The guinea pig farm.

Hyde, Hartley

Emeritus Professor Jonathan Anderson, of Flinders University, has been working with UNESCO to assist the growth of Information and Communication Technologies in developing countries. His book ICT Transforming Education: A Regional Guide (2010) can be downloaded from: http://unesdoc.unesco.org/images/0018/001892/189216e.pdf. In Chapter Four he identifies four stages that can often be identified when teachers, faculties, schools and even whole systems gradually integrate technologies into their curriculum.

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Some of us went through the emerging stage in 1979 when our school purchased its first Apple ][ computer. My wife and I spent our summer vacation touring Victoria and visiting other teachers emerging at Apple II schools in Myrtleford and Swan Hill.

It was our common experience that using computers in classrooms also changed our teaching style. Over the years, we acquired more machines and software and we gradually adapted our pedagogy and our approach to our curriculum to gain the most from the emerging technologies. The development of pedagogy with technology is depicted on the two axes of the graph shown above.

In the mid 80s, provision of more technology could only be justified if we took our school communities with us and showed others how technology could be applied across their curriculum. This also meant that many of us became computing teachers rather than teachers of our original subject. More and more time was spent teaching about computers rather than using computers to teach our various subjects. In 1987, Victor Czernezkyj predicted that computers would become as commonplace as telephones and that we would just use computers without needing to mention how they worked.

In 1990 I returned to teaching mathematics full-time and experimented with using computers to teach the existing curriculum. I was working in large schools and found an increasing number of colleagues with the same interest. Slowly we adapted our curriculum around a use of computers and graphing calculators. This is identified as the infusion stage.

Most schools have now reached the stage that Victor prophesied so long ago. It may have taken longer than he thought, but we now take technology for granted. Very few teachers know where their software is stored on their machines let alone how to write their own. Manufacturers are making it increasingly difficult to access root directories and actively discourage 'tampering'. Most people do not care how an iPad works--they just use it. This is the stage that Jonathan Anderson has identified as the transforming stage because the ubiquity of technologies has changed our approach to so many tasks.

This journal has also moved through the same stages and has led the way by several years. This series of articles has described our infusion stage. We have shared our attempts to integrate a use of technology with the evolving mathematics curriculum. The first article appeared in October 1991. This is therefore the eighty-first article. The name CACTUS was suggested by Rod Sinclair and has been used since 1992.

Twenty years later many classrooms and, in particular, this journal are already transformed. Many AMT articles assume a use of software to assist research and teaching practices. The CACTUS pages in their present format have therefore served their purpose. Since I am retired and have never worked in a completely transformed school I am not the person to suggest changes. A modern day Joshua may emerge to lead a new generation into the promised land, but in my opinion most readers are already there. There is no longer a need for a specific article about using technology. This is therefore the last article I plan to write for CACTUS.

One of the most rewarding aspects of writing CACTUS has been the effect on a generation of my students. When they knew that their teacher was always experimenting and writing there was a constant Hawthorne effect that inspired many to do their best.

A similar effect switches in when we encourage students to publish their own work on the net. I am interested in the notion of homework blogs where students publish their project work to a blog and their teachers and parents comment on each blog entry.

I have not attempted to provide any sense of 'best practice' because I do not believe in such a concept. Each of us has our own approach to teaching and what works for one teacher doesn't necessarily work for another.

Michael Trucano has recently suggested (http://blogs.worldbank.org/edutech/worstpractice) that we may do better to identify worst practice--the approaches that we have learned do not work! At the top of his list is the assumption that if you just dump hardware into schools some sort of magic will happen. If there is any 'magic' it is the hard work of a few teachers who recognise an opportunity and work well beyond the call of duty.

I am sometimes asked for PDFs of past articles. One disappointing issue has been the availability of AMT articles from very strange, expensive net sources. I am seldom fussed about intellectual property rights, but I am angered that the copiers do not include any diagrams and most CACTUS articles are meaningless without their diagrams. If you do need a proper back issue, the AAMT office can usually provide a journal or make a PDF for a sensible, small charge. I wonder if the 'rip-off merchants' will copy that bit?

The best of the CACTUS articles have been rewritten, in much more detail, as worksheets for the Casio Classpad Corner. This is a joint project and you will find many interesting mathematical investigations. Most are easily adapted for use with a range of alternative software.

The article which has received the most positive comments from teachers is Introduction to Spreadsheets (AMT Vol. 56, No. 3) which appeared in August 2000. It attempts to provide some simple examples that should get students started using spreadsheets. The Classpad version can be downloaded from www.casio.edu.shriro.com.au/products/classpad_Corner/ pdf/Birthday_Pizza.pdf.

The article which gives me the most satisfaction is Modelling Biological Control (AMT Vol. 53, No. 4) which appeared in October 1997. The Australian CSIRO has used exactly the same technique to completely eradicate Water Hyacinth from the Tanzania section of Lake Victoria. The Classpad version can be downloaded from www.casio.edu.shriro.com.au/products/classpad_Corner/ pdf/Biological_Control.pdf.

The project which best caught the imagination of my students is This Can't be Maths, (AMT Vol. 58, No 4) which appeared in October 2002. A group of 'slow learners' finished their course early and we made up an investigation to plan a Eurail tour of Europe. Such investigations are now called Web Quests but few use the variety of web based tools that we were able to incorporate. The PDF of the original article can be downloaded from my website at www.users.on.net/~hhyde/cactus/. Follow the links to Downloads. I plan to leave this website in place for a few years.

Finally, I have been asked for one more spreadsheet. My wife suggested this one.

The Guinea Pig Farm Spreadsheet is designed as a game. We start with two male and two female guinea pigs (cavia porcellus, also called cavy). Each female will almost certainly produce three or four young within a few weeks (columns E and F). Expect four or five litters per year. The young will be ready to participate in the next breeding cycle.

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Columns G and H assume that there will be losses to predators and this is controlled at cell D4. Columns I and J simply add the new cavys to the parents.

Now assume that at some stage we wish to sell cavys. The pet market is not that extensive and guinea pigs are seldom used for research these days. The best market is in South America where they are considered a delicacy. However we do not want to venture into the live meat export trade. It is a game!

At cells H4 and I4 we can specify how many guinea pigs we wish to sell each cycle and at L4 we can say at which cycle we wish to start selling. It is kinder if we sell the guinea pigs in pairs because they prefer to mate for life.

The cells in Columns C and D in the next row are simply bookkeeping to determine how many guinea pigs are left for the next cycle.

So far the spreadsheet is very simple and could be completed by most students. However, to keep the numbers positive, it does pay to check that there are still some males left to play their part in the process and some simple checks that we do not sell more guinea pigs than we have available.

The aim of the game is to achieve the highest total in Cell M18. A working version of this and other spreadsheets can be downloaded from my website.

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To build this spreadsheet put the numerals 1-11 in Column B and a 2 in cells C4 and D4.

E7=F7=IF(($C7<1),0,INT(0.5*$D7*(2+3*RAND()))) calculates a random number of each gender in the litter based on the number of females breeding and the availability of at least one male,

G7=INT(E7*$D$4*RAND()/100 and H7=INT(F7*$D$4*RAND()/100 calculate the losses.

I7=C7+E7-G7 and J7=D7+F7-H7 calculate how many of each gender are still present.

K7=IF($B7<$L$4,0,IF((H$4>(I7-2)),I7-1,H$4)) and L7=IF($B7<$L$4,0,IF((I$4>(J7-2)),J7-1,I$4)) calculate how many guinea pigs are sold from each litter.

M7=K7+L7 calculates the total sales for the litter.

The next cycle is started with some bookkeeping: C8=I7-K7 and D8=J7-L7.

Copy Cells C8 and D8 down to Row17. Copy the other columns down to Row 16. Cell K18=SUM(K7:K16), Cell L18=SUM(L7:L16) and Cell M18=K18+L18.

Hartley Hyde

cactus.pages@internode.on.net

www.users.on.net/~hhyde/cactus