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Presentation 2B4. Building a Better Foundation for Advanced Statistical Techniques

Anthony Harradine (Australia)


Presentation Abstract

Can Australian (or any) secondary school students learn about the Normal Distribution and the Central Limit Theorem in a way that leaves them with more than what has been traditional - a very superficial understanding of the concepts, a purely mechanical understanding of the calculation of related probabilities and little ability to use the concepts and skills in a meaningful manner?

Yes, yes, yes!

Some Australian students in secondary schools are taught how to calculate the probability of the occurrence of events that can be modelled by a Normal Distribution. Most of the students are those who find real mathematics too challenging and opt for a softer course. Statistics has been perceived as something to do for those who can't do real mathematics or the topic you do if you finish all the algebraic ones- what a shame.

Many text-books outline what the Standard Normal Curve looks like, it properties (especially the 68 - 95 - 99.7 rule), how to standardise and how to use tables or a graphic calculator (which makes standardisation redundant for this purpose) to find areas under it to solve invariably boring questions of little importance to the student (or anyone). One can only wonder what impression this leaves with students. They end their relationship with the Normal Distribution with little appreciation of why the bell shape occurs, why the area under the curve gives a probability value (the term density curve may be mentioned but is rarely understood) and little experience in using the knowledge they do gather in a meaningful way. This, or nothing, is often the foundation upon which many students try to build when they enter University and study Statistics. This seems absurd, given the importance of statistical ideas in many of the courses students study at University. In South Australia the number of students studying to become statisticians is at an all time low.

A normal textbook is unlikely to be able to provide students with the learning experiences required to do anymore than they presently do. However, by using the electronic technology now at our fingertips we can make learning about the Normal Distribution so different and so rich and as a result allows students to build a wonderful foundation for more advanced statistical ideas.

Interacting with Mathematics (IWM) is a web-based environment that makes the most of the many learning conduits now at our disposal. It employs a learning cycle that we believe the students of today respond well to.

The learning cycle can be summarised as follows:

  • Students are challenged to complete a Stenduser, which is an engaging problem that they will only be able to partially complete and hence provides the impetus for the students to undertake new learning within the learning journey on offer.
  • The learning journey is constructed in manner that takes the students from reality to mathematical model in sensible increments and then educates them on how the model can be used to solve problems. Traditionally, most teachers start at the model and show how to use it. The "Where did that come from?" is rarely considered. The students cycle in and out of the learning journey, returning to the Stenduser when they think they can make more progress toward it solution. This is where the real foundation building occurs.
  • Once the students have completed the learning journey and the Stenduser they practice skills and routines.
  • Finally students are challenged to apply their new skills (and some old ones to) to a new, interesting, real and challenging problem.

Among many other things, IMW provides the scaffold that enables students to benefit from the many excellent electronic gadgets already available on the net, that are only useful if you already have an understanding of the fundamental concepts.

During my talk I will demonstrate all of the above ideas using the IWM environment created for the Normal Distribution and the Central Limit Theorem.


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