Sometime in the 1990s, the head of our Department reported the results of a longitudinal study that showed the best indicator of a student’s success in tertiary education (regardless of discipline!) was that student’s success/mark in mathematics when matriculating from high school.

]]>I don’t know what your son’s experience is, but mine, with gifted students, is that they learn faster and deeper at the same time.

As for tolerance: that’s another story completely. But I would not want to sacrifice mathematical learning for learning of tolerance. And I don’t think we have to. That’s another story completely.

]]>I have always told students that there is a VERY simple reason they find mathematics hard, namely, mathematics IS hard! There would be something wrong if they did NOT find mathematics hard. However, mathematics is also the simplest subject they’ll ever study, for if you understand what you are doing, and forget a formula or result, you can work it out. But if you do NOT remember the German word for a table, you are truly stuck in an exam, or if you forget the details of some law and you are sitting for a law exam, you’re in trouble.

You don’t need to be clever to learn and use mathematics, only to create it. Because extremely clever and capable people, including genuine geniuses, have developed mathematics painstakingly over centuries, even lesser mortals, like us, can learn, understand and apply mathematics.

The hardest part of mathematics is to find the perspective that lays bare the underlying simplicity.

I am really disturbed by the number of ad hoc tricks used to “explain” things in mathematics that actually mask what is really going on, such as the “explanation” so often used for the arithmetic equality -(-a) = a. Typically, -a is “explained” as turning to face in the opposite direction, so doing it twice has you facing in the original direction. This is a trick that works only in this case. It cannot be used to show why 1/(1/a) = a, or why the inverse of the inverse of a function is the original function. Yet there is a simple underlying universal argument that explains all of these (and any similar!) statements. This universal argument is conceptual and requires more care to introduce and explain, but not inordinately so, and it makes many things much easier later.

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