teaching, learning, studying

f(x) = ax + b
Year ago when I was a pupil myself, math used to be writing down what the teacher said:[br]"If a is positive the graph is ascending".[br]"The greater the absolute value of a, the steeper the line".[br][br]Next lesson there was a quiz and you got points for correct answers [br]question 1: "WHen is the line ascending?"[br][br]Maybe you miss some chances to learn teaching this way...
two alternatives for slope
in this applet two variables a are defined:[br][list][*]aslider to have the slope defined as a slider[/*][*]abox to have the slope defined by an Input Box.[/*][/list]By a checkbox [i]show[/i] with caption 'show as slider' the slope of the graph a is defined as[br][code]a = If(show ≟ true, aslider, abox)[/code]
Slider in reserve
If you show just the variant with the schuifknop, you trow immediately all aces on the table.[br]In previous applet you can build up learning stepwise asking questions and controling the answers.[br]- "What if a = 2 ?"[br]- "Wat is a = 1/2 ?"[br]- "What if a = 0, or negative? "[br]Option: Show the slider de schuifknop just after formulating a hypothese upon the role of a, summarizing the different situations.[br]This way it summarizes what a student has learned instead of preventing the reasoning and the learning.
a version to use at home
Studying at home is different from exploring and learning at school so maybe we should make a different applet for a different learning fase. [br]In this 'homeversion' multiple choice questions are a way to control if you really understand what you should have learned at school.[br]- Can you do it without using the slider and trying out in the applet?[br]- Do I need the slider to assist me?

Information: teaching, learning, studying