Not good at math? The teacher is the key.

There are quite a few "scholarly teachers" around us (usually within schools), who only touch on all the content superficially and use an启发-style to let students learn. However, the hints given to inspire students are not enough, with too many steps skipped too quickly, especially when students are just starting to encounter a new field. This can cause their confidence to be shaken, leading them to easily give up. It's also possible that the teacher explains principles in too much detail, making mathematics overly complicated and causing most students to lose their intuitive judgment of math and thus lose interest. This is why tutoring centers have such good business; it's really thanks to these teachers!

In fact, if one can earnestly follow the content taught by these teachers, they usually have strong thinking abilities and are good at solving problems independently. But there aren't many students like this! These scholarly teachers always believe that anything involving memorization is not pure mathematics.

To them, true mathematics is about complete understanding and should not rely on any memorization!

However, without memory, how would one know the definitions of mathematical terms? Without memory, does one have to derive the quadratic formula every time? I think this kind of "philosophy" is overly extreme, after all, memorization is also a method of learning.

As for the other small group of teachers in schools who are just going through the motions, they are not included in my commentary. Frankly, I look down on such teachers! (This ties back to the teacher evaluation system. Alas!)

But there are indeed quite a few flexible-minded, selfless, and excellent teachers. They appropriately incorporate the methods from tutoring centers (question types, formulas, mnemonics) into their courses, mainly using guidance and inspiration (with the goal of "understanding") while supplementing with appropriate problem-solving practice. At the same time, they exercise students' thinking ability, rigorous reasoning ability, and strengthen their problem-solving intuition. These teachers are usually very popular star teachers in schools. And under this kind of teaching, most students are trained to become top students with flexible thinking, excelling not only in test scores but also having a thorough understanding of the course rather than just rote memorization.

My teaching style is similar to this kind.

Therefore, appropriately harmonizing philosophy with practice, and widely learning and absorbing the tricks and experiences of other teachers, is the only way to truly provide students with the most comprehensive teaching. Don't be closed-minded or self-righteous, thinking you're the best or the orthodox. That's nothing more than a narrow-minded view! There's no such thing as the best, only better!

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