Scientific Computing World: Education

Stonehenge - mathematics and environmental education

August 27, 2007 on 6:45 am | In A-level, A2-level, AS-level, Environment, GCSE, Public Understanding of Science, critical thinking, discussion starters, geography, mathematics, physics, practical activities, secondary education, user stories, wider context | No Comments

This is a brief description of the Stonehenge trip mentioned on May 1st this year under the heading Sun, moon and stones.

A much fuller description is provided on the Articles and papers page.

The Field Visit

A-Level and pre-GCSE Mathematics students took part in a Field Visit to Stonehenge in 1^st May 2007, one day before Full Moon. The curriculum comprised practical project-based activities integrating content from mathematics, astronomy, climate science and history¹. The party was permitted full Stone Circle Access in the evening – and an opportunity to observe moonrise and sunset from the centre of the monument. These activities were documented on film, and students were encouraged to take part in its production. The Field Visit had two main aims:

to improve mathematics motivation;

to afford learners a powerful affective experience of the natural world.

The latter goal features prominently in certain understandings of environmental education.

Summary of findings

The Field Visit was highly rated by student participants.

There is some evidence that the Field Visit improved interest in mathematics within both pre-GCSE and A-Level cohorts. In the case of the pre-GCSE cohort, however, this effect seems to have been temporary, although situational interest was stimulated on the day. This cohort seemed to especially appreciate the opportunity of using mathematical tools. Some amongst the A-Level cohort expressed a preference for contextualising mathematics within integrated project-based curricula.

Stone Circle Access afforded a majority of student participants a powerfully affective experience. Here are some of the words that students chose to describe their experience: inspiring, fabulous, stunning, intriguing, mystical, awesome, epic, great, fascinating, indescribable.

The experience of some individuals might be characterised in terms of cosmological based identification. For example, one student reported
…it was like in Physics when you talk about the Universe. Inside the circle she felt small. The builders of Stonehenge were probably smaller than her. But still managed to put up those big stones. She felt small in comparison to them.

[1] The objective of the A-Level mathematics activity was to calculate the azimuth (bearing East of True North) of the Summer Solstice sunrise in 2000 AD, 2000 BC, 3000 BC as seen from the centre of Stonehenge using a theodolite and trigonometry. The sunrise azimuth slowly varies over millennia due to oscillation of the tilt of the earth. This oscillation is one of the three Milankovitch cycles and it is thought to have been a causal factor in the alternation of glacial and inter-glacial periods between one and three million years ago.

Global warming and the Prisoner’s Dilemma

June 19, 2007 on 7:20 am | In AS-level, KS3, KS4, Public Understanding of Science, critical thinking, discussion starters, game theory, user stories, wider context | 5 Comments

Yesterday’s early morning email included a message from Pauline Laybourn of Minnesota, pointing me to the following video:http://www.glumbert.com/media/global

I recommend watching it through, viewing it as an educational resource. Thank you, Pauline.

Having watched the clip, I followed Mike Willcox’s ‘YouTube’ example and used it as the departure point for a discussion session with some thirteen year old students within a “Public Understanding of Science” strand.

Which side you happen to sit on the global warming debate doesn’t matter; nor does whether or not you are persuaded by the argument in this presentation. The important point is the number of themes which are here.

There is, of course, the straightforward global warming issue which the presenter is addressing. In my group of young teenagers, there was a lot of very intelligent and perceptive discussion around the examples, choices and language involved in completing the four cells of the decision grid shown on the whiteboard in the video. Are the “worst case” squares really the worst cases? Are they exaggerated? Are they understated? Are they off the track altogether? Are they both so unacceptable that the whole exercise breaks down?

There is also a very accessible entry point to game theory (game theory is a branch of mathematics, but you can go a long way in general educational terms without any explicit mathematical work). The result is an introduction to What he’s sketching out is what game theorists call a saddle point - more specifically, the type of saddle point known as a “minimax”. A minimax is a decision which minimises the maximum harmful outcomes in a given situation. A well known example of a situation where minimax may apply is the Prisoner’s Dilemma thought experiment: a good Prisoner’s Dilemma link, with an very accessible introduction leading to deeper material, can be found here at the Stanford Encyclopedia of Philosophy; other links include a Wikipedia entry, an online game at Princeton University, and a page of links connecting the dilemma to public ethics issues at the Constitution Society site.

Looking away from science to the wider context, the decision consideration process involved here is a valuable tool for thought in general. The video would be a valuable trigger for an AS level Critical Thinking session with sixteen year olds, but the critical thinking which it involves is an equally valuable component for any study, of any subject, at any school level. I plan to try it with eight year olds later in the week.

[contributed by Felix Grant]

Using video in teaching

June 6, 2007 on 6:44 am | In discussion starters, engineering, online video | 1 Comment

I was interested recently in the use by a colleague of video record from his own lectures and demonstrations.

I sometimes use clips from ‘You Tube’ as a way of demonstrating subjects I am teaching. For example, when explaining about the heat produced from an engine there is a good clip of an F1 engine revving to the point where the exhausts are glowing white hot with flames coming out of them.

Some other clips I have used are;