The new A level Mathematics course started this September. It is accompanied by brand new textbooks, freshly printed and delivered to schools. We can have a look into one of them thanks to the publisher providing access to the full text online here: http://en.calameo.com/read/0007777215f36d2bc2a39?authid=2lkMzyC7Nxrh®ion=uk Chapter 5 is about logarithms. This is how they are introduced: Well, […]

N is in Year 5. “What are you doing at school now?” “Umm, we are still converting fractions to decimals and back” “Show me an example” “Well, it’s something like \( \mathrm{\frac{1}{2}=0.5}\), \( \mathrm{\frac{1}{4}=0.25}\), \( \mathrm{ \frac{7}{10}=0.7}\) ” “I see. Can you write \( \mathrm{\frac{1}{8 }}\) and \( \mathrm{\frac{3}{40 }}\) as decimals?” He can. Without much effort. “The interesting […]

A new edition of a Pearson A level textbook has been published recently, and although there have been some changes made to the text, the mystery surrounding square roots has not been fully resolved. The good news is that the ambiguity about the meaning of the square root sign is gone as the book clearly […]

This is a chart called “100 square” that you can find in every primary clasroom: Children mostly use it for simple sums. Say, if you need to do 45+7, you find 45 on the chart and simply move 7 steps forward. Oops, sorry, you move only five steps forward, then you have to move your […]

You have certainly seen this bright-coloured toy called an abacus: It can usually be found in shops as an entertaining toy for three-year-olds. Despite a respectful past as a calculating device, using it for a serious purpose would probably be ridiculed as inappropriate for the 21st century. Indeed, an abacus like the one shown above […]

It is always a pleasure to find someone of the same mind. My amazement at the UK university application system is shared by the Guardian: Historians will laugh at us when they look back at our university application system. With only one in six young people getting the exam results their teachers predict, the current […]

My son sat the Key Stage 2 tests this year. It was the second run of the tests based on the new primary curriculum. In mathematics, two “reasoning“ papers and an “arithmetic” paper replaced two written general mathematics papers (one allowed use of a calculator, the other did not) and a mental mathematics test. The […]

Here is a question from A level Edexcel Core 1 January 2013 paper: The equation \( (k+3) x^2+6x+k=5 \) where \( k\) is a constant, has two distinct real solutions for \(x\). Show that k satisfies \( k^2-2k-24<0 \) Hence find the set of possible values of \( k\). This is a question […]

Jo Boaler continues her mission to bring meaning into maths teaching and joy into its learning. The Stanford University project YouCubed draws attention to common problems in maths teaching and offers some insight into what works best, supported by educational research. Her enthusiasm is highly commendable, and I would encourage everyone interested to visit the website. You […]

One remarkable fact about school maths is that students are hardly ever given definitions of the objects they are dealing with. Instead, students are presented with some sort of descriptions. Here is an excerpt from BBC Bitesize which is a typical example of what school textbooks say: Students need to know properties of squares, but […]