16
   

I'm an idiot -- stupid math question.

 
 
Thomas
 
  1  
Reply Thu 10 Sep, 2009 02:08 pm
@CalamityJane,
Calamity Jane wrote:
Thomas, it's mind boggling how they teach the children simple math here. I find our German system so much easier - only thing you have to be good at is memorizing the multiplication tables. Now in the U.S. it is taught more visual, yet more confusing (to me at least).

It seems you were lucky to go to school in conservative Bavaria, and to get out of Germany just in time. In 1975, when I joined my elementary school in Konstanz, Baden, that school was already of the "New Math" persuasion. We had a box with blocks of wood that were one centimeter high and wide, and 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 cm long respectively. We added and subtracted by laying two blocks side by side, and comparing its length with that of some other block. It's a graphic way of doing arithmetics, and it's intuitive for addition and subtraction. But multiplication was awkward (to me at the time).

It would be interesting to see studies investigating if students really find it easier to learn the "new Math" way of arithmetic calculations rather than going straight to the multiplication table. (Obviously you have to learn the multiplication table eventually, because you need it for multiplying and dividing numbers of arbitrary length.)

Personally, I never got anything out of the graphical stuff. But if some students learn better that way as littlek suggests -- so be it.
boomerang
 
  1  
Reply Thu 10 Sep, 2009 05:24 pm
@engineer,
I don't think the teacher is an idiot, engineer.

In fact, I think I'm really going to like her! Early appearance indicate that she's a bit unorthodox (she lets them chew gum in class (which studies show improves concentration) and lets them wander around while "thinking"). She talks about the worst teacher she ever had, the nuttiest thing she ever saw at school, the blahbedeblah.

Mo adores her.

True story: she used to live in the house next door to where I live now. My neighbors who have been around here a while all rave about her.
sozobe
 
  1  
Reply Thu 10 Sep, 2009 06:29 pm
@boomerang,
Encouraging!
0 Replies
 
FreeDuck
 
  1  
Reply Fri 11 Sep, 2009 07:42 am
@Thomas,
Thomas wrote:

Calamity Jane wrote:
Thomas, it's mind boggling how they teach the children simple math here. I find our German system so much easier - only thing you have to be good at is memorizing the multiplication tables. Now in the U.S. it is taught more visual, yet more confusing (to me at least).

It seems you were lucky to go to school in conservative Bavaria, and to get out of Germany just in time. In 1975, when I joined my elementary school in Konstanz, Baden, that school was already of the "New Math" persuasion. We had a box with blocks of wood that were one centimeter high and wide, and 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 cm long respectively. We added and subtracted by laying two blocks side by side, and comparing its length with that of some other block. It's a graphic way of doing arithmetics, and it's intuitive for addition and subtraction. But multiplication was awkward (to me at the time).

It would be interesting to see studies investigating if students really find it easier to learn the "new Math" way of arithmetic calculations rather than going straight to the multiplication table. (Obviously you have to learn the multiplication table eventually, because you need it for multiplying and dividing numbers of arbitrary length.)

Personally, I never got anything out of the graphical stuff. But if some students learn better that way as littlek suggests -- so be it.

I think that establishing a graphical base can help immensely when it comes to adding and subtracting large numbers that require carrying and borrowing (composition and decomposition). If you have a sense that a 10 is made up of 10 1's then borrowing makes more sense. For multiplication -- I can see how that could be awkward.
0 Replies
 
Eorl
 
  1  
Reply Wed 16 Sep, 2009 08:05 am
I think maybe y'all missed the point on this one. To work out the answer was 39, did you count 1,2,3 tens plus .. 1,2,3,4,5,6,7,8,9 units...

No, you recognized the shapes... a group of 3, and a block of nine. Apparently it's called "subitizing" (pronounced like a contraction of submarine advertising). My 7 year old had to teach me about it. When she was 5. It's a technique you can use to count without actually counting.
Eorl
 
  1  
Reply Wed 16 Sep, 2009 08:10 am
@ehBeth,
Cuisenaire rods by chance? Loved 'em. Can't imagine why. Laughing
0 Replies
 
Chumly
 
  1  
Reply Wed 16 Sep, 2009 09:29 pm
@Eorl,
Nope you're wrong.

There is no text reference to subitizing, in fact just the opposite.

You can't take part of the question (in this case the graphical element) out of context of the text element, and argue simply because some kid was at one time taught that the graphics may have only one given meaning, that this given meaning must hold true irrelative of the text.

Recall the text precedes the graphics and recall the text poses the question.

The question as asked "The number pictured here" does not reference relative size, but only quantity. There is no reference to magnitude processing, thus no reference to subitizing.

That would be like graphically representing the planets, then asking how many planets are in the solar system, then claiming that Saturn counts as more planets than Mars, because it's bigger.

That teacher is an idiot! Here are the correct answers as the question as asked: Question 6 = 12 and Question 12 = 9.

It matters not one iota how well a teacher is or is not liked in terms of whether they are an idiot for posing the question as asked.

It matters not one iota how popular the underlying graphics are or are not, what matters is whether the text is congruent with the graphics...it's not.

Have a look-see at the definition of "number", there is no reference to relative size, in fact just the opposite as relative size can be ignored as per "7. the full count of a collection..."

1. a numeral or group of numerals.
2. the sum, total, count, or aggregate of a collection of units, or the like: A number of people were hurt in the accident. The number of homeless children in the city has risen alarmingly.
3. a word or symbol, or a combination of words or symbols, used in counting or in noting a total.
4. the particular numeral assigned to an object so as to designate its place in a series: house number; license number.
5. one of a series of things distinguished by or marked with numerals.
6. a certain collection, company, or quantity not precisely reckoned, but usually considerable or large: I've gone there a number of times.
7. the full count of a collection or company.
8. a collection or company.
9. a quantity of individuals: Their number was more than 20,000.
oolongteasup
 
  1  
Reply Wed 16 Sep, 2009 09:40 pm
@boomerang,
i'm thinking you're going to struggle in high school again
0 Replies
 
Eorl
 
  1  
Reply Wed 16 Sep, 2009 11:30 pm
@Chumly,
I wouldn't say I'm wrong, although I think you are right.

The question was poorly put, if it could be said to have been put at all. I'm just guessing as to what was meant, and the kid may well recognize something they do in class all the time.
0 Replies
 
DrewDad
 
  1  
Reply Thu 17 Sep, 2009 07:03 am
@Chumly,
Chumly wrote:
That teacher is an idiot!

You're taking one data point (a worksheet with no written instructions) and extrapolating to infinity.

Don't be an idiot yourself.
0 Replies
 
boomerang
 
  1  
Reply Tue 20 Oct, 2009 06:27 pm
Okie dokie --- my next stupid math question is:

Adria is in the school band. She knows the band has 7 people in each row and that there are 10 rows.

(insert diagram of children's heads:)

x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x

<sample question>

There are two rows of flute players. How many flute players are there?






Obviously it is either 20 or 14. But since the preface tells that "rows" run each way there is no way to be sure what they want. I was taught that rows run across and columns run up and down.

Judging by the rest of the sheet I'm pretty sure the answer they want is 14.

But couldn't 20 be correct too? Really, wouldn't 20 be the better answer?
oolongteasup
 
  1  
Reply Tue 20 Oct, 2009 06:33 pm
@boomerang,
your diagram shows 7 rows and 10 columns

it should be vice versa

2 rows of 7 is 14

0 Replies
 
littlek
 
  1  
Reply Tue 20 Oct, 2009 06:33 pm
<oops, looks like a typo?> The rows go left to right.
0 Replies
 
JPB
 
  1  
Reply Tue 20 Oct, 2009 06:35 pm
@boomerang,
boomerang wrote:


x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x
x x x x x x x x x x

<sample question>

There are two rows of flute players. How many flute players are there?






Obviously it is either 20 or 14. But since the preface tells that "rows" run each way there is no way to be sure what they want. I was taught that rows run across and columns run up and down.

Judging by the rest of the sheet I'm pretty sure the answer they want is 14.

But couldn't 20 be correct too? Really, wouldn't 20 be the better answer?


Nope, it's:

x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x

so two rows = 14
boomerang
 
  1  
Reply Tue 20 Oct, 2009 06:36 pm
If rows go left to right, then there are 10 per row and the answer is 20.

I'm with ooootea (hope that's okay to use rather than looking up the correct spelling) -- it should be reversed but it should also define rows and columns.
0 Replies
 
boomerang
 
  1  
Reply Tue 20 Oct, 2009 06:38 pm
@JPB,
But the diagram has 10 across and 7 down -- not the other way around.

And besides, they call them both "rows" in the introduction.
CalamityJane
 
  1  
Reply Tue 20 Oct, 2009 06:40 pm
@boomerang,
boomerang wrote:

But couldn't 20 be correct too? Really, wouldn't 20 be the better answer?


No! There are only 7 people per row - and there are 10 rows of 7 people each -
making it 14 people.

Example: there are 7 apples to one cake, and there are 10 cakes.
2 cakes are filled with peaches. How many peaches are there?

I am sure your answer will be 14 right away.
0 Replies
 
JPB
 
  1  
Reply Tue 20 Oct, 2009 06:41 pm
@boomerang,
As a statistician I'd yell loudly if they were presenting rows vertically rather than horizontally but you can only work with what they gave you. I'd stick with 14 because.... well, that's how they described it even if the graphic didn't fit.
0 Replies
 
JPB
 
  1  
Reply Tue 20 Oct, 2009 06:45 pm
@boomerang,
Quote:
Adria is in the school band. She knows the band has 7 people in each row and that there are 10 rows.

(insert diagram of children's heads:)


Ok... no dilemma. There are 7 people in each of 10 rows. 2 rows of flutists equals 2 times 7 = 14. Pretend they didn't give you a faulty graphic.
boomerang
 
  1  
Reply Tue 20 Oct, 2009 06:53 pm
It still seems to me that by defining them both as "rows" that either answer would work.

I know math isn't my forte, but when I first previewed the problems I thought the answer was 20. It was only after reading the rest of the questions and realizing that someone had to be playing both the drums and the trumpets that by "row" they meant "column".

Just weird.
 

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