Forest_Dump wrote:Alan Masterman wrote:Yes, the only way you just "know" that 6 x 5 = 30 is because you learned it by heart in primary school. In no sense do you just "do the calculation".
Absolutely. I have been trying to figure out how you would really do it any other way other than mechanically adding six objects five times (i.e., imagining 30 objects - in five rows of six?).
When talking in childlike language, I explain it as the biggest number is the boss, the sign (x, multiplication) is the orders the boss gives and the second number is the one being told how many times to replicate or divide (or simply, being told what to do).
After a few hours of tutoring my 8 and 6 year old daughters are able to understand how to figure out 6 x 5 without memorising it.
So there are two number 30's.
The first number 30 is handed to you, in the equation 6 x 5 = 30.
It is pointless to learn this number 30 because it does not come with any understanding what so ever, and this number 30 should not be memorised.
The second number 30 comes from the question, what is 6 x 5?
It is fine to memorise this number 30, because of the way memory operates.
We can simply think of the process involved with multiplication without actually doing it, to remind our selves of the number 30.
Or if that fails you can simply redo the whole process.
But if you forget the first number 30, you fail the test.
I did a total of 3 hours home work over the period of 4 years in high school, yet I was one of 2 Maori's in the top mathematics class and I was able to pass every test handed to me. (I was the only Maori in the last year, as Hemi moved over seas)
The rest of our classroom students were all white, but if there were multiple teaching techniques, I'm sure there would have been more Maori's in the top mathematics class.
Most of my homework was for English class, and that was during lunch time for a project that I was supposed to spend two weeks on.
Many people are not able to just memorise everything handed to them.
These are the people that fail in class and where I come from, there are a lot of them.
Even in class, I was able to teach pupils my age to learn simple techniques that helped otherwise failing students.
These students who are able to learn in different ways are Imo, just as clever as someone who has good memory, but the current education system just labels them as dumb, unable to learn and are brushed aside for the students with a good memory.
The reality is that we do have to learn all kinds of seemingly arbitrary things like the difference between there and their or that 1 is a single object, etc. We memorize vocabulary (ever have to pass french or spanish? How else did you learn all the verbs?), math, what the signs at the side of the road mean, even what buttons to push on a calculator or computer. The trick is not in how much we need to memorize but rather in how to do it quicker and more painlessly.
When babies learn words, they are praised every single time the speak and so it is easy to learn by simply memorising.
But that later develops into mimicking which is another process of learning.
When adults learn a new word, they don't just memorise the word itself.
Instead we associate that word with a memory, and every time we use this memory we are reminded of the word.
This is probably the best technique for dealing with numbers too, where you associate numbers with memories.
Simply memorising 6 x 5 = 30 does not enforce the use of this memory technique.