paeddr . lilla korenova, phd . comenius university in bratislava [email protected]
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Using of digital technologies and their effectiveness in solving mathematical problems on secondary schools. PaedDr . Lilla Korenova, PhD . Comenius University in Bratislava [email protected]. Recommendation of the European parliament :. - PowerPoint PPT PresentationTRANSCRIPT
Using of digital technologies and their effectiveness in
solving mathematical problems on secondary schools
PaedDr. Lilla Korenova, PhD.Comenius University in Bratislava [email protected]
Recommendation of the European parliament:"Mathematical competence is an ability to
develop and use mathematical thinking for solving various problems in everyday situations. Based on well developed numerical skills, the emphasis is laid on methods and activity, as well as on knowledge. Mathematical competence includes the ability and willingness to use mathematical models of thinking (logical and stereometric thinking) and presentations (formulas, models, diagrams, graphs, tables) on many levels. "
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
What to teach? How to teach?Focus the content of the lessons on tasks from
everyday life- Adjust not only the form but also the content to opportunities using new technologies- To use: -constructivist didactic approaches -experimental methods -Interactive Lecture Demonstrations method -Peer Instruction method -Workshop method etc.
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Resource:MATH + ICT on high school
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:
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?
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
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%
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Exercise 3: New roadField 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. )
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€.
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.
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Solution 1:Cabri geometry
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Solution 2:MS EXCEL
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Solution 4:Graphic calculator ClassPad300
using Graph&Table we draw the graph and find the maximumImportant is that the students will be looking for the domain for xThey can be solving under the circumstances that the road can be marked only in integers or in stepping by 5, 10, 20 km
We are looking for the function – dependency of the price from x
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Do you think that a graphic calculator helped you in understanding mathematics?1.definitely yes2.rather yes3.rather no4.definitely no5.I don't know
31%
29%
20%
6%
14%
12345
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Do you think, that a graphic calculator helped you during your calculations?1.definitely yes2.rather yes3.rather no4.definitely no5.I don't know 20
%
20%
20%
20%
19%
12345
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Do you think that teaching mathematics with a graphic calculator is more interesting?1.definitely yes2.rather yes3.rather no4.definitely no5.I don't know
64%
29%
7%
1234
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Do you think that you have learned more on the lessons of mathematics using a graphic calculator then you would learn without it?1.definitely yes2.rather yes3.rather no4.definitely no5.I don't know
42%
33%
25%
1234
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Do you think that GeoGebra has helped you in understanding more in mathematics?1.definitely yes2.rather yes3.rather no4.definitely no5.I don't know
43%
20%
31%
6%
1234
CADGME, Hluboka nad Vltavou, 29.6. - 1.7. 2010
Thank you for yorr attention!