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Estimation comes before calculation

Nothing demonstrates the lack of mathematical education more than overly exact calculation.
Carl Friedrich Gauss

Many students think that the only thing that matters in math problems is the result, i.e., the students are primarily concerned with the recipe for quickly arriving at a certain result, namely the correct result. However, this basic attitude in learning mathematics is a mistake that often leads to problems later on, because in many students the indispensable control mechanism of understanding through the existing formulas is switched off, i.e., the students only orient themselves on the way to the result, but not on the process.

Therefore, one of the most important foundations in learning mathematics is to learn to estimate and to develop a feeling for the plausibility of a calculation process. In this context, one could also say that what matters most in any calculation process in mathematics is the meaning of a calculation, not the numbers or formulas alone.

Study shows great importance of feeling for numbersPrimary school students learn arithmetic by estimating. In mathematics lessons, elementary school students mainly learn to calculate exact results. Just as important in everyday life is the ability to estimate the approximate magnitude of numbers.

The problem is that very many people have no conception of large numbers and, in connection with this, do not give any thought to meaningful accuracy in these orders of magnitude. Hofstadter calls this widespread phenomenon mathematical illiteracy, which includes not only no feeling for numbers, but at the same time also the missing conception over sizes.