kitchen table math, the sequel: please explain

Tuesday, March 16, 2010

please explain

You really have to see it to believe it.

What happened to "Show your work"?


source: Math Problem of the Week
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13 comments:

SteveH said...

"Explain" doesn't bother me in this case because you can do the problems in your head. There is no work to show. Perhaps explain means to say which postulates or theorems or definitions you used - kind of like an informal proof.

March 16, 2010 at 7:19 PM
Barry Garelick said...

Right; "explain" in this case is different than explaining how 2/3 x 4/5 works and drawing a picture to illustrate it.

March 17, 2010 at 2:43 AM
Ricki Ricardo said...

Luceeeee, somebody has some 'splain to do!

March 17, 2010 at 2:44 AM
lgm said...

Agree. Explain means tell 'why' you did what you did as well as document 'how'. The request "explain how you got your answer" is misleading. Essentially the student is asked for his solution, not just his calculations.

#1 for ex: B/c a straight angle is always 180 degrees, angle AB =180=x+80+y. Since angle x is congruent to angle y, their measures are equal and thus 180=x+80+x using the transitive axiom of equality. Gathering like terms, 180=2x+80. Using the addition property of equality, add -80 to both sides of the eqn to get 100=2x. Using the property of equality, divide both sides by 2 to obtain 50=x.

If this is for below 9th grade, don't refer to properties and just use 'simplify' as the explanation.

March 17, 2010 at 6:22 AM
Catherine Johnson said...

an informal proof

"Russian Math" had those!

(Mathematics 6)

It was great.

That was a 6th grade book - same as this one.

March 17, 2010 at 5:16 PM
Anonymous said...

I don't see the problem with asking for an explanation. If you get the wrong answer, your explanation can show the teacher where you went wrong.

ari-free

March 17, 2010 at 6:10 PM
Catherine Johnson said...

I say Do the damn arithmetic!

March 17, 2010 at 6:21 PM
Catherine Johnson said...

Or an informal proof!

March 17, 2010 at 6:22 PM
Catherine Johnson said...

Or just dump the whole thing and teach Singapore Math!

March 17, 2010 at 6:22 PM
Catherine Johnson said...

Here are the Singapore Math problems for 6th grade.

March 17, 2010 at 6:25 PM
Ari-free said...

In Singapore math you have to show your model diagram. I read somewhere that some kids were upset because they couldn't use algebra to solve some very complicated problems on a test.

ari-free

March 17, 2010 at 7:22 PM
Barry Garelick said...

In Singapore math you have to show your model diagram. I read somewhere that some kids were upset because they couldn't use algebra to solve some very complicated problems on a test.

The bar modeling approach used in Singapore is a nice method--for relatively straightforward problems it does two things. It helps the student see what's happening mathematically and helps the student solve the problem. For more complex problems, such as in the 6th grade book, it gets in the way, in my opinion. It isn't apparent what is happening mathematically for some of these problems and students would be better served to use algebra, which is the end goal anyway.

When I was using SM to teach my daughter, she didn't like the bar models because she had trouble drawing. She said she could solve the problems without the drawings, and indeed she could; she knew the reasoning required (i.e., what the bar model would show) and just went ahead and did it without the bar model. Which was fine with me.

March 18, 2010 at 2:47 AM
Catherine Johnson said...

Speaking as a person who worked every single problem in Challenging Word Problems Grade 3, I love, love, LOVE the bar models. For awhile there, any time I looked at a simple algebra problem a bar model would pop into my mind's eye.

Saxon Math uses bar models to teach fraction word problems.

I had the same experience Barry describes with word problems for 6th grade. It was much more difficult to figure out what the bar model would look like than to solve the problem using algebra.

I remember once asking Carolyn to figure out how to construct a bar model representing a ducks-and-dogs type problem. (X number of legs; how many ducks versus dogs?)

March 18, 2010 at 5:32 AM

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