Reform Math

March 21, 2007

Recently compiled statistics show that more than 60 percent of recent Traverse City high school graduates who are enrolling in math classes at the local college are starting at the remedial level.
Those percentages are much higher than national averages. Thirty-seven percent and 22 percent of incoming students take remedial math at community and four-year colleges, respectively.
Some people believe that the statistics reported by Northwestern Michigan College simply reflect the fact that more kinds of students are going to college.
Others think it owes to the Traverse City school district’s reform curriculum, which they say emphasizes conceptual thinking at the expense of learning math basics.
Using a different set of statistics – the number of remedial math students divided by total college enrollment – NMC still has significantly higher numbers when compared to North Central Michigan College in Petoskey: 5.9% compared to 16.2%.
The statistics are conservative because they don’t include students who take intermediate algebra, which isn’t considered college credit by most four-year universities.
The NMC statistics are difficult to interpret for many different reasons, but it serves as a starting point for a very touchy subject right now – reforming math reform.

TO COLLEGE WE WILL GO
As background, NMC students must demonstrate a mastery of intermediate algebra in order to get an associate degree. Certain students are able to meet that requirement with a sufficient score on the ACT math test or existing college credit.
If not, they have to take what’s called a COMPASS test on the computer. The test is a dynamic affair. If the student does well, the problems get progressively harder, moving toward calculus. If the student is getting the problems wrong, they are moved back toward pre-algebra.
NMC has used the COMPASS test since 2000. Prior to that, only about 30 percent of incoming Traverse City students were enrolled in remedial math classes. However, the former paper tests didn’t adequately asses a student’s full knowledge, said NMC math instructor Jack Berman.
The number of remedial classes at NMC has grown steadily each year, nearly doubling from 10 years ago.
An NMC college official believes that the high percentages reflect a shifting student body. The less academically inclined students, who might have chosen factory jobs 30 years ago, are now going to college, primarily because the jobs and wages aren’t there anymore.
“When I graduated from high school, there was an expectation that not everybody was going on to college,” said Kari Kahler, director of NMC’s Learning Services. “Nowadays, almost all students are encouraged to attend, and some of those kids aren’t prepared.”
Kahler said that even though these kids do need remedial classes, statistics show they are doing well in the rest of their college career.

WE ALL COUNT
These statistics come at a time when a group of parents in the group, We All Count, have met with Traverse City administrators to complain about the reform math curriculum at the elementary and middle school levels. (A previous parent group was able to get a traditional math alternative offered at the high school level six years ago.)
More than 500 parents signed petitions asking the district for a blended curriculum of reform and traditional math.
Their concern is that students seem to lack a fluency in basic skills, such as fractions, multiplication and division.
Yet the NMC math instructors can’t attribute the high numbers of kids in pre-algebra and beginning algebra classes – around 200 recent Traverse City grads per semester – to the reform curriculum. As a note, Traverse City students are required to take two years of high school math, typically algebra one and geometry.
“It’s hard to say why,” Berman said. “We’ve always had a diverse population in community college. From term to term, hour to hour, it could be an entirely different make-up. To categorize a class’s ability and point it back to a certain cause is sort of hard.”

SCORING HIGH
Traverse City administrators point to the fact that the school district does very well on the Michigan Education Assessment Program (MEAP) tests compared to school districts across the state.
MEAP scores for third graders, for example, ranged from 75.6% at Blair Elementary to 98.4% at Westwoods Elementary (the percentage of students meeting or exceeding state standards). Most of the 15 elementary schools hit above 90%.
Ninety percent of eighth graders exceeded state standards on the Michigan Education Assessment Program (MEAP) test, said Dan Fouch who oversees the math curriculum for TCAPS.
“The one statistic showing very nicely for us is if you looked at the advanced placement scores 10 years ago. In math, we had 11 students get advanced placement credit in mathematics. That was about the time we were making the change to a more reform math program. At this point, we have 195 kids getting advanced placement college credit. When kids can walk on campus with AP credit, that’s a big boost for them.”
But critics say that “exceeding standards” on the MEAP doesn’t tell the whole story about basic math skills. It’s possible to exceed standards, but only get 70% of the answers correct.
They are hoping to work with the district to get a closer look at specific questions on the MEAP test to see how students are doing on “non-calculator” skill questions, such as fractions.

Other parents say their kids have done well, but only because they were tutored or received additional help at school.
“My son, in his senior year, was taking calculus, and he had to come into the school every day at zero hour with other kids to learn algebra so he could pass calculus,” said Phil Rodgers, an area judge. “And he’s not an average kid. He scored in the 97th percentile on his LSAT and is going to one of the country’s best law schools.”

ANSWERS
Traverse City School Superintendent Jim Feil has been particularly receptive to complaints. He often tells parents that he comes from a unique perspective – two of his children were academic stand-outs, while another dropped out of high school.
Feil said he wants all students to succeed and has promised to take a number of steps to make the reform curriculum more parent-friendly, such as providing elementary students with glossaries. The district also plans to hire a retired teacher to investigate how well Traverse City graduates are doing in college.
The district recently piloted software to improve basic math skills at one of the elementary schools. But Feil has not announced how soon the curriculum could be evaluated and whether parents would be involved.
The criticism of the math curriculum comes at a time when the district is struggling with budget problems that may shutter as many as three elementary schools.
The money crunch is due to a hugely unfair funding scheme that has hurt the district.
Enrollments have also stagnated, but it isn’t due to people leaving the area. In fact, the population of Grand Traverse County swelled by 30 percent from 1990 to 2005 (64,273 to an estimated 83,971 people). Yet the school’s K-12 enrollment has stayed nearly the same–10,271 students in 1990 to 10,653 students in 2005, a 3.7% increase.
CALCULATORS
There was a time back in the 1970s when calculators were introduced, and manual slide rules became extinct. No one raised a fuss. So why bother with long division if you can punch in numbers?
NMC Instructor Jack Berman believes that doing basic math problems – what’s called algorithms – is now much less important.
“I’m trying to get my students out of the hokey-pokey mindset of doing disembodied steps to get the right answer. That’s because it’s totally meaningless down the road,” Berman said.” I tend to show my students a lot of different ways to get an answer.”
He gives this example: “Instead of multiplying 28 x 32 with columns, I can think of a lot better way to multiply those two numbers. It’s the same as (30 + 2) (30 – 2) or 900 – 4 or 896. This is using algebra for a reason, and it requires that you understand the relationship of numbers.
“Math is like any subject–there is more than one way to do things. Some people can do very well with the traditional, formalized manipulation. They may not know what it’s good for, or what they’re doing, but they can do it. In calculus it’s the same way. They can do the problem, but have absolutely no idea what their answer means.”
Jane Porath, who teaches eighth grade math at East Junior High, believes the reform math helps students think out of the box.
“There is meaning behind what they’re doing. With all that they’ve learned, from elementary through junior high, they’re equipped with the tools to attack a problem, in a way that makes sense to them — to think about solving it in a way that I wouldn’t have when I was an eighth grader. I had a lot of knowledge, but it was kind of pigeon holed. If a problem didn’t fit into a pigeon hole, I had no way of attacking it. Our students are just good thinkers.”

GAPS IN THE FOUNDATION
But Pat Dolanski, founder of Grand Traverse Dyslexia, said she tutors many more older kids in math than she ever used to. She sees lots of gaps in their foundation of knowledge.

“The older kids are getting into advanced classes and don’t know how to do so many things,” she said. “There is just so much I have to teach before I can even get to the level of where they’re supposed to be at.”
These basics are important because there are many things a calculator can’t tell you, such as the order of operation in an equation, or that .3333 means 1/3, or that the square root of 16 is both four and negative four.
Dianne Walker, who heads up We All Count, also believes that students need to understand basic math facts in order to succeed at higher-level math. As a high school teacher, for example, she often had to teach fractions before beginning the algebra lesson.
Walker said she was trained in the 1990s to teach reform math, but was frustrated.
“I was very uncomfortable with having my students work in groups all of the time. It seemed the smarter kids did most of the work. … Even with the teacher manual I sometimes still did not understand the questions and how they arrived at the answers. Many times the answer was listed as ‘answers will vary.’ That’s it!”
Lauren Steffey, a senior at Central High School who is getting tutored for her AP calculus class, said she wishes she had the quick fluency in basic math that some other students have—students who did do the “kill and drill” in their earlier years.
“I think we wasted a lot of time doing group activities when we could have been practicing. I’m struggling because I don’t have a good foundation.”
Fouch responded that the issue of basic skills is very complex. Should kids be expected to do multiplication in the traditional way, when another way might be faster and easier? How much time should teachers spend on long division at the expense of more advanced concepts?
Calculators are an educational tool, he added, allowing kids to do far more advanced graphing and functions than they could 20 years ago.

NATIONAL PERSPECTIVE
The so-called math wars heated up last fall when the National Council of Teachers of Mathematics–representing 100,000 teachers–reversed itself last fall and said that students do need to learn basics.
This was the same group that started the math wars in 1989 when it announced that teachers should focus on open-ended problem solving rather than kill-and-drill exercises.
The president of the NCTM, Francis Fennell, has said the group’s original report was misinterpreted. It was never intended as an excuse to drop the basics. Its primary intent was to say that students must understand what they’re doing. The newly published goal is for a student to get the right answer, repeatedly, and in a reasonably fast way.
Discussions with curriculum directors are immediately humbling. They are hog-tied by state standards, which now spell out, grade by grade, exactly what each student is expected to know. And the standards just keep on increasing.
These standards, instituted a few years ago, are called Michigan Grade Level Expectations or what’s pronounced as glickees. These skills are then tested in the MEAP at every grade level, 3 through 9.
That makes trying to match a certain textbook to the specific expectations very difficult. Petoskey schools chose a book, “Michigan Math,” to better meet the standards, said Jane Bailey, curriculum director.
Schools are now going to have another challenge: every single high school kid graduating in 2011 must have four years of high school math unless they get a special exception, and it’s going to take more than, “I’m not good at math.”

BLENDED?
NMC Instructor Jack Berman believes that even though he stresses concepts over basic operations, he agrees a blended curriculum of reform and traditional math may be the best way to go. A number of districts use blended curriculums, such as Elk Rapids and Petoskey public schools.
Many parents are hoping for a parent-friendly curriculum. Right now if a child doesn’t “get it,” there are often no sample problems, correct answers for a student to check against, or a glossary. That’s because the nature of reform math is to “discover” the answer. At the elementary level, there is no textbook, leaving some parents feeling there’s no coherent direction.
“A lot of people pooh-pooh what I call the efficient algorithm,” said one parent, whose wife works in the district and didn’t want his name used. “But I think that once you teach a child what’s going on with a long, drawn-out transparent method, at some point, you’ve gotta move on and say, ‘Now here’s the fastest, easiest way to get it done.’ Eventually, you’ve got to get to that point.”

Disclosure: Anne Stanton is involved in the group, We All Count, a citizen group that has urged the Traverse City public school district to consider a new math curriculum.