Examples, examples, examples! But, of the right type!
Why is mathematics and physics so boring sometimes?
The question is hard to answer to me: as far as I've seen in my professional life, mathematics' and physics' applications are widespread and, most often than not, fascinatingly useful.
Just to give an example: if you connect to the site of the environmental protection agency of Lazio, after some browsing you'll discover a wonderful collection of maps illustrating pollution forecasts for the next hours. Like these:
These maps are the results of a sophisticated mathematical models, fed using data which underwent extensive data acquisition and processing work. Behind the scenes, an entire world of scientific knowledge is deployed seamlessly at your finger's command. There is a great deal of physics of the atmosphere, of course. But also, of quantitative chemistry. Of computer sciences.
On the other (darker) side, you open a mainstream high-school textbook on physics and yes, you find a lot of applications, but (in random order):
- About how quickly a soccer ball will travel from a point to another
- On whether a car launched at a crazy speed will stop before or after a (supposedly impenetrable) wall
- If it is better for an artillery round being shot with an angle of more or less than 45 degrees to hit a target
And more on the same line.
In my times you might have be even less lucky: there was no application at all. My high school physics textbook began with a phrase more or less like this:
"Kinematics is the study of the movement of collection of points in the space. A point is a dimensionless object occupying a position in space. Space is..."
If you endured the first lessons, you finally arrived to dynamics where you were told you may deduce anything about "material points" (points "dimensionless", but "with a mass") from few basic "Nature's laws" (your teacher may also have done his best to convince you that anything in the world, made of objects definitely not as dimensionless as points, was also deducible from the same rules).
Well. I hardly know soccer rules. Don't like to take risks when I drive. Prefer discussing (animately, Italian style) with people rather than destroying their lives and properties and killing their beloved with artillery rounds.
And, cordially detest the idea of "deducing physical reality from basic principles".
I'm not so an uncommon type of person, as I discovered! Many friends of mine share the same lack of passion for these things presented as "absolutely compelling".
Is it we lack good examples?
Delving a bit in a (Mauri-logic-style: crank, haphazard and diverging) assessment of common ways of presenting mathematics and physics through examples, I found some common factors I'd like to share. I try exposing them in (apparent) order.
1.Many example are highly gender-stereotyped (that is: unfriendly to most girls and many boys).
More precisely: they deal of arguments assumed to be interesting to boys: cars smashing somewhere, bullets crazily wandering in space, sport events. That they really are interesting to boys, or all of them, is an interesting question (I have some doubts).
Surely to many girls, these example seem contrived, extraneous and uninteresting.
To both girls and boys, they tend to seem marginal and puerile. This leads me to the next point.
2.Where the Real World is?
We all know "human kind has reached the Moon" (vaguely, and with some perplexity, by the generation of who "was not there"): a huge application of physics! We are accustomed to money, a tool of mathematical and quite abstract nature. We know (and sometime expect) weather forecasts - another highly matheatical and physical application.
Very few of these real-world applications are used as examples.
But these are precisely the kind of things mathematics and physics are used for.
Amusingly, to get examples from the real world could be much easier than inventing the next artificial self-standing puzzle: there is literally a sea of scientific and industrial publications from which to get inspiration. All what needed is, presenting things in an interesting way.
It takes some time to realize that "deducing physical reality from basic principles" is not exactly the same as "creating reality", and rather is "building a simplified model of it".
Unless you are highly deductive, as a young girl (or boy) you haven't yet realized this conceptual shift. At least, I didn't until early adulthood.
I wonder whether initially teacher would do better to insist on the experimental side of physics and mathematics. Incidentally, this is closer to how science is actually built: collecting and organizing "facts" by experimentation first, then sorting them out and formulating hypotheses to be tested. "Laws of Nature" may emerge when a discipline has matured a lot - but even then they should be considered as nothing more than models, valid until something better is found.
Like what happened with classical mechanics, whose "laws" have been extensively revised in the transition to special and general relativity, and completely replaced by a different thing in quantum mechanics.
Interestingly, classical mechanics has not been "replaced" by relativity or quantum mechanics: these theories (models!) co-exist, and are applied wherever it makes sense to. Sending humans to the Moon and back occurred when both relativity and quantum mechanics were well available and established, but required "nothing more" than classical mechanics.
I'd like to get feedback from "girls of today" (and yesterday, too) about this point.
My impression is, that accepting theories as models required me to mature a lot. I found a very interesting framework for "modeling the acceptance of models" in the wonderful book
"Women's Way of Knowing"
by Mary Field Belenky, Blythe McVicker Clinchy, Nancy Rule Goldberger and Jill Mattuck Tarule (as the title suggests, it's women-centered, but deals of men too - it may be hard following at times, but I found this book inspiring, to say the less).
In their terms, changing your own view so that you accept knowledge as something "constructed" is a relatively late moment. When (if) you reach that stage, it feels just "obvious" considering theories as nothing more, but also nothing less, than models.
But more important, it may be much more compelling to devise example and test cases which allow a great deal of experimentation. Of data-collection, organization, and sorting-them-out. Of distilling provisional truths (all acceptable, provided they can be falsified with some experiment). Of assimilating them "from the inside".
Nice, isn't it? Unfortunately, it collides with this:
4.What a hurry!
In classes we had to complete our works or tests under tight time constraints.
To get to the classes we have to "fight against" a clock ticking all the seconds we lose in traffic during our commute (if you happen to live in Milan).
We always feel the relentless pressure of time and haste.
And many examples seem to convey the same message. They're designed as "puzzles", to be "solved" in some short time (sometimes even specified).
A very competitive way of conceiving examples, that's true. But, not necessarily fostering deep creative thought. Just useful for contests, provided a real usefulness of them can be found (in some cases I've seen, the puzzle was used to build or confirm some pecking order based on some kind of pretended "mental prowess" - almost always by boys in early adolescence).
THen, if you scrutiny just a bit, you notice almost no real world intriguing problem manifests as a "puzzle" to be solved quickly.
Neither they are "competitive", too!
Rather, the more their complexity the higher the need to cooperate with others in organized ways to just even understand them.
In addition to being essentially contrived and unrealistic, examples of "shoot-an-answer" type may be deeply unfriendly to the more reflective and less status-poised people.
My fantasy and competence are limited, and our time scant, so it's better I don't go any further listing reasons. We all will have opportunities to add more.
I may try a synthesis, however: examples as they are commonly conceived tend to be unfriendly to a certain type of people.
These "people" may not form a random sample of the overall population: they are likely to be mostly female.
On average, it is the girls who "stay quiet" in a class, being less impulsive and more reflective. It is also them who, on average, do not get crazy for sport heroes. Again on average, it is girls who love thinking at a calm pace, interacting, trying ideas meanwhile...
The morale of this post may be, we need many more examples.
For them to be inspiring, we may need to deconstruct the way mathematics and physics are presented, and build on the new awareness.
In my opinion, we may try looking for examples which are:
- Taken from real-world, interesting applications
- Presented as open-ended problems, with possibly many, or no, solutions; as medium- and long-term projects anyone may follow at their own pace
- Not imbued of stereotypes on "what the kids would like to learn"
- Very "experimental" in nature, and respectful of the experimenter.
As the "Math Support Gals" group, we may have a role in inventing new examples!
A part of the group's sister site will be devoted to them.
I guess this is not sufficient. Time ago, on Pulsewire, I and my friend Jackie had a very interesting exchange about the subject. She pointed out a very important thing: teaching to girls demands patience. It requires staying in synch with a child time, not pushing, but in a sense (my addition) "pulling" her, gently.
It demands using the proper tone of voice, the sensible pauses, and neglect of the clock.
The reward, you can imagine, is immense. An "oxytocin-intensive" experience.
I realize this may not be easy to do, in the rigid frame of institutional school.
Should we work on this, too?
Cheers to all,
and let's dig the world, looking for interesting treasures!