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This bottleneck relates to the following intended learning outcome: Students always check whether a given formula comes with prerequisites for its applicability and whether these prerequisites hold in a given situation. | This bottleneck relates to the following intended learning outcome: Students always check whether a given formula comes with prerequisites for its applicability and whether these prerequisites hold in a given situation. | ||
== | ==Examples== | ||
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#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=|a|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2</math> and, hence, does not equal <math>a=-2</math>. | |||
#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]] | |||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
[[Category:Bottleneck]] | |||
Latest revision as of 16:30, 22 July 2024
Description of Bottleneck
When using a mathematical formula students don’t check whether the prerequisites for the applicability of this formula apply.
Intended Learning Outcome
This bottleneck relates to the following intended learning outcome: Students always check whether a given formula comes with prerequisites for its applicability and whether these prerequisites hold in a given situation.
Examples
- Square root and square are inverse to each other for nonnegative real numbers, i.e. for : . Without the prerequisite the formula would read . In fact, many students use without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a=-2} . There Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2} and, hence, does not equal Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a=-2} .
- Scope of quadratic formula as described in DecodingWork:Scope of quadratic formula
