Spiral practice, not instruction

Spiraled instruction stifles learning, writes Coach G in Ed Week.  “We touch on lots of topics each year,” then review the same material the next year and the year after that.  In his first teaching job, “Algebra 2 was such a rehash of the district’s Algebra 1 course that some teachers called it ‘Algebra T-o-o’.”

Consider, for example, area and perimeter, which students are first exposed to in third or fourth grade, and see again in middle school. Yet when area and perimeter come up in high school, most teachers–including me at first–teach them from scratch.

The problem, of course, goes back to the disconnect between kids seeing something and actually learning–and retaining–it. But if it didn’t sink in for them the first, second, or third time a teacher presented it, why should we present it again?

Instead of spiraling touch-and-go instruction, teachers should spiral practice, Coach G writes. “Instead of limiting assignments to recent content from the current course, we should also include problems on earlier content from that course AND previous courses.”

Why math tutors prosper

Many elementary students never learn basic math facts,  writes Lynne Diligent on Dilemmas of an ExPat Tutor.  They end up in remedial math classes in college. She advocates drill on math facts, more homework and no calculators till 11th grade.

I no longer teach Grade 3; I am now a private tutor. Unfortunately, I am now running across a number of 14-year-olds who are using calculators to add 5 + 3, or 7 + 6, or 9 + 2.

 Diligent also calls for requiring students to learn concepts before moving on, instead of  “spiraling” through the same things year after year.   

And she believes teachers should “instruct and explain, and then follow up with practice to master the skills,” rather than putting students in groups and telling them to figure out problems on their own. But group work is great for math tutors, she writes.


In defense of Everyday Mathematics

The Case for Everyday Mathematics is made by Andy Isaacs of the University of Chicago Mathematics Project in response to Barry Garelick’s critique.

Isaacs writes:

The highly efficient paper-and-pencil algorithms that have been traditional in the U.S. may no longer be the best algorithms for children in today’s technologically demanding world. Today’s elementary school children will be in the workforce well into the second half of the 21st century and the school mathematics curriculum should reflect the technological age in which they will live, work, and compete.

I’m not sure what that means. That kids should use calculators all the time? Or something quite different?

Isaacs defends spiraling:

Research shows that students learn best when new topics are presented at a brisk pace, with multiple exposures over time, and with frequent opportunities for review and practice.

The program offers more supports for teachers and parents, he writes.

Lots of comments, including a response from Garelick on whether research supports EM’s effectiveness.