If you want your learner to achieve true fluency with multiplication bonds try this...

This is not a manual it’s an approach. 

And it’s EASY to do this with your children - just look and listen to this 👀   

How do we now help our learners reach an automatic level of proficiency to allow for the recall of facts from memory without conscious effort? 

Automaticity: Strengthening the association of the fact in memory to make  RETRIEVAL automatic. 

How fast is fast enough to be automatic?

An essential component of automaticity with math facts is that the answer must come by means of direct retrieval, rather than following a procedure and one of its most notable traits is speed of processing - "immediate recall".

 Van de Walle (2007) and other educational researchers (Isaacs & Carroll, 1999; Rightsel & Thorton, 1985; Thorton & Smith, 1988) consider facts to be automatic  if an answer is produced in under three seconds.

However, other educators, cognitive psychologists, and mathematicians point out that three seconds is too long to demonstrate true automaticity because it gives time to consciously construct a response - clearly not the immediate, unconscious response defined by automaticity (Isaacs & Carroll, 1999; Shapiro, 1989).

I start by focusing on small sets of known facts my learners aren’t proficient with YET.  ALWAYS just small sets to avoid overloading the working memory 

Research shows that effective math facts practice proceeds with small sets of no more than 2 –4 facts at a time. During practice, the answers must be remembered rather than derived. I try to encourage RELATIONAL THINKING ⬇️

Our MULTIPLICATION BONDS are double sided to encourage relational thinking - the rule of commutativity! 

Gradual mastery of small sets of facts at a time is fundamentally different than the typical kind of facts practice. Because children are learning only a small set of new facts it does not take many repetitions to commit them to memory. This build success quickly. Because they see success in small increments after only a couple of days practice, students remain motivated and encouraged. 

Results from research (e.g., Chard & Kameenui, 1995; Cooke & Reichard, 1996; Koscinski & Gast, 1993; Williams & Collins, 1994) also show that the interspersion of known and unknown facts in each practice session increases the speed at which facts are committed to, maintained in, and retrieved from long- term memory.

 

 

 Although it is not possible to anticipate the perfect spacing schedule, effective spacing schedules typically involve providing sufficient practice with the learning material during the learning sessions and enough time between sessions such that the information is still familiar but not fresh in mind.

 The combined powers of retrieval and spacing are embodied in the method of successive relearning. First introduced four decades ago*, successive relearning is becoming known as a straightforward and effective learning strategy, particularly for building retention of factual materials.

*Bahrick, H. P. Maintenance of knowledge: Questions about memory we forgot to ask. Journal of Experimental Psychology: General 108, 296–308 (1979)

Now would be the right time to... 

At this stage children develop the capacity to simply recall the answers to facts without resorting to anything other direct retrieval of the answer. one of the most notable traits that automaticity has been developed is speed of processing. 

By observing learners RESPONSE TIMES  you are clearly able to distinguish between the  “figuring out” vs. the immediate retrieval of facts that have become automatic.

Activities specifically geared toward  rapid recall of a set or cluster of facts are ideal - try these... 

This process of developing automaticity with multiplication facts could proceed with relatively little pain and considerably less drill than is usually associated with learning “all” the facts.

Cooke and colleagues also found evidence in practicing math facts to automaticity, “suggesting that greater fluency can be achieved when the instructional load is limited to only a few new facts interspersed with a review of other fluent facts (1993, p. 222).” Stein et al. indicate that a “set” of “new facts” should consist of no more than four facts (1997, p. 87).

TRY THIS...

If the learner responds correctly but takes longer than 3 seconds or so, the grown up places the card back two or three cards from the front of the pile. Likewise, if the learner responds incorrectly, the grown up tells the learner the correct answer and then place the card two or three cards back in the pile. Cards placed two or three back from the front will receive intensive review. The grown up would continue placing the card two or three places back in the pile until the student responds within the time limit (3 seconds)  three times in a row.

(Silbert et al., 1990, p. 130)