(I copy-pasted this comment from The Atlantic article on New Math. How mathematics is taught in school is a very important issue and I think one ignored by most people in the general public. FYI, our school district uses a horrible "new math" program but as it is taught with emphasis on knowing the algorithm as well as the memorization of addition/multiplication tables and the like, our district test scores are deceptively high. My take-away from the article and comments is that it is best to master the lower-level maths completely before moving on to fulfill some graduation requirement list.)
I've been a classroom teacher for 15 years and spent the 7 years ahead
of that working in a Math Tutorial Lab in a state university, helping
undergraduates as they struggled with math. I saw big time calculator
dependence and continue to see that phenomenon in our high school
students. I recently invited four faculty from our university to speak
to our secondary (junior high and high school) math teachers about
preparation for college math and STEM fields. They unanimously said,
"Don't let your students become calculator dependent." "Don't let them
have calculators all the time." They also said, "We don't care if they
take calculus or not in high school, but please teach them algebra!"
And trying to teach algebra to students who are not prepared for it is
very difficult. In the recent decade (when students who learned from
NSF-funded math programs reached secondary schools), we have noticed a
drop in elementary math skills, including basic operations. We see
students who cannot multiply without a lattice (they frequently can't
multiply with it, placing decimals incorrectly or adding incorrectly)
and we see students who cannot do long division. We see students who
cannot multiply at all, and do repeated addition such as
1000+1000+1000+1000+1000+1000 instead of 6 x 1000.
They don't know when
to multiply, either. When it comes to multiplying fractions, we see
things like 2.666666... x 33 = ? because they can't manage the
fractions, continuing their love affair with decimals (and calculators).
They don't understand the concept of remainder and how to express it
as a fraction, as one would in changing an improper fraction to a mixed
number. They have to be taught long division at the algebra 2 level
because it is needed for polynomial division. The structure of the
standard algorithms (as those of us who learned math before the current
reform era got here) is necessary for students to work with polynomials
and rational functions.
Trying to teach students the difference between
vertical asymptotes and holes in rational functions is extremely
difficult when they are not in the habit of writing fractions in lowest
terms or knowing how to convert improper fractions into mixed numbers.
We cripple them for learning algebra (and hence, bar the door that leads
to STEM careers) when we don't prepare them with the standard
algorithms. I have seen it time after time -- students whose parents
can afford tutors or Sylvan come prepared to learn algebra much more
often than those who are dependent on whatever gets taught in school.
I've taught honors classes and very low-level, slow-paced classes over
the years. Those students in slow-paced algebra 1 are there mainly
because they have absolutely nonexistet computational skills.
pretty tough to add -6x + 10x in your head if you don't know how to add
-6 + 10. We see transfer students from states where nothing lower
level than algebra 1 is taught in high schools. They will have passed
algebra 1 and geometry from their previous schools, and they can barely
pass prealgebra in ours.
It's an equity issue and we will not
narrow the achievement gap until we have high expectations for ALL
students. Watering down the curriculum will not do it. Pretending that
everyone in a high school is taking algebra 1 or higher level math
classes is such a disservice to those students who have not mastered
prealgebra material. We can't pretend we are preparing students for
STEM fields or college or even careers that do not require some
vocational post-secondary education by not giving them a strong basic
math education at the K-8 levels.