Without trying to sound like too different a person, I understand why we need to simplify this and a working set of tools is very important. However, take my example from above. I can't think of a way to make that into an application that would actually teach the repeated addition concept. I would really like to hear from an educator as to how they show that multiplication is really just repeated addition. If there are any in this mailing list I'd love to hear your ideas on this topic so I can get writing some code.<div>
<br></div><div>Jason</div><div><br><div class="gmail_quote">On Sat, Mar 14, 2009 at 4:26 PM, Greg Dekoenigsberg <span dir="ltr"><<a href="mailto:gdk@redhat.com">gdk@redhat.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div class="im"><br>
On Sat, 14 Mar 2009, Jason Rock wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
My personal opinion on this is that you might be simplifying it too much. <br>
</blockquote>
<br></div>
Oh, I'm absolutely simplifying it too much. Very deliberately so.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
It is exceptionally easy to create a "flash card" system for learning<br>
multiplication tables, but I know for sure that that didn't work for me and<br>
it doesn't really teach multiplication. What worked for me was thinking<br>
about repeated addition (at least to start off, then I memorized by use). I<br>
think most people would say that the best way for children to learn single<br>
digit multiplication *is* memorization, and that may well be true, but I<br>
think it is important that we don't overlook some better way of doing it.<br>
</blockquote>
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You are absolutely right.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
And these discussions need not slow down work. I am all for a "flash card"<br>
set of multiplication tables. I just think it is also important to show<br>
that 3*2 = 3+3 = 2+2+2 so the student can appreciate how addition and<br>
multiplication connect.<br>
<br>
Jason<br>
</blockquote>
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Understand that the precise nature of the activities *themselves* can be somewhat arbitrary to start, so long as they align with a curriculum objective. I start with "flash cards", which in truth is what the first iteration of Mongo will be, only because it's the simplest place for me, myself, to start creating a reference activity. That's all.<br>
<br>
What is *crucial*, however, is the notion that activities -- regardless of how they are built and how they teach -- must be (a) aligned to *quantifiable learning objectives*, (b) modular (ergo SWAPPABLE), and (c) able to measure mastery of the objective.<br>
<br>
Why is this important? For precisely the reason you cite!<br>
<br>
Let us say that the goal is to learn the following module:<br>
<br>
"4.N.11. Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500."<br>
<br>
We can have two activities aligned to this objective. One for the kids who are better at memorizing facts, and one for the kids who are better at treating multiplication like rapid repeated addition.<br>
<br>
There must be a half-dozen effective ways to teach this concept. But if we are going to build an ecosystem of activities in Sugar that are *useful*, we *must* be able to map activities *directly* to these concepts -- and ultimately, we should provide *multiple activites* for learning each concept, each geared to different learning styles.<br>
<br>
First, though, we must get coverage. Until we can say "we have a complete set of activities to teach fourth grade math," we don't really have much that's useful for the likely targets: charter schools, homeschool associations, poor rural schools -- i.e. underserved markets who are willing to try to use computers to teach kids in nontraditional ways.<br>
<br>
Sorry for the length. :)<br><font color="#888888">
<br>
--g<br>
</font></blockquote></div><br></div>