Monday, October 24, 2011

Effective Math Practice

Bike Ride
"Bike Ride" by Courosa on Flickr
We all know that effective practice is the key to learning something first to mastery, and then to automaticity.  Reaching automaticity means that one can do something naturally and fluently, in an automatic way.  When students reach automaticity in single digit addition, for example, they can quickly answer that 4+3 is 7.  Students can reach automaticity through repeated practice, but it must be high quality practice.  What are the hallmarks of high quality practice?
  1. Clear expectations- students should see the skill modeled and know clearly what skill they are developing.
  2. Supported practice- Think about when learning to ride a bike.  Usually there is an adult's hand stabilizing the bike, or training wheels to keep every wobble from ending in scraped knees.  In learning, this is often the "We Do" in a skills' development.  This can be with the teacher and then with a partner or small group.
  3. Purposeful Feedback- When students begin to practice the skills for themselves, it is essential that they receive immediate feedback.  This feedback should tell them what they are doing right, and what they need to correct.  Think of a basketball coach teaching a player to shoot a free throw.  Basketball coaches often give pointed feedback that is different for each player, depending on what they see-  "follow through by snapping your wrist," "place your left hand here," "bend your knees," etc.
  4. Upward Basketball 
    Credit: Jason Tromm on Flickr
  5. Assess progress- Keep a clear eye on where students are in their skill development.  Be prepared to move some along as they master this particular skill, and offer more time for practice for those who still don't perform the skill naturally.  With the right amount of high quality practice (with specific and immediate feedback), they'll get there!

What does all this have to do with math?  Well, this process repeats itself over and over with each new skill or concept.  Technology gives us one way to give students immediate feedback on whether they're on the right track, or whether they need to refine their process, by telling students if they have the correct answer or not after every problem.  Here are some sites to check out that may be useful to you in providing students with practice and immediate responses:

FactMonster Flashcards
Calculation Nation (use Guest Pass)
Khan Academy (also on this website, explanatory videos for concepts)
AAA Math
Free Rice (choose Math- multiplication or basic math)
Education City (go to student webpage to choose your school: )

What other ways do you have to help students get the practice they need?


  1. One of our favorite sites is
    My class loves the logic games. Whenever my students find a math website they like, they add it to the personal math website they created using Google Sites.

  2. Thanks Shauna. It looks like there is a lot of fun practice on that website, with immediate feedback to help students as they practice with math facts. Love the idea about having students keep track of good sites. The only question I'm left with is what is the criteria that students apply when deciding that a site should be added? I think that's a great way to have students take ownership of the class website, and it can also help them develop the skills of discernment and analyzing quality. Thanks for sharing!