The building blocks of understanding are memorization and repetition • Hacker News Board

Re: The building blocks of understanding are memorization and repetition

#61

Post by intellegacy » Fri, Sep 16, 2016, 2:12 AM UTC

anonymid wrote: post #48

TLDR: This seems to be a strawman, at least in how it presents common core. However, I have to give a concession to the criticism that superficial understanding is often what common core implementations look like. Still, in my opinion fluency comes from understanding, not the other way around. >The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an i…

>One recent example I saw (a colleague works on coaching teachers in common core) was a class of elementary students who could correctly multiply 4/7 * 5/9, but couldn't shade in 1/4 of a square. They memorized and rehearsed the procedure for multiplication, but never built understanding of what they were doing.

the author's argument is that you build understanding by doing. learning the forms and perfecting your "doing" of them is fundamental to developing insights into what is going on

some students make the leap themselves, some students need it explained to them, either way, the student needs to know the HOW before they can understand the WHY

Re: The building blocks of understanding are memorization and repetition

#62

Post by BirdieNZ » Fri, Sep 16, 2016, 2:31 AM UTC

tsumnia wrote: post #58

It's nice to see people agreeing with Oakley, considering I had developers ready to tar and feather me for suggesting code snippets should be images to prevent copy/paste. By no means is memorization the end all be all. Oakley even writes "In the United States, the emphasis on understanding sometimes seems to have replaced rather than complemented older teaching methods". The techniques should be used hand and hand.…

Having seen the results of a system that focuses entirely on memorization without comprehension, a balance definitely needs to be struck between understanding and memorization. Pure memorization is useless, but so is conceptual teaching without practical application (which helps to reinforce the concepts and ensure real understanding).

Re: The building blocks of understanding are memorization and repetition

#63

Post by hyperpallium » Fri, Sep 16, 2016, 2:36 AM UTC

Reminds me of "mathematical maturity", that you can't understand mathematics on its own, but need much background. In this way, maths is more like an Arts than Science subject, and evaluated similarly.

And is perhaps a reason mathematics seems to simply and "unreasonably powerfully" explain the world - it's not simple.

Re: The building blocks of understanding are memorization and repetition

#64

Post by tamana » Fri, Sep 16, 2016, 4:47 AM UTC

lokiboi wrote: post #44

piedradura wrote: post #35

In maths you learn to solve problem by expanding the abstractions by adding new elements. There is a crucial difference between problems easy to solve by repetition and problems that require some insight.

Exactly, otherwise all those IOI and IMO contestants would be pure geniuses, probably they are, but they practiced a lot to be good at a single task - problem solving in programming or mathematics for competitions. That's a good foundation built on insane amounts of repetition and memorization, but still, not many turn out to be Terence Tao or Peter Shor. Although https://en.wikipedia.org/wiki/List_of_International_M…

You don't get to the IMO by mere memorization.

Re: The building blocks of understanding are memorization and repetition

#65

Post by ivansavz » Fri, Sep 16, 2016, 4:49 AM UTC

daveguy wrote: post #22

lake99 wrote: post #4

Earlier quoted context omitted.

Some people extoll the virtues of long-form writing. But even a site like HN is far too information dense to spend so much time reading one article. It's a different matter when we're learning something of an academic nature, of course. That's why I love summaries such as yours.

I completely agree. I have found a speed reading extension to be quite valuable in getting a quick overview of an article. The speed reading time for this article was 5 minutes at 600 wpm (practiced up from 300 wpm). The speed read is good enough to get the TL;DR and a little more depth about the article. This is the extension I use (it lets you rewind with k and pause with space -- helpful for getting more understan…

Have you tried text-to-speech software? The built-in one for Mac OS X is quite good (Alex, the default voice is not annoying).

I set the words per minute to a very high rate, and I get my hacker news while exercising or doing chores around the house. I've completely stopped reading long articles, except when there are intersperced code samples.

I highly recommend.

Re: The building blocks of understanding are memorization and repetition

#66

Post by [deleted] » Fri, Sep 16, 2016, 5:21 AM UTC

SamBam wrote: post #56

bsder wrote: post #39

Earlier quoted context omitted.

While I tend to agree with the thesis, personal anecdote does not make a valid conclusion. We probably have decent research on this at this point. Anybody versed in it weighing it?

... the author wrote a book on the topic, and teaches a fairly famous course on it. I'd hope you'd give those credentials at least as much weight as some HN self-proclaimed expert.

[deleted]

Re: The building blocks of understanding are memorization and repetition

#67

Post by nickledave » Fri, Sep 16, 2016, 5:31 AM UTC

danmendes wrote: post #57

nickledave wrote: post #51

Earlier quoted context omitted.

+1 for storytelling. This article is pretty much my life story, and I constantly tell that story to other people, because my own painful personal experience suggests our educational system does not do a good job of delivering the same message. Maybe tucaz doesn't need to hear it. But there are a lot, a lot , of people that do. How many times have you heard someone say "I'm just not good at math" or "I'll never be abl…

I suggest that author's personal experience does not give any insight into large phenomena affecting many more lives than the author's own that could not otherwise and more succinctly come forward without the addition of the overly personal voice into the prose. This style of delivering information is called gonzo journalism and has taken over a large part of the media. What people forget is that gonzo journalism was…

So you don't know any people that are mathphobes? You are right that it would be nice to have some hard science to back up the author's claims. Maybe we should read her book. I'm sure it's basically "Fear and Loathing in Calculus".

Re: The building blocks of understanding are memorization and repetition

#68

Post by Falkon1313 » Fri, Sep 16, 2016, 5:47 AM UTC

I liked this article because it was in direct opposition to my beliefs (based on my own experience) and yet it gave me a different point of view and convinced me that there was some truth and value there.

I grew up in an era when we wasted a lot of time on mindless rote repetition of meaningless things (meaningless because we were not taught to understand them, only to repeat them). It was boring and useless. I learned by understanding and then applying that understanding. If you understood it, then there was no need to memorize something like f = ma because it was then obvious. But this is a whole new way of looking at it:

>If m and a were big numbers, what did that do to f when I pushed it through the equation? If f was big and a was small, what did that do to m? How did the units match on each side?

That's not thoughtless memorization, that's gaining understanding. But the author did it by active exploration via repetitively examining something from different angles. Not just rote repetition (doing the multiplication over and over again), but seeking understanding. So in a sense, the author is arguing in favor of teaching by emphasizing understanding, but explaining how to use directed repetition to do so. That makes a lot of sense. The key is that it is not mindless rote repetition, but directed, inquisitive repetition.

Re: The building blocks of understanding are memorization and repetition

#69

Post by exmuslim » Fri, Sep 16, 2016, 6:00 AM UTC

I absolutely agree that memorization and repetition trump conceptual understanding when dealing with intermediate level of mathematics (I am taking a course on probability and integration and even though I have a good grasp of the basic concepts, if I don't keep up with the nitty gritty details and properties, I completely go astray when the teacher introduces a new concept built using those details.)

I.e. you need to master your tools (theorems, formulas etc) by repeating them so that you can use them to build something. Even if you knew what a hammer is good for (conceptual understanding) but didn't know how to hold it, it would still be pointless.

Re: The building blocks of understanding are memorization and repetition

#70

Post by WillPostForFood » Fri, Sep 16, 2016, 6:28 AM UTC

anonymid wrote: post #48

TLDR: This seems to be a strawman, at least in how it presents common core. However, I have to give a concession to the criticism that superficial understanding is often what common core implementations look like. Still, in my opinion fluency comes from understanding, not the other way around. >The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an i…

Common core encourages repetition through its focus on multiple representations.

Not sure if I'd say Common Core itself encourages any particular method, nonetheless many modern math curricula take this approach. I have an elementary age kid at a school using Everyday Math which is like this, and it is pretty terrible. The homework is, like you say, a few problems of one type, then jump to something else, then jump to something else. There is never mastery of anything. Not basic operations, not coloring squares, not anything. I'm not opposed to multiple representations, but there isn't enough focus or repetition, so there ends up being no mastery.

While most of the kids could color 1/4 of a square and understand that conceptually, if I said color 40/160 of a square, they'd freeze because they don't work with numbers or basic operations enough to figure out that it is the same %.