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PaedDr . Lilla Korenova, PhD . Comenius University in Bratislava korenova@fmph.uniba.sk

Using of digital technologies and their effectiveness in solving mathematical problems on secondary schools. PaedDr . Lilla Korenova, PhD . Comenius University in Bratislava korenova@fmph.uniba.sk. Recommendation of the European parliament :.

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PaedDr . Lilla Korenova, PhD . Comenius University in Bratislava korenova@fmph.uniba.sk

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  1. Using of digital technologies and their effectiveness in solving mathematical problems on secondary schools PaedDr. Lilla Korenova, PhD. Comenius University in Bratislava korenova@fmph.uniba.sk

  2. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 RecommendationoftheEuropeanparliament: "Mathematicalcompetenceisanability to develop and usemathematicalthinkingforsolvingvariousproblems in everydaysituations. Based on welldevelopednumericalskills, theemphasisislaid on methods and activity, aswellas on knowledge. Mathematicalcompetenceincludestheability and willingness to usemathematicalmodelsofthinking (logical and stereometricthinking) and presentations (formulas, models, diagrams, graphs, tables) on manylevels. "

  3. What to teach? How to teach? Focusthecontentofthelessons on tasksfromeverydaylife- Adjustnotonlytheformbutalsothecontent to opportunitiesusing new technologies- To use:    -constructivistdidacticapproaches    -experimentalmethods    -InteractiveLectureDemonstrationsmethod    -PeerInstructionmethod    -Workshopmethodetc. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  4. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 Resource:MATH + ICT on highschool

  5. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 Exercise 1: We would like a big yard for our pet! Siblings Eva and John would like to build a fence for their pet's yard. Their parents allowed them to build a fence around an area in the shape of a rectangle next to the stable, but they have only 15 meters of netting. What should be the size of the paled area if they want to have it as large as possible for their pet to play on? See picture:

  6. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 If we choose x as one side of the rectangle, then we get the function of the area y depending on the side x. How will the values of x and y look if we can measure only with a precision of 1m? 0.5m? 0.1m? Let's make a table. Where will be the maximum for the area?

  7. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 Exercise 2: How do our assets grow in the bank? Mary's father put 1000€ on her bank account when she was born. How much money will she have after 18 years, if the interest rate stays constant 7% p.a. • First, we are going to create a table and a graph using CASIO CP300

  8. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 We will try to derive the formula with the students we will draw the graph using Sequence for K0 = 1000 €, 'p = 7%

  9. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 Exercise 3: New road Field road between two villages consists of two perpendicular straight stages. The longer stage measures 19,3 km and the shorter one 3,9 km. In the point of right angle of this two stages, there is a forlorn house (see pict. )

  10. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 A committee decided to substitute this field road with a tarmac road. Deputies of committee have a problem where the new road should lead. Experts estimated that 1km of the new road built on the original field road would probably cost about 182 500€,1km of the new road built out of the original field road would probably cost about 219 000€.

  11. CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010 • The deputy Ferkova proposed a different route: a new road would lead at first on original field road from Svodin and from the specific point would gain a new direction and would lead straight to Bruty. In relativity, where is the specific point, formulate the price of this road. The distance from the point of diversion to the forlorn house mark with letter x (pict.). Calculate the price of building of this road.

  12. Solution 1: • Cabri geometry CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  13. Solution 2: • MS EXCEL CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  14. Solution 4: We are looking for the function – dependency of the price from x • GraphiccalculatorClassPad300 using Graph&Table we draw the graph and find the maximum Important is that the students will be looking for the domain for x They can be solving under the circumstances that the road can be marked only in integers or in stepping by 5, 10, 20 km CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  15. Do you think that a graphic calculator helped you in understanding mathematics? • definitelyyes • ratheryes • rather no • definitely no • I don'tknow CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  16. Do youthink, that a graphiccalculatorhelpedyouduringyourcalculations? definitelyyes ratheryes rather no definitely no I don'tknow CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  17. Do youthinkthatteachingmathematicswith a graphiccalculatoris more interesting? definitelyyes ratheryes rather no definitely no I don'tknow CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  18. Do youthinkthatyouhavelearned more on thelessonsofmathematicsusing a graphiccalculatorthenyouwouldlearnwithoutit? definitelyyes ratheryes rather no definitely no I don'tknow CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  19. Do youthinkthatGeoGebra has helpedyou in understanding more in mathematics? definitelyyes ratheryes rather no definitely no I don'tknow CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010

  20. Thankyouforyorrattention! korenova@fmph.uniba.sk

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