Re: Math Education: A response to "An Inconvenient Truth" Part1

[alleyghost]

Traditional algorithm is perfect for resolving quickly on paper, while most other methods are better suited to mental calculus or estimation, in my opinion...

Both methods have their merits.

One does not condemn the other, it should complement.

[grichard24]

He must have studied that "new math" in elementary school!

[jamesblackburnlynch]

Nah, he's too young. that "new math" was early 70's. Way long ago. That's some old junk.

[BruceDeitrickPrice]

It's so bizarre to me the way some people set up these fake oppositions. As if a kid who memorizes what 4 x 6 is, can't then go on to a more conceptual handling of the same problems.

[sleeper2345]

I don't think this is a general consensus. Does it matter how students memorize their facts? For example, if I learn 5, 6, 7, 8, so 7 x 8 = 56 do you care? Or is math just learning simple tricks to remember the facts?

[RedwoodTheElf]

The concept of "borrowing" is very strictly controlled...how could you NOT know that you always borrow to the left? The zero becomes a -1...which in turn becomes a 9 when IT borrows to the left.

[RedwoodTheElf]

So...where does "planning a world tour" come into a math book?

[jamesblackburnlynch]

It's an APPLICATION of mathematics. It's the thing everyone is always saying they want. What is math good for? When will I ever use this? And here we have a large section on applications (it's a reference book, so the teacher picks the relevant section for percents or means or multiplcation or fractions etc.) that is all connected.

It's so sad that people complain about the very thing they demand in their math education.

[Conuly]

I don't know. I imagine that at some point you have to figure out how much money you have left after buying various sorts of tickets or hotel rooms (and what the better bargain is - so and so much money for this hotel for 3 nights or so and so much money for 5 nights), and you have to calculate... I don't know, fuel and food costs and miles traveled and whatnot.

You think you don't use math when traveling?

[scrapbook11]

Yes, you are right that some of the algorithms are complicated in math. But reducing them is one approac. Another approach is the environment the students are in. Unstable families, neglected by parents as well as by teachers. Also some students learn best one on one or at least in a small group.

[sintofg]

Also I was taught in my 5-6, 7-8 math classes that writing out problems on paper in steps is a much easier way to find errors more quickly if an answer is wrong, than always relying on a calculator, because it shows that you can think and also it shows your ablility to mentally solve a problem and feel comfortable w/your results, and this ability really comes in handy if you forgot to bring a calculator to class o/if you didn't have one. Comes in handy in High School.

[sintofg]

I agree w/iortizvictory on this because when you have students and I am one of them,that just doesn't get math, for me I just can't learn from a curriculum entirely-based on an in-the-textbook apporach,because it never did click right away,and that when my class did qroup activities that involved hands-on work while at the same time it helped me understand forumlas & concepts more easily, because they were implied in real-life situations where they would be needed.

[MoAnabre]

I somehow doubt that you'll see this, but your method of doing 201-130, while basically how I do it mentally, would confuse the hell out of kids just learning the subject (inverting the difference 1-30 to 30-1 and then subtracting that from 200-100).

[iortizvictory]

We all have different learning styles. As a kid the algo method for subtraction was confusing. Reasoning is a good skill to have when kids are out of school. Not everything in the real world is multiple choice/connect the dots in a pretty package. Thanks for your post! I really appreciate your comments.

[TheMathGuy]

...you do when you reason it out, it just happens in a more controlled, standardized way.) Personally I think it's good to know both the method and the logic, so I can use whichever method/technique I think suits the problem best.

[truthseek2007]

I totally agree, both methods are good to know. especially if you can't remember which number to borrow from. Hey better yet a calculator. It's very rare in the real world that people do math by hand. The business math I see is done on Excel or via a computer program. I think grasping the concept and knowing when to use it as a tool is the most important thing. That's just my opinion though.

[TheMathGuy]

... That being said, the standard algorithm is fast and efficient for larger numbers (like 23457-1281) provided you have a strong enough grasp of it to not have to think about which number to borrow from (such as in this example where the 5 in the ten's place of the minuend would need to borrow one from the 4 in the hundred's place, and since one hundred is ten tens, the 5 becomes 15, and now you can take 15-8 to get the ten's digit of the difference. (This is really no different than what...

[truthseek2007]

Just different paths that lead to the same place.

[TheMathGuy]

The first thing I thought to do when I saw 521-275 was to think of 275 as 25 cents less than 3 dollars (thinking of it as money). If I subtract 3 dollars from $5.21, that would be $2.21, but I'm subtracting 25 cents less than that, so I really have $2.21 + 25c = $2.46. I think most people naturally think about it this way once they have a firm grasp of what subtraction means.

[vampireofminds]

If education in america wasn't so bad you would have been taught better

[truthseek2007]

I really think what educators should do is integrate real world problems and challenges into math circs. As a kid I got so confused remembering algo's and always asked the question, "Why am I doing this?" Thanks for you comment!

[Escuerd]

If education in America weren't so bad we'd all be using the subjunctive mood in proper places.  Ok, just kidding.

[SebFinnegan]

I don't understand your method. Yes 201-130 is really cute to do(then again doing 3 substractions instead of 1 just puzzles me). Try this : 5784134 - 248414 using your method. Where will you start ?

[iortizvictory]

What I'm saying is that you can reason through solving a problem rather than using the standard algo.

[CorfitzUlfeldt]

Bugger! Sorry about the spam. When I posted the first time, my posts didn't show up, so I reposted.

[CorfitzUlfeldt]

Now you can go through the standard algorithm, and instead of "borrowing" and "carrying", you pick up a larger bundle, and remove the elastic band.

Lets subtract 130 matches:

Starting in the 1s place we remove 0 single matches. Nothing to do. We move on to the 10s place. We need to remove 3 bundles of 10 matches, but there are none. We then take a bundle from the 100s place, remove the plastic band, and we have 10 bundles of 10. From those we remove 3, and we have 7 left.

(continued)

[CorfitzUlfeldt]

It seems to me that you want to make it less abstract and more concrete.

How about taking a large bunch of sticks or matches, and let them represent your number.

Take 10 matches, put a rubberband around them, and you have one 10.

Take 10 of those bundles of 10, put a rubberband around them, and you have one 100.

The number 201 would be 2 bundles of 100s, and a single match.

(continued)

[CorfitzUlfeldt]

We then move on to the 100s place:

In the 100s place we now have 1 bundle left, and we need to remove one. So we take it away.

In our hand we have 130 matches. Left on the table is 71 matches.

[CorfitzUlfeldt]

Now you can go through the standard algorithm, and instead of "borrowing" and "carrying", you pick up a larger bundle, and remove the elastic band.

Lets subtract 130 matches:

Starting in the 1s place we remove 0 single matches. Nothing to do. We move on to the 10s place. We need to remove 3 bundles of 10, but there are none. We then take a bundle from the 100s place, remove the plastic band, and we have 10 bundles of 10. From those we remove 3, and we have 7 left.

(continued)

[CorfitzUlfeldt]

It seems to me that what you want is to make it less abstract and more concrete.

If you want to make subtraction concrete, then how about having a bunch of sticks (or matches). Individual matches are your 1s. Bundles of matches (elastic band around) would be your 10s. Collect 10 of those bundles in a new bundle (additional elastic band), that would be your 100.

So your number 201 would be 2 large bundles of 100, 0 bundles of 10, and a single match.

(continued)

[xghoulxx]

well how I see it is that in the problem 201-130 all I see if someone asked me is that i always get the number and make it in the hundreads tens or thousands etc like i would see 30+70 = 100 add 1 and u get the 201 so answer is 71 if its wrong plz dont bash me im still a teen i just solve those problems like that :D

[iortizvictory]

That is very cool! See you did it too! You reasoned through the problem without having to using an algo. I really struggled in 5th grade because I could never remember which one to borrow from. Reasoning through it makes it so much easier for me. Thanks for the post!

[earlyphilosophy]

are you in a space station?

[iortizvictory]

hehehehe I love it. 10..9..8.. lift off!

[iortizvictory]

Great hearing from you James! The problem at the end of the video addresses how to solve it without borrowing. Unfortunately the video compression makes it hard to see problem. To avoid subtracting from 100 I would tell them, subtract $99 and hold on to the $1 which which we will bring back. It's easy to subtract a large number from a smaller number. Much easier then remembering which number borrow from. It gives them another route to go if they forget the process for the official algo.

[jamesblackburnlynch]

I'm very happy to see you thinking about other ways to do subtraction since the "borrowing" process hides the actual thinking involved. Question: In 201-130, it's clear why 200-100=100 is relevant, but it's not at all clear 1) why you are doing 30-1 (rather than 1-30) then 2) subtracting (instead of adding) 100-29 (which gets us back to the borrowing problem). Obviously, you've thought it through. But can you explain it to 3rd graders?