Digital technologies for learning mathematics

The issue of whether to use calculators when teaching students maths seems to worry a lot of people.  The argument for is often presented as the use of calculators is part of the modern world and, by having access to answers to calculations rapidly, students are more likely to be able to understand relationships.  The argument against is that they reduce students' calculation skills which can impact negatively on understanding and also that they over-rely on them and are unable to spot errors as they believe the number on calculator must always be the correct answer. I think that this is a false dichotomy that is caused by a misunderstanding of what mathematics is and the low quality of many of the questions that students are asked to do in mathematics classes. A question Here's a fairly typical question: what is 36 × 9? Do you think students should do this with or without a calculator? My answer is (to both questions) - I don't care! This is an absolutely point...

This a video featuring Charlie Stripp and me talking about integrating technology into the teaching and learning of mathematics, recorded at this year's MEI Conference.

Last weekend was the annual MathsJam Conference.  If you haven’t been (or even if you have) I highly recommend it.  For more details see: http://www.mathsjam.com/conference/ The format is talks of maximum length 5 minutes on anything you find interesting.  This year I gave a talk on “How to Break Excel”. How to Break Excel A commonly occurring “error” in Excel happens when you type 1 into cell A1, =A1-0.1 into cell A2 and then drag this down to cell A11. This problems occurs due to the way Excel stores numbers: it uses floating point arithmetic with 1 bit for the sign, 53 bits for the mantissa and 10 for the exponent.  This means that the number we think of as 0.1 in base 10 is actually stored in binary as: 0.0001100110011001100110011001100110011001100110011001101 Similarly 0.9 in base 10 is stored in binary as 0.11100110011001100110011001100110011001100110011001101 This means that every time you use 0.1 in base 10 Excel is actually using: At...

There’s been a lot of talk on Twitter this week about an app called PhotoMath.  It scans mathematics live and then gives an “answer” to the question.  This is a screenshot of it: Some comments on Twitter seem to think it’s cheating whilst others think it’s the future (although to be honest most seem to mirror my experience of struggling to get it to read anything sufficiently accurately to evaluate or solve it). Any question that can be answered by a computer should be Arthur C Clarke once said “Any teacher that can be replaced by a computer should be”. It’s a great quote and I’d like to offer a variation on this: Any question that can be answered by a computer should be. The whole point of mathematics is to investigate the relationships between mathematical objects or solve real problems (I’ll skirt round the definition of “real” here!).  There are many processes that are useful in doing this but where they can be reduced to algorithms (such as solving linea...