These were my notes for the workshop. Most of the links are poiting to Mathcad files so in order to read those you'll have to have Mathcad.

 

1.        Objective - future mathematics teaching

As a point of view I believe that schools shall use the most sophisticated software available at a reasonable price. On the other hand it’s not my goal that a specific kind of software is to be used in future mathteaching. At the moment I will recommend Mathcad and Smartsketch but this may very well change in the future. It is just that they are the most general user friendly mathtools at the moment which I hope you’ll have this opportunity to experience.

I will also try to demonstrate when you use software like in this case CAS and CAD it has an impact on what it is relevant to teach.

2.        Set-up in the participating classes - an ongoing development.

           a.        Facilities

                      i.         Great opportunities in Danish curriculum

One of the most important facts is how Danish teaching is regulated. We do not have inspections, material do not have to be approved, and despite curriculum the teacher can design his or hers own teaching within a very flexible frame close to unlimited. In general there has been a great belief to the teacher in Denmark the past 10 to 15 years but sadly this is changing at the moment.

                      ii.        computers versus calculators

Most CAS experiments are carried out on calculators. They do have some advantages but the big downside is that the pupil have to learn to use a specific tool. I don’t think it’s the way to go. The more general and standard a tool the better. This is why I prefer computers.

But of course this implies access to computers. Best if they are in the classroom (in Denmark the classes do have their own room and the tearchers are nomad) or in the surroundings.

           b.        Software

No further remarks on this.

           c.        directions (or instructions) for the teachers

This time my only directions were: Teach the way you would without the tool, but promise to let the pupils use Mathcad and Smartsketch..

           d.        levels

3.        Mathcad - basic editing

           a.        Word processor (text editor)-publisher mixture

           b.        electronic books and where to get help

                      i.         educational books

                      ii.        drag design of lessons - calculation off

                      iii.       buttons programming

           c.        regions - math versus text

                      i.         identification by cursors

                      ii.        principles for cursors - space

           d.        equals

4.        Smartsketch - basics                                              

           a.        relationships - check maintenance              

           b.        simple drawing - triangle

                      i.         Can Varignon’s sentence be about space

           c.        measures

           d.        active use of relationships                                                 

                      i.         Equilateral triangle

5.        Mathcad and other applications (eg. Smartsketch)

           a.        Components - pentagon - interactive area triangles - three bar linkage

6.        Mathcad and communication

           a.        Skolekom (First Class)

7.        Some examples - findings

In the first case the teacher quickly found out that she had to make another kind of exercises. To solve an equation became very easy so instead she changed it to things like: Given some information make a mathematical expression that contains the information. Her pubils actually became both strong in solving equations not only with computers but also in their mind and in making mathematical expressions.

These pupils never draws a graph with pencil and paper but what we don’t know anything about at the moment is if they have pictures in their mind.

           a.        beginner

Later on things like this have showed up... same file... and finally this is an example of how the tools were used in the final examination.

           b.        final

The pupils unanimously say that these tools should be presented much earliere in schools.