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Difference between revisions of "Scope of formula"
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==Examples== | ==Examples== | ||
| − | #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 and, hence, does not equal <math>a=2</math>. | + | #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]] | #Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]] | ||
Revision as of 13:31, 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 <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