genius" in the 1990's which includes
her demise as one of their case studies. Some individuals have an innate
ability to remember pretty much anything that interests them.
>
> When does one expect kids to be able to "think for themselves"?

Some people never seem to master that skill.

--
Regards,
Martin Brown

On Wednesday, March 2, 2022 at 10:56:06 AM UTC, Martin Brown wrote:
> On 02/03/2022 04:02, Don Y wrote:
> > I have to develop a curriculum for a (non-credit) high-school STEM class.
> >
> > I'm trying to decide how much hand-holding is appropriate vs. "unaided
> > discovery".

> There was a BBC Horizon? programme "Genius" in the 1990's which includes
> her demise as one of their case studies. Some individuals have an innate
> ability to remember pretty much anything that interests them.

That was a great programme.

To teach high-school STEM, I presume we are not required to take safety risks.
I can't think of acids or noxious gasses. The power supplies can
be voltage & current limited; the power demands kept modest.
Stored energy release can be controlled. But I concede, if there's
some way to overload or overextend something, some enterprising
fool hardy youth will find it. So teaching safety should be part of the
course.

Re syllabus, One aspect is the adaptability. I recall my 7th-grade
math class. It was modular and 100% self paced. Each student
worked independently thru each module (basic algebra, etc.).
The teacher was there, as 1-on-1 coach, as needed.
May not work for entirely disinterested student, but then, they
wouldn't be forced into a STEM class, would they?

On Wednesday, March 2, 2022 at 2:41:39 PM UTC, Rich S wrote:
> On Wednesday, March 2, 2022 at 10:56:06 AM UTC, Martin Brown wrote:
> > On 02/03/2022 04:02, Don Y wrote:
> > > I have to develop a curriculum for a (non-credit) high-school STEM class.
> > >
> > > I'm trying to decide how much hand-holding is appropriate vs. "unaided
> > > discovery".
> > There was a BBC Horizon? programme "Genius" in the 1990's which includes
> > her demise as one of their case studies. Some individuals have an innate
> > ability to remember pretty much anything that interests them.
> That was a great programme.
>
> To teach high-school STEM, I presume we are not required to take safety risks.
> I can't think of acids or noxious gasses. The power supplies can
> be voltage & current limited; the power demands kept modest.
> Stored energy release can be controlled. But I concede, if there's
> some way to overload or overextend something, some enterprising
> fool hardy youth will find it. So teaching safety should be part of the
> course.
>
> Re syllabus, One aspect is the adaptability. I recall my 7th-grade
> math class. It was modular and 100% self paced. Each student
> worked independently thru each module (basic algebra, etc.).
> The teacher was there, as 1-on-1 coach, as needed.
> May not work for entirely disinterested student, but then, they
> wouldn't be forced into a STEM class, would they?

And another option is STE(A)M, add the Art component.
Some artistic types I knew were terrible at math.
But maybe, giving them such a mix would've found an entre' for math,
science, etc. Many maker faires are also
arts & crafts shows. The creative mind encompasses all.

On 3/2/2022 3:55 AM, Martin Brown wrote:
> On 02/03/2022 04:02, Don Y wrote:

>> I'm trying to decide how much hand-holding is appropriate vs. "unaided
>> discovery".

> If you are good at the subject it really doesn't make much difference but if
> you are not too bright discovery quickly becomes "accident".

How they "get there" isn't important -- *if* they learn, in the process.

>> For example, one approach is to introduce a subject/problem space, let
>> them explore it and help them develop solutions. Then, challenge those
>> solutions with different problems known (by me) to be poorly addressed
>> by their previously developed solutions.
>>
>> Lather, rinse, repeat.
>>
>> In this case, any "testing" would simply be regurgitating one of the
>> many scenarios explored during the class to see how well it is recognized
>> and whether or not the "correct" solution is forthcoming.
>
> A quick one that will find the very brightest is draw an ellipse using only a
> piece of string and two pins. For physics and engineering things involving
> pendulums are not a bad choice with little scope for damage.

I quote "testing" as the intent isn't to quantify their knowledge but,
rather, to coerce them into applying it. I think if you just push
information AT them and never put them in a position to "think for
themselves", they don't embrace the material taught.

And, I think putting a "number" (score) on a "test" sends the wrong
message. You want them to understand what they've "missed" and not
make them feel like they failed.

>> A *different* approach is to present the new challenges as *test* material
>> to see if they: recognize that their solution(s) don't work; why; and
>> see if they can adapt new solutions, on-the-fly.
>>
>> This seems like it would lead to a more lasting impression and reinforce
>> "how to learn" (instead of "how to remember what you've been taught").
>> But, I'm afraid it may be overly harsh on too many students given the
>> conditions typically encountered for testing.
>>
>> ISTR the latter being how much of my later education was based -- though
>> the earlier years were more "regurgitation".
>
> The transition between learning by just remembering stuff and having to really
> think out the right answer is quite a tricky one.

Yes -- hence the question.

The point of the "class" is to spark an interest in STEM... to show them
that these are *tools* that can be used to solve real problems. (unlike
"History" which only bears fruit later in life)

[I can recall stumbling on the notion of "similar triangles" when I
was a youngster -- before it had a *name* (trig) -- and the sorts
of things that it allowed me to do that would, otherwise, have been
effectively impossible: "How tall is that oak tree? If it was
to fall/be felled, what might it fall *onto*?"]

You measure the success of the *class* ("program"), not the success
("test scores") of the students! I.e., "Is this a good way to increase
interest in STEM?"

A participant who may not have a great skill set can still be a
"successful result" if his/her attitude towards STEM is enhanced
by the experience.

> I know one genius class
> individual at school who failed to make the transition to university
> successfully. I still don't understand why. She was in addition a gifted
> musician as well as being (very) good at the sciences.

I met an "idiot savant" whose skill was arithmetic. He could do
math in his head *instantly*. But, needed a constant companion to
navigate the simple tasks in "life".

> There was a BBC Horizon? programme "Genius" in the 1990's which includes her
> demise as one of their case studies. Some individuals have an innate ability to
> remember pretty much anything that interests them.
>>
>> When does one expect kids to be able to "think for themselves"?
>
> Some people never seem to master that skill.

For them, we have knitting, needlepoint, basket-weaving, etc.

On 3/2/2022 7:41 AM, Rich S wrote:
> Re syllabus, One aspect is the adaptability. I recall my 7th-grade
> math class. It was modular and 100% self paced. Each student
> worked independently thru each module (basic algebra, etc.).
> The teacher was there, as 1-on-1 coach, as needed.

The curriculum isn't linear. "Classes" expose students to ideas,
challenges, etc. Each pursues the material at their own level
of interest -- and, hopefully, brings that *back* to share with
their classmates.

> May not work for entirely disinterested student, but then, they
> wouldn't be forced into a STEM class, would they?

Exactly. The fear is that "superstars" can intimidate the less
capable (though interested) others.

There's a robotics club, here. The "advisor" largely drives the
design of their robot (there is a national competition) with
input from the kids. They all feel a part of the result -- but
have different levels of participation/contribution.

If the ideas of the "superstars" are the only ones that make it
into *the* (robot's) design, then those others have a hard time
seeing how they contributed to the result.

While the "team" concept might be valuable to instill in them
(for use later in life), it's important to also foster faith
in their *own* abilities -- as they will eventually be employed
as *individuals* (even if they eventually serve on teams).
Let them see the products of their peers as inspiration
(not intimidation).

On 3/2/2022 1:37 AM, Don Y wrote:
> On 3/1/2022 9:30 PM, Tom Biasi wrote:
>>> When does one expect kids to be able to "think for themselves"?
>
>> I would always encourage critical thinking as long as they have the
>> proper tools to accomplish. When would one expect kids to be able to
>> think for themselves? As far as I am concerned; at birth.
>
> I think a lot depends on "motivation".
>
> E.g., I'd give good odds that a *toddler* could figure out how
> to get into the "cookie jar".  OTOH, put a bar of SOAP (for
> "bath time") there and it will likely remain unchallenged!
>
> If thinking for themselves was so commonplace, one would
> expect all students to do well in all fields -- as there
> is an incentive ("good grades") to doing so.
>
> So, I see a big part of the problem as being one of generating
> "buzz"... motivation to make them WANT to figure out the problems
> laid out for them.  Putting *cookies* in the jar instead of
> bars of soap!  The flip side is avoiding confrontations
> that they might see as "discouraging".
>
> I.e., "tests" -- with "grades" -- will likely do more harm than
> good.  So, need to be designed to reinforce their grasp of the
> material and not try to trip them up (even if that's only just a
> perception).
>
> As this is not-for-credit, they have to *want* to return.
If they are not thinking for themselves who is thinking for them?
I'm not saying who forces their actions.

On 3/2/2022 6:45 PM, Tom Biasi wrote:
> On 3/2/2022 1:37 AM, Don Y wrote:
>> On 3/1/2022 9:30 PM, Tom Biasi wrote:
>>>> When does one expect kids to be able to "think for themselves"?
>>
>>> I would always encourage critical thinking as long as they have the proper
>>> tools to accomplish. When would one expect kids to be able to think for
>>> themselves? As far as I am concerned; at birth.
>>
>> I think a lot depends on "motivation".
>>
>> E.g., I'd give good odds that a *toddler* could figure out how
>> to get into the "cookie jar". OTOH, put a bar of SOAP (for
>> "bath time") there and it will likely remain unchallenged!
>>
>> If thinking for themselves was so commonplace, one would
>> expect all students to do well in all fields -- as there
>> is an incentive ("good grades") to doing so.
>>
>> So, I see a big part of the problem as being one of generating
>> "buzz"... motivation to make them WANT to figure out the problems
>> laid out for them. Putting *cookies* in the jar instead of
>> bars of soap! The flip side is avoiding confrontations
>> that they might see as "discouraging".
>>
>> I.e., "tests" -- with "grades" -- will likely do more harm than
>> good. So, need to be designed to reinforce their grasp of the
>> material and not try to trip them up (even if that's only just a
>> perception).
>>
>> As this is not-for-credit, they have to *want* to return.
> If they are not thinking for themselves who is thinking for them?
> I'm not saying who forces their actions.

That was the point of the question.

"For example, one approach is to introduce a subject/problem space, let
them explore it and help them develop solutions. Then, challenge those
solutions with different problems known (by me) to be poorly addressed
by their previously developed solutions."

This would be an interaction between their minds and the instructors'.
But, primarily the instructors *guiding* their thinking. They are
never in a "responsible" position as the instructors have to keep
the course moving, despite any real engagement from the *whole* of
the class.

By contrast:

"A *different* approach is to present the new challenges as *test* material
to see if they: recognize that their solution(s) don't work; why; and
see if they can adapt new solutions, on-the-fly."

leaves them largely on their own to develop solutions without immediate
feedback. I.e., they are relied on to come up with *a* solution instead
of waiting to hear what the instructors offer.

But, it is more confrontational. And, can intimidate students.

On 3/2/2022 9:04 PM, Don Y wrote:
> On 3/2/2022 6:45 PM, Tom Biasi wrote:
>> On 3/2/2022 1:37 AM, Don Y wrote:
>>> On 3/1/2022 9:30 PM, Tom Biasi wrote:
>>>>> When does one expect kids to be able to "think for themselves"?
>>>
>>>> I would always encourage critical thinking as long as they have the
>>>> proper tools to accomplish. When would one expect kids to be able to
>>>> think for themselves? As far as I am concerned; at birth.
>>>
>>> I think a lot depends on "motivation".
>>>
>>> E.g., I'd give good odds that a *toddler* could figure out how
>>> to get into the "cookie jar".  OTOH, put a bar of SOAP (for
>>> "bath time") there and it will likely remain unchallenged!
>>>
>>> If thinking for themselves was so commonplace, one would
>>> expect all students to do well in all fields -- as there
>>> is an incentive ("good grades") to doing so.
>>>
>>> So, I see a big part of the problem as being one of generating
>>> "buzz"... motivation to make them WANT to figure out the problems
>>> laid out for them.  Putting *cookies* in the jar instead of
>>> bars of soap!  The flip side is avoiding confrontations
>>> that they might see as "discouraging".
>>>
>>> I.e., "tests" -- with "grades" -- will likely do more harm than
>>> good.  So, need to be designed to reinforce their grasp of the
>>> material and not try to trip them up (even if that's only just a
>>> perception).
>>>
>>> As this is not-for-credit, they have to *want* to return.
>> If they are not thinking for themselves who is thinking for them?
>> I'm not saying who forces their actions.
>
> That was the point of the question.
>
>    "For example, one approach is to introduce a subject/problem space, let
>    them explore it and help them develop solutions.  Then, challenge those
>    solutions with different problems known (by me) to be poorly addressed
>    by their previously developed solutions."
>
> This would be an interaction between their minds and the instructors'.
> But, primarily the instructors *guiding* their thinking.  They are
> never in a "responsible" position as the instructors have to keep
> the course moving, despite any real engagement from the *whole* of
> the class.
>
> By contrast:
>
>    "A *different* approach is to present the new challenges as *test*
> material
>    to see if they:  recognize that their solution(s) don't work; why; and
>    see if they can adapt new solutions, on-the-fly."
>
> leaves them largely on their own to develop solutions without immediate
> feedback.  I.e., they are relied on to come up with *a* solution instead
> of waiting to hear what the instructors offer.
>
> But, it is more confrontational.  And, can intimidate students.
Good luck.

On 3/2/2022 7:22 PM, Tom Biasi wrote:
> On 3/2/2022 9:04 PM, Don Y wrote:
>> On 3/2/2022 6:45 PM, Tom Biasi wrote:
>>> On 3/2/2022 1:37 AM, Don Y wrote:
>>>> On 3/1/2022 9:30 PM, Tom Biasi wrote:
>>>>>> When does one expect kids to be able to "think for themselves"?
>>>>
>>>>> I would always encourage critical thinking as long as they have the proper
>>>>> tools to accomplish. When would one expect kids to be able to think for
>>>>> themselves? As far as I am concerned; at birth.
>>>>
>>>> I think a lot depends on "motivation".
>>>>
>>>> E.g., I'd give good odds that a *toddler* could figure out how
>>>> to get into the "cookie jar". OTOH, put a bar of SOAP (for
>>>> "bath time") there and it will likely remain unchallenged!
>>>>
>>>> If thinking for themselves was so commonplace, one would
>>>> expect all students to do well in all fields -- as there
>>>> is an incentive ("good grades") to doing so.
>>>>
>>>> So, I see a big part of the problem as being one of generating
>>>> "buzz"... motivation to make them WANT to figure out the problems
>>>> laid out for them. Putting *cookies* in the jar instead of
>>>> bars of soap! The flip side is avoiding confrontations
>>>> that they might see as "discouraging".
>>>>
>>>> I.e., "tests" -- with "grades" -- will likely do more harm than
>>>> good. So, need to be designed to reinforce their grasp of the
>>>> material and not try to trip them up (even if that's only just a
>>>> perception).
>>>>
>>>> As this is not-for-credit, they have to *want* to return.
>>> If they are not thinking for themselves who is thinking for them?
>>> I'm not saying who forces their actions.
>>
>> That was the point of the question.
>>
>> "For example, one approach is to introduce a subject/problem space, let
>> them explore it and help them develop solutions. Then, challenge those
>> solutions with different problems known (by me) to be poorly addressed
>> by their previously developed solutions."
>>
>> This would be an interaction between their minds and the instructors'.
>> But, primarily the instructors *guiding* their thinking. They are
>> never in a "responsible" position as the instructors have to keep
>> the course moving, despite any real engagement from the *whole* of
>> the class.
>>
>> By contrast:
>>
>> "A *different* approach is to present the new challenges as *test* material
>> to see if they: recognize that their solution(s) don't work; why; and
>> see if they can adapt new solutions, on-the-fly."
>>
>> leaves them largely on their own to develop solutions without immediate
>> feedback. I.e., they are relied on to come up with *a* solution instead
>> of waiting to hear what the instructors offer.
>>
>> But, it is more confrontational. And, can intimidate students.
> Good luck.

I suspect we will be hugely successful; the current/legacy approach
of teaching these subjects is the "regurgitation" mode. Clearly that
isn't working if (US) math/science competence is at such a low!

Clearly, one can't "memorize" all there is to know re: math
so methods haven't been successfully taught. And, the way it has
traditionally been taught somewhat intentionally segregates
students ("college prep" and "other").

On 02/03/2022 22:28, Don Y wrote:
> On 3/2/2022 3:55 AM, Martin Brown wrote:
>> On 02/03/2022 04:02, Don Y wrote:
>
>>> I'm trying to decide how much hand-holding is appropriate vs. "unaided
>>> discovery".
>
>> If you are good at the subject it really doesn't make much difference
>> but if you are not too bright discovery quickly becomes "accident".
>
> How they "get there" isn't important -- *if* they learn, in the process.

The syllabus I mentioned was all about guided discovery. Certainly much
better than rote learning but still a minority interest in the UK.

My school was unusual in doing Nuffield syllabus. I still have my copy
of the Nuffield Data book (recommended) although I have long since
graduated to CRC Handbook of Chemistry & Physics and Abromvitch & Stegun.

https://www.amazon.co.uk/Nuffield-Advanced-Science-Book-Chemistry/dp/058235448X/

Secondhand they are about £3 rather than £30 new.

>>> For example, one approach is to introduce a subject/problem space, let
>>> them explore it and help them develop solutions.  Then, challenge those
>>> solutions with different problems known (by me) to be poorly addressed
>>> by their previously developed solutions.
>>>
>>> Lather, rinse, repeat.
>>>
>>> In this case, any "testing" would simply be regurgitating one of the
>>> many scenarios explored during the class to see how well it is
>>> recognized
>>> and whether or not the "correct" solution is forthcoming.
>>
>> A quick one that will find the very brightest is draw an ellipse using
>> only a piece of string and two pins. For physics and engineering
>> things involving pendulums are not a bad choice with little scope for
>> damage.
>
> I quote "testing" as the intent isn't to quantify their knowledge but,
> rather, to coerce them into applying it.  I think if you just push
> information AT them and never put them in a position to "think for
> themselves", they don't embrace the material taught.

It depends on the context whether or not score is important.

Theoretical physics is very tough and competitive so the first week of
the final course was followed by a very difficult exam to put off anyone
not going to make the grade. This was deliberate policy by the
department. It got a bit easier after that if you were any good at it...

Two of us dug our heals in and insisted that the dozen or so who got the
answer correct according to the physics should also get full marks. My
more practical colleague turned up with the circuit nailed to a plank.
Mine was a sheet of paper with the algebra on it- our point was the
same. His method was a lot more convincing though.
> And, I think putting a "number" (score) on a "test" sends the wrong
message. You want them to understand what they've "missed" and not
make them feel like they failed.

Depends what the purpose of the test is. I have been an examination
marker in the past. The really controversial questions are the ones
where the marking scheme "correct" answer is itself in some way
incorrect. Only happened once in the years I did it but it was fun!
>
>>> A *different* approach is to present the new challenges as *test*
>>> material
>>> to see if they:  recognize that their solution(s) don't work; why; and
>>> see if they can adapt new solutions, on-the-fly.
>>>
>>> This seems like it would lead to a more lasting impression and reinforce
>>> "how to learn" (instead of "how to remember what you've been taught").
>>> But, I'm afraid it may be overly harsh on too many students given the
>>> conditions typically encountered for testing.
>>>
>>> ISTR the latter being how much of my later education was based -- though
>>> the earlier years were more "regurgitation".
>>
>> The transition between learning by just remembering stuff and having
>> to really think out the right answer is quite a tricky one.
>
> Yes -- hence the question.
>
> The point of the "class" is to spark an interest in STEM... to show them
> that these are *tools* that can be used to solve real problems.  (unlike
> "History" which only bears fruit later in life)

One which might suit although it is strictly more of an engineering
problem is "The Great Egg Race" where the challenge is to transport an
egg from one side of a gymnasium to the other as quickly as possible and
unharmed. It was the basis of a UK TV science programme mid 70's.

https://en.wikipedia.org/wiki/The_Great_Egg_Race

Obviously some of the failures are more entertaining that the winners.
>
> [I can recall stumbling on the notion of "similar triangles" when I
> was a youngster -- before it had a *name* (trig) -- and the sorts
> of things that it allowed me to do that would, otherwise, have been
> effectively impossible:  "How tall is that oak tree?  If it was
> to fall/be felled, what might it fall *onto*?"]

I recall being horribly bored by high school mathematics.

One challenge that did test me was construct the triangle with ruler and
compasses given only two sides and the radius of the inscribed circle.
That did not come from school though - but from a bank manager!

> You measure the success of the *class* ("program"), not the success
> ("test scores") of the students!  I.e., "Is this a good way to increase
> interest in STEM?"

Solving problems with computer programs will interest some of them.
Building hardware that does something interesting will get you a
different subset of your audience. No one size fits all.

> A participant who may not have a great skill set can still be a
> "successful result" if his/her attitude towards STEM is enhanced
> by the experience.
>
>> I know one genius class individual at school who failed to make the
>> transition to university successfully. I still don't understand why.
>> She was in addition a gifted musician as well as being (very) good at
>> the sciences.
>
> I met an "idiot savant" whose skill was arithmetic.  He could do
> math in his head *instantly*.  But, needed a constant companion to
> navigate the simple tasks in "life".

I know a dyslexic professor of mathematics. His skill is in visualising
solutions and then writing down the algebra describing it. Strangely his
reading dyslexia for words did not affect his mathematics much at all.

He went to a very prestigious public school on a scholarship after
having been identified with this highly unusual combination of skills.

--
Regards,
Martin Brown

On 3/3/2022 2:46 AM, Martin Brown wrote:
> On 02/03/2022 22:28, Don Y wrote:
>> On 3/2/2022 3:55 AM, Martin Brown wrote:
>>> On 02/03/2022 04:02, Don Y wrote:
>>
>>>> I'm trying to decide how much hand-holding is appropriate vs. "unaided
>>>> discovery".
>>
>>> If you are good at the subject it really doesn't make much difference but if
>>> you are not too bright discovery quickly becomes "accident".
>>
>> How they "get there" isn't important -- *if* they learn, in the process.
>
> The syllabus I mentioned was all about guided discovery. Certainly much better
> than rote learning but still a minority interest in the UK.

I chased down the URL but it looks like I will have to make a fair bit of
time to chase down all of the downloads (I didn't see a "download all" link,
anywhere).

> My school was unusual in doing Nuffield syllabus. I still have my copy of the
> Nuffield Data book (recommended) although I have long since graduated to CRC
> Handbook of Chemistry & Physics and Abromvitch & Stegun.
>
> https://www.amazon.co.uk/Nuffield-Advanced-Science-Book-Chemistry/dp/058235448X/
>
> Secondhand they are about £3 rather than £30 new.
>
>>>> For example, one approach is to introduce a subject/problem space, let
>>>> them explore it and help them develop solutions. Then, challenge those
>>>> solutions with different problems known (by me) to be poorly addressed
>>>> by their previously developed solutions.
>>>>
>>>> Lather, rinse, repeat.
>>>>
>>>> In this case, any "testing" would simply be regurgitating one of the
>>>> many scenarios explored during the class to see how well it is recognized
>>>> and whether or not the "correct" solution is forthcoming.
>>>
>>> A quick one that will find the very brightest is draw an ellipse using only
>>> a piece of string and two pins. For physics and engineering things involving
>>> pendulums are not a bad choice with little scope for damage.
>>
>> I quote "testing" as the intent isn't to quantify their knowledge but,
>> rather, to coerce them into applying it. I think if you just push
>> information AT them and never put them in a position to "think for
>> themselves", they don't embrace the material taught.
>
> It depends on the context whether or not score is important.
>
> Theoretical physics is very tough and competitive so the first week of the
> final course was followed by a very difficult exam to put off anyone not going
> to make the grade. This was deliberate policy by the department. It got a bit
> easier after that if you were any good at it...
>
> Two of us dug our heals in and insisted that the dozen or so who got the answer
> correct according to the physics should also get full marks. My more practical
> colleague turned up with the circuit nailed to a plank. Mine was a sheet of
> paper with the algebra on it- our point was the same. His method was a lot more
> convincing though.

We're not trying to "teach" them anything, in particular. Rather, we
are trying to spark their interest in STEM by showing them that it is
*practical* knowledge and not just a bunch of sterile abstractions.

Our interest in "testing" is in having some mechanism to gauge how well
they are *engaging* in the material. It's too easy (when there are no
"grades" involved) to just "be present" and not "be engaged".

>> And, I think putting a "number" (score) on a "test" sends the wrong
>> message. You want them to understand what they've "missed" and not
>> make them feel like they failed.
>
> Depends what the purpose of the test is. I have been an examination marker in
> the past. The really controversial questions are the ones where the marking
> scheme "correct" answer is itself in some way incorrect. Only happened once in
> the years I did it but it was fun!

Ideally, we will create "problems" that have no "right" answer. The goal
is to coerce them into *trying* things with an eye towards being able to
identify why something worked -- or not.

We want to develop critical/analytical thinking that yearns for application.

>>>> A *different* approach is to present the new challenges as *test* material
>>>> to see if they: recognize that their solution(s) don't work; why; and
>>>> see if they can adapt new solutions, on-the-fly.
>>>>
>>>> This seems like it would lead to a more lasting impression and reinforce
>>>> "how to learn" (instead of "how to remember what you've been taught").
>>>> But, I'm afraid it may be overly harsh on too many students given the
>>>> conditions typically encountered for testing.
>>>>
>>>> ISTR the latter being how much of my later education was based -- though
>>>> the earlier years were more "regurgitation".
>>>
>>> The transition between learning by just remembering stuff and having to
>>> really think out the right answer is quite a tricky one.
>>
>> Yes -- hence the question.
>>
>> The point of the "class" is to spark an interest in STEM... to show them
>> that these are *tools* that can be used to solve real problems. (unlike
>> "History" which only bears fruit later in life)
>
> One which might suit although it is strictly more of an engineering problem is
> "The Great Egg Race" where the challenge is to transport an egg from one side
> of a gymnasium to the other as quickly as possible and unharmed. It was the
> basis of a UK TV science programme mid 70's.

We have no shortage of "problems" to solve. What we need are:
- metrics by which we can quantify how well we are meeting our stated objective
- (to that end) metrics by which we can quantify how well the students are
engaging in the program

You can't (practically) look at performance in the regular school program
(which they are attending in parallel with this) and draw conclusions about
the impact you are having (how do you know there has been a change? how do
you know that you are the reason for that change??)

[There are also privacy issues governing what we can see/report]

You *can*, however, notice how many participants stay with the program
for the full term -- if they are bored with it, they will likely stop
coming as the time spent comes out of their "personal" time allotments
("I'd rather be playing with my friends!")

You can notice whether or not they "re-up" with the program in
their next school year.

You can notice if *other* kids want to join the program (in
subsequent years).

On a larger scale, you can look to see if you have any impact on the
graduation rate and, even longer term, on the careers chosen.
(but, that can only happen if the program can demonstrate some
potential for making positive changes, in that regard).

> https://en.wikipedia.org/wiki/The_Great_Egg_Race
>
> Obviously some of the failures are more entertaining that the winners.
>>
>> [I can recall stumbling on the notion of "similar triangles" when I
>> was a youngster -- before it had a *name* (trig) -- and the sorts
>> of things that it allowed me to do that would, otherwise, have been
>> effectively impossible: "How tall is that oak tree? If it was
>> to fall/be felled, what might it fall *onto*?"]
>
> I recall being horribly bored by high school mathematics.

Math is almost always taught in a boring/sterile manner.
Even the "problems" are contrived.

This persists through college -- likely because the assumption is
that you can think in abstractions ("Wombats are crossing a highway.
Each wombat requires 15 seconds to cross the roadway. It is vulnerable
to death/injury for the entire time it is on the roadway. Vehicles
pass with interarrival times defined by the following PDF. Assuming
the vehicle arrivals are independant events, what is the probability
that a particular wombat will survive the transit...")

On the other hand, if you present a *real* problem needing solution,
students can "see" how a problem that they are facing can benefit
from such analysis.

"How many marbles are in this container?"

"How many popsicle sticks will we need to fabricate a bridge for
this model train to traverse this chasm?"

> One challenge that did test me was construct the triangle with ruler and
> compasses given only two sides and the radius of the inscribed circle. That did
> not come from school though - but from a bank manager!

Martin Brown wrote:
<snip>
>> The point of the "class" is to spark an interest in STEM... to show them
>> that these are *tools* that can be used to solve real problems.  (unlike
>> "History" which only bears fruit later in life)
>
> One which might suit although it is strictly more of an engineering
> problem is "The Great Egg Race" where the challenge is to transport an
> egg from one side of a gymnasium to the other as quickly as possible and
> unharmed. It was the basis of a UK TV science programme mid 70's.
>
> https://en.wikipedia.org/wiki/The_Great_Egg_Race
>
> Obviously some of the failures are more entertaining that the winners.
>>
<snip>

Horizontal transport is key.

Back in the long ago, UBC had a shiny new physics lab / lecture hall
building called Hebb. On one end, it had a four-story tower with glass
walls, containing only a staircase and a Foucault pendulum running the
full height of the building.

They had a competition for lower-level undergraduates for who could get
an egg from the fourth floor to the ground fastest without breaking it.
They had a couple of He-Ne laser / photodiode gizmos and a CAMAC crate
to do the timing--all very physicsy and all.

There were imaginitive solutions such as arrows with sculptured foam
noses and so on, and it went on for a few years like that. Then one
bright spark took his egg, wrapped it in paper towels inside a foam
container that had formerly housed a Big Mac, taped it to a flimsy mylon
rucksack full of rocks, and dropped that. Four stories down, inside a
narrow tower with all-glass walls and a concrete floor.

That was the last year for the competition.

Cheers

Phil Hobbs

(Who came along the following year, 1976. Honest.)

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On 3/3/2022 5:12 AM, Don Y wrote:
> On the other hand, if you present a *real* problem needing solution,
> students can "see" how a problem that they are facing can benefit
> from such analysis.

Imagine setting out to design a cart/conveyance.

Start out with 4 wheels (you can, later, challenge that assumption).

How do you allow the cart to travel in anything other than a straight line?

You can implement a crude mechanism to change the angular orientation
of two of the wheels (e.g., put them on an axle that has a central?
pivot point and add a means of adjusting that pivot).

Gee, it has a large turning radius! How large? *Why*? How can we decrease
that? Hack together a mathematical expression that relates the physical
parameters of the design to the effective turning radius and "graph" the
result. Where is the minimum? What *limits* the minimum attainable?

What if we allowed the wheels to pivot "locally" (e.g., like rack and pinion)?
What does this buy us? What does it cost (mechanism complexity)

What if we allowed front and rear wheels to pivot? Why did we initially
assume the *front* wheels had to pivot?

Why does the wheel on one side get "scuffed" in turns?

E.g., with this sort of approach, you can move from a "straight-line" vehicle
to one with a "swerve" drive -- and SHOW the advantages and costs of each.
(What *technology* do you need to implement each?)

No need for computers or advanced math so you can involve kids of various
different capabilities without intimidating some.

On Friday, 4 March 2022 at 11:46:56 UTC, Don Y wrote:
> On 3/3/2022 5:12 AM, Don Y wrote:
> > On the other hand, if you present a *real* problem needing solution,
> > students can "see" how a problem that they are facing can benefit
> > from such analysis.
> Imagine setting out to design a cart/conveyance.
>
> Start out with 4 wheels (you can, later, challenge that assumption).
>
> How do you allow the cart to travel in anything other than a straight line?
>
> You can implement a crude mechanism to change the angular orientation
> of two of the wheels (e.g., put them on an axle that has a central?
> pivot point and add a means of adjusting that pivot).
>
> Gee, it has a large turning radius! How large? *Why*? How can we decrease
> that? Hack together a mathematical expression that relates the physical
> parameters of the design to the effective turning radius and "graph" the
> result. Where is the minimum? What *limits* the minimum attainable?
>
> What if we allowed the wheels to pivot "locally" (e.g., like rack and pinion)?
> What does this buy us? What does it cost (mechanism complexity)
>
> What if we allowed front and rear wheels to pivot? Why did we initially
> assume the *front* wheels had to pivot?
>
> Why does the wheel on one side get "scuffed" in turns?
>
> E.g., with this sort of approach, you can move from a "straight-line" vehicle
> to one with a "swerve" drive -- and SHOW the advantages and costs of each.
> (What *technology* do you need to implement each?)
>
> No need for computers or advanced math so you can involve kids of various
> different capabilities without intimidating some.

I once read that one could throw a raw egg over the roof of a house and if it
landed on a grass lawn it would not break.
I tried it. It really was true (but only some of the time because there were some
stones in the lawn).
Less good were the trials where it didn't quite make it over the top.

I also found a way of shooting a hole through a glass light bulb with
an air pistol without completely shattering it - just leaving an entry and
exit hole. All it needed was sufficient precision in aiming so that
the pellet was perpendicular to the glass at the point of impact. And ways of
making the pellet emerge from the barrel at supersonic speed. And explode
on impact with a target.
Nowadays of course I would have been arrested for these - and other - activities
that involved the rapid expansion of hot gases.

John

On 3/5/2022 1:11 PM, John Walliker wrote:
> I once read that one could throw a raw egg over the roof of a house and if it
> landed on a grass lawn it would not break.
> I tried it. It really was true (but only some of the time because there were some
> stones in the lawn).
> Less good were the trials where it didn't quite make it over the top.

There are lots of novelty "tricks" you can do with eggs... balancing on end,
checking freshness without cracking, hollowing, scrambling in shell, dissolving
shell, etc.

Because eggs are so ubiquitous, they are good for challenging preconceived
notions regarding their nature/characteristics.

> I also found a way of shooting a hole through a glass light bulb with
> an air pistol without completely shattering it - just leaving an entry and
> exit hole. All it needed was sufficient precision in aiming so that
> the pellet was perpendicular to the glass at the point of impact. And ways of
> making the pellet emerge from the barrel at supersonic speed. And explode
> on impact with a target.

I always liked the pin-in-balloon trick (but, it really *is* a trick).

Or, slicing an unpeeled banana.

etc.

Each of these are good -- yet simple -- puzzles to get kids to challenge their
conventional thinking.

[Favorite is: given a box of thumbtacks and a candle, mount -- and burn -- the
candle on a cork-covered wall]

> Nowadays of course I would have been arrested for these - and other - activities
> that involved the rapid expansion of hot gases.
>
> John
>

John Walliker wrote:
> On Friday, 4 March 2022 at 11:46:56 UTC, Don Y wrote:
>> On 3/3/2022 5:12 AM, Don Y wrote:
>>> On the other hand, if you present a *real* problem needing solution,
>>> students can "see" how a problem that they are facing can benefit
>>> from such analysis.
>> Imagine setting out to design a cart/conveyance.
>>
>> Start out with 4 wheels (you can, later, challenge that assumption).
>>
>> How do you allow the cart to travel in anything other than a straight line?
>>
>> You can implement a crude mechanism to change the angular orientation
>> of two of the wheels (e.g., put them on an axle that has a central?
>> pivot point and add a means of adjusting that pivot).
>>
>> Gee, it has a large turning radius! How large? *Why*? How can we decrease
>> that? Hack together a mathematical expression that relates the physical
>> parameters of the design to the effective turning radius and "graph" the
>> result. Where is the minimum? What *limits* the minimum attainable?
>>
>> What if we allowed the wheels to pivot "locally" (e.g., like rack and pinion)?
>> What does this buy us? What does it cost (mechanism complexity)
>>
>> What if we allowed front and rear wheels to pivot? Why did we initially
>> assume the *front* wheels had to pivot?
>>
>> Why does the wheel on one side get "scuffed" in turns?
>>
>> E.g., with this sort of approach, you can move from a "straight-line" vehicle
>> to one with a "swerve" drive -- and SHOW the advantages and costs of each.
>> (What *technology* do you need to implement each?)
>>
>> No need for computers or advanced math so you can involve kids of various
>> different capabilities without intimidating some.
>
> I once read that one could throw a raw egg over the roof of a house and if it
> landed on a grass lawn it would not break.
> I tried it. It really was true (but only some of the time because there were some
> stones in the lawn).
> Less good were the trials where it didn't quite make it over the top.
>
> I also found a way of shooting a hole through a glass light bulb with
> an air pistol without completely shattering it - just leaving an entry and
> exit hole. All it needed was sufficient precision in aiming so that
> the pellet was perpendicular to the glass at the point of impact. And ways of
> making the pellet emerge from the barrel at supersonic speed. And explode
> on impact with a target.

Good luck making a pellet supersonic with a gas charge that starts at
ambient temperature. You need the propellant to stay in contact with
the pellet as it goes down the barrel.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On Sunday, 6 March 2022 at 01:15:29 UTC, Phil Hobbs wrote:
> John Walliker wrote:
> > On Friday, 4 March 2022 at 11:46:56 UTC, Don Y wrote:
> >> On 3/3/2022 5:12 AM, Don Y wrote:
> >>> On the other hand, if you present a *real* problem needing solution,
> >>> students can "see" how a problem that they are facing can benefit
> >>> from such analysis.
> >> Imagine setting out to design a cart/conveyance.
> >>
> >> Start out with 4 wheels (you can, later, challenge that assumption).
> >>
> >> How do you allow the cart to travel in anything other than a straight line?
> >>
> >> You can implement a crude mechanism to change the angular orientation
> >> of two of the wheels (e.g., put them on an axle that has a central?
> >> pivot point and add a means of adjusting that pivot).
> >>
> >> Gee, it has a large turning radius! How large? *Why*? How can we decrease
> >> that? Hack together a mathematical expression that relates the physical
> >> parameters of the design to the effective turning radius and "graph" the
> >> result. Where is the minimum? What *limits* the minimum attainable?
> >>
> >> What if we allowed the wheels to pivot "locally" (e.g., like rack and pinion)?
> >> What does this buy us? What does it cost (mechanism complexity)
> >>
> >> What if we allowed front and rear wheels to pivot? Why did we initially
> >> assume the *front* wheels had to pivot?
> >>
> >> Why does the wheel on one side get "scuffed" in turns?
> >>
> >> E.g., with this sort of approach, you can move from a "straight-line" vehicle
> >> to one with a "swerve" drive -- and SHOW the advantages and costs of each.
> >> (What *technology* do you need to implement each?)
> >>
> >> No need for computers or advanced math so you can involve kids of various
> >> different capabilities without intimidating some.
> >
> > I once read that one could throw a raw egg over the roof of a house and if it
> > landed on a grass lawn it would not break.
> > I tried it. It really was true (but only some of the time because there were some
> > stones in the lawn).
> > Less good were the trials where it didn't quite make it over the top.
> >
> > I also found a way of shooting a hole through a glass light bulb with
> > an air pistol without completely shattering it - just leaving an entry and
> > exit hole. All it needed was sufficient precision in aiming so that
> > the pellet was perpendicular to the glass at the point of impact. And ways of
> > making the pellet emerge from the barrel at supersonic speed. And explode
> > on impact with a target.
> Good luck making a pellet supersonic with a gas charge that starts at
> ambient temperature. You need the propellant to stay in contact with
> the pellet as it goes down the barrel.
>
That is where the fuel air mixture in the compression chamber comes in. I used the diesel fuel intended for model aircraft engines, atomised in the compression chamber by firing once without a pellet after introducing the fuel. The atomised fuel would ignite on the next firing if soon afterwards.
John

> Cheers
>
> Phil Hobbs
> --
> Dr Philip C D Hobbs
> Principal Consultant
> ElectroOptical Innovations LLC / Hobbs ElectroOptics
> Optics, Electro-optics, Photonics, Analog Electronics
> Briarcliff Manor NY 10510
>
> http://electrooptical.net
> http://hobbs-eo.com

torsdag den 10. marts 2022 kl. 00.30.45 UTC+1 skrev John Walliker:
> On Sunday, 6 March 2022 at 01:15:29 UTC, Phil Hobbs wrote:
> > John Walliker wrote:
> > > On Friday, 4 March 2022 at 11:46:56 UTC, Don Y wrote:
> > >> On 3/3/2022 5:12 AM, Don Y wrote:
> > >>> On the other hand, if you present a *real* problem needing solution,
> > >>> students can "see" how a problem that they are facing can benefit
> > >>> from such analysis.
> > >> Imagine setting out to design a cart/conveyance.
> > >>
> > >> Start out with 4 wheels (you can, later, challenge that assumption).
> > >>
> > >> How do you allow the cart to travel in anything other than a straight line?
> > >>
> > >> You can implement a crude mechanism to change the angular orientation
> > >> of two of the wheels (e.g., put them on an axle that has a central?
> > >> pivot point and add a means of adjusting that pivot).
> > >>
> > >> Gee, it has a large turning radius! How large? *Why*? How can we decrease
> > >> that? Hack together a mathematical expression that relates the physical
> > >> parameters of the design to the effective turning radius and "graph" the
> > >> result. Where is the minimum? What *limits* the minimum attainable?
> > >>
> > >> What if we allowed the wheels to pivot "locally" (e.g., like rack and pinion)?
> > >> What does this buy us? What does it cost (mechanism complexity)
> > >>
> > >> What if we allowed front and rear wheels to pivot? Why did we initially
> > >> assume the *front* wheels had to pivot?
> > >>
> > >> Why does the wheel on one side get "scuffed" in turns?
> > >>
> > >> E.g., with this sort of approach, you can move from a "straight-line" vehicle
> > >> to one with a "swerve" drive -- and SHOW the advantages and costs of each.
> > >> (What *technology* do you need to implement each?)
> > >>
> > >> No need for computers or advanced math so you can involve kids of various
> > >> different capabilities without intimidating some.
> > >
> > > I once read that one could throw a raw egg over the roof of a house and if it
> > > landed on a grass lawn it would not break.
> > > I tried it. It really was true (but only some of the time because there were some
> > > stones in the lawn).
> > > Less good were the trials where it didn't quite make it over the top.
> > >
> > > I also found a way of shooting a hole through a glass light bulb with
> > > an air pistol without completely shattering it - just leaving an entry and
> > > exit hole. All it needed was sufficient precision in aiming so that
> > > the pellet was perpendicular to the glass at the point of impact. And ways of
> > > making the pellet emerge from the barrel at supersonic speed. And explode
> > > on impact with a target.
> > Good luck making a pellet supersonic with a gas charge that starts at
> > ambient temperature. You need the propellant to stay in contact with
> > the pellet as it goes down the barrel.
> >
> That is where the fuel air mixture in the compression chamber comes in. I used the diesel fuel intended for model aircraft engines, atomised in the compression chamber by firing once without a pellet after introducing the fuel. The atomised fuel would ignite on the next firing if soon afterwards.

sound like it would be far too much oil, oiled pellets should be enough