# Soon Children Will Learn Math Without Talking About Marbles, Coins or Apples

Soon, will children learn math without talking about marbles, coins or apples? According to the convincing results of a new Franco-Swiss scientific study, this is quite possible.

At the beginning of recess, a little boy has 24 marbles before putting them in play with his friends. In the first game, he loses 4 marbles but in the second game, he wins 7 marbles. How many does he have left at the end of recess? (Spoiler: he gained three more, so he has 27.) If you had a little trouble solving this fourth grade math problem, you might have had to follow this new learning method tested by Swiss and French researchers. According to these students, the fact that some primary school students have difficulty solving certain complex problems is linked to their perception of mathematics. Mental simulations (talking about marbles rather than numbers or proportions) can help them see solutions to simple problems. But they also prevent them from concentrating on more complex thinking exercises, where transposition becomes harder to imagine. The University of Geneva and its researchers have thus developed an alternative method, called ACE-ArithmEcole, which is based only on arithmetic principles and semantic coding (i.e. using only numbers and letters in the statement of a problem). Thus, the fact that the exercise is too complex to use a mental simulation is no longer a problem.

For one school year, ten French classes of CP-CE1 were mobilized to test this hypothesis. The results were recently published in the scientific journal ZMD Mathematics Education. Five classes followed the classical program where mathematical problem statements are filled with mental simulations. The other five learned the new method. To teach them semantic encoding, we used online or boxed diagrams,” explains Emmanuel Sander, professor at the Department of Education at the University of Geneva, in a statement. Students should be able to detach themselves from the imagery of marbles or apples and the idea that subtraction is always a loss. They had to be able to consider the latter rather as the calculation of a difference or distance. “The teachers focused on learning this technique in three categories of exercise, each at varying degrees of complexity: combination (how much is the sum total of the addition of two different quantities?), comparison (what is the difference between two different quantities?) and monetary problems (how much did a person earn between having so much money and then having so much money?).

At the end of the school year, the researchers studied the results presented by the teachers of the two groups of classes. In the first, educated in the classical mathematical method, only 42.2% of the pupils had answered correctly to the problems considered simple against 63.4%, in the classes having followed the ACE-ArithmEcole method. For the more complex mathematical problems, the gap was even more massive: 29.8% of pupils in the first group managed to solve them compared with 50.3% of pupils in the second group. “Thanks to the schematic tools provided by the new method, students were able to detach themselves from informal mental simulations and avoid falling into the traps that they may later encounter,” says Katarina Gvozdic, a researcher in psychology at the University of Geneva. Based on these results, the researchers now want to test the new method in higher grades but also apply it to other subjects, such as science and grammar.

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