[math4] FourthGradeMath Digest, Vol 2, Issue 15

[Greg Dekoenigsberg]

On Sat, 14 Mar 2009, Jason Rock wrote:

> My personal opinion on this is that you might be simplifying it too much. 

Oh, I'm absolutely simplifying it too much.  Very deliberately so.

> It is exceptionally easy to create a "flash card" system for learning
> multiplication tables, but I know for sure that that didn't work for me and
> it doesn't really teach multiplication.  What worked for me was thinking
> about repeated addition (at least to start off, then I memorized by use).  I
> think most people would say that the best way for children to learn single
> digit multiplication *is* memorization, and that may well be true, but I
> think it is important that we don't overlook some better way of doing it.

You are absolutely right.

> And these discussions need not slow down work.  I am all for a "flash card"
> set of multiplication tables.  I just think it is also important to show
> that 3*2 = 3+3 = 2+2+2 so the student can appreciate how addition and
> multiplication connect.
> 
> Jason

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.

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.

Why is this important?  For precisely the reason you cite!

Let us say that the goal is to learn the following module:

"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."

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.

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.

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.

Sorry for the length.  :)

--g