Alberta's experiment seems similar to the approach in Common Core.

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When school returns next month in Alberta, for example, the requirement for students to memorize the multiplication tables will be reinstated, following an awkward climb down by the province's education ministry in March.

One critic of the government�s adoption of "discovery-based learning," Ken Porteous, a retired engineering professor, put it bluntly: "There is nothing to discover. The tried and true methods of addition, subtraction, multiplication and division work just fine as they have for centuries. There is no benefit and in fact a huge downside to students being asked to discover other methods of performing these operations and picking the one which they like. This just leads to confusion which ultimately translates into frustration, a strong dislike for mathematics and a desire to drop out of any form of mathematics course at the earliest opportunity."

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A new study demonstrates that memorization is not some crude manner of learning, but rather one that remains vital. They monitored the brains as young children did simple math by various means, from counting on fingers to applying memorized rules. They monitored them over a period of time as the kids advanced in mathematical sophistication.

The hippocampus, the part of the brain associated with factual memory, appears important in stimulating the higher reasoning functions of the brain.

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"In particular, the hippocampal system appears to be critical for children�s learning of mathematics in ways that are not evident in adults who have mastered basic skills," the authors write. It appears to play a "critical, time-limited, role� in fostering "the gradual establishment of long-lasting knowledge represented in the neocortex," a brain area of higher order functions.

This process is "time-limited" because the hippocampus�s role seems to taper off once this knowledge has been "consolidated" elsewhere in the brain...

In effect, as young math students memorize the basics, their brains reorganize to accommodate the greater demands of more complex math. It is a gradual process, like "overlapping waves," the researchers write, but it clearly shows that, for the growing child's brain, rote memorization is a key step along the way to efficient mathematical reasoning.

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So if I understand that, the hippocampus -- the repository of simple memorized facts -- eventually imprints its memory into the neocortex, the higher-level reasoning part of the brain. And thus memorization is just the first step (in the hippocampus) that leads to actual understanding (in the neocortex).

I've argued this before, so I won't belabor the point, but I think this is where the Education wonks (and I use that term advisedly) keep going wrong:

1. They notice that higher-performing kids don't actually seem to use memorized times tables to do simple math, but instead seem capable of quickly intuiting an answer.

2. Therefore, they assume, the memorization process actually retards learning, and so if you want to make lower-performing kids into higher-performing kids, you just teach them insight and intuition (true understanding) and skip that boring memorization step.

This, I contend, is wrong. This is Cargo Cult -- mistaking the end-product of the process for the process required to achieve it.

The actual thought process should be:

1. Higher-performing kids don't actually seem to use memorized times tables to do simple math, but instead seem capable of quickly intuiting an answer.

2. This is because higher-performing kids have already incorporated and then surpassed the simple memorization stage of problem analysis.

2a. The higher-performing kids began as memorized-answer-repeaters, but eventually their memorized answers simply became incorporated into their working knowledge/intuition base.

3. Higher performing kids reach this step in cognitive evolution before their peers because they're higher performing kids, not because they're doing things differently than lower-performing kids. They're just going through the steps of cognition faster than their peers. (Many high-performing kids, by the way, come into first grade already having memorized a lot of the addition tables and times tables, because their parents already taught them that -- no government school needed.)

4. Ergo, we really should make sure that lower-performing kids master the memorization process, too, so that they too can eventually move on to true understanding.

I don't know how hard it is to understand that memorization is something that can be taught rather easily, whereas insight, intuition, and deep understanding is not something that can be taught easily. In fact I don't think it can be taught at all, and certainly not by people who themselves are only capable of teaching the second grade.*

Understanding must arise from within the student himself. You can only prepare his mind for that leap, and you prepare the mind by the tried and true methods.

I think Common Core will fail in teaching kids actual mathematical insight, while simultaneously failing to teach them the memorized facts required to achieve that insight on their own.

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