# What is the opposite of math thinking

## Number beam ignites flashes of inspiration

Max Planck Institute for Human Development examined how children learn mathematics

Mathematics has always been a problematic subject not only for many students, but also for education - and for a long time it was believed that mathematical thinking was primarily a matter of innate talent, but otherwise only to a limited extent. This is contradicted by studies on primary school children, carried out at the Berlin Max Planck Institute for Human Development under the direction of Elsbeth Stern: They showed that even weaker pupils, if they are properly instructed, learn to understand mathematical concepts and learn to use them correctly.

Around 200 children from the fifth grade of primary schools in Berlin took part in the project. Elsbeth Stern, cognitive psychologist at the Max Planck Institute for Human Development in Berlin, and her colleagues had designed various learning experiments that were intended to show how children grasp new mathematical relationships and the difficulties they have to overcome.

For example, the aim was to correctly position numbers on a number line - a series of experiments aimed at showing the interactions between the so-called procedural and conceptual knowledge of children. Procedural knowledge consists in using certain "cooking recipes" routinely and without deeper insight into the underlying facts; Conceptual knowledge, on the other hand, is based on insight into fundamental relationships and is ultimately what characterizes mathematical thinking.

This conceptual knowledge must and can be learned. Because without learning, on the one hand, even mathematicians do not get very far, and on the other hand, only average intelligent people achieve very good performance through appropriate motivation and practice.

Arousing deeper understanding contributes most to long-term learning success. A lesson that aims at a simple, everyday program with consideration for the weaker ones and omits abstract mathematical concepts is a mistake. Elsbeth Stern: "Because the opposite of good is not bad in this case, but well-intentioned: Especially with weaker children, everyday lessons have the least effect, rather an abstract program brings the greatest progress. This is due to the fact that high-performing students in simple tasks Recognize mathematical structures on their own, but the weaker ones need targeted support and stimulation. "

The false restraint, especially in mathematics lessons, is essentially due to the work of the child psychologist Jean Piaget (1896 to 1980), according to whose opinion primary school children should remain at the concrete operational level in all areas of knowledge and be incapable of abstraction - a prejudice that has since been refuted by several investigations.

If it were true that children develop in a programmed way, stimulating lessons would not be needed, says Elsbeth Stern: "Then the gifted would learn everything by themselves, and the rest would lose hops and malt. But word should gradually get around that knowledge, Motivation and practice are crucial for any learning success - and that good, that is to say, demanding lessons, especially in mathematics, provide children with valuable thinking tools. "

Because mathematics, as Francis Bacon judged at the beginning of the 17th century, is a language that can be used to describe areas that otherwise one would only have to marvel at without a word. The English philosopher and writer could not have guessed how much more his insight would apply at the beginning of the 21st century.

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