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.
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.
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.
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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.
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.
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.
How they "get there" isn't important -- *if* they learn, in the process.
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.
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 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".
For them, we have knitting, needlepoint, basket-weaving, etc.
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.
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).
"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.
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").
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.
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Secondhand they are about £3 rather than £30 new.
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.
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!
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.
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Obviously some of the failures are more entertaining that the winners.
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!
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.
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.
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.)
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.
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 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]
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
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