Re: Programming languages for the very young

From: Samuel Walters (swalters_usenet_at_yahoo.com)
Date: 01/19/04 

Date: Mon, 19 Jan 2004 02:24:16 GMT

First off, Thank you for writing a well-considered response. I'm glad to
find someone intelligent of opposing views. One cannot, after all, trust
one's own views until they are tested against someone who can
intelligently criticize them.

Now, I'll put my experience in this matter into context. I have worked
for many years, with a couple of breaks, as a math tutor at the university
and community college level. The community college is in rural Florida
and connected to a magnet high school where they lump the troubled and
exceptionally bright students together and treat them with a bit more
respect than is afforded them at public schools. I have helped some with
these students, and have worked with many students who couldn't add or
subtract. In a strange coincidence, it seems that almost every girl I've
dated seriously has been from a family deeply involved in education. This
has given me some insight into what grade school and middle school
teachers worry about.

I also spent a good deal of my time during high school assistant coaching
P.E. and teaching reading to Kindergarten and First grades. I worked
closely with the head start program. That was, to say the least, an
eye-opening experience. It's the sort of thing that makes you want to
side with Communist China and require people to be licensed to have
children. I won't go that far, but it does make one reconsider the idea.

I said elsewhere that I could charge $50/hr for my services, and I have at
times. I'm well known for my tutoring ability. I prefer, however, to
decide how much of my time is available and dedicate that time to students
who need the services of a great tutor, rather than just any tutor. Then
I charge the average rate for tutoring in this area, $20/hr. In this
manner, I often tutor middle and high school students. I don't mean
to be immodest. I used to deny it every time someone would compliment me.
 Then I realized that by some strange quirk of divine grace, I was given a
gift and to deny the depth of that gift would mean wasting some of it. I
am still a humble person, I just know that I have a gift and that it is
for others, not me.

After several times of being bitten by the career bug, I keep finding
myself back here, living in poverty and loving every minute of it. It's
time to turn teaching into my career.

| Brian Mastenbrook said |
> Unfortunately due to the prevalence of graphing calculators, many
> students these days never develop any sort of proficiency at graphing
> by hand, which means they lose out on a very important intuitive
> understanding of spatial relationships in numbers. So I would be of the
> opinion that a trig class should be taught with only scientific
> calculators (used well, too - being able to calculate some basic
> sines/cosines without the calculator is important for calculus). Other
> than that, I agree with you.

The instructors here have come up with a clever way around this. They
have two portions of the test, each on a different colored sheet of paper.
 One is sans-calculator. The different paper allows one to see who's
working on which portion of the test so that the no calculator section is
enforcible. Trig is just the first place

> There are some excellent, non-anecdotal reviews of mathematics
> curriculum linked from the Mathematically Correct site. A lot of the
> information is indeed anecdotal, but I think the purpose of the
> Illinois Loop site is to encourage parents to question the curriculum,
> not provide mountains of research. Leave that to the Fordham Foundation
> et al.

I will find it, I will read it and then report back. I promise.

>> What I don't think that you understand is that teaching mathematics solely
>> by rote is not only ineffective, it's counterproductive.
>
> I never disputed that. However, I am sick of trying to teach algebra to
> students who quite simply can't add and subtract - not because they
> were "drilled and killed", but because there was no drill and all.
> Critical thinking requires a solid, intuitive understanding of the
> basics - you can't possibly visualize algebra, or do simple
> trigonometry, if you can't rattle off what six times seven is without
> thinking. By the time you get to an Algebra II course, you should be
> able to solve simple linear equations without much thinking as well.
> Intuitive understanding is the key to higher-order thinking; without
> our intuition, we wouldn't think at all.

I agree that one cannot effectively learn algebra if one is still baffled
by basic issues of arithmetic. I, however, think that addition,
subtraction, multiplication and division are much more than skills learned
by rote. Tim Hayes responded to this point, and you will find my thoughts
in the response I'm about to write to him.

> This is a great aim for the later grades in mathematics education;
> however, the goal of a third grade mathematics classroom is not to
> produce critical thinkers, it's to produce people who are ready for
> critical thinking. The kids I tutor in the seventh and eigth grades,
> who are placed into advanced track algebra, are not. They can't be
> expected to use any sort of the critical thinking that you and I do,
> because mathematics is totally counterintuitive to them - even basic
> operations.

I actually believe that numeracy *is* intuitive. I think that the proper
mental models are not being provided. Again, more in my response to Tim
Hayes.

> It's not the teachers who are the problem, it's the people who train
> the teachers and write the curriculum. There is no even ground there -
> it's been getting more and more progressive over the past fifty years.
> There is no essential debate anymore /inside/ the education colleges. I
> would argue that this is not a good situation.

If it is as you describe it, then I would agree with you. I do not have
any experience inside any large education college. My experience is
distinctly small-town. I cannot assert anything about this without more
research.

> Don't mistake me as being against many of the progressive ideas - focus
> on the individual is good, developing critical thinking is good. I am,
> however, against the overtly philosophically-driven curriculums we now
> have, which are demonstrably worse in some cases than what we had
> fifteen or twenty years ago. Phonics /works/ as a means of teaching
> reading - study after study has shown that. Whole language replaces
> this solid method of reading instruction with activities like
> "modeling", where the teacher is supposed to go up to the front of the
> class and read silently, to model reading for the student. It's cargo
> cult reading, and does nothing for the student who is falling behind.
> However, it does make less work for the teacher.

I agree with each point here, save perhaps one. That is your definition
of "philosophically-driven curriculums." This "cargo-cult reading" you
describe is a poor replacement to phonics if only for breaking the maxim
that learning is not a spectator sport, if not on more fronts I don't
intend to dig up at the moment.

>> Where we *should* be concentrating is on problem-solving skills. The
>> teachers themselves don't possess those skills.
>
> We aren't in a place where we can do that. Have you actually tried to
> teach or tutor in the middle school / early high school grades lately?
> The students have gone through so much diluted, project-centered,
> integrated crap that they don't have the basic command of literacy and
> mathematics to actually approach problem solving skills. The
> curriculums attempt to teach basic mathematics with an overt focus on
> "algorithms", under some mistaken assumption that something other than
> repeated practice can build intuition. The /only/ way to build
> intuition is through practice, practice, and more practice - and by
> understanding what skill you're practicing when you're practicing.
> "Drill and kill"? Hardly so.

My work with students below the college level is fairly low. One or two
paying customers a term, and a few that the local magnet school sends my
way.

Again, rebuttal deffered to my next post.

>> I end up tutoring a lot
>> of students going for their teacher's certification, and luckily, the head
>> of that department often sees me to ask how well her students are using
>> problem-solving skills. A student must be taught not only that a thing is
>> true, but why it is true. Students are not being taught that math,
>> science, and history are anything more than a loose collection of facts.
>> That's why I can (though I don't) charge $50 an hour for private tutoring.
>> I make it all fit together. I make it all make sense.
>
> What school district are you in? The local districts here are as
> progressive as can possibly be. The closest university's teaching
> department is purely progressive, and their professors give us such
> fine gems as "I don't like gifted programs - they're elitist", "I don't
> like math", and "I don't think teaching facts is important."

I'm not sure our districts are *anything* alike now. When I see students
entering college, they have a strong memorization of their times tables,
but no earthly clue what multiplication means. For instance, I'll be
damned if I can find more than a handful of freshmen able to tell me why
multiplying length and width gives us area of a rectangle. The ones I
*do* find are probably going to be resident aliens or immigrants. I'm not
asking for deep understanding here. I just want a student to understand
that counting by five is the same as the fives table in a multiplication
table. It's truly baffling how little understanding they possess.
 
>> A teacher is a facilitator. They are not a mystical font of knowledge in
>> whose mere presence a student will become magically enlightened. It is an
>> instructors job to lead students from their current understanding to a
>> deeper and more powerful understanding. I am sick of seeing students who
>> are afraid to do anything on a math problem because they're afraid that
>> they will be wrong. A student should explore, not quake in their boots.
>
> I'm not arguing for a "mystical font of knowledge"; but I do argue that
> teachers should be the primary guide for the student's learning. The
> "facilitator" theory is that students can direct their own knowledge.
> This would be great if young children knew anything at all about what
> they didn't know, but they don't. The reason we have teachers is that
> young children /can't/ reasonably direct their own learning, due to
> inexperience. The teacher is then the guide which makes the decisions
> about what the student will learn - paying attention to feedback, yes,
> but still creating the overall direction.

It seems you were using a technical term whose mundane meaning was coopted
by a theory. I was reading it as the colloquial sense. It is obvious that
you are far better read on theories of education than I am. I hope this
won't diminish your view of my ideas. :-P

Just beware, if you use a technical term with a common usage, I'll
probably read it with the common meaning. Hopefully, though, I will spot
those landmines of miscommunication since I know they're there now.
 
> I agree that "students should explore", but honestly, if you're
> learning how to add and subtract, there isn't much exploring to be
> done. It takes repeated problem solving to get it under intuitive
> command, and once you have it, you are much better prepared to think
> critically about higher mathematics.

To this, and the last point: I think that there is reasonably more
exploration to addition and subtraction than it first appears. This
assertion will be elaborated, you guessed it, in the next post.

> Peer review is also known as mutual masturbation. The problem is that
> right now, testing is tied into teacher and district funding, which
> immediately destroys the scientific validity of the test. If we viewed
> tests as merely a measurement of curriculum on a broader scale, they
> could be much more valid measurements.

*chuckle* Well, that certainly is a colorful way of putting it. And here
I thought that explaining to statistics students the reason statistics was
required "is not so that you could find the standard deviation of a data
set ten years down the road, but so you can call 'bullshit' when a
consultant tries to pull the wool over your eyes with bogus statistics," was a
brazen thing to say.

All I have to say is that there are effective ways to conduct peer review
and there are horrifyingly poor ways to conduct it. While I support the
former, sadly bureaucracy favors the latter.

I agree wholeheartedly with your point that standardized testing loses all
effectiveness when tied to funding. In Florida right now, there's a
disturbing system that ties school funding, individual teachers jobs. The
problem comes from two fronts. One is that the large number of senior
citizens will never vote for an increase in funding for schools. The
other is our "education governor." You know him as Dubya's brother, Jeb
Bush. Big headlines came recently when Bush announced an 8% increase in
funding for Community Colleges. After the 25% cutback at the beginning of
his last term, an 8% increase still leaves us with a 19% deficit. It
seems he's not only hoping to keep the children from learning arithmetic,
but he's hoping that the general population is bad at it too. (I leave it
as an exercise to the reader to connect this with the last presidential
election.)

> As for what's worth measuring, the local education union wants lots of
> open-ended questions on the test which have to do with the application
> of mathematics, and they shun all questions which have to do with
> mathematics in the abstract. Of course, our local teacher college
> teaches that public school education's purpose is merely to prepare the
> average student for their future career, so what's the point of
> teaching exponentation or any other abstract concept?

I despise the overkill manner in which mathematics has moved toward an
emphasis on "applications." Mathematics involves a visceral, visual and
tactile understanding that these methods obscure. Strange, you'd think
that "applied" problems would be more grounded in experience, but they're
not.

> I disagree with the way you phrased that - the correct algorithm is
> more important than an incorrect result. Our district penalizes
> students who obtain correct answers but did so intuitively. This is,
> from what I understand, part of the Everyday Mathematics curriculum. In
> their world, for even the simplest of mathematics problems, you need to
> write out a detailed explanation of how you came to the answer.
> Penalizing intuition is the precise opposite of what I would do if I
> wanted to encourage critical thinking. A solid intuitive understanding
> of mathematics builds the ability to think critically about a wide
> range of ideas. Of course, it's important to understand your intuition
> too, but penalizing it is highly counterproductive or even dangerous.
> Most everything you or I do with mathematics, we do so intuitively. It
> enables us to extend our thinking to more complex ideas - programs,
> circuits, differential equations, et al. Without this ability we can't
> extend that far - we're always having to count on our fingers to add or
> subtract, or write out multiplication.

The true utility of mathematics is that it allows us to take small
intuitive steps to discover surprising and often counter-intuitive truths.
 
>> I am very confused as to how the thesis of this paragraph has *anything*
>> to do with totalitarianism.
>
> It was poorly written. Sorry.

S'okay. I hope you are so lucky that this is the worst of your
transgressions on usenet. :-P

> I wasn't arguing about computer technology at all! You can teach the
> lambda calculus on a blackboard. But if the students have not
> sufficiently developed their mathematical and anylitical intuition to
> the point where they can work with the conceptual underpinnings of a
> computer, then we are producing a society which doesn't understand its
> own operation - a sure danger to freedom.

Here, I think I let some of the context of the greater thread bleed into
your posting. The topics were different, I apologize.

Ah! Now you connect the dots. I can see why you were talking about
fascism. I advocate computer programming as a required high school
course. Perhaps there are bigger fish to fry at the moment, but an
understanding of the nature of the beast is imperative for students to
function in any future society. I'm not talking about web-surfing or
using a word processor, though those are useful skills. I'm talking about
the tools necessary to build a mental model of what a computer does. My
personal political beliefs see the Internet as either the future
choke-point for all information, or the liberating conduit that breaks the
bonds of political spinsmen and double-speak. Education is the key to
the outcome, as we both agree.

>> But the problem facing many educators these days is that the
>> students know more about computers than they do!
>
> From my experience, students know a lot about using certain things on
> the computer, but little about the computer itself - how to fix
> problems, etc. Some students are quite gifted with computers, and their
> attention should be directed towards programming.

And my point was that the stewards of knowledge in this area are incapable
of effectively educating students because they themselves do not
understand that which they claim to teach.

> Ah yes, Lakoff. His ideas are interesting, but a lot of
> neuropsychologists tend to see him as kind of on the edge - in
> particular, he attaches a great deal of importance to mirror neurons
> that are not yet fully understood or explored. I think his ideas will
> only be evaluable ten or twenty years from now, when cognitive
> psychology has caught up with the areas he's speculating in.

I haven't read any of his other works. I found the first half of "WMCF"
solidified a lot of ideas I had a subconscious grasp on. The ideas have
proven very useful in my day-to-day experience. In the second half of the
book, Lakoff and Nunez dig into some areas of mathematics that are clearly
over their heads. This makes their assertions interesting, but not
compelling. Overall, I felt the first half was well thought out and well
researched. The second half seemed cobbled together at the last minute
from loose notes. YMMV.

Sam Walters.

P.S. I did not intend this as a "me-too" post, but I felt it was
important to map out the areas we agreed on so that we can focus in on
those where we disagree. 

-- 
Never forget the halloween documents.
http://www.opensource.org/halloween/
""" Where will Microsoft try to drag you today?
    Do you really want to go there?"""

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