## ‘Using Technology to Foster Mathematical Meaning through Problem Solving’

In the article “Using Technology to Foster Mathematical Meaning through Problem Solving” by Rose Mary Zbiek, it is mentioned that using mathematics technology how encourage to students’ learning and interest. Thanks to using technology, students learn clearer and quicker. Moreover, it also has a lot of instructional opportunities such as the capability of storing, sharing and changed the problems and solutions. As technological sources, there are a lot of devices, tools and programs such as; several types of calculators, Cabri Geometry, The Geometer’s Sketchpad, PowerPoint, word processors and so on.

In the article, two examples which consist of a sequence of two or more related problems are also mentioned. In first example, it is wanted from students that image of given triangle under a reflection must be found between given other triangles. This example related with Euclidean transformations especially reflections. By this problem, students consider about preimage and image of triangles under transformations. After students identify triangle as the image under reflection, they discuss the other triangles. Then, they find image under rotation and they begin to think about relation between images under reflection and rotation. They realize that rotation equivalent to a composition of two reflections. By using technology, such as the Geometer’s Sketchpad or Cabri Geometry, we provide students to think about reflections line and rotation points more deeply and they also see clearer this relationship by visually thanks to technological programs. After these steps, composition of other types of transformations might be given with geometry construction program.

In second example, it is wanted that students find relations between parameters of function and its perspective on coordinate system. For example, on the equations such as f(x) = ax+b or f(x) = ax2 +bx +c, changing the value of “c” results in moving up /down of graph. Moreover, students find vertical intercept by storing 0 in “x” (on the equation f(x) = ax+b). In addition, on the function f(x) = C abx , students investigate the sign of equation by checking signs of “C”, “a” and “b”.  Thanks to the Geometer’s Sketchpad, students realize relations quicker and clearer since they have opportunity to see directly and a lot of examples and equations visually.

All in all, it is mentioned that technological devices and programs provide a lot of advantages to students when they learn mathematics and geometry. I totally agree with the writer because of three main reasons. First of all, thanks to using technology in mathematics, students see their mistakes, reasons and results visually by trying. Therefore, they learn permanently since they learn not only by doing but also by seeing. I think, if a student learns by discovering on your own, reasons/results are catchier. Secondly, dynamic tools provide a lot of examples, new problems and different ways to solve problems. Hence, students learn to solutions by not only one way but also a lot of ways and concepts. When, one way is not appropriate for one problem, students use another way they learned by using technological programs. This is very good because when a student cannot solve one way to question, s/he sees and applies other ways directly. Finally, thanks to technology, students see relationships between geometry and algebra visually by sliding points, lines in dynamic geometry. I think, realizing relations in geometry is the most important thing when understanding and solving a problem. Since, if a student cannot realize relations between points, lines or something else, s/he cannot put forward an idea in any way. Because of all these reasons, I think, using technology encourages students to mathematical meaning through problem solving.

http://www.jstor.org/discover/10.2307/27969542?uid=44902&uid=3739192&uid=5909400&uid=2&uid=3&uid=67&uid=29476&uid=62&sid=21102093905141