SOL (Self organized learning)
(Prof. Dr. Diethelm Wahl,
University of Weingarten)
Concentration of students during a lesson
Learning velocity (Bloom, 1973 und Wahl 2005)
Speed in which students are able to understand a topic, varies:
Primary school
Factor 1:5
College
Factor 1:9
(depending from the Heterogenity of the students)
Four consequences for teaching
1. Teaching structure
„Sandwich principle“
Teaching and Transfer
alternate constantly
Four consequences for teaching
1. Teaching structure
„Sandwich principle“
Systematic Change of
impart and transfer units
2. „WELL“ (mutual
teaching and learning)
Four consequences for teaching
3. Knowledge should be
structurized
Four consequences for teaching
3. Knowledge should be
structurized
4. „Advance Organizers“
Advance Organizer
• Learning aid
• Summary of the most important results at the
beginning of a unit.
• Without any details
• Connection with still existing knowledge.
Advance Organizer for Integral Calculus
What is the size of the area marked?
Advance Organizer for Integral Calculus
1
A   3 4  3 4 18(FE)
2

Advance Organizer for Integral Calculus
What is the size of the area marked?
Advance Organizer for Integral Calculus
Here it is necessary first to create the antiderivative.
1
x1  x2
2





1
x2  x3
3
x3 
1 4
x
4
1
x4  x5
5
1 n1
n
x 
x
n 1
Advance Organizer for Integral Calculus
f (x)  x 3

Advance Organizer for Integral Calculus
Creating the antiderivative
1 4
x  x
4
3
Advance Organizer for Integral Calculus
Calculating the area marked:
1 4 1 4 1
1 15
A   2   1   16  
4
4
4
4 4
Advance Organizer for Integral
Calculus
The following page shows an
Advance Organizer to this topic
which has been used in class.
“Traffic lights method“
The “Traffic lights method“ is
used to repeate a certain topic.
„Traffic lights method“
The antiderivative of f(x) = x² is
F(x)  2x


1 3
F(x)  x
2
1 3
F(x)  x
3
„Traffic lights method“
Now the students have to select and raise a card of the
colour of the corresponding answer.
F(x)  2x


1 3
F(x)  x
2
1 3
F(x)  x
3
„Traffic lights method“
The correct answer:
The antiderivative of f(x) = x² is
F(x)  2x


1 3
F(x)  x
2
1 3
F(x)  x
3
„Traffic lights method“
Next task:
3
The antiderivative of f(x) = x is
1 4
F(x)  x
 4
F(x)  3x 2


1 3
F(x)  x
3
„Traffic lights method“
Correct answer:
3
The antiderivative of f(x) = x is
1 4
F(x)  x
4

F(x)  3x 2


1 3
F(x)  x
3
„Traffic lights method“
The marked red area of the graph from f(x) = x² is
8
3
4

14
3

„Traffic lights method“
The marked red area of the graph from f(x) = x² is
8
3
4

14
3

„Traffic lights method“
The marked blue area of the graph from f(x) = x² is
1
3

2
3
4
3
„Traffic lights method“
The marked blue area of the graph from f(x) = x² is
1
3

2
3
4
3