Should Math Skills Be
'Integrated,' or Taught Step-By-Step?
daughter is in fourth grade. She has trouble remembering basic math facts like
7 x 8, and gets tripped up by simple processes like finding the mean of three
numbers, etc. Yet her math curriculum ventures regularly into algebra, and has
for over a year. Can this be good? I think she's getting confused, and more and
more "down" on herself. I don't like it when schools teach higher-level, more
abstract math like algebra, when the students haven't had a chance to master
the more concrete, basic fundamentals.
growing number of people agree with you. In early 2010, the Spokane (Wash.)
Public Schools considered getting rid of its "integrated" math curriculum -
which, as you remark, combines algebra with basic computation on the
the high school level, "integrated" math textbooks combine the skills of algebra,
geometry, and algebra II in the same course of study, which many observers
criticize as confusing and out of order.
of that "integrated" curriculum, the Spokane schools are considering moving to
one of two "traditional" math curricula, which teach math skills step by step.
two more-traditional curricula that the district is considering are Holt
Mathematics and Prentice Hall Mathematics as the two finalists.
advantage of the more-traditional texts that proponents cite is that "discovery
learning" is reduced in them. In "integrated" math curricula, also known as
"discovery math" or "whole math," teachers don't directly teach, but set up
activities and lessons in such a way that students are expected to "discover"
math concepts and skills on their own. It is thought that working in groups and
"discovering" the answers on their own is more relevant and interesting for
proponents of traditional texts say students who have "integrated math" texts
don't do as well as those who've been taught traditionally. They say students
deserve to be taught math by a competent teacher using good curriculum, not
just "luck in" to concepts and skills or rely on more math-savvy peers to
learn. They say it is not very enjoyable or interesting to be "innumerate" -
unable to apply math skills to one's everyday life.
more traditional texts, teachers are the ones who guide the students in the
skills, directing them and overseeing their work, instead of the more liberal
philosophy of letting them learn by doing.
of traditional math texts also say that the more liberal texts are harmful in
that they emphasize a lot of calculator work, which denies students the
repetition and practice that they need to make math concepts automatic.
the traditionalists say, the "integrated" and "discovery" style texts set up
far too much group work, as the students "discover" math together - saying that
the groups are more like "the blind leading the blind" than effective
instruction of math concepts and skills.
is possible that Spokane will keep the curriculum that it already has, Core-Plus
Mathematics Project, and supplementary materials. But those who want to see
the curriculum changed back to a more traditional approach predict disenrollment
problems and continuing underachievement in standardized test scores, if
something isn't done.
math developments in Spokane on this blog: