NCETM article on the use of calculators in A level Mathematics
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My article for NCETM: "Ten calculations that A level students should be doing on a calculator: can yours?" can be read at: https://www.ncetm.org.uk/resources/54231
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One of the fantastic features of dynamic graphing software is that you can animate how a graph changes as some aspect of it is varied. I'm particularly keen on making short GIFs of animated graphs that demonstrate interesting properties. One advantage of animated GIFs is that they are really easy to distribute via Twitter. There are loads of them if you have a look at the hashtag #mathgif . Parabolas I've been posting animated Maths GIFs to Twitter for quite a while now. Here are some of my favourites featuring parabolas: The midpoint of the points of intersection of y = x ² and y = mx + c lies on the line x = m /2. The tangent at point P to a parabola with vertex Q can be constructed by finding R, the point of intersection of the vertical through P and the horizontal through Q, finding the midpoint, M, of QR and then drawing the line through P and M. If the tangents at two points A and B on a parabola are perpendicular then the line AB goes through t...
There are a lot places on the internet where the are negative opinions about Powerpoint. I don't want to repeat these arguments here, instead I wish highlight particular problems relating to the use of Powerpoint in the teaching and learning of mathematics. These are that: It reinforces a view of mathematics that it is a series of algorithms to be rote-learned; It can reduce the amount of student-centred use of ICT in learning mathematics; It is usually a static form of mathematics and there are many easy tools for creating equivalent dynamic forms of mathematics. Reinforcing a limited perception of mathematics Many Powerpoint presentations for mathematics feature a question with the stages of a solution presented. This can have a negative impact of students' perceptions of mathematics. There is a link between students' perception of mathematics and how successful they are. Students who perceive maths a series of unrelated recipes for solving probl...
Most graphing tools have a feature to add a variable constant in a way that can be changed dynamically. In Desmos and GeoGebra this is by using sliders; in Autograph it is via the constant controller. When the parameter is changed you can view its effect on the graph and this can be discussed with students. You can even animate the change so you don't need to do it manually! This feature of being able to dynamically change a variable constant is a very powerful tool to help students build their understanding; however, to make the best use of it, it is useful to have some questions to ask to direct students' thinking. Effective questions when using dynamic graphs When I vary … how does it move and why? For what value of … will …? If I vary … how will it move? Examples using the intersection of a line and a parabola To exemplify this I'm going to use the intersection of the parabola y = x 2 with the line y = mx+c . To do this I've plotted: y = x 2 y...
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=> Minimal WD 20.000
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