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Should Math Skills Be 'Integrated,' or Taught Step-By-Step?


Q. Our 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.


A 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 grade-school level.


On 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.


Instead of that "integrated" curriculum, the Spokane schools are considering moving to one of two "traditional" math curricula, which teach math skills step by step.


The two more-traditional curricula that the district is considering are Holt Mathematics and Prentice Hall Mathematics as the two finalists.


Another 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 students.


But 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.


With 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.


Proponents 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.


And, 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.


It 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.

Homework: Follow the math developments in Spokane on this blog:



By Susan Darst Williams Math 18 2010


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