I often speak about
fluency and math facts. Recent articles address the conflicts between memorization,
the need for fluency and math drills, especially timed ones.
In this course we
stress the load on memory that retrieval of verbal information causes and the
fact that some students will not benefit from timed drills. Their unique
learning differences make them unsuitable candidates for the pressures of
automatic retrieval in timed settings. These timed drills can create
stress and anxiety, feelings of defeat and loss of self-worth. That does not
mean we should give up on gradual and incremental growth toward fluency and
fact retrieval. Rather it would suggest that by using the same facts
repeatedly in problem solving activities and through games, children can
eventually achieve the fluency we desire.
Remember that
"chunking" is a viable study skills strategy. We chunk those
facts or a specific number of facts that a child can master with relative
ease. We review mastered facts periodically to preserve fluency. We
do not drill without meaning attached.
Woodin Math has a
book aimed at teaching multiplication tables to students with disabilities and
there are a variety of vehicles available other than "drill and kill"
and timed Mad Minute exercises.
Here is a link to
one of the two articles on timed drills and fluency. It includes research links
which you may follow if you wish. At this time, the article is a
free pdf download.
You can also find
some very interesting research on numeracy in the UK which more than likely
would be replicated here in the USA. The simple graphics make the lack of
numeracy awareness in the general population to be quite shocking. The
research from the UK is an outgrowth of Brian Butterworth's work on
numeracy.
I definitely feel like I have encountered a number of students who had a lot of difficulty retrieving math facts, and it wasn't for lack of effort. Thank you for sharing the thinking behind and strategies for helping these students.
ReplyDeleteFluency is a very sensitive issue, and I also have kids who struggle with addition and subtraction fluency. I have an almost third grader who uses her fingers for facts such 5+3 and 9-2. She is an anxious child, she doesn't need any pressure on her, but I feel we still need to work gently to make those facts easier to recall so she can use them efficiently. Her mom (an educator) feels that fingers are fine; and while I don't want to contradict her, I am hearing Marilyn's voice reminding me that 'the purpose of manipulatives is to get rid of them'.
ReplyDeleteWhile this is true, I feel for this child. Those who have been taught to count on as an initial strategy have difficulty releasing themselves from it. Lots of dice and domino games, explicit practice in numeracy patterns will help...and especially targeted practice on a few number facts at a time. I even review the composition of 7, 8 and 9 with my middle school students as we begin fraction work and work with integers.
DeleteMy daughter has dyscalculia--addition and subtraction facts (even those to 10) are still so much more challenging for her than multiplication facts. I plyed tons of games with her but never focused on a few at a time. There are materials from Stern Math that have been so helpful. They are durable and beautifully made (and expensive) but the 7-10 frame boxes have been game changers for her and they make for excellent warm-up activities. I wish I had known about pattern recognition and subitizing sooner because the counting with fingers compensation has been difficult to undo and it seems to limit the decomposing and composing of numbers ability.
DeleteI struggled with memory retrieval as a child and still do to a degree. I remember dreading the times table and drills where I was timed or competing against others because I always lost. Many times I would completely shut down and not participate out of fear of failure and embarrassment.
ReplyDeleteMe too! I missed recess for six weeks once b/c of the mad minute. It takes sustained practice...and for many students...practice with a small set of facts over a period of time for them to begin to master fluency.
DeleteThank you so much for sharing this article by Jo Boaler. I appreciate her emphasis on number sense rather than rote memorization of facts.
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