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