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Q&A #332

Teachers' Lounge Discussion: Place value and different bases

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From: Noorali Jiwaji <njiwaji@hotmail.com>
To: Teacher2Teacher Public Discussion
Date: 2000091619:04:39
Subject: Re: memorization problems

Memorisation can only be acheived by exposing the mind to
multiplication tables as often as possible.  This means the best (and
only?) way is by chanting the tables starting from a very early age. 
Once the tables are memorised, the mind is then free to use these
"mathematical facts" to do higher problems.  My focus has been how to
monitor the child's ablility to do simple arithmetic problems.

I give below my experience in this and have some queries arising from
it:

Memorizing multiplication tables to 12 starting from a young age
allows one to be comfortable and confident about real life arithmetic
problems encountered in adult life.  This is irrespective of whether
or not you really understood the meaning of multiplication as a young
child.  

When testing young children on multiplication tables, I have been
facing a problem about how to quantify this learning and what to
expect at various age levels.  The main factors are:
-	accuracy and
-	speed of answering.

The problem is quantifying these parameters and getting a single
number for each student which can be tracked for progress and to set
targets for each age level.

I administer 5-minute tests each with 100 simple multiplication
questions (upto 12) to 10 to 15 year olds.  I then get a number by
dividing the number of correct answers by thinking time (in minutes)
multiplied by accuracy ratio.  I illustrate this below with a specific
example:

T = Total time for doing the questions = 5 (minutes)
Q = Number of questions attempted = 79
C = Number of correct answers  = 82
W = Time to write 82 answers = 1 minute 38 seconds = 1.63 minutes

Then multiplication proficiency (M) is:

M = [C/(T-W)] * [C/Q]

For our example, M = 22.6

Basically this means that the pupil can think up answers to 22 simple
multiplication questions per minute.  The maximum I have encountered
is 150 for a 15 year old with most falling in the range 30 to 60. 
Similar numbers are also encountered in addition and subtraction
tests, though I have found some pupils with multiplication
difficulties with surprisingly better subtraction abilities.

I would like to know if anyone has done a similar type of assessment
or any other type quantification of such arithmetic and speed skills. 
What kind of targets can be expected for various age groups?  Can
training methods be assessed using this type of numerical technique?
And any other comments on improving the deteriorating mental dexterity
of our children. 


Dr. Noorali Jiwaji
(Physicist)


On 7 Jun 00 14:41:31 -0400 (EDT), Terrie Palmer wrote:
>My son has just finished the four grade.  His teacher has stressed
>that he didn't memorize his multiplication table and needs to
>accomplish this or he will have problems and keep falling behind. 
How
>can I teach him to memorize his basic times table?	It hurts me to see
>him count on his fingers and struggle.  
>



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