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Skills Practice and Review - SPR

This component of Think Math! is key to mastery of computational skill. It is essential every day.

This should be brief, frequent, fun, lively, and regular. It is best done not during math-time, but during otherwise "lost" time: cooling down after recess, waiting in line, in the hall before or after a special, as a morning warm-up. Always do the SPR of the day, but also keep a list of past SPRs and revisit them occasionally. The aim is for students to feel totally competent and confident! Advance the difficulty just enough (or alternate practices) so that children always feel slightly challenged but competent (never bored). The idea is for children to own these skills and ideas.

To become good at piano or soccer or mathematics, one needs both the big picture -- playing the game or the music in some simplified-enough form to be possible for a beginner, or doing age-appropriate mathematical research and genuine puzzling through an intriguing problem -- and to develop the basic skills. Developing skill takes practice, and lots of it.

In sports, music, and math, there are potentially so many tiny skills that one can easily get lost focusing on them alone. Practice, if it is overly repetitive, also loses the learner's attention, and students don't actually get the practice when their brains are asleep, even if they are participating in the activity. The challenge for teachers and curricula is to design practice in such a way that it

  • is focused and strategic, building the skills that give the most "mileage" first;
  • keeps students intellectually alert (interested) while they are practicing; and
  • develops competence and confidence in that competence (generating motivation for the hard work);
  • is faithful to the subject, neither ruining nor hiding the point or fun or beauty of the subject.

(See difference of squares for one example of practice--in this case, of multiplication facts--that meets these four criteria. It focuses first on particular facts--not all of them at once--that lead to a pattern that helps students remember the facts. Surprising patterns keep students intellectually alert, looking for more, doing a piece of mathematical research as they acquire, and feel, skill.)

Practice does not have to be dull if it is designed thoughtfully and done in the right spirit. (Soccer drills are often designed to be game-like.) One way to keep practice lively is to vary it. Another is to keep it short.

Most of the daily, brief, Think Math! skill-practices focus on mental math skills.