Monday, June 30, 2014

Multiplication In Other Countries (Exemplar)

Multiplication In Other Countries

One thing that I have found to be extraordinarily interesting is the topic of multiplication.  I got to thinking about what it really is and why we do it the way we do. It seems like everyone that I have every met has learned to do it the same way.  There are, of course differences in terminology and sometime the order that things are done, but for the most part it's the same.  You take your numbers and stack them up like a cake and then slowly work your way across, devouring each place value until you you get the very end (or beginning).  What you find yourself with then is an empty plate...or a number, depending on what we are still talking about.  Anyhow, I got to wondering if we all do multiplication that way because that's the only way to do it...that didn't seem logical, so there must be another way.  Then it came to me! A calculator...that's how most people do multiplication these days. I include myself in that blanket statement.  It honestly wasn't until my teacher assisting in a second grade class this past semester that I really had to retrain my brain to do multiplication like I learned at that age.

I couldn't possibly be building up this whole "how to do multiplication" thing, just to say that people use calculators, surely not.  So what then? Well it turns out that there is another way, a pretty cool way, in fact, that doesn't involve writing numbers at all.  At least in the way that we are used to.  From my understanding, this multiplication has it's origins in China.  So how do you do it?

Well basically it's like writing tallies.  Lets say you wanted to multiply 14 and 12, you would start by writing one tally and then four tallies, representing 14.  Then you would do the same thing for the 12 except crossing the lines horizontally over the 14 like this:

You then count up the intersections like the illustration below.  The red indicates the hundreds place, the blue added up represents the tens place and the green represents the ones place.  Of course you can do this same process with larger numbers, but then there is "carrying" involved.  But! I thought this was a really cool, visual way to teach students how to do multiplication differently.

Exemplar Additive:

One thought to consider when looking at these different methods of multiplication is, how might this look in a practical, educational setting?  Would there be any benefit to teaching this type of multiplication over other types?  Well to begin explaining what this might look like in a classroom, it would be helpful to know and look at the different types of learning that students fall into, or the umbrella of learning style under which they take refuge.  The explanation of these is a research paper in and of itself, so I am going to just say that this type of multiplication would in fact be a major benefit to any students who fall under the visual or bodily kinesthetic learning types.  Students who learn better from moving with learning, or seeing with learning would be able to step into a realm of understanding that they would be unable to in the traditional teaching of multiplication (memorizing facts, place value line ups, etc). Though younger students may not benefit from an explanation of why the line crossings work, they would benefit from being able to see what it is that they are counting up and how to place the numbers they had counted.  It works well because students can literally see a number of objects, rather than a set of numbers to be multiplied.  This approach also takes pressure off of students as they come into the stigmas associated with learning and doing multiplication.  It's not always numbers, it can be things or objects as well.  Even with larger numbers which can become more complicated, a teacher could provide students with pipe cleaners to use as their lines, which they can then physically move and count out.  Pretty slick for a student who is intimidated by numbers.

In terms of students who learn in a kinesthetic fashion, the pipe cleaners or other objects (maybe even large, movable objects in a gymnasium or on a playground) would allow them the movement that they require for valuable and meaningful learning.  Again, with younger students, the explanation of why these lines work may be above them, but the activities that are made possible with this form of multiplication would certainly not be. I would recommend this type of multiplication education for any students who fit into either of these learning styles.  This is actually a great way for teachers to diversify their teaching, even with students who learn more traditionally.  Seeing information presented in different ways can help to solidify a concept for any student. 

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