How to raise a mathematical genius
Stanford University Professor Joe Bowler is the general director and co-founder of YouCubed. This is a university project that is created to provide resources for mathematical education to students, parents and teachers. In his column, Bowler tells how a finger count can be useful for children, why visual mathematics is clearer and more interesting, and gives several exercises for training memory with fingers.
A few weeks ago a bell rang in my office in Stanford. The mother of a five-year-old girl called: her daughter came from school in tears, because at the lesson she was forbidden to count on her fingers. This is not an isolated case. Quite often teachers do not allow students to use their fingers when counting - it's somehow "childish", unprofessional. However, studies in the field of neurology prove that this is at least foolish.
A study by American scientists Ilaria Bertheletti and James R. Booth, published last year, emphasized the direct relationship between the somatosensory cortex and the activity of the fingers. In particular, they found out that the process of counting in our brain is always reflected as finger, even if in fact when calculating the fingers do not use.
The somatosensory cortex is the area of the brain that is responsible for the actions of all parts of the body (from the lips to the toes).
According to another study, the academic performance of schoolchildren and students also depends on finger counting skills: the more successful junior students coping with the score on their fingers, the better they think in the future.
Scientists note that it is necessary to pay special attention to the skills of finger counting in six-year-olds: the training of perception at this age will guarantee future success in mathematics.
The skill to perceive information with the help of fingers and display it in the brain can be trained. For this, neurologists have developed a set of exercises that improves the quality of perception of information through fingers. These exercises can be practiced in school and at home.
First, mark the pupil's fingers with different colors, as shown in the picture.
1. Now ask the student to press the piano keys so that the color of each finger matches the color of the key.
2. Ask the student to go through the labyrinth with that finger, the color of which corresponds to the color of the figure.
3. Ask to show the number with that finger, the color of which corresponds to the color of the figure.
The above developments are part of a large group of studies on the process of cognition and reflection of the information received in the human brain. Our brain consists of a complex of networks that begin to interact in the process of processing information. When we are engaged in mathematical work, this activity affects those networks of the brain that are responsible for the visualization process and are located in the visual cortex. This means that when studying mathematics, you always need to use visual methods.
"Warm-up" of the visual system of the brain
Visual mathematics is effective for everyone. In 1983, Howard Gardner proposed a theory of multiple intelligence that allows people to differently assimilate information - visually, tactilely or logically. This idea expanded our knowledge of intellect and human abilities, but when it came to practice, it was misused. So, in schools, students were classified into types, and then presented with information most convenient for each type. This is fundamentally wrong: because people who are weak in visual thinking, this thinking needs more than someone else.
Mathematics has been presented for decades as a set of numbers and symbols, and the potential of visual mathematics has simply been ignored.
It's no wonder that students consider mathematics to be incomprehensible and uninteresting, because in the classroom they are immersed in the world of abstraction. They are forced to cram the facts, solve endless sheets with numbers, examples, using the minimum amount of visual aids and creativity. Even if teachers resort to visual methods, then, rather, as a prelude to the same abstract ideas.
To involve students in the process of visual thinking, they need to regularly ask how they see mathematical ideas, and ask them to draw what they see. It is very useful to ask questions and get answers to them using visualization. Last year the team of Stanford scientists launched a free course on visualization of mathematics, and the result was stunning: not only was the course downloaded 250 thousand times and used by teachers across the country. According to surveys, 89% of respondents, schoolchildren (3-9 class), noted that these classes "pumped" their mathematical skills, and 94% said that they learned to "move forward, even if the work is difficult and I make mistakes."