Transcript www.whatworks.ae

How we use an algorithm
approach to improve
students maths skills ?
E. Suquet & B. Cadet
Organizing your thinking
Create an algorithm which calculates
the length of a side knowing the
length of the two others
Step by step process ...
Some students are more motivated in making
a program work than in solving an exercise ...
Helping to learn lessons
How to solve
quadratic
equation ?
Compute ∆
Easy to program on a graphic calculator
If ∆ < 0
Impossible to program without
knowledge
If ∆ = 0
If ∆ > 0
End
x0 = -b/(2a)
Final product is useful by the student
x1/2 = (-b±sqrt(∆))/(2a)
Helping to make strong conjectures
Making conjectures
Having ideas
Starting to solve the problem
http://scratch.mit.edu/projects/688054/
Raising new mathematical questions
Syracuse conjecture :
15 46 23 70 35 106 ...
How to explain if an integer is odd or even ?
Developing logical skills
Put 3 numbers a, b and c of your
choice in order
Understanding what being rigorous is
Computers make no difference between
little or big mistakes.
It is not because your program gives an
answer that it is right
How to find mistakes
Helping with abstraction
Abstract problem to solve
Trying to find real life
illustration to help the
student understand
But it is not always possible ...
Using an algorithm
- Function limit
- Derivative number
- Sequence
How to bring students to use algorithms ?
● There is a need to be progressive : not a one year work
● Do not mix mathematical and algorithm difficulties
● We use 3 others tools :
○ Scratch
○ Lego
○ Beaver challenge
An easy programming software : Scratch
The beaver computing challenge
1S
Move 1 case to the south
3E 1W
Move 3 cases to the east, then 1 case to the west
http://www.beaver-comp.org.uk/
3S 2E 1N
Move 3 cases to the south, then 2 to the east and then 1
to the north
3E 4(3S 2E 1N)
Move 3 cases to the east, then execute the above
programme 4 times
2(3E 4(3S 2E 1N)) 1N Execute two times the above programme, then move
one case to the north
http://www.cemc.uwaterloo.ca/contests/bcc.html
http://castor-informatique.fr/
The use of Lego Mindstorm
● Easy and progressive introduction to algorithm
● Possibility to bring new student to maths
● Ability to evolve during the project
● Students are proud of their final product
http://www.lego.com/en-us/mindstorms
Algo as a tool for teachers
http://scratch.mit.edu/projects/688054/
Algorithm helps us to :
Bring back students to maths
Strengthen and improve their skills
Students/Teachers move with the times
Background
Long time algorithms practice in our curriculum in middle and high school
But there was a big change in 2009 :
2009
2010
The words “algorithms”
and “programming”
appears in the French
curriculum in high
school
2011
2012
2013
New sort of
questions in final
exam of french
baccalaureat
A change for students but also for teachers ...