[justify]The researchers stimulate the students to use different main strategies for creating new mathematical problems, such as:[/justify][list=1][*][i][/i][justify][i]Changing the constraints: [/i][/justify][/*][/list][list][*][i][/i][justify][i]Constraint manipulation[/i] - systematic manipulation of the task conditions or implicit assumptions (Silver, Mamona-Downs, Leung, & Kenney, 1996);[/justify][/*][*][justify][i]Changing[/i] the given data or the required data; [i]Varying[/i] the conditions or the context of given problems (Gonzales, 1994);[/justify][/*][*][justify][i]Goal manipulation[/i] - manipulation of the goal of a given or previously posed problem where the assumptions of the problem are accepted with no change (Kontorovich et al., 2012, p. 152; Silver et al., 1996);[/justify][/*][*][justify][i]Symmetry[/i] - a symmetric exchange between the existing problem's goal and conditions (Silver et al., 1996);[/justify][/*][*][justify][i]Numerical variation[/i] - creating a brand-new problem by substituting the given numerical values with the new ones (Lavy & Bershadsky, 2003);[/justify][/*][*][justify][i]"What-If?" or “What-If-Not?[/i][i]“ - creating new problems by systematically asking the questions “What would be If a particular condition is Not true?" or "What If a particular condition or implicit assumption would be different?[/i][i]” (Brown & Walter, 2005). Southwell (1998, p. 527) offers[/i][i] [/i][u]Step 1:[/u] [i]Solve the problem[/i][i]. [/i][u]Step 2:[/u] [i]Pose a similar problem and solve it; comment on the problem posed and solved[/i][i]. [/i][u]Step 3:[/u] [i]Write a comment on the problem given, the problem posed, or any other relevant matter;[/i] etc.[/justify][/*][/list][list][/list][justify][i]2. Generalisation [/i]– creating a problem for which the given problem is a special case (Harel & Tall, 1991; Kontorovich et al., 2012);[/justify][justify][i]3. Posing [/i]of new auxiliary problems, combination and disassembly[i] [/i](Song, Yim, Shin, & Lee, 2007, p. 193);[/justify][justify][i]4. Transformation:[/i][i][/i][/justify][list][*][i][i]t[/i][i]ransforming [/i]a given solved problem into an investigation problem (Leikin & Grossman, 2013, p. 517);[/i][/*][*][justify][i][i]transforming [/i] a given problem from one mathematical area to another one (Bilchev & Velikova, 2007);[/i][/justify][/*][/list][justify][i]5. Analogy; Association [/i](Abu-Elwan, 1999, p. 4; Kilpatrick, 1987);[/justify][justify][i]6. Targeting a particular solution[/i] - creating a new problem the solution of which would require the use of a specific theorem, solution or mathematical approach (Koichu, Leikin, Levav-Waynberg, & Appelbaum, 2008);[/justify][justify][i]7. Chaining[/i] - expanding an existing problem so that a solution to the new problem would require solving the existing one first (Singer et al., 2013, p. 3); etc.[/justify][justify]In connection to the need for increasing the activities in mathematics education and improving the quality of training of future teachers, the following question arises "How the integration of GeoGebra in mathematics education can be used for creating a rich environment that stimulates students' professional competence development?".[/justify]