If
only Mounds View could live by one simple rule, our lives would be easier: If
it’s not broke, don’t fix it. Alas, the
Integrated Math System is a reflection of this form of unplanned enterprise. This system interferes with learning the
math it is designed to teach, demoralizes and ruins good math students and
fails to prepare math students for calculus and the SATs. A whole generation of lab-rat high school
students has been forced to run around in this maze of mathematical
ambiguity. Obviously, the Integrated
Math System should never have been implemented at Mounds View High School.
In
trying to transcend application and directly teach concepts, the new math
system leaves a large obstacle in the way of learning the math. There are two problems with transcending
application. One is, concepts need to
be taught by teachers, not books. If a
student has a question, or is struggling with a concept, he or she needs a
teacher to explain it and then a math problem to refine it. The supporters of the system claim that it
allows students to learn more concepts and improve their retention. Diana Fogler, a teacher at La Habra High
School, notes “Two of the author’s . . . claims are that students can learn
more mathematics than before and can have better retention of what they’ve
learned. I couldn’t use a standardized
test this year: there are too many topics on it we’ve not covered. And retention is way down: I write tests
which are like the problems we do in class assignments, but my failure rate has
skyrocketed (Fogler 3).” By skipping
over the refinement process students are forced to learn about things they are
not yet confident in. The other is that
concept-only questions like ‘why?’ and ‘explain.’ force the students who
understand the concepts to waste their time trying to put it into words, while
the students who are struggling become frustrated and fail because the book
does not allow them to refine their skills while learning concepts through
repetition. When asked to comment, Charlotte Osborne, Mounds View math teacher
for eleven years and a strong supporter of the new math system, admitted that
she would add more basic skills drilling if she could (Osborne).
The new system also tries to
teach student’s to use technology, but succeeds only in making them calculator
dependent. Student’s go from being able
to function with or without a calculator to being dependent on the calculator.
As Fogler put it, “I’m a bit leery of mindless button pushing after seeing students
in some low level classes compute a quotient like 75/15 on a calculator: about
40% of those who do will give an answer of .2 instead of 5. Anyone who thinks
better technology will produce smarter students should spend a week with
another colleague to use graphing calculators, checking them out and back in
each period, switching calculators with good batteries for those with dead ones
and later recharging the dead ones, and solving all the ‘My calculator is
broken’ problems that arise from strangely set ranges, modes, etc. that some
malevolent elf contributed during the previous period (Fogler 2).” Even Osborne
expressed doubts concerning the calculator-based curriculum. She cited as reason for her concern the
remarkable drop in grades on a no-calculator test in a subject just covered in
class (Osborne). The students are also
aware of the lack of arithmetic skills involved, as jokes about “Calculator
101” and “TI-I Math [Texas Instruments Integrated Math]” circle the halls in
small variations. Three of the students
on Bachalis’ survey suggested that all they had learned over four years of Core
Plus was how to use a TI 82 calculator.
As mental muscles grow stiff from long disuse, Calculus continues to
loom on the horizon, and the technology-based curriculum has left students with
little more than the ability to play Tetris.
The new system not only fails
to achieve its goals, it also ruins students who could have flourished in the
older math system. It, in short, provides the youth of Minnesota with a new and
improved way to lose their confidence in their math skills. By switching to the new system, designed to
concentrate on teaching the concepts as opposed to the application, Mounds View
has, in a sense, disguised the subject.
Questions like ‘explain’, ‘describe’, and ‘why?’ stump students who
would normally enjoy and flourish in math.
Those who are interested in
math (or science) are often interested because of its black and white
nature. These people prefer the
security of having one right answer, rather than the uncertainty of ‘explain’.
The new math system was in part intended to help students develop the ability
to verbalize what they understand and explain it to others. This is a valid goal, and it may freely be
admitted that verbal skills are important.
But if a student has poor verbal skills, he or she should be failing
English, not Math. Students like this have perfectly valid math skills and it
is inexcusable to confuse and demoralize them by mixing verbal skills with
math. Math classes have enough to
cover without heaping on assertion abilities. As one student who responded to
Gregory Bachalis’ survey said, “I am concerned with the direction taken in Core
[Plus math] classes. Math has become secondary to learning how to write about
math. I am embarrassed and not the
least bit confident with my math ability.
I am upset that I was ever placed in a Core [Plus math] class (Milgram
6)!”
If the system is going to try
to blend classes in spite of these issues, it should at least be made clear
what the students are expected to put into words. Even students with excellent verbal skills have difficulty
deciphering what is asked for by the cryptic questions of the new system. Alex
Pimentel, a student in the second year of the advanced Integrated Math course,
explained “It’s horrible to have to write down the same answer dozens of dozens
of times (Pimentel).” The problem of vague questions is compounded by the fact
that any given assignment can repeat the question four to six times with small
differences. But the repetition is very
frustrating because it sends the message that they were either too stupid to
learn the first time or else our time is not worth enough to justify new
questions. Pimentel commented, “Obviously they’re insulting our intelligence by
asking over and over for an answer my six year old sister could have gotten on
the first try (Pimentel).” The new system doesn’t boost the “average” students
confidence, it insults their abilities. Unlike the repetition in the old
system, which was skill building and practice, this is just writing down the
exact same answer multiple times.
Numbers can’t be changed around on “describe the relationship”
questions.
The Integrated system tries to
generate interest with “real world” examples, but again fails and leaves behind
an unpleasant legacy of offended students. Said Fogler, “The authors’ puffery,
blithely accepted by fans of the [Core Plus] sequence, claims that students can
now ‘solve problems that are much more realistic and interesting’. We’re asked to calculate the probabilities
that a salvage boat will anchor directly over a sunken barge in a river and
that a bead dropped in a grocery bag will fall through a circular hole cut in
the bottom. These are so realistic:
I’ve taken a salvage boat out to hunt for a barge dozens of times this year
alone and I plan to stay up late tonight cutting circular holes in my grocery
bags (Fogler 2).” A student from Bachalis’ survey of Core Plus Alumni echoed
this sentiment “It [The Integrated System] tried to apply math to real life ~
but it didn’t make a great attempt. I
live on my own in [Location Withheld], use math in all my taxes and bank
account things, and I learned all that outside of the math program (Milgram
5).” Often these real world examples detract from the material rather than add
to it. Fogler also pointed out, “In
place of simple examples and more practice problems, we get overwhelming
clutter. Students are asked to research
the Braille alphabet or gravity on other planets (for which they lack the time
and resources) or are asked why skateboarding is popular or told what the fuzz
on a tennis ball accomplishes (Fogler 3).” This has the same flaw as mixing in
English, math has too much to cover and not enough spare time to put these
exercises in futility in at regular intervals.
The New Math System does not
teach the needed math, both to progress to college math and in terms of
standardized placement testing.
Integrated Math fails most notably in not achieving its goal of better
preparing students for college level math courses, specifically calculus. In Bachalis’ survey, respondents were asked
to mark the type of class they chose to take as a college freshman. It is compared with the results from a sister
high school nearby, with similar demographics.
Leaving high school the Core Plus students from Andover, of which 50%
responded to the survey, had an average GPA of 3.23. The sister school, Lahser, had 30% respond to the survey and an
average GPA of 3.29, nearly identical. The step into college math however
reveals a dramatic change: 27% of the Lahser students took calculus their
freshman year, where only 3% of the Andover students did. 70% of Andover’s graduating class were
forced to take remedial courses, some of which they could not receive credit
for, and only 40% of the Lahser graduates chose a remedial course. When asked to rank the usefulness of their
math course on a scale of 1 to 5, five being the highest, the average score was
1.75 for Andover Core Plus students compared to 3.46 for Lahser students. Each ranking had an average deviation of
approximately one full point. This
matches perfectly with the fact that only two Andover grads even attempted
calculus their first year. The average GPA
in college math is also disturbing: 1.90 for Core Plus students (less than a C)
and 2.6 for Lahser (about a B-). These
numbers should be considered taking in mind that the classes for Lahser
students are, on average, more difficult classes. Of the 67 Andover student’s who responded to the survey, 26 felt
they were inadequately prepared for college math, eleven felt they were lacking
in basic math skills and three more felt that all they had learned was how to
use a graphing calculator. Only two
seemed to feel that college math had failed them rather than high school
math. Furthermore, Andover is ranked
between the top ten and the top fifteen high schools in the country, and Lahser
between the top 200 and the top 220 in the country. Integrated math failed the Andover students, and there is no
reason to think that Mounds View bears some mythic charm of safety. (Milgrim
1-6)
This systematic failure also
showed up on standardized placement and entry tests such as the SAT and
ACT. Bachalis’ survey also showed
dismal results on these tests with the Core Plus students scoring lower than
average on nearly every test. The
average SAT math scores for Andover Core Plus students was 531, where the
Lahser students averaged 590, nearly a 60 point gap on math. And the SAT scores also demonstrate the
failure of the integrated system to significantly improve verbal abilities,
with the average verbal score being 585 for Andover students and 611 for
Lahser. ACT scores were not broken down
in the survey, but the gap is still evident, with 23.35 for the Andover
students and 25.09 for the Lahser group.
The median percentile SAT math scores were 49 for Andover, and 76 for
Lahser. As one student commented, “My math experience was not advantageous.
Although I received good marks in the courses, they did not prepare me for the
SAT or the ACT.” (Milgram 1-6)
The mournful complaint of one student summed the issue up perfectly, “I have never been so disappointed in a type of schooling such as this course. I am the epitome of mathematical ignorance in a top ten high school in the country with a 4.0 in math.” The new system doesn’t work. It was a nice idea, but it needs work to fix the practical issues surrounding its implementation. Mounds View should never have put the Integrated Math system into place. I wonder how the people who decided that the system by which they were taught was flawed felt so eminently qualified to change it that they did not even consult the students before implementing their ‘solution’?