Teacher2Teacher 
Q&A #494 
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From: Noorali Jiwaji <njiwaji@hotmail.com> To: Teacher2Teacher Public Discussion Date: 2000091119:07:17 Subject: basic arithmetic skills 11th September 2000 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 5minute 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/(TW)] / [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)
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