Contributed Commentary on
Volume 4 Number 8: Stone Developmentalism: An Obscure but
Pervasive Restriction on Educational Improvement
27 April 1996
Les McLean
lmclean@OISE.ON.CA
Thanks to Rick Garlikov for taking the time to respond to John
Stone's "Developmentalism" article. Among the good qualities of Rick's
response is that it is an illustration of how to follow the Edpolicy
Guidelines! I hope all who took the time to read Stone's article will
also take the time to read Rick's response (the response is only about
one-quarter as long!). My purpose in this post is to branch off from both
of them to follow the question, "In any given situation, just WHAT is
being taught?" In the direct instruction lessons I have observed, myself
or via videotape, I was convinced that the overriding outcome, the one
that would last (if anything did) was, "Do what the teacher says, believe
what the teacher believes; don't think too much because it will slow you
down."
YES--I know that is not what most instructors intend. I know that is
not all that happens. But I have been convinced by the tasks and the
methods that it is mainly what happens. Rick's example of Saxon math and
the follow-up questions illustrates my point. No teacher can take the
questions seriously and keep to the essence of direct instruction; nor
should they, any more than whole language teachers should avoid word/sound
correspondences. My question, "What is taught?", however, came from
Rick's "statistics" example. I put in the quotation marks because I
argue that Rick's 100-box problem does not teach statistics in any
meaningful sense of the term. I will argue that it teaches, "None of the
most important and difficult problems in life are statistical, but
sometimes you can use statistics to understand them better, maybe even
solve them". Here is the task, as set out in Rick's response to Stone:
"Likewise, here is a statistics question that might work better to help
teach statistics. I have been trying to work out ways to get kids to see
that one must take into account not only probabilities, but the value of
outcomes, when assessing choices. For example, should you play a game
where you get to choose a box to open if there are 100 boxes to choose
from, $1000 in each of 99 of the boxes, but a bomb that will be fatally
detonated in one of the boxes? If kids say, "yes, because those are good
odds", I lower the amount of money in each box, which does not change the
odds, but which starts to make them reconsider, and get the point.
My stats question derives from different variations on this game: Is
there any difference between having 100 kids who think this is a good game
to play each choose a box (all at the same time, so that all the boxes are
spoken for), and having 100 kids play the game separately? Why or why
not?" (Rick goes on to explain...) "If they play simultaneously one kid
will for sure get killed, which seems like it makes the game not a good
game for any of them, since they will be guaranteed to lose a friend, if
not their own life. But if they play individually (with different sets of
boxes, replacing the chosen box each time), maybe no one will get killed,
and maybe two or eight or 100 of them will be killed. Yet the game may
still seem like a good risk to some kids to play on this basis. IS THERE
a statistical difference between the two ways of playing the game? If so,
what? And if not, why does it seem okay to play it one way to a kid but
not another way? This is the sort of thing I consider to be a purposeful
interventionist, proactive sort of teaching question, but one which is
consistent with Dewey and which would perhaps lead to students learning
about statistical analysis better. Yes? No? It is not a "natural"
question, but one which I think is of the sort that works "naturally" to
get kids more interested and thinking about statistics issues and more
readily receptive to learning them, however else they are taught."
My point: Except for the first, simple situation (one person choosing one
box from 100), people I know (from 'kids' to graduate students), cannot or
will not learn enough probability to arrive at the correct odds
themselves. Even if they arrive at an intuitive acceptance of the odds as
stated by the teacher, the crucial question remains, "How do you put a
value on human life?" Even as a class exercise, this belongs in Decision
Theory, and here again, "kids" and graduate students I know will not gain
more than an exceptionally superficial feeling for the "statistics". If
the teacher can engage their interest, however, they WILL see how crucial
the value question is and how, IF they can answer that question THEN they
can apply some simple statistics to arrive at an answer. My prediction is
that most people will decide that they should not play the game at all,
any more than they would play Russian roulette. If you really want to
teach statistics, there are, IMHO, better examples, e.g., error estimates
in opinion polling, bias resulting from non-random sampling in comparative
studies.
Here is an example from the National Pilot Mathematics Test, elementary
school, in the U.K., 1992. (The 'sign' was presented in a box so it
looked like a sign. Use of a calculator was allowed. 'lift' =
'elevator')
--------------------------------------------------------------------
This is the sign in a lift at an office block:
This lift can carry up to
14 people
In the morning rush, 269 people want to go up in this lift.
How many times must it go up?
---------------------------------------------------------------------
The expected answer is 20, but notice how many assumptions are required
for this to be correct (always full when people waiting, no one takes the
stairs, no large parcels...). The best approach is to assume maximum
simplicity, divide 269 by 14 and round up, still not an easy question for
young people. But what is being assessed? What is being taught? The
example appeared in the article by Patricia Murphy (1995), "Sources of
inequity: understanding students' responses to assessment" (Assessment in
Education, 2(3), 249- 270), where she presents evidence that girls pay
more attention to context than boys and hence take more time with this
task, maybe get it wrong, maybe omit it. Mathematics tests are full of
such examples, and the successful student has to learn to ignore most of
the contextual information and get directly to the simple calculations.
Few would argue that mathematics teachers should be teaching this. Just
one more example of an item that might be authentic in some circumstances
but not desirable in any:
Billy steals Joe's skateboard. As Billy skates away at 15 mph,
Joe loads his 357 Magnum. If it takes Joe 20 seconds to load his
Magnum, how far away will Billy be when he gets whacked?
Best to end with another quotation from Rick's response:
"I think teachers need to be able to recognize and create teachable
moments and then know what to do with them when they have them." Right
on, Rick.