One of the Year 11 classes I teach is what we call a withdrawal group. They all got a Grade 0 in their Higher GCSE mock back in November so we moved them to Foundation tier. This was definitely the right decision. I teach them for two double periods a week. The pupils in this particular group are very complex. Trying to teach them has been the most challenging thing I have ever done. I'm crossing my fingers that they all get a Grade 4 this summer.
Last week I attempted to engage this class in a revision lesson with one of the
revision mats I recently made. This required calculators, which I lent them. This particular revision mat was deliberately designed to identify gaps in their knowledge of how to use basic calculator functions. I very quickly discovered that there were indeed many gaps. In this post I hope to help teachers of similar GCSE classes be aware of things to look out for and address.
The first question to cause me concern was this one on multiplying fractions:
The answer they wrote down was 4.2. There are two worrying things about this:
- that they don't recognise that the answer should be greater than 21 (an area model would be a good way to demonstrate this)
- after almost five years of using calculators at secondary school, they don't know where the mixed number key is.
Their answer of 4.2 came from them inputting the fraction ½ and then using the cursor to move back and put a three in front of it. The calculator sees this as 3 x ½ rather than the intended 3 + ½.
In this country (though apparently not all others), writing 3½ means 'three and a half' and we call it a 'mixed number' - I'm pretty sure my pupils know this much. But when I went round and corrected each of them individually they all swore blind that they had never before been shown the mixed number button.
Now, I have been teaching teenagers long enough to know that the old 'we've never been taught this' line is normally nonsense. However in this case it may well be true. When we teach fraction arithmetic we do so in lessons that deliberately don't involve calculators. So unless these pupils have had a 'calculator skills' lesson then perhaps they haven't been shown it.
The second question to cause me concern was this one:
Thankfully all but one pupil wrote down the correct answer without using a calculator because they have some understanding of place value (phew!). The pupil who got it wrong wrote one seventh.
He could have typed 7% in his calculator and then pressed the S-D button and it would have done it for him. The percentage button simply divides by 100. It's nothing special but it's there if they need it. For example, think about the various ways to do this question:
We know that the most efficient thing to type into your calculator is 43 x 1.16. If pupils are not au fait with multipliers then perhaps they can type 16% x 43 instead, making use of the percentage button, and then add their answer to 43.
Do they do this? Hell no. Interestingly this is a topic where most students working at Grades 1 - 3 are very good at non-calculator methods. They will have done a lot of work on using multiplicative reasoning to find 10%, 5% and 1%. I'm super pleased that they can do this, but it's frustrating to see them use this method when they have a calculator at their disposal.
The next question that alerted me to a knowledge gap was this one:
There were two issues here: 1. not knowing where the cube root button is (I've known pupils to do 3√64 in the past) and 2. not following the order of operations. Some of them wrote 15 x 4, having worked out the cube root of 64 on their calculator after asking me the whereabouts of the button. I reminded them that their calculator has 'been taught the order of operations and understands it well', so we can trust it to correctly evaluate the multiplication first if we type in the whole calculation in one go. The problem of course comes with something like this:
In this case the calculator does indeed follow the order of operations, so if you type -32 then it will correctly square the three before multiplying it by negative one. But of course that's not what we wanted it to do. So if we insist on squaring negative three using a calculator, then we must put it in brackets. In fact if using a calculator I'd suggest putting all substituted values in brackets ie typing in 5(-3)2 -2(-3). I'd prefer to see this one done without a calculator really though.
Evaluating the square of a negative incorrectly using a calculator is a problem that persists. We know that GCSE students make this mistake all the time when asked to plot quadratic graphs. They end up with weird looking 'parabolas'. I remind them that they know they've gone wrong if their graph isn't symmetrical. Pupils must use brackets if they use a calculator to square a negative! I feel like I've said this a million times and I will keep saying it until I'm blue in the face.
The next question is one that I deliberately included in the resource to draw my pupils' attention to a useful calculator button. In my question about prime numbers, most of them assumed that 51 is prime. I pointed out that using the FACT button will show the prime factorisation of that number, which is rather exciting. If they're asked to write a number as a product of primes it will probably be in the non-calculation paper, but it's still helpful to know this function. It gave me the opportunity to have a helpful conversation with my pupils about what prime numbers are.
I think they were impressed by this button. 'This button is peng, fam'.
I had shown them it before, back in January. I'd also shown them the button they can use for time conversions. They were impressed then too, but had clearly forgotten all about these buttons which is unfortunate.
The final question of interest is this one on standard form.
Like fractions, standard form is often taught in a non-calculator context. And even if we have a calculator, it doesn't help us convert between standard form and ordinary numbers. However, if we're asked to use standard form in a calculation and we have a calculator to hand, it might be helpful to know how to use the x10x button.
On reflection, this resource ended up being more than just a revision mat. It helped me identify and address significant gaps in calculator knowledge, albeit much more last minute than I would have liked. They should have been using these buttons for years.
I should mention that when I took on this class at Christmas there were even more gaps in their calculator knowledge. At first they weren't making use of the Ans button. Plus, to do say 5.72 they would type 5.7 x 5.7 because they didn't know about the x2 button. So we have made some progress.
Ironically, as they left the classroom I reminded them that they should bring compasses and a protractor to their maths exam and they told me that they don't need to because it is all provided for them in a pencil case. 'Oh. In that case just make sure you bring your calculator. It has to be the one you've been using for the last five years - the one you know how to use'. 'Nah miss - they provide calculators too, we'll just use whatever they give us'.
This lesson got me thinking. I have a feeling that many schools don't do enough with calculators. In every school where I've taught Year 7 we haven't used calculators at all for the entire year - this is such a shame when there are many opportunities to explore and make sense of numbers in Year 7 using calculators. Also, although we need to build fluency with arithmetic in Year 7, I am convinced we should allow calculators for topics such as angles. It makes sense, and pupils like it.
Pupils need to be explicitly shown how to use their calculators throughout secondary school - I think that teachers often assume pupils already know the main keys. We need to bear in mind that much of it may not be obvious to a novice.
If you currently teach Year 6 or Year 7 then you might want your class to take part in MEI's
Calculator Crunch in June. In this challenge there will be nine daily problems to solve using a calculator. MEI will be providing two lesson plans too.
There are lots of fun '
know your calculator' activities in my resource library. These are great, but we must make sure that calculator use is embedded throughout the topics we teach too, not just covered separately. I'm sure that some schools already do this really well.
Note that the calculator pictures in this post are from my 'peng' Casio fx-83GTX which was kindly given to me by
Science Studio (and engraved with Mrs Morgan, which I love!). The buttons I've featured are in the same position on the Casio fx-83GT and fx-85GT (the ubiquitous calculators in the current Year 11 cohort).
