Memorization is not learning. It is a part of learning. Being able to memorize things and understand their relationships in context is learning.
How I Rewired My Brain to Become Fluent in Math
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Re: How I Rewired My Brain to Become Fluent in Math
#22I thought thus would be about the guy on HN who used a psychedelic trip to gett over math anxiety. Still a good read.
Re: How I Rewired My Brain to Become Fluent in Math
#23Memorization is not learning. It is a part of learning. Being able to memorize things and understand their relationships in context is learning.
My German teacher at school did an accelerated course from scratch at university (no previous knowledge) - a full language degree. It involved rote memorisation of German texts. It worked! She said that the advantage was that you later recognised phrases and grammar and were able to analyse what was previously just rote memorisation.
I spent a couple of years in Italy in my early 20s and learnt fluent Italian in that time. I took a couple of classes a week in the evenings, but spent the day programming with a team of English colleagues and perforce spoke English. I made an effort to socialise with Italians outside of work.
I went out with groups of Italians many a time, and experienced many a boring evening where if people didn't speak to me specifically I couldn't understand a thing.
I realised that after 9 months I could hold a good 1-to-1 conversation but that it was another 9 months before I was comfortable in a group situation - in your native tongue you can keep tabs on the various threads of a group conversation with ease, whereas if you are having to explicitly process it, it's so easy to fall behind and then you're lost.
Re: How I Rewired My Brain to Become Fluent in Math
#24I come from a very similar background as the writer. As a young man, I showed high potential for languages. So when I went to college, I loaded up on languages, graduating with 6 different languages at at least the 200-level and fluency in 3 of those languages. Unlike the writer, I chose neither military nor government work upon graduation, but instead worked as an ATA-certified translator for 10+ years, primarily tr…
> But I am in total agreement with the writer that modern education does a grave disservice to young learners by discarding rote learning and repetition.
I've come to appreciate the importance of rote learning over the past couple of years... but despite its simplicity, I would call it a very advanced technique.
You don't need rote learning to get to understand something. You don't even need rote learning to become very good at something. You only ever need it to be able to think faster about certain advanced topics or if you'd like to become fully fluent in a language.
These are not things a high school student should necessarily spend much time on. Especially considering that rote learning, if not self-motivated, can be incredibly demotivating and have the opposite effect of what was intended.
Re: How I Rewired My Brain to Become Fluent in Math
#25What an incredibly short-sighted sentence: "Sorry, education reformers, it’s still memorization and repetition we need.". I could not disagree more with this article. Memorization helps, but MAKING CONNECTIONS between concepts is _HOW YOU MEMORIZE EFFECTIVELY_. Memorizing is great for learning different languages. NOT MATH. Sure, maybe students are bullshitting in understanding concepts, and forgot quickly since they…
This is why the education system will never ever change. Too many people learn too many different ways. Some people can read a formula and instantly memorize it. Other's need a connection to that formula. Some need to figure out how that formula was derived in order to understand and memorize it. And some know the formula before you even show it too them. Not to rehash what you hashed, but it depends who you are. If…
This is very true. A corporate trainer once told me there's specific kinds of learners. They've actually identified each type, and which specific methodologies you need to reach each one. The best teachers find a way to synthesize it all into an effective single presentation. (This may also be why tutors are so helpful -- they can customize their material to the audience...)
Re: How I Rewired My Brain to Become Fluent in Math
#26I believe that math is something a lot of people can learn and become effective at using, way more than Americans currently believe about themselves.
I think it all comes down to making sure people understand the actual abstractions and concepts rather than formulas and rote learning. The advantage of math is that you can figure stuff out using what you already know, without having to learn every little detail - while that's impossible in other subjects, such as history.
The missing piece is, in fact, granularity and feedback. And real world studies support my position:
http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way...
http://opinionator.blogs.nytimes.com/2011/04/21/teaching-mat...
If you want to read how I'd reform education and improve the economy, these are my thoughts:
Re: How I Rewired My Brain to Become Fluent in Math
#27Nice!
FYI: This comment will get downvotes. Not because people here are senselessly mean. But, because the HN community takes a strict approach to comments that add noise without contributing signal to the conversation. Downvotes on "Nice article!" comments frustrate many new users. So, here's your explanation. Welcome to Hacker News!
I was simply replying to the explanation that the article is available for free and I care nothing for points or votes, thanks anyway
Re: How I Rewired My Brain to Become Fluent in Math
#28I think those of us who aren't a fan of "memorize/repeat" is that it is extremely inefficient. And you lose as many people as you gain.
The classic example is long division. In elementary school I did a thousand long division problems, but I never understood it. I just knew the pattern. I didn't really know the math. It wasn't until much later did I learn how and why it worked. Having done those thousand problems didn't really help my understanding at all. And honestly, it's not a skill I use today.
Rote learning is useful when what you memorize is useful in itself. Learning what 2+2 is useful, but because adding 2 to another small number, including itself, is something you do a lot.
Addition/times tables are great because the scope of numbers is something you will run across a lot of day to day. A thousand long division (or multiplication) problems is just rote work for little benefit. It's better to teach the concepts, and then build on them.
Re: How I Rewired My Brain to Become Fluent in Math
#29"Sorry, education reformers, it’s still memorization and repetition we need."
This is very true. For example, doing the advanced engineering calculus can often boil down to manipulating polynomial, which are still arithmetic. A person with "understanding" but no fluency in basic arithmetic is setup to fail.
Re: How I Rewired My Brain to Become Fluent in Math
#30As a thank-you present to our readers on HN, Nautilus wanted to give you exclusive full access to this Prelude article from our latest print Quarterly online "preview". Subscriptions to our print edition are how we make all our online content free. We thought the HN audience would like this piece so in appreciation for your traffic and your comments, here it is.
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