Are mathematicians gifted people
The relationship to mathematics remains ambivalent even in modern knowledge and information societies. It is generally accepted that we owe technical progress to mathematics as the language of science. People with good math skills can also be sure of admiration. But that is where the ambivalence begins. Mathematical skills should actually be as natural as written language skills, since both are taught from the first to the last day in general schools with a large number of hours.
There are large differences in literacy among pupils, but only a few pupils leave school completely illiterate. People with a high school diploma would hardly claim that they cannot really read and write. On the other hand, even people with academic training admit to mathematical illiteracy surprisingly lightly, and this assessment is entirely in line with reality, also in Switzerland. The Evamar Study II, in which 3800 Swiss schoolchildren who passed their Matura in 2007 took part, showed that almost a quarter of the participants achieved mathematics below the minimum requirement. But even among the students who have taken the hurdle, you will only find a few who have more in-depth mathematical skills. Most of them manage to apply procedures to familiar types of tasks, but new tasks quickly reveal the thin ice on which they are moving.
Is math really only for a particularly gifted minority? Such an assumption is widespread - especially among math teachers - and it corresponds to the human tendency to simplify things. Inferring permanent characteristics of a person from observed behavior without considering the various environmental influences that can influence behavior, is referred to in psychology as correspondence bias or attribution error. But mathematical and other academic competencies in particular can only be met if they are viewed against the background of cultural development. For all we know, the blueprint for the human brain was created 40,000 years ago. The first traces of mathematics date back less than 3,000 years, and much of what is now on the curriculum in general schools was only developed a few centuries ago. In the Roman Empire there was probably neither arithmetic weakness nor outstanding mathematical skills, because the Roman number system could be used to quantify discrete quantities, but otherwise hardly offered any opportunities to develop mathematical concepts. Even the most intelligent Roman could hardly imagine a prime number.
But even if our brain has not been prepared directly for the acquisition of mathematics and written language, it obviously has quite good prerequisites for acquiring them. This is the only way I can explain to myself that in just a few school years, normally gifted children can learn what has been developed over thousands of years. School learning brings together what was intended in the blueprint of our brain as independent competencies 40,000 years ago. At that time we were given a sense of numbers that enabled us to distinguish between quantities of different sizes. In carefully designed experiments it can be shown that infants can quantify precisely even in the small range of numbers and estimate them well with larger quantities. These two basic competencies can now also be identified as independent mechanisms in the brain. The ease with which almost all preschool children learn to count spontaneously and without systematic instruction speaks in favor of prepared, universally available learning mechanisms.
Severe arithmetic disorders, as they show up in a few children later at school, very often originate in the brain. The big differences in mathematics performance at school, on the other hand, are not so easy to explain. Mathematical skills are based on our innate sense of numbers. But mathematical competencies can only arise in combination with our specific human intelligence, which is shown above all in conclusive thinking, if the appropriate learning opportunities are offered. In general intelligence, there are also large and largely genetically determined differences among high school students. But an above-average or even very high intelligence can only be used for the development of mathematical skills with good, understanding-oriented teaching. This can be optimized at all school levels. Too often, students practice routines that never lead to understanding. Anyone who knows curve discussions cannot necessarily interpret or even construct graphs correctly.
Esther Ziegler, a doctoral student in my research group, recently showed how small changes can have a big impact in the transformation of algebraic terms in mathematics lessons at secondary level 1. Instead of introducing addition and multiplication one after the other, the tasks were given in parallel and thus enabled the learners to make systematic comparisons that led to a deeper understanding, as demonstrated by the performance in transfer tasks. There were still differences in performance, but at a higher level.
Conclusion: To speak of a mathematical talent is neither sensible nor justified from a scientific point of view. Mathematical competencies arise when people are given the opportunity to invest their intelligence in building mathematical knowledge in which concepts and routines are well integrated.
To the author
As a 15-year-old she already knew that Elsbeth Stern wanted to become a researcher or professor. She achieved this goal: The native German has been a full professor for learning and teaching research at ETH Zurich since 2006. She graduated from high school in Schwalmstadt (Hesse) in 1977. She studied and earned her doctorate in psychology in Marburg and Hamburg. After completing her habilitation in 1994, she worked as a professor at the University of Leipzig and at the Max Planck Institute for Human Development in Berlin. Establishing teaching and learning research as a serious scientific field has long been a central concern of her. A fundamental question about learning is one of the most fascinating for her: How does the human brain, which is at least 40,000 years old, learn things that have only been part of human culture for a few decades, such as operating a computer ?
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