Mathematica in danish highschools

Kurt Bøge
kurt.boge@icloud.com

Abstract:
The publishing house ‘Forlaget Matematik’ has for some years been working on how to use Mathematica in the primary schools up to K10.
We have recently started a new project in the danish highschools, aiming at how to improve the educational outcome using Mathematica.
The primary goals are
-how to adjust Mathematica to the existing national curriculum
-to examine the pedagogical potential of Mathematica in this context
-teach the teachers how to create their own educational materials
-to dive into ‘Computational thinking and Mathematica’
-to start a discussion on ‘Mathematics after Mathematica’. Impact on curriculum?

Students and teachers at Sønderborg Statsskole are invited to participate

Adjusting Mathematica to the national curriculum
-
setting the scene

Why?

The fair question is why do we want to adjust anything

Because

We need to reduce the threshole. Mathematica is a very powerfull and overwhelming tool - for students as well as teachers at this level

We need to comply with Danish terminology - in Denmark we don't 'Plot' anything, we 'tegner grafer' and we don't 'Solve equations', we 'Løser ligninger'.

We can have a language issue - especially for the younger students.

We have to impose certain constraints on Mathematica. For example we must make sure, that the equation 
	(x^2)+1 = 0
has 0 and not 2 solutions

and in general: 
We must make ie easier to interpret results from calculations

If you 
FactorInteger[123456789123456] 
you’ll get
{{2,7},{3,1},{10303,1},{31204703,1}}

-but students a this level  can’t intepret the result
They need it in another form
(2^7)·(3^1)·(10303^1)·(31204703^1)

How?

I’ll show you in a minute, but just for the record:
We have developed a lot of specific functionality 
We have made it easy to use the functionality by designing new palettes, taking advantage of templates and with build-in help - adjusted to the highschool level and - of course - in Danish
We have worked a lot on making the output from certain functions more easy to interpret for students at this level
And recently we started using the dynamic possibilities in Mathematica to make it easier to Plot, to illustrate consequences of changing parametervalues, to work with mathematical modelling and to understand algorithms

More to come

Right now we are working on two things 
-	video guides - invoked from inside Mathematica:
	 - click on a button and you’ll get a relevant video
	The hard work here is to produce the video guides
-	Integrating our own help-pages in Mathematicas documentation
	The tools are Wolfram Workbench and Eclipse
				 +

Distribution

All materials are distributed as Paclets from our own paclet-server. It is - by far - the best and easiest way to distribute and update materials of this kind.

Adjusting Mathematica to the national curriculum
-
Demonstration

Demo

Install and activate dkGym paclet

Show
-New palettes: Gymnasiet > Grafer, Ligninger

Creating materials in  Mathematica

Demo

Install and activate demonstration paclet

Showcases
	verhulst.nb - on logistic growth
	pest1711.nb - the plague in Copenhagen 1711
	[SIR.nb - on epidemics]

Computational thinking and  Mathematica

Demo

Install and activate demonstration paclet

Showcases
The Sieve of Erastothenes



On calculating approximations to π

Mathematics after  Mathematica

A way of starting this discussion is to look at some math problems from the national written exams in the danish highschool

Demo

Install and activate demonstration paclet

Showcases
Dive into the solutions in the folder ‘eksamensopgaver’.
What makes sense and what doesn’t?

Makes no sense

Makes sense