[IAEP] [Sugar-devel] versus, not

[Edward Cherlin]

On Sun, May 10, 2009 at 9:46 AM, Costello, Rob R
<Costello.Rob.R at edumail.vic.gov.au> wrote:
> We’ve had some of this discussion before : Alan has mentioned the arch
> metaphor before–as a key insight in building / architecture, that is
> distinct from mere brick laying, and so is never reached through repetition
> of laying however many bricks  - as an analogy for a type of learning or
> mathematics that is not reached by mere repetition of lower order skills

+1

> Also used a related metaphor that the real test of learning is the ability
> to do the ‘real thing’ at some level, not just reciting learning ‘about’ a
> topic (or switching to a music analogy he has also used, can the student do
> more than play scales? as useful as that may skill and drill may be…

There was a company that said it only hired math and music majors,
because they were the only two subjects you couldn't fake. Proven
ability to learn and perform meant that they could learn pretty much
anything and then do it.

> (and also do more than the air guitar version which might get smuggled in
> (or even advocated) as a watered down version of the topic that is easier to
> ‘teach’ and ‘learn’)
>
> Anyway, re-reading some of the previous discussions, I find we have all
> generally been in agreement that there is a place for “skill and drill”

Yes, we agree that it has a place, but not what that place is. And
even where we might agree in part, as in the case of musical finger
exercises, we will still disagree on when and how much, and whose.
Bach, Chopin, Brahms, Bartok all wrote wonderful exercises for a wide
range of skill levels, but no Czerny for me, please.

> So an argument that perhaps needs to be put to rest, as one that no
> educators seem to actually hold, as far as I can tell, is the suggestion
> that there is no role for direct instruction

I have direct experience that you cannot claim that any idea has 100%
acceptance, or conversely, 0% opposition. Nobody here objects to
direct instruction wherever we actually know how to do it effectively,
which includes the idea of not leaving anything out, not dumbing the
topic down to only include what we know how to do by direct
instruction. But some people do object.

> My own observation is that while it is indeed possible to structure
> curriculum in a way that is more self directed and still has enough
> structured scaffolds (such as well sequenced materials that can accessed on
> demand, and mixes in some project driven enquiries) , in most cases a strong
> thread of direct instruction can be justified and is often needed

Schools that allow the student to choose subject matter still offer
proven teaching methods. Suggesting that children should learn from
_unguided_ exploration alone is ludicrous, and yet I have personally
been accused of such nonsense when I tried to talk about _guided_
exploration, even on this mailing list.

> However a curriculum that does not go beyond this, that does not encourage
> performance or real competence as a test of learning, is, in these terms,
> the equivalent of only ever playing scales or brick laying, - ie it does not
> reach the ‘arch’ of understanding which gives new meaning and beauty to the
> brick laying exercise, or allow students to reach an authentic performance
> with some musical feel –
>
> Idit Harel : “even "successful" pupils within this approach are often left
> with a kind of knowledge which some have called "inert", mathematical
> knowledge which may suffice for passing tests but which is not useful or
> available outside the classroom context in which it was originally learned.
>
> (Educational Studies in Mathematics 24: 319-327, 1993)

If you only teach how to get The Right Answer, it should surprise
nobody that children are helpless in dealing with questions that have
no right answer, where judgment is required.

> Some feel it’s the state of teachers that leads to this –-

Teachers are just as much victims as are children. Their own education
and training has been dumbed down over two centuries, under the
guiding principle that they don't have to understand what they teach;
they just need to be able to present it as set forth in the textbook.

This is the same principle that was widely applied in factory
automation, and for the same reasons. "Efficiency" on the one hand,
and no backchat from the workers on the other. Of course, that means
that when the time comes, you can't employ all of Total Quality
Management, which requires that the workers understand what they are
doing and at a minimum report deviations, or better still be able to
suggest improvements. You are left with the portions of quality that
it occurred to you to measure. You also get workers who won't listen
to management even when it has a good idea.

Thus No Child's Behind Left. Obama proposes to change the measures
away from just "standard" tests, but it does not appear to have
occurred to him or to his advisers to ask the children for their
input.

> others hope that
> new and innovative software will transform the field

There is nothing more feared and loathed in education than genuine
innovation. As soon as XOs and Sugar start getting good results
reported from the field that make their way into the public
discussion, as soon as they threaten to become part of the
"mainstream" of ideas, I expect to see an organized campaign against
them. Several, actually. From all the segments of society whose fears
they expose.

> So this sense that state of traditional education  is selling us short on
> real learning, or at least under doing the potential  - is what I suspect
> informs many here at some level, in an attempt to better resource education.
>  And yes, education has often swung too hard and simplistically from one
> position to another …which is where some of us want to try to understand and
> contribute
>
> Rereading a previous round of this (archives June 2008 on ‘reconstructing
> maths- http://lists.sugarlabs.org/archive/iaep/2008-July/001303.html’)
>
> has got me going to back to a Papert article on possible math educations  …
>
>  http://www.papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html
>
> and following a provocative paragraph
>
> “A particularly clean example is an apparent paradox in the report by Sfard
> and Leron (in press). They ask which of the following two problems is
> harder:
>
> P1: Given three points, (2,3), (-1,4), and (0,-1), in the plane, find the
> center and the radius of the circle through them.
> P2: Write a computer program that accepts any three points in the plane
> (given by their coordinates) and returns the center and the radius of the
> circle through them.
>
> Since P2 asks for more than P1, one could argue that tautologically it must
> be harder. But Sfard and Leron report that more than half of their students
> failed at P1 and nearly all succeeded at P2. Why? It is not any magic of the
> computer except the fact that working at the computer transforms the stance
> of the students from "solving a problem" to "pursuing a project."

I disagree. Telling a computer an algorithm is much easier for people
than following an algorithm. We are good at communication using names,
but bad at keeping track of anything with multiple steps and a varying
collection of intermediate numeric results. Computers understand
nothing, but are nearly infallible at remembering sequences of steps
and large numbers of values. We copy numbers incorrectly, copy the
wrong value, mix up signs, and so on. They don't.

One method of solving this problem is to find the equations of the
perpendicular bisectors of line segments joining two of the three
points, and then finding the joint solution of these equations. The
radius comes from the Pythagorean formula. Compute all three distances
if you want to check your work.

Point midway between (a,b) and (c,d) is (0.5×(a+c), (0.5×b+d). Slope
of line segment joining them is (a-c)/(b-d). Slope of perpendicular is
negative inverse of this slope. Line with slope s through point
(x0,y0) in vector notation is (x0,y0) + k×(x,sx). Or
s=(x0+kx)/(y0+ky), which we can easily convert to standard form. Use
Gaussian elimination to solve the pair of equations.

I did not write all that in an attempt to explain it to you. I hope,
in fact, that you understand how impenetrable all of this is to the
non-initiate.

On the other hand, if the student is permitted to solve the program on
graph paper with ruler and compass, it is actually fairly easy.

Center A, radius AB, draw circle.
Center B, radius BA, draw circle.
Connect points of intersection to get perpendicular to original line.
Same for BC.
Find point of intersection of the two perpendiculars.
QEF (which was to be done)

> Reading through some of the work of these authors and colleagues in Journals
> – some via uni library – but some is also open online
>
> http://symbolicspecies.com/?The_2006_conference:Speakers_and_abstracts_2006:Uri_Leron
>
> http://edu.technion.ac.il/Faculty/uril/papers/JRME_Actions_vs_Functions.pdf
>
>
>
> leads further to the interesting idea of mathematics is built on more homely
> metaphors
>
> http://www.cogsci.ucsd.edu/~nunez/web/PME24_Plenary.pdf
>
> this is seemingly very non practical – as the logical discipline of
> mathematics itself can appear to be - but for some educators such as myself
> its all valuable learning, - we share a role in engaging in better IT
> mediated learning experiences (of math and other areas), so I at least find
> this compelling research, even in a parallel universe where software is not
> necessarily ‘free’-
>
>
>
> [eg someone mentioned the need a while ago to do the ‘unsexy work of
> uploading and mapping n curriculum against x activities’ – that’s been
> exactly my role for the last 4 months in that parallel world – I wrote some
> tools to help  – I often see the same general issues coming up all over the
> place – [ie what philosophy of learning? What system structure? Do
> developers really need to bother with this? ] it clarifies my thinking to
> see the issues in other contexts – helps try to find the superstructure that
> these issues are derived from] … I think there are common concerns about
> learning, and developing systems that are more readily and deeply accessible
> to students as learning tools

Where is that information? We need it for the Earth Treasury-led
textbook project.

> So the reflective thinking / debate about IT and learning has been worth
> hanging around for – risking these questions might lead to better answers
> for those who are gripped by the questions, in whatever context
>
> [I had hoped to run a school sugar trial and may still do so if I can ..but
> either way all this is learning that will underpin some kids learning].
>
> cheers
>
> rob
________________________________
>
> From: iaep-bounces at lists.sugarlabs.org
> [mailto:iaep-bounces at lists.sugarlabs.org] On Behalf Of Bill Kerr
> Sent: Friday, 8 May 2009 6:37 PM
> To: Martin Langhoff
> Cc: iaep; Sugar-dev Devel
> Subject: Re: [IAEP] [Sugar-devel] versus, not
>
> I'm not sure what is meant by a "big tent"

I'm not one of those proposing a big tent. I want a tent that is just
big enough for what works, not for every unproven theory floating
around, nor for faulty implementations of what works.

> Why do some people want a big tent for learning theory but not a big tent
> which accepts both FOSS and proprietary software? Phrasing it that way is
> intended to encourage people to think about what sort of thing is learning
> and hopefully will not be interpreted as just being provocative for its own
> sake.

I would have no complaint about proprietary software if it were not
simply legal monopoly under the copyright and patent laws. With very
rare exceptions, the developers behave just like the monopolists in
the Econ 101 textbooks, withholding product and driving up prices. The
result is educational shovelware. Instead of powerful learning tools,
we mainly get canned lessons on minimal amounts of subject matter at
unconscionable prices, and unseemly boasting about how much good the
company is doing. (I first published this set of complaints in a
market study of so-called Educational Software in 1981. Nothing has
changed on the proprietary side in the last 28 years. In another
report, I claimed that Smalltalk was the future, and here we are.)

I have never known much good done by those who affected to trade for
the public good.--Adam Smith

> you can have a big tent where people don't discuss learning theory because
> it's too hard to reach agreement
>
> you can have a big tent where people passionately argue about learning
> theory but actually listen to what each is saying and argue rationally
>
> when I look at minsky's theory of mind I see that he supports multiple
> models of thinking but also argues against models of thinking that he thinks
> are incorrect or which emphasise only one way of doing things, eg. although
> he helped create connectionism he now thinks it has too much influence
>
> that suggests another version of a big tent which I favour - cherry picking
> the best parts out of different learning theories / activities based on
> criteria (not stated here) that are substantial

+1

> I don't believe that thinking people are agnostic about how people learn
>
> it seems to me that alan kay has presented a possibly strategic view of
> progress on these questions (that learning about bricks will not
> automatically lead to building arches, that we need more than just focusing
> on building blocks) - but that for various reasons we are not in a position
> to implement the learning materials based on that view in practice in the
> activities

That is in fact the intent of our project. As I understand what he has
told me, Alan does not think that it is impossible to do it, but he
doesn't know how to get schools to accept it.

> for me to sit in the big tent holding a strategic view feels different to
> "too hard basket", agnosticism or a tower of babble - teaching with an
> underlying strategic view is very different to just going along with the
> tide
>
> that would mean work to understand and implement that strategic view but
> also accept that we are not there yet (it will take some time) and so it is
> perfectably understandable and desirable that people will use and develop
> whatever is at hand or which they think important to develop - no one can
> stop that anyway accept by successful arguing someone out of a POV
>
> Does the "big tent" phrase add clarity to this conversation?
>
> On Tue, May 5, 2009 at 4:59 PM, Martin Langhoff <martin.langhoff at gmail.com>
> wrote:
>
> On Tue, May 5, 2009 at 3:03 AM, Walter Bender <walter.bender at gmail.com>
> wrote:
>> Fair enough. I agree that *most* people on the list agree that there
>> is not just one right way. And to use a metaphor that has been
>> oft-spoken in the US news of late, Sugar Labs has to have a "big
>> tent."

Unfortunately, the primary users of that phrase are those intent on
driving all opposition out of the Republican "big tent". I don't think
that the metaphor will help our discussion.

>> Sugar itself has affordances that can be used in support of many
>> educational approaches and virtually any content area.
>
> Completely for the big tent, and wide ranging use models. It also
> means I have to swallow hard when people use things I build in ways
> that I consider... not particularly good. You might hear me mention
> that "that's a practise that I don't emphasize" ;-)

I am greatly encouraged by the report from Ethiopia that Sugar and
other software leads teachers trained in strict rote memorization to
accept and even embrace questions from students. Only sustained
experience can convince large numbers of people of a new truth.

> cheers,
>
>
>
>
> m
> --
>  martin.langhoff at gmail.com
>  martin at laptop.org -- School Server Architect
>  - ask interesting questions
>  - don't get distracted with shiny stuff  - working code first
>  - http://wiki.laptop.org/go/User:Martinlanghoff
>
>
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