ACE-ArithmEcole- Easier Way to Teach Arithmetic to School Students

The University of Geneva (UNIGE) has
developed a new system to make learning of arithmetic easier for school
students. Titled ACE-ArithmEcole, the programme is designed to help school
children surpass their intuitions and informal knowledge, and rely instead on
the use of arithmetic principles. The approach based on semantic re-encoding
helps students to gain knowledge in arithmetic at a very young age.
A study was conducted among ten classes of students in the age group of 6 to 7
in France (second grade). Five classes were given conventional training in
addition and subtraction known as the control group and the other five classes
the teachers encouraged them to favour abstraction. “To get the students to
practice semantic re-encoding, we provided them with different tools such as
line diagrams and box diagrams,” says Emmanuel Sander, professor at the
Department of Education of the FPSE at UNIGE. The idea is that when they read a
problem, such as “Luke has 22 marbles, he loses 18. How many marbles does he
have left?”, the pupils should detach themselves from the idea that subtraction
always consists in a search for what remains after a loss, and should instead
manage to see it as the calculation of a difference, or a distance that has to
be measured. It’s all about showing students how to re-encode this situation.”
After a year of teaching based
on this practice, the UNIGE researchers evaluated their intervention by asking
the pupils to solve problems that were divided into three main categories:
combine (“I have 7 blue marbles and 4 red marbles, how many do I have in
all?”), comparison (“I have a bouquet with 7 roses and 11 daisies, how many
more daisies do I have than roses?”) and change problems (“I had 4 euros and
Iearned some more. Now I have 11. How much did I earn?”). In each of these
categories, there were some problems that were easy to represent mentally and
to solve using informal strategies, and others that were difficult to simulate
mentally and for which it was necessary to have recourse to arithmetic principles.
At the conclusion of the tests,
researchers observed undeniable results. Amongst students who had learned to
solve mathematical problems with the ACE-ArithmEcole method, 63.4% gave correct
answers to the problems that were easy to simulate mentally, and 50.5% found
the answers to the more complex problems. “In contrast, only 42.2% of the
pupils in the standard curriculum succeeded in solving simple problems, and
only 29.8% gave the right answer to the complex problems,” exclaims Katarina
Gvozdic, a researcher at the Faculty of Psychology and Education (FPSE) in UNIGE . “Yet their level measured on other aspects of maths was exactly the
same,” adds Emmanuel Sander.
This discrepancy can be
explained by the frequent recourse to the use of mathematical principles rather
than to mental simulations by the students who had taken part in the
ACE-ArithmEcole intervention. “Thanks to the representational tools that had
been offered to them and to the activities they had recourse to in class, the
students learned to detach themselves from informal mental simulations and
avoid the traps they lead to,” comments Katarina Gvozdic enthusiastically.
The results are promising and
they provide a foundation for promoting abstraction and breaking away from
mental simulations. “Now we want to extend this teaching method to higher
classes, incorporating multiplication and division as well,” continues Gvozdic.
“Moreover, the method could be applied to other subjects-such as science and
grammar—for which intuitive conceptions constitute obstacles,” adds Sander. The
idea is to put semantic re-encoding to widespread use in schools and to
incorporate it more amply into teaching methods.
Source: University of Geneva
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