Monday, April 9, 2007

Algebra Aptitude Test scores decline under Connected Math

The Iowa Algebra Aptitude Test (IAAT) is used as a placement test in the Columbia Public Schools and is administered to all students in 7th grade to help identify honors vs. regular math placement in 8th grade. CPS secondary math curriculum coordinator Chip Sharp expressed it this way: “It is a readiness test. This means it was designed to measure how ready a student is to study abstract concepts in the algebraic strand of mathematics."

The chart below shows the percent of CPS 7th graders that scored above the national 50% rank on the Iowa Algebra Aptitude Test (IAAT) from 1999 to 2006. Under the middle school math curriculum in use from Fall 1999 - Spring 2002, 42.1% scored above the national 50% rank. Under the experimental Connected Math curriculum in use from Fall 2002 - Spring 2006, that dropped to 38.4%. A simple statistical test shows that this is a significant difference, and represents approximately 100 additional students scoring below the 50% rank every year.

Important points to note: the Missouri DESE has declared that the MAP test is out for 11th graders and will be replaced with an end-of-course exam in Algebra I by 2009 (http://columbiamissourian.com/news/story.php?ID=2435) so looking at the test results for an "algebra readiness test" makes sense.

Another point: the line between the previous curriculum and Connected Math in this data isn't fuzzy as is often the case with comparisons--students scored lower using Connected Math, and the difference is significant. Connected Math (CMP) was implemented at CPS in 6th grade in 01-02 and in 7th grade in 02-03. Therefore, students tested in 7th grade in 01-02 had used the "old" curriculum exclusively, and students tested in 7th grade in 02-03 had 2 years of Connected Math in middle school. The data represent over 9,000 student test scores over 8 years. The original data is available at the CPR-Math google group pages (http://groups.google.com/group/cprm/files).










Another way of looking at the results:

Math curriculum

Testing Year

How many more students in bottom half than top half each year?

Number students in bottom half-number students in top half adjusted for cohort size

“old”

99-00

178

185

“old”

00-01

186

196

“old”

01-02

151

154

CMP

02-03

262

249

CMP

03-04

245

239

CMP

04-05

295

293

CMP

05-06

260

255

CMP

06-07

285

283

The average number of students scoring in the "bottom half" under the "old" curriculum was 172. That increased to 269 when students studied a Connected Math curriculum as 6th and7th graders. So a simplified way of viewing the results is that on average, approximately 100 more students score below the national 50% NPR each year that Connected Math is in use in the CPS middle schools. NOTE: The IAAT is normed for 8th graders, so the results do not indicate that CPS students score below the national average, but that CPS students are tested earlier than most students.

7 comments:

Anonymous said...

All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness and proficiency.

JohnL said...

Michelle, what was the "old" math curriculum? Why did the curriculum change had such salutary effects? Would the students in, say, 6th and 7th grade not have brought with them the competence they acquired from the previous curriculum?

Please understand that I'm not opposing what you seem to be proposing. I'm simply hoping to understand these data.

Michelle Pruitt said...

Hi johnl,

I'll try to address each of your questions:

I don't know the name of the "old" math curriculum. Since it's well established that CMP is a significantly different approach to math education, I let the comparison stand on that basis.

My personal opinion of why the Connected Math curriculum made scores go down is that it doesn't prepare kids to move from concrete "example driven" learning to the abstract reasoning required to master algebra. The IAAT measures "readiness" for algebra, not actual algebra skills, but students who are "ready" for algebra need to have a strong grasp of symbol manipulation (something that can be aided by learning standard algorithms) so that they can grasp the idea that, for example, 1/(1-x)=x is a solvable problem even though you may not be able to mentally visualize the solution. It's this point that more than anything compels me to ask for change in the math curriculum. There are many innovative ideas that have gone into the CMP and similar curricula; however, their antipathy toward showing children the power of abstract symbol manipulation seems counter productive.

As for the skills the middle schoolers brought with them from elementary school, I looked at whether the adoption of TERC Investigations in the elementary schools would have had an effect upon these results because it was adopted around the same time. I have a detailed explanation of which students in which years would have had x number of years of TERC vs. the "old" elementary curriculum, but it boils down to the first year of testing, there would have been NO difference between elementary education among all the students tested, and thereafter, a small percentage of students would have had 1 or 2 years of TERC in 4th and 5th grade, depending on which elementary school they attended (Fairview Elementary was an early adopter of TERC). So it looks to me that the real difference is the impact of CMP in just 2 years.

Whew! More than you bargained for? I'd be happy to continue the conversation via email if you'd like, or send you the spreadsheet of data I used.

Anonymous said...

Michelle,

Please give your blog a grammatically correct title. If you cannot accomplish this, how is anyone to take you seriously? Especially when you, a layman, continues to criticize trained professionals.

Michelle Pruitt said...

Since I plans to continues to criticize, perhaps anonymous should visit a different blog. Seriously.

P.S. I'd like to clarify that I'm not criticizing math education researchers or teachers; I'm criticizing math curricula.

anotherstudent said...

That was the best comeback ever, Mrs. Pruitt.

Michelle Pruitt said...

I wondered why the "anonymous" comment posted on April 11 sounded vaguely familiar (and somewhat preachy) to me. Anonymous has cut and pasted "The Overarching Goal of the Connected Mathematics Project" from their website. Sounds great doesn't it? Too bad the curriculum doesn't actually deliver.

Was that a test? Did I pass?