Gideon, my grandson, is almost nine-years-old and starting fourth grade this year. He loves soccer, baseball, online videos, hip-hop, and school because that is where his friends are during the day. His attitude toward homework, and I suspect any school assignment, is to get it done fast so he can move on to more important and interesting things.
On last year's New York State 3rd grade common core aligned math assessment Gideon scored in the proficient range, not the highest level, but not bad on a test where 70% of the students failed. I have been doing math homework with Gideon since school started and I noticed a couple of things that concern me about how math is being taught. I am not blaming his teachers or the school. I am certainly not blaming Gideon. But I worry that the problems he is having in math reflect the push for test prep for standardized tests.
The first problem is that Gideon seems to be convinced that there is only one right way to solve a problem and if he does not solve it that way he will be marked wrong. This problem he will get over either as he learns more about how the world works or becomes less interested in pleasing his teachers.
The second problem is a bit more serious to me as a teacher and grandparent. Instead of trying to understand a math problem and being willing to play with the numbers, Gideon is committed to remembering a long, complicated sequence of steps to finding a solution. If he makes a mistake somewhere in the sequence he gets the answer incorrect, but he does not recognize it as incorrect, because his goal was following the prescribed steps, not coming up with a result that makes sense.
Kids are supposed to be learning to estimate from the start of elementary school so they can stop and say this cannot possibly be the answer, but estimation requires both feeling comfortable with the relationships between numbers and a willingness to experiment and speculate, qualities that appear to be neglected in the test prep math curriculum.
One night recently Gideon had to figure out how many tens are in 540. He set up number groups. There are 10 tens in one hundred so he had five groups of 10 tens each. There are 4 tens in forty. He then added 10+10+10+10+10+4=54. I did not have a problem so far. But then he had to figure out how many tens were in 370 and he started to set up his number groups again instead of just saying if there are 54 tens in 540, there must be 37 tens in 370. He did not see or even look for the relationship between the two problems. They were separate entities.
The third question was how many twenties are in 640 and again he started by setting up his number groups. I asked him how many tens were in 640 and if there were more tens or twenties, but his response was "That's not the way we are supposed to do it."
Maybe that was what he was told, maybe he was misinterpreting instructions, but in either case, he would not play with the numbers and try to figure out a solution on his own. He was memorizing rules, not learning math.
Initially I thought the problem here might just be Gideon's stubbornness and anxiousness to be finished, after all there were other more rewarding things to be done. But email exchanges on the Long Island "Middle School Principals" listserv (email@example.com) point towards much more serious problems with the way math is being taught and assessed in the New World of Common Core and high-stakes assessments.
A principal at one affluent Nassau County middle school reported that in his school 235 eighth grade students took accelerated ninth grade math and 190 of them, 78.6% of the students, earned a grade of 80% or better. But inexplicably, 82 out of the 190 high scorers, 43%, scored less than proficient on the 8th-grade common math assessment. Three other middle school principals from similar districts reported the same phenomenon.
A fifth principal from another affluent high-performing Nassau County school district described the state math assessments as a "Kafkaesque system" that "does not make sense," as a "fake testing system" that "hurts kids" and their teachers. He has middle school students who passed high school math examines with mastery level scores but who failed the common core standardized test and now must be assigned to remedial classes. He also cannot figure out how when his school had the highest seventh grade English and math assessment results in the state on the common core test, only one out of six of his seventh grade ELA and math teachers was rated highly effective.
He charged that the current instructional and testing system "only enriched consultants, textbook companies and service corporations." He called it a "fiasco" that "only ensures further unfunded mandates, pushes schools to become test-prep centers, further institutionalizes an over-testing system that terribly hurts kids, and enshrines an unfair evaluation system that actually makes it harder to terminate unsatisfactory teachers."
Actually, I do not find the lack of correlation between the 9th-grade algebra test scores and the 8th-grade common core assessments inexplicable. I think the same phenomenon is at work that I saw in Gideon's homework. Students are not learning math, they are being prepped for tests to maximize test scores.
When you put different types of questions on the math test they are stymied because the procedures they were taught to follow do quite line up with the problems and they either do not know how, or are afraid to, adjust. They do not estimate, they do not hypothesize, they do not "do the math," they just get lost in the steps and get the answers incorrect.
I remember learning math the old-fashioned way, my friends and I had fun figuring out things we actually wanted to know and were very competitive at it. Back in the days before calculators and computers, the newspapers only updated baseball batting averages on Sundays, except for the league leaders. My friends and I were big baseball fans, our elementary and middle schools were about a mile from Yankee Stadium, and we needed to know the latest batting averages for Mickey Mantle, Roger Maris, Yogi Berra, Elston Howard, and "The Moose" Bill Skowron, so we calculated them every day during lunch (and sometimes when we were not paying attention in classes). It was not that we liked math -we loved baseball. Math was just a tool.
I walked into my high school 10th grade statewide geometry math test without having paid attention for most of the year (Bill Cosby used to tell the joke that when he was a kid his family was so poor he couldn't afford to pay attention). But I was comfortable with math, numbers and problem solving and actually figured out geometry while taking the test itself.
I like finding patterns in math, I enjoy problem solving, and I appreciate the way it helps me to think systematically and provide evidence to support my conclusions. But I am convinced my comfort level is rooted in my love of baseball and the Yankees.
The other night I asked a group of college students if Robbie Cano is batting .310 and goes one for three with a sharp single, two fly outs, and a base on balls, what happens to his batting average. Some of the students had no idea, some of them started to calculate, but I knew his batting average went up, by just a little bit, because I know the relationships between numbers.
That is what I am trying to teach Gideon.