Unlock your child's understanding of math, part 7

Practice should be done using a spaced repetition schedule and it should be interleaved

In my last post I discussed the importance of developing fluent performance of basic skills.  The next question to address is:   What are the most efficient means of achieving this goal?  Or, in other words, what are the characteristics of efficient practice?

In order to be able to recall new information easily, the best time to practice remembering it is when one is on the verge of forgetting it.  Initially, the interval between remembering something and forgetting it is quite small.  With children learning something like arithmetic facts, it can be just a few seconds.  But once some new information can be recalled correctly after a very short delay, the amount of time until one is about to forget it increases.  Moreover, the very act of trying to remember something is the primary means of strengthening the memory.  Therefore, the most efficient way to commit something to memory is to try to recall it at increasing intervals.

There are various recommendations for the best interval schedules, but a rough rule of thumb is to double the amount of time of the previous interval after each successful attempt to recall the information, from seconds to minutes to hours to days to weeks to months.  If at any point a person cannot recall the information, she should begin the process over again, returning to a very short recall interval.  This routine of increasing the interval between successive correct attempts to recall the information is referred to as “spaced repetition.”

The general idea behind spaced repetitions is quite easy to understand.  Our brains are inundated with an enormous amount of information every day, much of which is not very important.  It would be quite daunting if we remembered all the irrelevant details of our day, such as what we wore or had for lunch or who we passed on the street every single day.   It is important, therefore, for the brain to store only those memories that are important, and the way it does that is to make stronger connections with information that is repeated, that is, that appears again and again in our environment.  Once a memory is reasonably well-established, it requires very infrequent review to remain relatively strong and easily accessible.

Learning new material well, though, involves not simply remembering it as an isolated, decontextualized fact.  Rather, learning something well requires that a person apply the information in the right way and under the right circumstances.  There is overwhelming evidence that the best way to achieve this goal  involves doing a variety of different tasks during a different practice set instead of practicing just a single skill..  In a primary math class, for example, that might mean shunning review that focuses on calculations with just a single kind of calculation, such as a page with just addition calculations on it, and instead doing a randomly presented mixture of addition and subtraction calculations, and perhaps within each operation, a couple of different types of problems, such as those with just single digits and those with two-digits.

Unfortunately, teachers and students often avoid this sort of “interleaved” practice because in the short run, it is much harder, and therefore the student performs the task more slowly and with more errors than a practice session involving just a single skill.  It is slower, of course, because the student has to make more judgments about the situation in order to recall the correct information.  However, in the long run, a student’s ability to apply the new skill in a variety of appropriate contexts is greatly enhanced with interleaved practice.

The reason is that what really needs to be learned isn’t only HOW to do the task, but also judgment about WHEN to do the task.  And when this judgment or discrimination step is a regular part of practice because it is interleaved or varied, learning is more robust and durable and it is more readily mimics how the person will apply the knowledge outside the classroom or practice session.

So, to make practice as efficient as possible, space the intervals in which the student is asked to recall the information in increasing intervals, and also make sure that practice time is spent with “interleaved” material, in which several related skills are practiced at the same time.

In my next post, I will give examples of how to apply these principles to prepare practice routines for helping students develop rapid performance of some particular math tasks.