I have a master’s degree in teaching mathematics. In many and most of my college graduate level courses we discussed the reasoning behind why we do the things that we do, mathematically speaking.
The idea is not to teach the children that two times three is six but teach them why by showing the process of addition. All other mathematical concepts were also presented in this way. We kept math journals and recorded our mathematical thinking through difficult word problems and math puzzles.
I agree with the concept that children will learn and remember if they understand why. However, the concept of why is not always so easy to teach or understand.
Some of this idea comes from educational specialists are trying to lead teachers away from the “just do it” or “memorize it” phase and into the “reasoning” stage.
I completely agree that we need much more reasoning in our world. Higher order thinking is definitely something that all teachers can improve upon in their classrooms.
Saxon phonics looks at reading and spelling in the same manner as the math courses that I took. Instead of just stating a word, it gives rules to follow that explain why words are spelled and pronounced a certain way.
I will admit that when I became confident in the Saxon way of thinking (only from teaching it first) I became a much better speller and reader.
I also think that the concepts that I learned through my graduate math courses have strengthened my math teaching to some degree.
However, I also think that there are some things that one just has to memorize. There are some things that can be simplified and explained with “just because”. There is nothing wrong with using rote and repetition when learning math facts or how to spell certain words.
In fact, as Valorie has listed in homeschooling, there are many fun games that can be played to enhance the quickness and proficiency of these facts.