kitchen table math, the sequel: "Investigations" in Prince William County, VA

Wednesday, May 2, 2007

"Investigations" in Prince William County, VA

Prince William County, in Virginia, recently adopted Investigations for grades K-3. The school district has an online TV station that gives updates on what's going on. If you go here you can watch a video of the Superintendent and Deputy Superintendent of PWC school district talk about Investigations, including interviews with teachers about the program. It is on the first 5 or so minutes of the program. The rest of the program is devoted to other issues.

All the standard verbiage is there: "hands on", "inquiry-based", "build a foundation", "the way we learned was by memorization" . This last one, while employing the usual canard (i.e., the previous method didn't involve any understanding whatsoever, it was just pure memorization) is given a caveat: the Superintendent condescends to recognize that memorization "works for some students". Just not all.

So far there are only about two parents in PWC who are upset. One has protested and has done a good job doing so, to the extent that the school board wrote a written response to address his concerns. But Investigations is there to stay. Old story.

12 comments:

Catherine Johnson said...

I still can't watch that video.

Anonymous said...

http://www.youtube.com/watch?v=Ooa8nHKPZ5k
I thought this was really fitting:)

Anonymous said...

"the way we learned was by memorization"

They have this phrase memorized and repeat it by rote, parrot like.

I don't see how any problem can be solved without analysis and reasoning.

+++

Math help needed.

My students are trying to solve a CMP2 problem that involves d = r x t.

A fellow bikes from Point A to B at different speeds. He stops three times to record his time and distance.

First stop: 5 miles in 20 minutes
Second stop: 8 miles in 24 minutes
Third stop: 15 miles in 40 minutes

Someone tries to tie him at a steady rate. How fast would he have to go?

I solved this problem in a complex way by using r = d/t

Plugging in the numbers I get:

r = 28 miles/84 min

I converted the minutes to hours expressed in decimals (1.4 h) and ended up with 20 mph.

I also tried another approach trying to average the speeds in the three segments (15 m/h, 20 m/h, 22.5 m/h). That doesn't get me the 20 mph. Why doesn't averaging work here?

This and similar problems asking for t are intended for 7th graders. They are enormously complicated involving complex fractions and expressing hours in decimals. Too taxing for most or all of the students.

C.

SteveH said...

"...the Superintendent condescends to recognize that memorization 'works for some students'. Just not all."

Thank you Professor Umbridge.

All we need now is a Room of Requirement and some Saxon and Singapore Math books. We can call ourselves Milgram's Army.

[apologies to non-Harry Potter fans]

SteveH said...

Yes, they parrot these things back without any thought or analysis. They were probably directly taught in Ed School.

- - - -

"A fellow bikes from Point A to B at different speeds. He stops three times to record his time and distance."

I guess he stops, records this data instantaneously, and then starts right up?

SteveH said...

Average rate = total distance/total time

(d1 + d2 + d3)/(t1 + t2 + t3)

does not equal

(d1/t1 + d2/t2 + d3/t3)/3

You can't average rates. What if a car went 100 mph for 10 hours, then went 5 mph for 5 minutes and 15 miles per hour for 3 minutes. You can't average the rates.

Also, I wouldn't bother changing units. Miles per minute is fine.

Anonymous said...

"I guess he stops, records this data instantaneously, and then starts right up?"

I guess this is the fuzzy element.

Maybe there are breaks that account for the discrepancy. The text is silent on this point.

C.

Anonymous said...

"You can't average rates."

I should have known.

Many thanks for your help.

C.

SteveH said...

DRT problems can work very well for early algebra. They teach students about governing equations. If they keep going in math, they will see how it compares to things like Bernoulli's equation. You can start with simple problems and work your way to more difficult variations. The hope is that the students are writing down and solving equations and not just trying to figure it out in their heads or by guess and check.

Anonymous said...

All we need now is a Room of Requirement and some Saxon and Singapore Math books. We can call ourselves Milgram's Army.

I like this idea. It would be almost like having friends ... (more apologies!) :-)

-Mark Roulo

Sean Price said...

This is a great ambiguous questions

First stop: 5 miles in 20 minutes
Second stop: 8 miles in 24 minutes
Third stop: 15 miles in 40 minutes

What is the average speed?

Well my statistics training tell me that average = mean = sum(speeds for all N)/N.
= (5/20 + 8/24 + 15/40) / 3
The average of the speeds is 23/72 miles/min

But average speed could also mean what is the speed given the total distance and time?
Total distance = 5+8+15 = 28
Total Time = 20+24+40 = 84
Speed = distance/time = 28/84 = 1/3 miles/min

Who is right? Watch out for those ambiguities.

At least the problem writers tried to resolve the ambiguity with sentences "Someone tries to tie him at a steady rate. How fast would he have to go?" Although awkwardly (what does "tie him" mean?).

Sean

Instructivist said...

"Although awkwardly (what does "tie him" mean?)"

The way I understand it, it means ride the same distance in the same time.