If you ever want proof that the way you teach something determines whether or not students actually learn it, try teaching a room full of kids to say supercalifragilisticexpialidocious backwards (as Julie Andrews does during the famous song from Walt Disney’s Mary Poppins).

First, teach them badly, by simply writing the backwards version on the board:

If your students are like mine, when you ask them to read it - even by “sounding it out” - most of them will freeze up and draw a blank. Some, of course, will try to pronounce it, but they too will soon give up. In my 30 years as a teacher, exactly zero students have been able to read it correctly on their own the first time through - despite the fact that it has a regular English spelling.

Now draw the following on the board and ask them to try it again:

Most or all of the students will try it this time, and some will actually succeed (it’s pronounced doh-shuhs-al-i-ek-spee-is-tik-fraj-ee-kal-ee-roo-puhs). Pronounce it yourself several times and give the students some time to practice, and pretty soon they’ll all be saying it correctly. (Then, for an added challenge, try getting them to stop saying it. I apologize in advance!)

Imagine: a 0% success rate quickly converted to a 100% success rate by simply breaking the task into pieces. What’s the explanation for such different rates of success? It’s all based on the way our working memory works - or should I say, doesn’t. As George A Miller revealed in his famous 1956 paper The Magical Number Seven, Plus or Minus Two, there appears to be a limit to how many items we can hold in our working memories at one time, and that limit is about seven. A 33-letter, 14-syllable nonsense word simply doesn’t stand a chance.

But that’s only when we try to pronounce it in one go. If we apply our innate abilities to work with groupings of items (with no more than 7 items per group as a general rule), we can bypass our working memory limits and enable our minds to work with practically limitless amounts of complex material. By turning dociousaliexpeisticfragicalirupus into seven two-syllable groupings and stringing them together, the load on working memory is reduced and our natural ability to work with groups kicks in - and the correct pronunciation becomes a piece of cake. Notice that the number of syllables is key here, as we’re teaching kids to say the word. If we were teaching them to spell it, the approach would work just as well in this case; the longest grouping - “docious” - is exactly 7 letters long.

Scientists call the individual groupings of information “chunks,” and the act of breaking complex information into sub-groups and stringing them together into coherent groups “chunking”. There is evidence of both all around us. Consider phone numbers; instead of trying to memorize a number like 18423891224 we break it into a single-digit country code (1), a 3-digit area code (842), a 3-digit exchange code (389), and a 4-digit subscriber number (1224), producing the much more easily remembered 1-842-389-1224. (Seven digit telephone numbers were actually created to conform to Miller’s “magical number seven,” in order to make them easy to remember.) Zip codes, as well, contain easy-to-remember “chunks” now that they’ve created the extended “Zip+4” codes. Notice what the Postal Service didn’t do when they created them: they didn’t just tack on 4 extra digits to create 9-digit Zip codes.

Interestingly, the Sherman Brothers, the songwriters who wrote Supercalifragilisticexpealidocious, intuitively used chunking when they created the backward spelling. As you may have noticed, if you actually try to read the word backwards, the result doesn’t even come close to dociousaliexpeisticfragicalirupus; the actual backwards spelling is virtually unpronounceable. To navigate this dilemma, the Shermans broke the word into chunks and simply reversed their order - with the exception of “super,” which they “fake reversed” to “rupus,” which sounded funnier.

Chunking is a powerful memory device, of course, but to think of it as merely a memory device would be to miss its larger implications; chunking tells us how our brains master complex skills, namely by breaking them into sub-skills, mastering those sub-skills, and then putting everything back together.

Take the complex skill of playing softball. In order to master it, you first have to master sub-skills involving how to hold a bat, how to run the bases, how to throw the ball, how to field a grounder, and so forth. Then, on the field, you simply put all of those sub-skills together. If you fail to master any of the sub-skills - actually master them - you won’t be a good softball player; a player who can do everything except field a grounder will most likely spend a good deal of time “riding the pine.”

This is no different in principle from our dociousaliexpeisticfragicalirupus example; if you can pronounce every part of the word correctly except for “expe” (ek-spee), you're not pronouncing it correctly at all.

Of course, this is all very obvious, to the point of not needing to be said. So why don’t we teach math this way? Why aren’t students mastering math sub-skills, and putting them together to master the math skills themselves?

Because we haven’t been aiming for mastery at all! If I had a dime for every time I’ve heard an educator say, in private, that we’re really just “exposing them” to math; you don’t just “expose” a kid to softball - and then put them in the game. (There are subjects - like music, art, and computer science - where exposure to the subject may be sufficient; math just isn’t one of them.) How do I know math teachers in general aren’t shooting for mastery? Because they’re not employing the “see it, do it, check it” learning strategy that mastery requires. Students aren’t being given enough worked-out examples to refer to, practice problems related to those worked-out examples, and worked-out solutions or other immediate feedback so that they can check their work and nail down each individual concept. Isn’t that how you master new skills?

Imagine the complex math skills our students could master if they first mastered the “chunks” that math is made of. Imagine the life skills they could master if they mastered those math skills!

A supercalifragilisticexpealidocious future where all students know math backwards and forward is entirely possible - so long as we build it one dociousaliexpeisticfragicalirupus chunk at a time.