[math4] [utos-xo] 4.N.12 - Mutiplication

Thu May 28 06:24:21 EDT 2009

On Thu, May 28, 2009 at 04:04, Christian Horne
<blendmaster1024 at gmail.com> wrote:
> this is a good idea except that animation generally sucks on the XO.
> other than that...

I think that animations where only a small part of the screen is
redrawn will work fine.

Regards,

Tomeu

> On 5/27/09, Shawn Willden <shawn at willden.org> wrote:
>> At the Utah OLPC meeting my son and I volunteered (were volunteered?) to
>> cover
>> 4.N.12 in the curriculum, which is addition of up to five-digit numbers and
>> multiplication of up to three digits by two digits.
>>
>> This note is intended as both an update on our progress, and a request for
>> comments.  All suggestions/corrections/flames are welcome.
>>
>> Not satisfied with my own ability to effectively teach fourth grade math, I
>> enlisted the aid of my son's (fifth-grade) teacher, Mrs. Woody (copied on
>> this e-mail), and she pulled in a few other third and fourth grade teachers.
>>
>> I asked them how they teach multiplication, and we brainstormed a bit on how
>> we can effectively translate those techniques to software.
>>
>> By the way... I *highly* (highly!) recommend that anyone working on the 4th
>> grade math project find a local teacher who has experience teaching the
>> concepts to children.  Particularly with simple math, knowing how to do it
>> is
>> *very* different from knowing how to teach it.
>>
>> Some of the constraints that we think we're working under are:
>>
>> 1.  We are providing only a piece of software, and we can't know exactly
>> what
>> explanations will accompany it.  So, ideally, it would be good if the
>> student
>> could learn to do multiplication ONLY given the operation of the software.
>> This is a didactic activity not a practice activity.
>>
>> 2.  Any textual or verbal explanations provided by the activity will have to
>> be translated for every country that will use it.  So it makes sense to
>> minimize the use of text and speech, and to teach the process as much as
>> possible with numbers, arrows, and animations.  I do want to use audio cues
>> for emphasis, but those don't need to be verbal.
>>
>> 3.  XO storage capacity is limited, so extensive imagery and audio files are
>> a
>> bad idea (and outside of my skill set to produce in any case).
>>
>> Within those constraints, though, we think there is a lot that can be done
>> with animation and simple sound effects.
>>
>> One of the points that the teachers emphasized is the importance of teaching
>> children not only the mechanical process of long multiplication, but also
>> the
>> importance of place values, and their role in why the process works.  To
>> that
>> end, they recommended teaching long multiplication by "pulling apart" the
>> steps.
>>
>> For example, given the problem 284 x 48, that problem can be broken down
>> into
>> two sub-problems: 248 x 8 and 248 x 40, the results of which must be summed.
>>
>> Visually, we think we want to present the whole problem on the left-hand
>> side
>> of the screen and then pull it apart with an animation by having the
>> constituent sub-problems "fly" to the right side of the screen, leaving the
>> whole problem in place.
>>
>> Each sub-problem will then be worked separately, and as each result is
>> completed, it will "fly" over to slot into place under the whole problem.
>> Finally, the addition will be performed.
>>
>> Animation will also be applied to carries.  A digit-pair multiplication will
>> be performed by the student and the result written in its place underneath
>> the multiplicands, and then the carry digit will "fly" up to its place.
>>
>> For example, after the multiplication of 5 x 5, we'd have:
>>
>>  85
>> x 5
>> ---
>>  25
>>
>> And then the '2' would fly around, shrink a bit and settle above the '8' in
>> the carry location.
>>
>> The teachers also suggested an incremental teaching process, whereby the
>> computer does more of the work at first, eventually leading to the child
>> doing the problem entirely without help.  We envision this proceeding
>> according to the following steps:
>>
>> 1.  Fly-apart demonstration mode, no carries.  This might be used by a
>> teacher
>> to demonstrate the process, without student or interaction, or by a
>> student "self-teaching".  At this first level, the problems would have no
>> carries.  The computer would perform all of the animations, step by step
>> with
>> the click of a "next" button, and it would break the problem apart as
>> described above.
>>
>> 2.  Fly-apart handhold mode, no carries.  The computer walks the student
>> through each step of the process, visually highlighting, for example, pairs
>> of digits to be multiplied or added and prompting the student to enter the
>> answer.  Still no carries.
>>
>> 3.  Fly-apart corrective mode, no carries.  The student performs all of the
>> steps in order, and the computer indicates whenever the student makes a
>> mistake, not allowing the student to proceed in an incorrect manner.
>>
>> 4.  Fly-apart demonstration mode, with carries.
>>
>> 5.  Fly-apart handhold mode, with carries.
>>
>> 6.  Fly-apart corrective mode, with carries.
>>
>> 7.  Normal demonstration mode, with carries.  In this mode we would start
>> the "normal" long multiplication process, performing it in place rather than
>> separating out the sub-problems.
>>
>> 8.  Normal handhold mode, with carries.
>>
>> 9.  Normal corrective mode, with carries.
>>
>> 10. Drill and practice mode.  Just like normal corrective mode, but without
>> the corrections, just a correctness indicator after the problem is complete.
>>
>> 11. Test mode.  The student answers a series of problems and receives a
>> score
>> at the end.
>>
>> In the above sequence, each demonstration mode would normally occur only
>> once,
>> followed by a handhold mode 2-3 times, followed by a corrective mode
>> repeated
>> until the child does it without making process errors.
>>
>> There is probably value in having the demonstration modes be "shareable", so
>> that a whole class can watch a demonstration, but we're not sure we see
>> collaborative value in any of the rest of it.  I'd think all problems worked
>> and the results should probably be logged to the journal.
>>
>> Those are our current thoughts on multiplication.  Addition is similar, but
>> simpler, with fly-apart and animated carries.  And, obviously, long addition
>> must be mastered before long multiplication is attempted.
>>
>> Any comments?  Are we overthinking this?  Any other ideas about how
>> collaboration might be usefully incorporated?
>>
>> Thanks,
>>
>>       Shawn and Ethan
>>
>>
>>
>> P.S. from Shawn: This project will probably take many months to complete.
>> Ethan, my 11 year-old son will be doing nearly all of the programming, under
>> my close guidance.  He's just learning to program, so it will proceed
>> slowly,
>> especially at first.
>> _______________________________________________
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>> utos-olpc at utos.org
>> http://mail.utos.org/mailman/listinfo/utos-olpc
>>
>
>
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> the blendmaster
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