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Two prescriptions for fixing a procedural/declarative knowledge mismatch.

22nd Jun 2018

10Said Achmiz

8habryka

1Andrew Quinn

2gianlucatruda

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4 comments, sorted by Click to highlight new comments since: Today at 7:38 AM

Great post and helpful synthesis of the difference in procedural- and declarative- directed approaches. The matrix multiplication example earns a 10/10 too. I trust the exams went well!

## Prescriptions

more procedural knowledgethan declarative:more declarative knowledgethan procedural:## Rationale

In whales' excellent Book Review: How Learning Works, each one of the 7 Principles gets expanded upon with a "Research consensus". In the first principle, discussing how prior knowledge affects a students' learning, they write:

(Emphasis whales', not mine.)

I've noticed this to be an especially useful asymmetry to keep in mind myself, since a lot of what I do is filling one, then using that to bootstrap the other. So I thought I would share my two "prescriptions" for it.

They're nothing groundbreaking, but they might help someone who's stuck in a state of analysis paralysis decide what to do next.

## EDIT: The Feynman technique and a variant

My apologies, I thought this was a little better known than it was. To summarize very quickly, the Feynman technique is where you

as if you were explaining it to a generally intelligent layman, who doesn't know most of your fancy words;That was all taken from this helpful link from commentator habryka below. (Thanks!) Let me add a bit of my own value, by suggesting a variant for people with a lot of "know-how".

thatat the top of the page.This might be a little easier if you're really in the weeds, so to speak. It can be difficult to just pick "a concept" and run with it without motivating examples; here, you invert the process, and use an example to

findconcepts to explain.## Personal examples

(You can probably safely skip this, if you have more important stuff to do.)

## Matrix multiplication (declarative > procedural)

I used to have trouble remembering how to do matrix multiplication by hand. (I think this is very relatable!) I have a lot of

declarative knowledgeabout what matrices "really" are, linear transformations and all that, but I lacked the practice to effectively turn that intoprocedural knowledge.To fix this, I generated concrete examples to practice. Specifically, I wanted examples I could do in just a few seconds of mental calculation, and that I could throw into Mnemosyne, using its LaTeX formatting; so I wrote a Python script to generate a bunch of very easy, random matrices and ask me for the value of their multiplication at a specific row.

That allowed me to make a Tab-Separated Value text file of 50 such cards I could import in to Mnemosyne, which would give me more than enough practice and retention to never have to worry about the skill again.

## Circuit analysis (procedural > declarative)

In the days leading up to my final exam last quarter, I realized that while I had a pretty good sense of

whatto do by hand when analyzing an electronic circuit with an AC power source, I had very little ability to explainwhythat was the way it was. I hadprocedural knowledge, but I was lacking indeclarative knowledge.I sat down about a week before the exam, and used the Feynman technique - I tried to explain back to myself (for example)

whyandhowwe did things using complex numbers instead of the "raw" real functions. When I couldn't generate the explanation myself, I went back to my textbook and read through theirs.The next day, I got a new sheet of paper, and tried again. This time it went much smoother. I began to push my reasoning abilities, with questions like:

Where I wasn't sure, I tried α or β and if I got the right answer I'd mentally class it as "leaning towards correct". But the final litmus test was always to take a technique that spat out the correct answer and explain

whyit had to be so. (Come to think of it, it's a similar epistemic style to proof writing, which as we all know is a skill in itself!)I did this each day leading up to the exam. And by the time the exam came around, I felt like not only did I know how to do the problems I saw, but I also understood deeply

whywe solved them these ways. That turned out to be useful, because the exam threw much harder problems at us than I expected. Being able to verbalize the logic behind the operations made it much easier for me to spot bottlenecks where I could solve simpler problems that would compose upwards into a full solution, so I was still able to breathe somewhat easy.