Teachers tell us how they approach the freedom of transition year.

Frank Ryan, St Mark's Community School, Tallaght: "Transition year is a year when much diversity is attempted in many subjects but, unfortunately, not too often in maths. Despite the Department of Education's guidelines, it has become the first year of the Leaving Certificate maths course in many schools.

"As a teacher of Leaving Certificate maths, I appreciate the pressures of getting the course covered in two years, but if transition year is used to open up students' minds to maths and develop a love of the subject, then surely that makes next two years a lot more pleasurable.

"By doing lots of surfing and reading, and using a bit of imagination, I have built up a lot of resources for use in transition-year maths. I divide the course up into six areas and move around between these as the need arises or the

mood requires. First thing on a Monday is a different world to last class on a Friday, even in transition year.

"The first area I cover is calculator work, which involves magic squares and cubes, number crosswords, sequences, equations with missing operators to fill in, versions of the 'four fours' problem and so on.

"I then delve into the whole area of counting around the world. We examine types of counting such as Mayan, Babylonian, Roman, Chinese and abacus, ending with binary, which can then lead into computer counting.

"Next I introduce students to the history of maths, involving such events as Fermat's last theorem, the Goldbach conjecture and Marilyn and the Goats. I also profile famous mathematicians, such as Euler and al-Khwarizmi, and look at the development of calendars over the years, a history of zero and other interesting lore from maths history.

"Students enjoy the chance to use maths in a cross-disciplinary context in transition year. Throughout history, for example, maths was employed in the development of artillery. Maths is central to computer-generated art, business, geography and map- reading, biology and forensic DNA, astronomy and probability in gaming.

"Another popular part of the transition-year maths course is the module on problems and puzzles. I have found lots of brain teasers from the internet and other sources. We now study the maths of card tricks and cryptorithms - sums where letters replace numbers.

"This leads quite neatly to the whole area of coding and encryption. We have a module on the history of code making and breaking, such as the scytale, Caesar and polysubstitution ciphers. I give students examples to break, all of which involve lots of maths.

"We work with Morse code, modern encryption which leads to prime numbers, the search for Mersenne numbers and Ireland's contribution, internet security and a range of related topics.

"This can also lead to the writing of simple computer programs in QBasic. Other topics in this module include the Enigma machine [ below] and the Zimmermann telegraph. The Code Book by Simon Singh is a great resource here.

"All of the above can be enhanced by the students going online, getting more information and using the many interactive sites that are available.

"To avoid the weaker student getting left behind, I pick teams at the start of the year and do a lot of the puzzles, code-breaking, magic squares, Countdown with

numbers and so on as team

events. The material changes every year, as different groups have different interests, and what works one year may be boring the next.

"For three periods a week, there is a lot of work involved, but if you like maths it's a great alternative to a fixed syllabus."

Send your thoughts on teaching in transition year to lholden@ irish-times.ie