[**note:** This week, I’m trying to catch up on posting about recent stories related to Providence Public Schools. This is the first of these posts. I hope you’ll take the time to watch the video and try to solve the math problem below!]

As **reported in the ProJo**** **and elsewhere, on Monday March 3rd the Rhode Island Department of Education released the results of the New England Common Assessment Program (NECAP) examinations give to 11th graders in the Fall of 2007.

The percentage of students scoring proficient or proficient with distinction were as follows: Reading: 61%, Writing: 37%, Mathematics: 22%

The results, particularly in math, are discouraging and have excited quite a bit of public comment. The reading and writing scores are approximately consistent with the scores for 8th graders, but the math scores represents a substantial drop (from 48% proficient or proficient with distinction in 8th grade).

Providence’s top scores were at Classical High School (Reading 92%, Writing 62%, Math 40%). Those Reading and Writing scores were on a par with, and in some cases better than, the other top schools in the state, Barrington and East Greenwich. Classical’s math scores, however, were 14 points below E. Greenwich’s and 20 points below Barrington. The worst news is that only 10% of Providence’s 11th graders were proficient in math.

While nobody will say this is acceptable, there are some caveats to consider. First, the exam was given to 11th graders for the first time this year. The test is generally regarded as significantly harder than the test previously given to 10th graders. (For an example of the questions, see below). New Hampshire, which also uses the NECAP, also saw a dramatic drop. There, 28% were proficient, a fugure not much higher than RI’s. It may be that we need a year or so to know how much of the problem is due to the testing instrument, as opposed to the students’ knowledge.

Second, while some are quick to blame teachers, it is not clear that this is appropriate. The math test covers algebra and geometry. The school department, however, steers many students into general math courses (sometimes called “math to nowhere”) and out of algebra and geometry, so that students are being tested on concepts they have never been taught. This, of course, is a matter of school department and school board policy over which teachers have little say.

Finally, it is probably time to look closely at the general math curriculum. Providence uses the “Math Investigations” curriculum, which was introduced by a previous superintendent. “Math Investigations” has been widely criticized as being unsuitable for developing the skills necessary for higher mathematics. For a nifty video demonstration, see the video link below.

Sample NECAP math problem:The manager of a music store ordered 20 new violins. She ordered some of two different models- the standard and the deluxe. Each standard violin costs $500, and each deluxe violin costs $800.

If the manager spent exactly $11,500 on these violins, how many deluxe violins did she order? Show your work or explain how you know.

Answer in the comment below.

Here, with a tip of the hat to Rhode Island Regent Angus Davis, whose blog “Passing Notes” covers education reform issues, is a brief video comparing traditional math with “Math Investigations”. I was quite astounded.:

on March 10, 2008 at 7:50 pmThomas SchmelingHere’s my solution to the problem. Other solutions might be more elegant, but I am sure this one is correct.

The manager of a music store ordered 20 new violins. She ordered some of two different models- the standard and the deluxe. Each standard violin costs $500, and each deluxe violin costs $800.

If the manager spent exactly $11,500 on these violins, how many deluxe violins did she order? Show your work or explain how you know.

X= number of standard violins

Y=number of deluxe violins

X+Y=20

X=20-Y

500X+800Y =11,500

500*(20-Y)+800Y=11,500

10,000-500Y+800Y=11,500

10,000+300Y=11,500

300Y=1,500

Y=5

5 Deluxe violins were ordered.

on March 14, 2008 at 7:24 amJustinYour reply leaves nothing to be desired, mathematically speaking.

But could someone work this one out logically, without knowing how to set up a system of equations and do a variable elimination like you did? Sure: think of *all* the violins as having a base price of $500, with the deluxe ones requiring a separate bonus payment of $300 extra. Then, the 20 violins have a base price of $10,000. But the manager spent $11,500, which is $1500 extra — so that implies she bought $1500/$300 = 5 deluxe models.

on March 14, 2008 at 10:48 amThomas SchmelingThat’s pretty clever, Justin. I don’t know that I would have come up with that on my own, though of course I didn’t think to look for alternatives to my approach.

Formally, it skips my first three steps and just goes:

10,000+300Y=11,500

300Y=1,500

Y=5 Cool.

It also goes to show that there are different approaches to problems. Does it say anything about “Math Investigations’ or other approaches that avoid algorithms? Did you look at that MI video and, if so, what did you think? My first reaction was that it was completely awful, but I’d like to learn more.

I’m a professional educator, but certainly don’t know anything to speak of about math instruction.

on March 27, 2008 at 8:15 amGayle GiffordAs someone who struggled with arithmetic and math facts throughout school, but did master calculus (back in high school, not any longer, though I do use some simple algebra frequently), I found some of the methods in Everyday math as outlined to be much more intuitive than the standard algorithm

method which is just memorization of numbers and no understanding of what those numbers mean. In particular, the Everyday math long division problem that she did made way more sense to me than the historic algorithm method.

Do I have any idea how to teach math? Absolutely not. But I do know this about teaching…

There are various ways of learning. Any one teaching method does not suit all. My kids struggled through math, in part, I think, because they were never able to conceptualize what all those math facts meant. And guess what… when I was in elementary, middle and high school way back in the 60s and 70s, lots of kids struggled through math then as well. We just didn’t have standardized testing to document how little students knew (not to mention that we had huge drop out rates then because you could get a low skilled, high pay union manufacturing job).

We should hold our teachers and schools accountable for results… and not dictate to them the way to teach. Right?