14.04.2008 Autor: Manfred Kricke Rational Unified Process Manfred Kricke.
Geometric construction in real-life problem solving Valentyna Pikalova Manfred J. Bauch Ukraine...
-
Upload
calvin-leonard -
Category
Documents
-
view
216 -
download
0
Transcript of Geometric construction in real-life problem solving Valentyna Pikalova Manfred J. Bauch Ukraine...
Geometric construction in real-life problem solving
Valentyna Pikalova
Manfred J. Bauch
Ukraine
Germany
Theoretical aspects
Practical realization
Theoretical aspects
Synergy of the two educational strategies
Content and structure of a dynamic learning environment
Different teaching and learning traditions
Interdisciplinary aspects
Dynamic mathematics software
Ukrainian side
German side
Joint work
Ukrainian side
Students' worksheets for secondary school geometry course
Dynamic learning environments with DG
Implementation at Ukrainian schools Intel “Teach to the Future”
German side
I –You – We concept
Dynamic learning environments with GEONEXT
Implementation at German schools
Evaluation and feedback
Joint work
Synergy of two educational models
Dynamic learning environments
Joint publications
Step-by-step (real-life) problem-solving tasks strategy
(Real-life) problem
Geometric model
Conjecture
Theorem
FormalizeConstruct
Investigate
Test
Deductive proof
Analytical solution
Generalizati
on
I – YOU – WE
I – individual work of the single student
You – cooperation with a partner
We – communication in the whole class
Synergy 1I YOU WE
Consider a problem +Formalize problem
Construct Geometric Model +Test Geometric Model +
Investigate +Make a conjecture +
Test the conjecture Formulate final result =
Theorem
Deliver a deductive proof or analytical solution
+
Try to generalize
- discussion between 2 pupils
check each other
- discussion with the whole class
PR
OB
LEM
-SO
LVIN
G S
TR
AT
EG
Y
Practical realization
The comparative study of the curricula in Ukraine and Germany
Selection of topics for explorative learning environments based on a combination of the two pedagogical-educational models
Collect the set of tasks for each topic
Practical realization
Consider different types of explorative learning environments
Design a learning environment
Implementation in German and Ukrainian schools
Dynamic learning environments
sequence of HTML pages including textgraphics dynamic mathematics applets (GEONExT)
collection of the dynamic models in DG
Types of explorative learning environments
Getting practical skills for working in dynamic geometry packages in constructing geometrical models
Gaining research skills through problem solving
Gaining new knowledge through investigation
Example1 . Vectors
Lesson1 Addition of Vectors. The Parallelogram Rule
Lesson 2
Solving Strategies with Vectors
Pedagogical Model
I – You – We
I You We
Step-by-Step
problem solving strategy
first lesson
situation 1 situation 2 situation 3
second lesson
situation 4 situation 5 situation 6
Lesson 1Addition of Vectors. The Parallelogram Rule
Situation 1 Construct the
sum of 2 vectors using the parallelogram rule.
Lesson 1 Addition of Vectors. The Parallelogram Rule
Situation 2.1 Investigate the sum of 2 vectors Make a conjecture about it properties.
*Situation 2.2 Repeat the same
steps for 3 vectors.
Lesson 1 Addition of Vectors. The Parallelogram Rule
Situation 3
Conclusions
*Problem discussion – more general problem construct and investigate the sum of 4, 5, …
vectors; create and save new tools the Sum of 2, 3, …
vectors by using macroconstructions.
Lesson 2 Problem Solving Strategies with Vectors
Problem: Investigate the position of point O in any given triangle ABC for which the expression is true
Situation 4Construct the given geometric model
Construct the sum of 3 vectors Test it
0 OCOBOA
Lesson 2 Problem Solving Strategies with Vectors
Situation 5.1 Investigate the geometric model
Investigate the position of the point O Make a conjecture Check it
in many cases
*Situation 5.2 Deliver
deductive proof
Lesson 2 Problem Solving Strategies with Vectors
Situation 6 Final conclusions *Related problems
4 vectors 6 vectors
DGGeometrical Place of points
Problem Construct two
segments AB and CD on the plane. Point E and F are points on the segments AB and CD respectively. Conjecture about the set of midpoints of the segment EF when dragging points E and F along AB and CD respectively
GEONExTGeometrical Place of points
DGPolygons.Tesselation
GEONExTPolygons.Tessalation
Real-life problem. Box
Thank you!
ObDiMat
Lehren und Lernen mit dynamischer Mathematik
Обучение с динамической математикой
Teaching and Learning with dynamic mathematics