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Web resources for a 14 year old girl struggling with maths & confidence

Yesterday on Twitter I asked a question that had been asked of me: “Help: looking for web resources for 14 year old girl struggling with maths, particularly fractions, & maths confidence.

I love Twitter for this kind of thing. People are so helpful. I am grateful to @SteelingSeconds, @Samuel_Hansen, @fittdr, @Domestic_jules, @ColetteWeston, @nick4glengate and @christianp for their answers. Also huge thanks to the following, who retweeted my question: @UKRC, @Hel_TCW, @kunglu, @Mwmyn, @afriquanwoman, @MoreUtterPiffle and @Loiscarter. Here are the responses I got:

The Khan Academy

Recommended by @SteelingSeconds and @Samuel_Hansen, The Khan Academy is a set of free videos explaining maths topics at a variety of topics, with a corresponding set of exercises. Here’s a description from the website:

The mission of the Khan Academy is to provide a world-class education, for free, to anyone in the world. It consists of 1700+ (and growing) videos on YouTube covering everything from basic arithmetic to advanced calculus, chemistry and biology, along with a series of exercises that allow students to practice and assess their knowledge at their own pace.

Since my specific question was about fractions, here is an example of multiplying fractions:

Primary Resources: Maths

Although it goes back to Primary Maths, @fittdr suggests Primary Resources and says she “found it to be good revision for my kids”. The site describes itself as “Free lesson plans, activity ideas and resources for primary teachers.” For example, here is an exercise sheet on adding and subtracting fractions.

BBC Bitesize

@Domestic_jules and @ColetteWeston both recommend BBC Bitesize, a site which covers KS1-KS4 in England. The site has a series of reading material, activities and quizzes for self-testing. For example, here is a link to the KS3 fractions section.

nrich

@Domestic_jules also recommends nrich, a site with hundreds of classroom resources indexed by topic. For example, this Fractions Jigsaw.

MyMaths

@nick4glengate says his 13 year old likes the MyMaths website. This is a subscription service. There are some free samples available on the website, for example this game on ratios.

Mangahigh

@christianp says Mangahigh “really is very good”. Backed by Marcus du Sautoy, the website says:

Mangahigh is the first maths games site to teach the UK National Curriculum entirely through games. Our unique, curriculum-compliant maths casual games go beyond the scope of any maths games previously developed, and inspire incredible enthusiasm in students.

The fractions game is Flower Power.

E-Learning in Mathematical Subjects online videos

I spent some time yesterday remaking the E-Learning in Mathematical Subjects (ELMS) website, which has had an extended period of downtime since my previous webhost deleted my server without warning. ELMS is a research seminar series at Nottingham Trent University which I set up with Dr. David Fairhurst in 2005 and the website contains videos of seminars. ELMS aims to appeal to a wider range of subject areas and allow discussion on issues in mathematical e-learning that are shared over a range of diverse disciplines. There are currently 11 videos of seminars online on topics including e-assessment, disability and accessibility, podcasting, electronic voting (audience response) systems, VLEs, GeoGebra & interactive whiteboards and more in the pipeline.

I took the redevelopment opportunity to add some new features such as an improved RSS feed, AddThis boxes, short URLs for video pages and video embedding code, as well as some backend changes to make the site easier to run behind the scenes. Consequently I am now able to embed the video of my ELMS talk in this blog. (I have embedded this half size due to the limitations of this blog layout, so you might prefer to view full size).

Wolfram|Alpha: Sometimes answering the question misses the point

Wolfram|Alpha was released today. This is a fascinating piece of technology and I am trying to work out how I feel about it. If you don’t know what it is, for a general overview you could read “Wolfram ‘search engine’ goes live” from the BBC or a little more detail from “Ask Alpha: Quizzing the world’s first answer engine” from New Scientist. The technology enthusiast inside me is giddy with excitement but there is a little voice inside me crying caution.

It doesn’t do everything very well yet. For example, it knows “number of people in Nottingham” but not “number of bars in Nottingham” (it doesn’t know how to relate the unit “bars” to a city). But that’s not really the point, we should be interested in potential here. I am interested in how it handles maths particularly and in whether when it fails to answer a question this is because it never can or just can’t yet.

I have been typing in some questions from a ‘fun’ maths quiz used at the University of Nottingham on open days. I shouldn’t list too many here (as they should remain useful!) but an interesting situation has occurred.

One question asks “What is the difference between six dozen dozens and half a dozen dozens?”

It’s a slightly silly question and I’m sure there are more mathematical examples, but I immediately wonder if it could be answered with no knowledge (or, importantly, without acquiring the knowledge) of what a “dozen” is.

I tweaked the question and got a correct response from “difference between half a dozen dozens and six dozen dozens.” I now know the answer is 792 and at no point have I either found out (or been told) what a dozen is.

[An aside: On the subject of an unfinished product: Strangely, “difference between six dozen dozens and half a dozen dozens” (the other way around) doesn’t work. Interestingly, “six dozen dozens minus half a dozen dozens” produces an erroneous result, by implying a bracket in the wrong place. It interprets it as “six dozen times (one dozen minus half a dozen dozens)”. Seems it needs to learn BIDMAS/BODMAS]

This example is merely illustrative. However, I wonder if there are situations where an answer (with “working”) can be received via Wolfram|Alpha by typing key phrases from a coursework question and that answer is completely satisfactory to the assessment method (and marker) but the student has at no point understood what is being asked or what is to be learned. Mind you, as Adam Partridge (AdamJTP) points out to me on Twitter, this is not too different from the many many university students up and down the land who are currently cramming ‘knowledge’ into their heads which will only remain for a few hours while they get through their exam.

The other caveat is that the same answer can be obtained through a Google search for “difference between half a dozen dozens and six dozen dozens” and the student is only slightly more likely to find out what the term means.

So perhaps it doesn’t matter. Google does stuff like this, we’ve had computer algebra for years and Wolfram|Alpha doesn’t work all that well anyway. But, remembering this is a first look at a new type of technology, it makes me uneasy.

Another question gives me another example: “The diameter of a circle of circumference 1 is…?” Wolfram|Alpha makes light work of “the diameter of a circle of circumference 1” (even gives a nice little diagram), a question Google doesn’t cope well with. It is very easy to plug the text of this question into Wolfram|Alpha and get an answer, without the student having to muck out developing an instinct for the properties of a circle. Another example you might give a student to tease out an understanding of the relationship between circumference and diameter is “the diameter of a circle of circumference 12 pi“.

I am glad it doesn’t seem to know how to “list pairs of prime numbers which sum to 999“, a neat little trick I picked up from Math_Bits on Twitter and used successfully with students in York. I am using questions here that are quite basic because Wolfram|Alpha isn’t doing so well with more involved questions – but in many cases there’s no reason it shouldn’t be able to in time. But I think the point I am trying to make here is that sometimes we ask questions so that the student will learn something while thinking about the answer (and the actual answer is immaterial).

In the same way that skill at mental arithmetic shortcuts (and corresponding easy familiarity with numbers) is largely lost in my generation by use of calculators, I worry what this means about more advanced maths. Still, perhaps my unease is just a sign I am getting old and all this means is that questions which explore mathematical concepts need to be better crafted, which we (should) know anyway.

Of course this technology isn’t going to go away. It is a fascinating device for the betterment of humanity and such is progress. But it might force a change in the way certain concepts are taught/learned.

How many of your questions are answerable by Wolfram|Alpha with no need for understanding? Rather, give Wolfram|Alpha your assessment – how well does it score?

Chalk and talk and interactive whiteboards

Last December I gave a talk to the E-Learning in Mathematical Subjects (ELMS) Seminar Series at Nottingham Trent University. This was based on an essay I wrote for my PGCHE on lecture delivery methods. It looks at chalk and talk methods vs. PowerPoint and winds up on some of the things that can be done with interactive whiteboards. You can watch my video on the ELMS website, also download my slides, etc. and view other ELMS talks through the website.

ELMS is something I have been involved with through my PhD in e-learning in maths at Nottingham Trent University. These aim to bring people together from around the university who teach mathematical content and have similar issues but no opportunity to otherwise meet, along with people who are interested in education and e-learning for research and those who work in e-learning support. We received funding from the Institute of Mathematics and its Applications in 2006 to support the seminars and allow videoing of these for distribution through the ELMS website at elms.org.uk. We also receive support from the Higher Education Academy Maths, Stats and OR Network who provide web space for the videos.

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