Variety In Mathematics Lessons Colin Foster, Association of Teachers of Mathematics, 2008, ISBN 978-1-898611-54-7 This book is a guide for teachers who wish to offer a greater diversity of experiences in their school mathematics lessons. It offers twelve different models or styles of lesson, with examples of how each one might be realised in practice. A 'must' for any maths teacher who feels that lessons are too 'samey' and wants to inject more variety and enthusiasm into their teaching. Click on the image to buy from www.atm.org.uk. “All teachers, from trainees to those with years of experience, will find ideas here that will add variety and interest for them and for their pupils. Every maths department should own a copy and every maths teacher should use it.” Mark Dawes, Advanced Skills Teacher of Mathematics, Comberton Village College, Cambridge; Association of Teachers of Mathematics – click here to read the entire review. “A fascinating and challenging set of ideas ... it would be impossible to read the book and not find something new on every page ... this book is a real gem and cannot fail to help develop our teaching.” Peter Hall, Advanced Skills Teacher of Mathematics, Imberhorne School, East Grinstead; Association of Teachers of Mathematics – click here to read the entire review. "A valuable resource for all teachers." Grant MacLeod (2008) Review in Mathematics in School, 37(5), 35

Singing Graphs! (see page 16)

SoundFunction © G Foster 2007

Many learners will be familiar with experiencing a graph as a static image or as a left-to-right developing line. (The impact of these alternatives can be quite different.) Often these pictures are linked to tables of numbers. A different non-visual way of experiencing a graph might be as a sound, where the pitch relates to the ‘y-value’, while the ‘x-value’ operates as time. The program SoundFunction (available for free download below) enables the user to enter a list of numbers (perhaps pasting in a column of values from a spreadsheet) and the software generates the appropriate soundtrack. (Zero is taken as middle C and an increase of 1 unit corresponds to a semitone musically.) To download the free program, click here and then click 'Install'. (You will need to have DirectX installed on your computer; if you haven't, you can download this for free from http://www.microsoft.com/downloads/.) Scroll down this page for some mp3 files produced by SoundFunction. Tasks learners might work on with this program could include: · Predict what particular graphs would sound like and then try them out. · Identify graphs from their sounds as precisely as you can (see below for ready-made examples). · Which graphs sound ‘boring’/'predictable'? Why? · Which graphs sound 'surprising'? Why? · Which graphs are ‘soprano’/’bass’ graphs? Why? · Which graphs are in your singing range? Which would be hard to sing? Why? · When do you need 'perfect pitch' to identify a graph; when is 'relative pitch' enough? · What are the aural effects of transformations such as f(x) —› f(x) + a and f(x) —› af(x) and f(x) —› f(–x), etc? It is also possible to use SoundFunction to represent sequences: · What do the square numbers ‘sound like’? · How could you tell the square numbers from the cube numbers? · How does an arithmetic series sound different from a geometric series? · What is the same and what is different about the sounds of different arithmetic series?

Identifying Graphs

Listen to the sound files (mp3) below and try to identify which graphs (or kinds of graphs) they might represent:

Function 1
Function 2
Function 3
Function 4
Function 5
Function 6
Function 7
Function 8
Function 9
Function 10
Function 11
Function 12
Function 13
Function 14
Function 15

© Colin Foster 2007