Sunday, March 20, 2016

Learning Math Facts

As I continue my investigation into cognitive science, I continue to run into the concept of “distributed practice,” sometimes called “spaced” practice.  One of my passions for a long time has been helping students learn their math facts.  Over the years, I’ve tried several approaches to teaching students their facts, with mixed results.  What follows is a suggestion based both on my recent experiences and my readings in cognitive science.

This will be a whole-class activity.  Begin with a numbered set of math fact drill cards (I have a homemade set to offer. See below).  Select 5 cards, one for each day of the week.  On Monday, present the first fact card and ask students to repeat the fact both ways (6+5=11 and 5+6=11).  After this introduction, find 5 or 6 opportunities on Monday to quiz the class on the first fact.  On Tuesday, present a new fact.  On Tuesday, your 5 or 6 later quizzes should include both Monday’s and Tuesday’s facts.  Repeat Wednesday through Friday.  In like manner, keep introducing the “fact of the day” through the next week.  At this point you will have introduced 10 facts and will be quizzing 10 facts.  On the second Friday, give an assessment to see which of the 10 facts have been learned.  Learned facts go into a separate stack to be randomly quizzed from time to time (perhaps once a week), just to keep students “sharp.”  

Keep adding daily cards to the “quiz stack” until you reach 10 facts.  You now have 3 stacks:  1.  new cards; 2. quiz stack; 3.  mastered cards.  Avoid letting the quiz stack get beyond about 12 cards.  Stop introducing until you can reduce the quiz stack to less than 10 cards.  Stop introducing if you can’t transfer cards from the quiz stack to the mastered stack.  An easy assessment would be done orally, giving just 10-20 problems combining recently added facts and those previously mastered- no fancy form needed.  Just use lined paper.

Because the introductions and daily quizzing would be very quick, it’d make a good transition activity.  I’ve written the above as succinctly as possible, so if anything is not clear, feel free to contact me:

Also, if you’d like a set of homemade flash card masters for addition and multiplication, send me an email and I’ll send you .pdf format masters.  They include numbered back-to-back masters which can be copied on to 8.5x11 cardstock to make serviceable flash cards for this activity.  If you’d like, of course, you could copy off additional sets for students who want them.

Again, if you have any questions, don’t hesitate to contact me.

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