The PSLE2009 item (see Page 32 PSLE Examination Questions 2005-2009) available from several publishers or the Popular bookshop in Singapore is a good illustration of when calculator use is expected and when calculator should not be used.
The problem is about Super Puff Shop where you can buy one curry puff for 80 cents but when you buy three curry puffs, you get to buy one more at half the price. The problem is to find out the gretaest number of curry puffs that one can buy with $50.
You do not expect 12-year-olds to use calculator to find half the price of 80 cents. That should be an automatic number fact. Students are also not expected to use any computational tool - whether it is a calculator or paper and pencil - to find the cost of three puffs. In fact, to find the cost of a set of four curry puffs should be done mentally. Although it is best to write down how one arrives at the value and this can be done by writing down the number sentence 3 x 80 cents + 40 cents = $2.80, the actual computation should be done mentally.
In order to find how many complete sets of 4 curry puffs one can buy, $50 divided by $2.80 is appropriate. This computation should be done using calculator. We should not want kids in the present technological age to waste time (and be frustrated in the process) to compute 50 divided by 2.8 using long division - it is simply not productive.
It is better to use the time to teach them that although the calculator shows a bunch of digits (17.85714...), only the whole number part (17) is of any meaning in the present situation.
That means 17 x $2.80 = $47.60 is used to buy 17 x 4 puffs or 68 puffs. I would expect most people to use calculator to do the former and do not need one to do the latter. 17 x 4 is easy to do using the doubling strategy - double 17 to become 34 and double 34 to become 68.
There is still a remainder of $2.40 - no 12-year old should need a calculator to know the change for $47.60 when one pays $50. We don't use a calculator in real life for this situation. Most adults know what the change is in this situation.
The remainder gets you another 3 puffs. Does that need the use of a calculator? We would have failed if kids need a calculator to work that out!
There is a difference between having a calculator to use and using a calculator indiscriminately.
Wednesday, April 1, 2009
Wednesday, March 4, 2009
I have been asked too many times how the examination items will change with the use of calculator being allowed in the PSLE. Logically, with the use of calculators being allowed, computation is no longer the skill being assessed. The examiners is more interested in how students make use of a computation to solve a problem. In other words, in some problems, a computation is necessary but not sufficient to obtain a solution.
The examiners are also able to use authentic information which often results in tedious computation not easily done mentally in the problems. With calculators the issue of tedious computation is non-existent.
We have always encouraged investigative problems in the curriculum but do not really assess thsi aspect of problem solving. Often in solving investigative problems, a fair bit of exploration and repetitive computation is necessary. Without calculators, such exploration and computation make it not plausible for investigative problems to be included in a timed test. With calculators, there is nothing to stop examiners from assessing such problems in a timed test.
Of course many of the problems that have been included in previous PSLE can still be included even when calculators are allowed. In some problems, calculators are simply not useful. In others calculators will provide help to those who stuggle with computations but otherwise fairly successful in problem solving. In the era where technology is prevalent, if all one cannot do is tedious computation, it is no longer perceived as having a big handicap. After all this weakness can be overcome by a relatively cheap tool - the calculator.
These are of course my views based on the role of calculators in doing mathematics at primary levels.
PSLE stands for Primary School Leaving Examination. It is the sixth grade national examination in Singapore. It is compulsory for all children in Singapore to sit for this national test. From 2009 onwards, calculator use is permitted in part of the examination. Candidates may use a calculator to help them complete five short answer items (two marks each) and thirteen long-answer items (either three, four or five marks each). For short-answer items, it is not necessary to communicate the method in writing. Credit is given for a correct response. However, partial credit can be earned even if the final answer is incorrect if a correct method has been communicated. For the long-answer items, communication of solution mentod is necessary as the problems are fairly complex and/or novel. The level of difficulty of the paper remains the same,a ccording to a press release by MOE.