News

The Cambridge Mathematics newsletter has drawn our attention to stories of the lives and work of two mathematicians. They reinforce our proposition that school mathematics is about learning to work like a mathematician and that our document Working Mathematically (see Link List below) is indeed an accurate and appropriate lens through which any systemic curriculum can be interpreted.

• Dr. James Tanton, an Australian, begins his Cambridge Mathematics interview with a puzzle that captured him as a child. It lived with him into high school where he had a revelation about its solution - on the way to school, not at school - and on into university where he realised that it wasn't just a puzzle. It was mathematics and he had already been a mathematician for a very long time. Also in the article James makes poignant observations of his time teaching in schools post-university. (See Link List below.)

• In 2014, Hollywood brought the incredible code-breaking story of Alan Turing and his Bletchley Park team to public attention through the film The Imitation Game. As brilliant and important as the work of these mathematics was, it pales in the presence of the story of Dr. William Tutte (1917 - 2002), also a Bletchley mathematician. Enigma, the machine decoded by Turing, used 4 rotors to encrypt codes. Lorenz, a secret German machine used for the highest security signals, used 12. It was single-handedly decoded by Tutte. After a brief outline of Tutte's extensive career, the Cambridge article A network to catch fish in, offers insights into this remarkable work which remained classified until the 1990s.

Both these articles are short and readable and, as a maths teacher, you are encouraged to make them part of your weekend or holiday reading. Perhaps both will have a place in your future teaching.

Task 65, Shape Algebra

Shape Algebra is a simplified version of Task 71, Algebra Through Geometry, which was reviewed in the May News. It gives younger students easier access to the mathematical ideas and it can also serve as an introduction to the approach for older students. The shapes themselves, although still formed using square x and quadrant y, are simpler, but the mathematical concepts remain: concept of area, use of symbols (pronumerals) to represent area, like and unlike terms, manipulating algebraic symbols, concrete representation of algebraic addition, subtraction and multiplication by a whole number and the Distributive Law.

In the eTask Package this task is in the 'special' set because the most motivating equipment possible is the plastazote shapes shown in the photo. Some schools will have these. Of course if a school does have a set 'in the cupboard' the task immediately jumps into the 'easy to make' category. For the rest of us the eTask Package provides a master for printing the shapes on card, laminating and cutting. The master is also included in the cameo. A bit more work, but not much when it only takes one set to supply the task.

Task 145, Land of ET

A story shell is used in conjunction with equipment to hook the students into this investigation. An imaginary land has only two letters in their alphabet. That leads to a huge number of very big words! The letters are B and Y and they are represented by blue and yellow counters. The king and queen make a decision to simplify the language by creating spelling rules. Their rules certainly limit the language, but the result is something far beyond what they expect. Children discover an underlying structure in the modified language, including the need for a 'nothing' word. It's a wonderful, 'content free' example of how mathematicians

think and work and it can be used to link apparently disparate mathematical content such as modular arithmetic and the reflections and rotations of an equilateral triangle.

Search 'modular arithmetic' and you will soon see how critical this content is to mathematics which surrounds our daily lives. It may not appear in school curricula as such, but the wonder of this task is that it throws light on the structure that underpins it and that this structure is the connection that links the imaginary language with the special arithmetic and the special geometry of the equilateral triangle.

In the eTask Package this task is in the 'easy to make' set because it only needs counters in two colours. Further, schools with Poly Plug can immediately use it as a whole class investigation because Poly Plug includes a set of yellow/blue counters.