Sunday, January 21, 2007

Test your math knowledge

The Fordham Foundation's The State of State Standards 2006 has given California's math standards a top rating. (CA shares an A with MA and IN).

Here you can test your math knowledge with Practice Problems for the California Mathematics Standards Grades 1-8

An example from 7th grade:

A jacket is on sale for 70% of the original price. If the discount saves $45, what was the original price of the jacket? What is the sale price?
Let's see...

Here is an example from fourth grade:

What is the length of the line segment joining the points
(6, -4) and (21, -4)?
So the kids are already expected to know early algebra at that grade level? Pretty amazing!


Jonathan said...

I didn't look at the lower grades, but distance formula in 4th grade? Too early for that level of abstraction. I read the algebra practice. It looked inappropriate for 8th graders, anywhere.

California teachers and students were victimized by "constuctivism" in the middle and late 90's. This new stuff is from the other, back-to-basics extreme. It looks like California's teachers have utterly failed to hold the middle ground. I wish it were a surprise.

Instructivist said...

"I didn't look at the lower grades, but distance formula in 4th grade? Too early for that level of abstraction."

I was shocked, too.

On the other hand, graphing is appealing to kids brought up on arts and crafts. Algebra notions, like unknowns, are introduced (snuck in without fanfare) in the early grades. I am thinking of omitted addends.

The number line is also introduced in the early grades. A coordinate plane is nothing more than two perpendicular number lines.

I'd like to see if fourth graders would have trouble plotting an ordered pair when shown how. If they can plot ordered pairs with ease and draw the line, then the above problem isn't harder than reading temperature changes on thermometer. There is no need to formally introduce the distance formula.

I am speculating here about the cognitive abilities of fourth graders. I suspect they would be capable of grasping what I have described here. Actual trials would tell.

Anonymous said...

1) You don't need the distance formula to solve that problem. (6,-4) and (21,-4) form a horizontal line so the answer is |21 - 6| = 15.

Of course, it takes a bit of graphing knowledge to know that it's possible to treat (x,y) and (z,y) as an one dimensional problem. However, if nothing else, a quick sketch should make that fact easy to detect.

(Hey, constructivism does get one thing right--if you don't understand it, draw a picture. Unfortunately for the constructivists, kids also need a solid math background so they can deduce what in the heck they just drew.)

2) I help tutor at the local high school. There's no shortage of CA high school students who would not be able to solve the % off problem, alas.

Jonathan said...

You guys are right about the distnace - no formula involved. I looked too quickly. The link seems to be to local, not state documents. And some of the problems (in algebra at least) look like an individual's pet favorites. California may have swung way too far back-to-basics, but these documents may not represent those standards.

I was a math whiz in hs, one of the best in a strong, very traditional school (with all the scores to show it). There are big chunks of that 8th grade exam that would have had me guessing as a junior or senior. There is something wrong.

Instructivist said...

CA math standards: