Wednesday, April 11, 2007

Why I believe supplementing the Investigations curriculum would be an ineffective and frustrating strategy to improve math education in CPS

by Tere DeWitt

A well written mathematics textbook is a thing of beauty to the math teacher. It has many layers and nuances that might not be obvious to the casual observer. The components that make up a good lesson will include practice over the new concept, applying the new concept in application problems, an opportunity to be challenged with the new concept by more difficult practice and/or applications, review of previously learned topics to reinforce their learning, and perhaps foreshadowing, to borrow a literary term, or pre-requisite practice of the topic to be learned tomorrow. Truly good texts can layer 2 or more of these components into a single question. They give the teachers, who know their classes better than anyone, flexibility to choose the appropriate content to best further the education of their students. They also allow for different learning styles and provide a variety of means for the teacher to use to communicate the content, so no student is left out of the learning process all the time. This takes a lot of planning and editing and doesn’t just happen by accident.

Now, we are getting some of the school board candidates to speak out for the teaching of mastery of basic math facts and standards in our elementary schools. They have said that they think Investigations should be supplemented.

The Investigations curriculum is not designed to support mastery of basic arithmetic facts. It is designed to support their discovery methods and also the use of calculators. Therefore, the problems in the curriculum would be worthless for the teaching of basic math facts and could actually have a detrimental effect on the learning of basic facts by not being designed to reinforce them and to increase in difficulty as the student progresses.

One of the reasons the traditional algorithms have been used for thousands of years is that they are efficient, with fewer steps than other methods, and therefore have fewer places that an error could occur. If a student learns one of these algorithms and sees its efficient result, they will be very resistant to another, longer and perhaps more tedious method to solve a problem. Likewise, the Investigations curriculum, which is very calculator dependent, will encourage students not to learn the traditional algorithms because the calculator is more efficient than the algorithms and the algorithms become the tedious method. I would not want to be a teacher in this classroom fighting this battle day in and day out.

The Investigations curriculum does not build on previously learned knowledge. Their teachers’ resources say that the units may be taught in any order. We are missing the vital components of review and also of taking concepts to greater depths. They are a one size fits all package without allowing for the difference in learning styles. As a math teacher, I know that there is a lot of math out there to learn. I never get all the information covered in my classes that I want to. To devote six weeks for “discovering” a topic takes time away from developing any depth about that topic and then, to never revisit that topic during the school year, means that for many students that topic is all but forgotten. This is not good pedagogy and we can’t waste that precious time.

For these reasons above, I have come to the conclusion that Investigations is such a weak curriculum, we should replace it as soon as possible. We will have to phase in a new curriculum, because our students will be behind, so even more precious educational time is going to be lost. Investigations has done some good, in that the traditional textbook authors have responded to their methods and the “drill and kill” books are a thing of the past. The new blended texts, as some websites are calling them, include all the components I have listed above and also include discovery learning opportunities, writing to explain math, critical thinking exercises, and non-routine problem solving. Let’s encourage our curriculum review committee to look these resources over and see if we can’t come up with one strong mathematics curriculum. A curriculum that contains a variety of methods to best help the diverse student population of Columbia to learn math to the best of each individual student’s ability.

Tere DeWitt is a math tutor and member of the CPR-Math steering committee. Her opinions are her own, and we welcome discussion of the issues she raises.

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 ( 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 (

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

































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.