[size=100]In this activity you will explore the impact of parameters on a quadratic polynomial. You will experience how GeoGebra could be integrated into a ‘traditional’ teaching environment and used for active and student-centered learning.[br][br]Follow the instructions of this activity and write down your results and observations while working with GeoGebra. Your notes will help you during the following discussion of this activity.[/size]

[table] [tr] [td][size=100]1.[/size][/td] [td][center][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/center][/td] [td][size=100]Type [font=Courier New]f(x) = x^2[/font] into the [i]Input Bar[/i] and hit the [i]Enter[/i] key.[br][u]Task[/u]: Which shape does the function graph have?[/size][/td][/tr] [tr] [td][size=100]2.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][/size][/td] [td][size=100]Use the [i]Move[/i] tool in order to drag the graph of the polynomial in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] and watch how the equation in the [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] adapts to your changes.[/size][/td][/tr] [tr] [td][size=100]3.[/size][/td] [td][size=100][center][icon]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/120px-Menu_view_graphics.svg.png[/icon][/center][/size][/td] [td]Change the function graph so that the corresponding equation matches [br][list][*][i]f(x) = (x + 2)²[/i][/*][*][i]f(x) = x² - 3[/i], and [/*][*][i]f(x) = (x - 4)² + 2[/i].[br][/*][/list][/td][/tr] [tr] [td][size=100]4.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][/size][/td] [td][size=100]Double-click the equation of the polynomial. Use the keyboard to change the equation to [font=Courier New]f(x) = 3 x^2[/font].[br][u]Task[/u]: How does the function graph change?[br][/size][/td][/tr][tr] [td][size=100]5.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][/size][/td] [td][size=100]Repeat changing the equation by typing in different values for the parameter (e.g. 0.5, -2, -0.8, 3).[/size][/td][/tr][/table]

[list][*]How can a setting like this (GeoGebra in combination with instructions on paper) be integrated into a ‘traditional’ teaching environment?[br][/*][*][size=100] Do you think it is possible to give such an activity as a homework problem to your students?[br][/size][/*][*][size=100] In which way could the dynamic exploration of parameters of a polynomial possibly affect your students’ learning?[br][/size][/*][*][size=100] Do you have ideas for other mathematical topics that could be taught in similar learning environment (paper worksheets in combination with computers)?[/size][/*][/list]