I Had A Random Thought...

[jennegatron]

It took me a second to parse what that common core demo is doing because that isn't how I learned to do it, but when I did take a second to figure out what was going on (which is do small additions to count up to 32 from 12, and then take the sum of the additions you did) it makes a whole lot more sense than the old algorithm to me, as this is a much more intuitive way to think about subtraction, again for me. You can ask what you get when you take 12 from 32 OR you can ask what do you add to 12 to get to 32. If addition & subtraction aren't something you've been doing for decades, it makes more sense to move in chunks of 5's and 10's as those are the easiest patterns to remember, imo.

 

Multiple algorithms will get you to the correct answer, but you have to think about what does the algorithm obscure from the user.

I think people encounter math that they're not familiar with and just shut down instead of stopping to think about what is trying to be accomplished.

[tberton]

I guess I just don't really understand because math is my thing, but the old way (taking the more difficult form of your question, 32 - 13, breaks down like this:

 

32 = 30 + 2 & 13 = 10 + 3 (basic number construction)

32 = 20 + 12 (carry the one)

20 - 10 = 10 (subtract the tens)

12 - 3 = 9 (subtract the ones)

Answer = 10 + 9 = 19

 

So there is an underlying process going on there. It might not be taught very well, but there is a pattern there, and it feels like it extends to larger numbers a lot better.

 

Edit: Not that I'm against teaching the new way. I think that teaching things in as many different ways as possible is a plus. I just don't think we should just throw out the old way.

 

I agree completely that there's an underlying process in the standard algorithm. What I'm saying is that the way we write it obfuscates that, so that unless a teacher goes out of their way to continuously mention that, none of the underlying processes are made clear in the notation. And if every time somebody used the standard algorithm they broke it down into the steps you describe, it wouldn't look any less confusing on the face of it.

 

I'll also agree that it's silly to completely throw out the old way. Both should be taught in conjunction. 

 

What do you need to add to 12 to get 32? 20. 

 

Zeus, I'm singling this section out of your post because I agree with the rest of what you said about teaching multiple methods and ensuring that teachers are actually conveying information effectively.

 

But I want to point out that it is not at all obvious that you need to add 20 to 12 to get 32. It's only obvious to you and me because we've dealt with equations like that since we were children. But unless you can't just say to a kid "what do you need to add to 12 to get 32" and expect them to know it right off the bat. They could get 12 apples and keep adding to them and counting until they had 32 apples and then check how many apples they needed to add, but that's tedious and impractical. However, that works really well on the smaller scale, because we've all got at least a few fingers to count with quickly.. All this method is doing is splitting it into smaller steps to make it very obvious what's going on.

 

Basically, I just think a lot of the criticisms of Common Core math are rooted in the fact that certain ideas are so ingrained and practiced in us as adults that they seem obvious, when they are not at all obvious to children. To use a bit of a strange analogy, a Greek of Euclid's time would have been completely baffled by our use of symbols to represent numbers, but completely comfortable counting geometrically. 

[Dewar]

I can't imagine how difficult it would be to teach children math. 

[jennegatron]

As someone who tried to teach them math when their parents and their teachers were falling short, it's hard!

[Merus]

I rapidly became wary of this conversation because I've learnt most adults have very strong opinions on pedagogy and very few of them have any kind of training in pedagogy. It's one of the more accessible places the Dunning-Kruger effect rears its head: because most adults in developed countries went to school, we know a little about the teaching process, which makes us think we know a lot more than we do. Myself included! I constantly have to suppress the urge to assume that just because they gave us formulas in exams that this is the best way to go about teaching physics.

[Jutranjo]

Teachers of physics in all my school years except the last one, before uni, taught physics formulas by drawing this triangle and writing in F=m*a.

 

 

To find out what the formula for what you're looking for the task is, just cover that one up and the triangle tells you if it's m*a, F/m or F/a! It works for work, electrical currents, etc.

 

It's absolute garbage. Then you get to heat exchanges and this triangle does not work. You need to use formulas that have more than 3 variables like

 

 

Or more if you have vaporization, etc. I think most of the class ended up purely memorizing the equation and plugging numbers into it.

[tberton]

I actually found that triangle really useful for three-variable equations. You're right that it's not useful for more variables than that though.

[SecretAsianMan]

Here are my last thoughts on these topics.

 

On memorization: I think memorizing is a good way of knowing but not a good way of learning.  As evidenced by the above triangle examples, memorization is mostly useful in specific cases that fit what you've memorized.  When you start go outside of those cases, that's where you need understanding which usually doesn't come with strict memorization.  If something has been memorized because it's been used a lot, there's nothing wrong with that.  I learned a ton of things that way.  And there are going to be things that really can't be learned any other way besides just memorizing it, like Gormongous has suggested.  I think one of the traps of relying on memorization is it can lead to a narrow focus.  To bring up the programming example Zeus used, if I understand how a function works then maybe I can realize that there will be cases where it's not an optimal solution and instead use another or write my own.  That doesn't happen if I just know how to call the function.  Maybe both will give me the same answer but if you're calling that function thousands of times that adds up to a lot of potential savings.  I don't mean to suggest we have to know how everything works before we use it because that would be silly.  But memorizing a lot of things without having understanding isn't good either.

 

On common core vs traditional:  I don't think either is better than the other.  People learn in different ways.  The common core method makes sense to me because that's how I think.  I know that it won't to everyone.  My real complaint about teaching one method over the other is the "one size fits all" philosophy we have when teaching.  Some people are visual learners, some aren't.  Some people are hands on, some aren't.  Neither is wrong, neither is bad.  But forcing everyone to do the same is.  Unfortunately, for all my complaining I really don't have a better general solution because tailoring learning to each individual person is expensive, in both time and money.  Ideally I'd love to have students and teachers work together to figure out the best way for both but in reality neither one has the time to do that.

[Reyturner]

I used to like Christmas but now I hate it. Ben X you're a one man war on Christmas.

[SuperBiasedMan]

It's like the Sesame Street special where Elmo wishes every day was Christmas, and then he sees how that's terrible and undermines the special nature of being one day a year.

[Patrick R]

Ben has not and never will learn his lesson.

[Ben X]

It's like the Sesame Street special where Elmo wishes every day was Christmas, and then he sees how that's terrible and undermines the special nature of being one day a year.

 

If every day is special... then none of them is

 

[SuperBiasedMan]

Are you trying to hint that you found my Syndrome/Elmo slashfic.

[dibs]

Are you trying to hint that you found my Syndrome/Elmo slashfic.

 

I found it, but i re-released it with every reference to Elmo replaced with BenX.

[SuperBiasedMan]

I found it, but i re-released it with every reference to Elmo replaced with BenX.

 

You 50 Shades of Grayed me!

[Ben X]

Hee hee, tickle me Syndrome!

[Ninety-Three]

Thumbs! I have a question, a philosophical quandary for you!

 

I was on a Skype call with a friend, and we realized that my headset mic was faintly picking up audio coming from the headset speakers. Testing this phenomenon, I put on some music and asked "Can you hear that?" My friend responded "I can hear faint music, but I can't tell what it is." Then she guessed, correctly "Is that Never Gonna Give You Up?" Now to be clear, my friend could not actually recognize the song based on the audio, instead she used her knowledge of me to deduce "Ninety-Three is playing a song for someone else. It's probably Never Gonna Give You Up, that seems like a Ninety-Three move."

The question is: Did I successfully Rickroll my friend? Can you Rickroll someone who doesn't hear the (intelligible) audio?

[Twig]

i have a new avatar this is another good one imo

[Merus]

Thumbs! I have a question, a philosophical quandary for you!

 

I was on a Skype call with a friend, and we realized that my headset mic was faintly picking up audio coming from the headset speakers. Testing this phenomenon, I put on some music and asked "Can you hear that?" My friend responded "I can hear faint music, but I can't tell what it is." Then she guessed, correctly "Is that Never Gonna Give You Up?" Now to be clear, my friend could not actually recognize the song based on the audio, instead she used her knowledge of me to deduce "Ninety-Three is playing a song for someone else. It's probably Never Gonna Give You Up, that seems like a Ninety-Three move."

The question is: Did I successfully Rickroll my friend? Can you Rickroll someone who doesn't hear the (intelligible) audio?

 

I was going to say trick question, anyone still trying to Rickroll people in 2015 doesn't have friends, but there's a more fundamental problem.

 

The difference between Rickrolling and listening to Rick Astley's biggest hit is the subverted expectation. A Rickroll is when you're expecting one thing and get Rick Astley instead. If she can guess you're playing Never Gonna Give You Up, she can't be unpleasantly surprised by Never Gonna Give You Up, which means she hasn't been Rickrolled.

[syntheticgerbil]

HAH GOT YA

[Gaizokubanou]

https://www.google.com/webhp?sourceid=chrome-instant&rlz=1C1ASRM_enUS625US625&ion=1&espv=2&ie=UTF-8#q=gargled%20milk

 

HAHAHAHAHHAHAhahhahahahahahahhahahahah

 

hahaha

 

oh... sigh...

[Vasari]

I tried Spotify for the first time today and I'm not sure I understand the point. I wanted to listen to Run The Jewels 2, so I searched for that. It gave me a playlist that had some of the songs from that album, and some other RTJ songs, and some adverts, and then after a while it wouldn't let me listen to any more. Are you just supposed to hope it gives you what you actually want to listen to?

[jennegatron]

I don't know if you were listening on mobile or desktop, there are slightly different interactions available to you on each. Also I'm not sure the restrictions specific to locations other than the US.

[Vasari]

I was on mobile. I'm only confused because it's seems like a popular service and I can't believe that in 2015 this is the best we can do in terms of listening to music.

[Space Anchor]

I tried Spotify for the first time today and I'm not sure I understand the point. I wanted to listen to Run The Jewels 2, so I searched for that. It gave me a playlist that had some of the songs from that album, and some other RTJ songs, and some adverts, and then after a while it wouldn't let me listen to any more. Are you just supposed to hope it gives you what you actually want to listen to?

 

Good choice! (I know it's not really the point here, but do you know that they've made free downloads of their two LPs available right?)

 

Not a very frequent Spotify user but find the web app to be pretty decent. (i.e. http://play.spotify.com). Their library's gotten much better too - there was no Dylan for a good while, among other stuff.