3. The key to improving mathematical proficiency lies in the teacher’s competences. Teacher training and post-graduate courses have been seriously undermined.
The Ministry of Education, Culture and Science should subject teaching training programmes to a thorough investigation and encourage post-graduate training in mathematics and mathematics teaching.
I think the focus on better teachers is the single greatest flaw in education. Any normal profession focuses upon getting more with the personnel they have, or even doing more with lesser personnel. You'll never even see medical researchers complain about how their new technology requires better doctors.
We have this fantasy that no expense must be spared educating the children, but this is demonstrably false. A talented person usually avoids teaching high school. How many people get PhDs in literature? How many academic jobs are there? Where are the extras going? Quite clearly not high school teaching. It's far far worse in mathematics.
What is the purpose of mathematics education? Is it practical skills? Is it how to think logically? Is it what to do if your calculator breaks? Is it aesthetic?
Wow, see this is a very very very very very good example of integrating algorithms with pictorals, and of breaking down complex algorithms into simpler ones, and yet you still get ignorant people like in the comments at BB who hold problems up like this as something that is wrong with math.
I asked, at a teach conference, about getting him some material that was more on his level, and they said, and I quote "Well, we don't want to encourage him to get too far ahead of the kids that are still learning to count." What, what, WHAT?
The essence of the addition algorithm, like all standard algorithms, lies in the abstract understanding that the arithmetic computations with whole numbers, no matter how large, can all be reduced to computations with single-digit numbers.
... it leads seamlessly to the explanation of why students must memorize the multiplication table (of single-digit numbers) to automaticity before they do multidigit multiplication: in the same way that knowing how to add single-digit numbers enables them to add any two numbers, no matter how large, knowing how to multiply single-digit numbers enables them to multiply any two numbers, no matter how large.
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