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===Description of Bottleneck=== | ===Description of Bottleneck=== | ||
Students have difficulties to use derivative to calculate the change of function value. They believe the derivative is a magic transformation of one formula into another, e.g. | Students have difficulties to use derivative to calculate the change of function value. They believe the derivative is a magic transformation of one formula into another, e.g. x² into 2x. They do not have an idea of "derivative=slope" or in case they have it they do not know what exactly the slope means, because they do not calculate "change of function value=slope*change of argument value" | ||
Desired learning outcome: given that f(1)=2 and f'(1)=3 | |||
Desired learning outcome: Students should understand that the change of function value is proportional to the change of argument value, and the derivative is exactly the proportionality factor. They should be able to draw for a given graph of function a triangle to illustrate the changes in values and the slope | |||
Concrete problems may be, for example: | |||
* A) given that f(1)=2 and f'(1)=3 students should be able to make an estimation of f(1,01) as f(1)+f'(1)*0,01=2.003 | |||
* B) given the entities of function and entities of argument, decide on the entities of derivative | |||
* C) given the text, which describes the rate of change, deduce a differential equation. | |||
===People interested in this Bottleneck=== | ===People interested in this Bottleneck=== | ||
Revision as of 12:44, 16 April 2025
Description of Bottleneck
Students have difficulties to use derivative to calculate the change of function value. They believe the derivative is a magic transformation of one formula into another, e.g. x² into 2x. They do not have an idea of "derivative=slope" or in case they have it they do not know what exactly the slope means, because they do not calculate "change of function value=slope*change of argument value"
Desired learning outcome: Students should understand that the change of function value is proportional to the change of argument value, and the derivative is exactly the proportionality factor. They should be able to draw for a given graph of function a triangle to illustrate the changes in values and the slope
Concrete problems may be, for example:
- A) given that f(1)=2 and f'(1)=3 students should be able to make an estimation of f(1,01) as f(1)+f'(1)*0,01=2.003
- B) given the entities of function and entities of argument, decide on the entities of derivative
- C) given the text, which describes the rate of change, deduce a differential equation.
People interested in this Bottleneck
Inna Mikhailova
