People only see what they are prepared to see. Ralph Waldo Emerson

The chart shows the distribution of math scores in the four bands reported for the CSAP testing in Colorado. These bands are Unsatisfactory, Partially Proficient, Proficient, and Advanced. Within the bands are shown the percentage of students by grade in each grouping. I picked this chart because it has a nice, relatively symmetrical shape. However, in looking at similar charts for most of the large districts in the state the message is the same but the distributions can be skewed somewhat to the left or right. That message is that kids being taught math in Colorado (Colorado is not unique, just at the low rigor end of the distribution of the states) are not advancing a grade level in performance for each year spent in school. Thus, the longer the kids are “exposed” to the system the worse they perform against the standards.

Under NCLB each state was given the latitude to set their own standards. This means that there is a wide variation in their rigor. However, since the distribution of the performance of the states on their own tests shows much higher proficiency than those states do on the NAEP (National Assessment of Educational Progress) testing, you have to conclude that the states are “sandbagging” their tests to look as good as possible and avoid NCLB sanctions, some more than others. In The Proficiency Illusion (2007) done by the Fordham Institute and NWEA (Northwest Evaluation Association) where they studied 26 states’ standards for math and reading across all grades they found Colorado to have the lowest standards of those 26 states and South Carolina to have the highest standards in both subjects. In their concluding comments on Colorado’s standards they said,

“When setting its cut scores for what constitutes student proficiency in reading and mathematics for NCLB purposes, Colorado aimed low, at least compared to the other 25 states in this study. (This finding is consistent with the recent National Center for Education Statistics report, Mapping 2005 State Proficiency Standards Onto the NAEP Scales, which also found Colorado’s standards to be toward the bottom of the distribution of all states studied.) Colorado’s low cut scores have declined even further in recent years in several grades.

As a result, Colorado’s expectations are not calibrated across all grades; students who are proficient in third grade are not necessarily on track to be proficient by the eighth grade. In addition to better calibrating the state’s cut scores, Colorado policymakers might consider raising those scores across the board so that parents and educators can be assured that scoring at the NCLB proficient level means that students are truly prepared for success later in their educational careers.”

Thus, the terribly inadequate performance shown in the graph is against abysmally low standards. How could this go on year after year without some positive response to require serving the kids better? First, you have to appreciate that the education “experts” are more than happy to depend on the parents and the public not putting in the large amount of effort required to ferret out the truth. Oh, it is reported to be sure. However, you have to be willing to dig for the data you need among the infinite amount available and then be able to cast it into a form that will allow you to understand the consequences to the kids of the poor decisions being made by educators.

There are two gigantic problems in the teaching of math (will discuss at another time some similar problems in other subject areas). The first is that teachers, especially at the elementary level do not have adequate math knowledge to teach it to their students. This has been a well known problem of the education schools’ poor training of teachers for decades but no one with the power required has been willing to kick over that hornet’s nest and require the ed schools to improve their product immediately or go out of business. In an Associated Press article, Math Teachers Barely Ahead of Students,

“WASHINGTON (AP) 12/07/08 — Math can be hard enough, but imagine the difficulty when a teacher is just one chapter ahead of the students. It happens, and it happens more often to poor and minority students. Those children are about twice as likely to have math teachers who don't know their subject, according to a report by the Education Trust, a children's advocacy group. Studies show the connection between teachers' knowledge and student achievement is particularly strong in math. ‘Individual teachers matter a tremendous amount in how much students learn,’ said Ross Wiener, who oversees policy issues at the organization.”

This has been known for decades. Mortimore and Sammons in their 1987 report on research they had done on the effect of teachers on student learning found that the teacher was up to 6 times more important than student demographics in reading and up to 10 times more important in math.

Liping Ma’s book, Knowing and Teaching Elementary Mathematics: Teachers’ understanding of fundamental mathematics in China and the United States, reports on her research of American elementary math teachers selected from the best and those who were getting their masters degrees at the end of the current school term compared to Chinese elementary teachers. She found that the Chinese teachers who were predominately the product of 2 years of training beyond high school (similar to the Normal School training America had before the blossoming of the education schools in the twentieth century) had far more math knowledge than their “better educated” American counterparts.

The second major problem is that more and more American elementary schools have switched to constructivist or discovery curricula like Everyday Math. This has been attractive to school districts because it helps to mask the lack of math skill among teachers who were having great difficulty teaching with the direct instruction method that most adults experienced. The discovery method because students work in groups flailing about to “solve” problems with the aid of calculators for even the most trivial problems takes a lot longer. That is, you can’t cover as much material in the time available with the discovery method as with the direct instruction methods. Also, the algorithms that generations of students here (and abroad) were taught are not taught in the discovery math curricula. You might say, what is the problem, if they get the right answers for the problems they are trying to solve. The answer is that the study of math is hierarchical in nature. You build the foundation starting at the beginning and continue to build on it year after year. Now, algebra requires the manipulation of polynomials with all of those algorithms that the direct instruction method teaches are necessary in algebra and higher math. They can be used on the simple problems but also on the more complex ones—hats off to the people who were dedicated enough to develop these elegant approaches to solving both arithmetic and algebraic problems. So we send the kids into a very stressful transition in middle school where they are totally unprepared for the studies at hand. Also, manipulation of fractions is virtually a lost art among products of the discovery curricula. These skills again are essential for the study of algebra. While many educators consider algebra “advanced math” it is certainly not and it is something that will benefit every student whether they intend to go to college, trade school, etc.

An argument I often hear is that I must be wrong because the constructivist curricula are “research based” and have passed muster. And that is true. But the “research question” used to foist off this trash on our kids is flawed. That is, it asks if the curriculum allows kids to solve simple arithmetic problems with the aid of a calculator when it should and must for integrity ask, does the curriculum allow kids to solve simple arithmetic problems AND PROVIDE THE NEEDED FOUNDATION FOR THE STUDY OF ALGEBRA AND HIGHER LEVEL MATH? The answer there is a resounding NO!! These curricula are not suitable for any elementary school in the nation and should be banned immediately.

In reality, the education experts, especially in the education schools do not understand math (or many other subjects) well enough to be entrusted with decisions about curricula or anything else pertaining to the educating of our kids. Rita Kramer’s assertion in her famous book “Ed School Follies” that “our educators are not educated” is succinct and true if you base your evaluation on the results of our education system.

Since the educators are not going to change without significant pressure, who will stand up for the welfare of the kids? You?