Additional Math Pages & Resources

Tuesday, February 1, 2011

Easy-Hard, Easy-Harder, Easy-Hardest, Easy

Wah! I wrote 99% of today's blog and it inadvertently got erased. So now I have to start over, which normally means you get a better, more pleasing (shorter) blog.

Today I will explain some of the features of a typical Excel Math lesson. Here are both sides of a typical Lesson Sheet, for your viewing pleasure [click for a larger view].

After much tedious reading of research papers, I'd like to summarize three very important techniques we use to help students learn math.
  • Interspersal
Students can improve accuracy and have a more positive attitude when we mix simple problems in the midst of a bunch of complicated ones. Research shows students are more motivated to complete their lessons when there are a few very easy calculations among the difficult items. Click here.
  • Explicit Timing
Explicit timing involves setting a time interval for completion of an assignment, and then announcing time as it passes - "You've used 10 minutes; you have 5 minutes to go."  Explicit timing and interspersal assignments have been proven to enhance student math practice. When interspersal assignments with explicit timing were compared to interspersal assignments without timing, it was found that explicit timing raises achievement, but students did not maintain the higher work levels for long. The second phase of this study added rewards and set academic targets for students, but neither of these approaches reliably increased performance. Click here.
  • Incremental Rehearsal
Incremental rehearsal helps students build capability in math, by injecting new or novel problems into a continually-growing base of known items. The likelihood that a student will tackle the new difficult work is raised due to on-going success at solving familiar problems. What is not clear yet is the optimum ratio of known-to-unknown items (researchers have tested ratios ranging from 90-10% to 50-50%). In general, more unknown items (50-50%) mean students learn more in the short term. More known items (90-10%) mean students have better retention over the long term. Click here.

Excel Math uses both interspersal and incremental rehearsal approaches. In additional to our year-long spiraling approach to individual objectives, we also provide the Checkanswer which does two things: it allows students to check their own work, and the simple 3-4 item addition problem provides some respite from the challenging problems on the rest of the page.

The teacher can employ explicit timing whenever appropriate, especially on the Guided Practice part of the lesson.

NOTE: If you want to read more, click the links at the end of each paragraph, or search on the specific term to find the research papers that interest you most.

And that's enough for today.

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