Back to main page.

Comments

In my parents' basement, I found a copy of The World Book of Math Power, copyright 1983. This is what it says about spiralling:

-- RobynW - 14 Nov 2006

It says this:

"Another innovation also occurred in the 1950s. It is known that a series of short, spaced practice sessions produces longer-lasting improvement than does a single, long practice session. Based on this notion, educators reorganized the sequence in which math was taught so that an idea recurred several times, each time with increased complexity. They called this reorganization 'spiral learning.' Teachers disliked this approach, and students seemed to learn less when it was used."

-- RobynW - 14 Nov 2006

oh that's cool!

Thank you so much!

wow

-- CatherineJohnson - 17 Nov 2006

I have more interesting quotes about spirals.

In promotional material, the publishers of Everyday Math quote a special education teacher who says the following:

"I believe our special education students are achieving success with Everyday Mathematics because of its spiral structure that allows students to use a math strategy many times before they must achieve mastery."

Everyday Mathematics, Student Achievement Studies, Vol. 5, pg. 6.

If you're on the curriculum committee of a board of education, you might read that and assume that spiraling benefits the low performers.

In contrast to EM's anecdotal evidence on the benefits of spiraling, experts, like Englemann, who have formally studied spiraling conclude that it is ESPECIALLY BAD FOR KIDS WITH LEARNING DIFFICULTIES:

"The typical basal curriculum uses a spiraling approach to instruction; in other words, numerous skills are rapidly introduced in a single graded book.... Basal instruction using this spiraling curriculum approach is supposed to add depth to math topics taught, but in reality the result seems to be superficial coverage of many different skills....Research has demonstrated that this basal approach to teaching mathematics is particularly detrimental to students who have learning difficulties (Engelmann, Carnine & Steely, 1991; Silbert & Carnine, 1990; Woodward, 1991)."

S. Miller, C. Mercer, Educational Aspects of Mathematics Disabilities, Journal of Learning Disabilities, Vol. 30, pp. 47-56 (1997).

-- RobynW - 25 Nov 2006

So, according to McKnight^?'s research, spiraling harms the strong math students because they're spending too much revisiting old material and not enought time learning new material ... in contrast to kids from the high-performing Asian countries who master the curriculum and move on to more difficult stuff.

Then, according to the research of Engelmann and others, spiraling is bad for the weak students because they don't get enough practice and review and the coverage is superficial.

Of course, kids should still have review and distributed practice, but the schools should use a mastery-based math program.

-- RobynW - 25 Nov 2006

wow!

excellent!

future posts!

-- CatherineJohnson - 28 Nov 2006