When people ask, “Which is better?” for most anything, my response is, “Better for what?”
The same is true for any kind of debate about different teaching approaches, whether the subject is language, mathematics, or how we design classroom environments.
Take for example the whole debate about phonics versus whole-word approaches to reading. Each method is useful in different ways, and to different people. Phonics does give you tools to decode a great many words. But because English is not a strictly phonetic language, phonics can break down in the pronunciation ability, and especially in the spelling ability. One can usually come up a number of phonetically rational ways to spell a word, but only one or two will be correct (e.g. the British kerb and the American curb). So, let’s spell a word (I bet you can come up with even more ways than I’ve listed here!):
(Damn, now I have imaginary helicopters flying in my head.)
Not all people can use phonics effectively; their brains do not process the information the same way. In such cases the whole-word approach or a combination of whole-word and phonics can be better. Personally, I have to learn how to spell French words simply as whole words, including diacritical marks. For me, French words have certain shapes, which can describe pronunciation, but I can’t go from sounding out to spelling. (I still cannot fathom why it takes three vowels “e-a-u” to make the long O sound. I swear the French stole some of their vowel supply from the Welsh, who were then forced to draft W into service as a vowel.)
Too often we get caught in false dichotomies, thinking that if one thing is good, the other is bad, and if one is right, then the other is wrong. In real life, we end up using different tools for different jobs, and sometimes combinations of tools.
In education we also run into the whole problem of pedagogical fads, where we think that because a particular approach is new and has shown to be effective in some ways, that it is better than other approaches, and should be instituted by substituting it for other approaches. There may be any number of reasons why the New Method doesn’t work well, including teachers who are not adequately trained to use it, general resistance to change, students who have trouble transitioning from one teaching method to another, parents who don’t understand how the new method is supposed to work and thus cannot adequately help their children with homework, and of course, the whole issue of teaching methods that are neither adequate nor well-matched to the learning needs of all the students to whom they are being applied.
When poorly implemented, the open classroom was not the hoped-for freer, student-directed learning environment, but merely a school without walls between classes, as though they were held in an airport terminal. This created noisy and chaotic environments that were hell for the easily-distracted students, ditto the students with hearing or listening difficulties who couldn’t track and understand one speaker out of many voices. I furthermore had trouble because I couldn’t keep track of what my class and I were supposed to be doing because I couldn’t identify the students who were supposed to be in my “pod” (teaching group – our classrooms were an open plan of several pods surrounding a central library hub).
I started off mathematics under the New Math, where the focus was more upon understanding and applying concepts, rather than upon rote learning of exact processes. I also had a couple of teachers who understood mathematics AND the New Math teaching process. Life was great. (I still think in sets.)
Then we had one of those reversals in teaching approaches, and I next found myself in classrooms with math-phobic teachers who taught the subject by drills and memorising mechanical processes, and there I floundered in the maths until college. I was absolutely shocked the day I heard my college algebra teacher announce, “There are several ways you can solve this; pick whichever one works best for you.” Not only did I finally have a teacher who liked the subject and could explain it in different ways (so it made sense), but she also gave us the “radical” idea that mathematics was a tool that we could use in ways that made sense to each of us.
Once something makes sense to you, you not only own it for using it, but you can also figure out how to apply it to novel situations.
Applying math to novel situations is where the memorise-this-process approach falls apart, and likewise with story problems. Most math students are terrified of story problems, because they have to be able to understand both the “story” and understand the various mathematical tools they have learned, determine what they are solving for and which methods to use, and be able to figure out how to construct equations (or inequalities) to solve the questions. If you are used to being told which formula or process to use and then being given a set of problems that all use that process, then you are less familiar with decoding and evaluating situations.
Shockingly, real life doesn’t hand you a volume of problems all lined up, with answers to the odd-numbered problems in the back of the book. And that’s where the rote-process approach to teaching math fails. Aside from rote functions like bookkeeping, real life is almost nothing but story problems.
Despite that, there are some uses for simply memorizing steps. Most people find it easier to memorise the °C : °F conversion formulae than to re-create them every time by comparing the ratios of two or more pairs of known equivalent amounts (e.g. the freezing and boiling points of water). After decades of struggle, I have resigned myself to the fact that although I can memorise equivalencies involving monomials (e.g. 1 mole = 6.022 x 10^23 molecules), I can’t keep straight in my head the more complex formulae that involve fractions or ratios. So when I lacking a reference source, I end up reconstruction the formula needed each time. But there are a great many people who would find that process to be much more difficult than simply memorising an equation or rote process! On the other hand, I have the mathematical tools to reconstruct or even create de novo other formulae and conversion factors as I need them.
But regardless of whether a person is designing a classroom environment or selecting a pedagogical approach, the real answer to the question, “Which is better?” should be, “Whatever works best for the student.” This is not the same thing as, “What we think the student ‘ought’ to use.”