# Tanks, goats and buses- Anne Watson

Consistent use of images supports the understanding of mathematical structures. The outstanding examples of this in mathematics have become ‘canonical’, that is part of the mathematical canon. At school level these canonical images are: number line; function graphs (thankyou Descartes); 2-dimensional combination grids (thankyou Omar Khayyam and Cayley); Venn diagrams (thankyou Cantor and Charles Dodgson).  […]

# Handrails – Anne Watson

I have been floating the idea of treating key mathematics ideas as handrails for teachers and students.  Recently several positive comments about this perspective have floated back to me, so I am sharing the idea with you. In mathematics, teaching key ideas could be handrails. Handrails can be held, used as guides or supports, or […]

# Euclid and Sherwood – Anne Watson

When Euclid wrote about ratios of lengths and areas and similarity, without algebra, theorems were dependent on spatial representations. Five diagrams, all related to each other, appear in his text in various places, so I designed a ‘Match the theorem’ task in the manner of Malcolm Swan’s tasks.  There isn’t a one-to-one correspondence and you […]

# Exponentiation by Anne Watson

Exponentiation I was prompted by a recent tweet to think more about exponentiation. The problem being posed was how to convince students that the laws of indices apply even when the exponent is not a whole positive number. There is a deep issue lurking here, which is that the more abstract the mathematics, the less […]

Professor Anne Watson has two mathematics degrees and a DPhil in Mathematics Education, and is a Fellow of the Institute for Mathematics and its Applications.  She taught mathematics in challenging schools for thirteen years before becoming a teacher educator and researcher at the University of Oxford.  For most of those years she used a problem-based […]

# Five top tips for transforming your primary maths teaching

We summarise Professor Anne Watson’s webinar on the small adjustments that will transform your primary maths teaching, part of our Maths Adventure series.

# How can the use of manipulatives improve both mathematical understanding and mathematical language skills?

This blog summarises David Lyttle’s webinar on how manipulatives improve mathematical communication, part of our Maths Adventure series.