Calculator Woes

One of the Year xi classes I learn is what nosotros telephone phone a withdrawal group. They all got a Grade 0 inward their Higher GCSE mock dorsum inward Nov thus nosotros moved them to Foundation tier. This was definitely the right decision. I learn them for 2 double periods a week. The pupils inward this detail grouping are really complex. Trying to learn them has been the most challenging affair I receive got e'er done. I'm crossing my fingers that they all larn a Grade iv this summer.

Last calendar week I attempted to engage this bird inward a revision lesson amongst ane of the revision mats I of late made. This required calculators, which I lent them. This detail revision mat was deliberately designed to seat gaps inward their noesis of how to work basic information processor functions. I really chop-chop discovered that at that topographic point were indeed many gaps. In this post I promise to assist teachers of similar GCSE classes live on aware of things to hold off out for together with address.

The outset enquiry to displace me occupation organization was this ane on multiplying fractions:

The respond they wrote downward was 4.2. There are 2 worrying things well-nigh this: 

1. that they don't recognise that the respond should live on greater than 21 (an expanse model would live on a expert way to demonstrate this)
2. after almost v years of using calculators at secondary school, they don't know where the mixed number primal is. 

Their respond of 4.2 came from them inputting the fraction ½ together with and then using the cursor to displace dorsum together with lay a 3 inward front end of it. The information processor sees this every bit 3 x ½ rather than the intended 3 + ½. 

In this province (though patently non all others), writing 3½ means 'three together with a half' together with nosotros telephone phone it a 'mixed number' - I'm pretty certain my pupils know this much. But when I went circular together with corrected each of them individually they all swore blind that they had never earlier been shown the mixed number button.

Now, I receive got been didactics teenagers long plenty to know that the former 'we've never been taught this' line is unremarkably nonsense. However inward this instance it may good live on true. When nosotros learn fraction arithmetics nosotros practise thus inward lessons that deliberately don't involve calculators. So unless these pupils receive got had a 'calculator skills' lesson together with then perhaps they haven't been shown it.

The instant enquiry to displace me occupation organization was this one:

Thankfully all but ane pupil wrote downward the right respond without using a information processor because they receive got some agreement of house value (phew!). The pupil who got it wrong wrote ane seventh. 

He could receive got typed 7% inward his information processor together with and then pressed the S-D push together with it would receive got done it for him. The pct push exactly divides past times 100. It's null particular but it's at that topographic point if they demand it. For example, recollect well-nigh the diverse ways to practise this question: 

We know that the most efficient affair to type into your information processor is 43 x 1.16. If pupils are non au fait amongst multipliers together with then peradventure they tin give notice type 16% x 43 instead, making work of the pct button, together with and then add together their respond to 43.

Do they practise this? Hell no. Interestingly this is a theme where most students working at Grades 1 - 3 are really expert at non-calculator methods. They volition receive got done a lot of piece of work on using multiplicative reasoning to uncovering 10%, 5% together with 1%. I'm super pleased that they tin give notice practise this, but it's frustrating to encounter them work this method when they receive got a information processor at their disposal.

The side past times side enquiry that alerted me to a noesis gap was this one:

There were 2 issues here: 1. non knowing where the cube root push is (I've known pupils to practise 3√64 inward the past) together with 2. non next the enterprise of operations. Some of them wrote xv x 4, having worked out the cube root of 64 on their information processor afterwards quest me the whereabouts of the button. I reminded them that their information processor has 'been taught the enterprise of operations together with understands it well', thus nosotros tin give notice trust it to correctly evaluate the multiplication outset if nosotros type inward the whole calculation inward ane go. The job of course of report comes amongst something similar this:

In this instance the information processor does indeed follow the enterprise of operations, thus if you lot type -3² together with then it volition correctly foursquare the 3 earlier multiplying it past times negative one. But of course of report that's non what nosotros wanted it to do. So if nosotros insist on squaring negative 3 using a calculator, together with then nosotros must lay it inward brackets. In fact if using a information processor I'd advise putting all substituted values inward brackets ie typing inward 5(-3)² -2(-3). I'd prefer to encounter this ane done without a information processor actually though. 

Evaluating the foursquare of a negative incorrectly using a information processor is a job that persists. We know that GCSE students brand this error all the fourth dimension when asked to plot quadratic graphs. They goal upward amongst weird looking 'parabolas'. I remind them that they know they've gone wrong if their graph isn't symmetrical. Pupils must work brackets if they work a information processor to foursquare a negative! I experience similar I've said this a ane K k times together with I volition proceed maxim it until I'm blueish inward the face. 

The side past times side enquiry is ane that I deliberately included inward the resources to describe my pupils' attending to a useful information processor button. In my enquiry well-nigh prime numbers, most of them assumed that 51 is prime. I pointed out that using the FACT push volition present the prime factorisation of that number, which is rather exciting.  If they're asked to write a number every bit a production of primes it volition likely live on inward the non-calculation paper, but it's notwithstanding helpful to know this function. It gave me the chance to receive got a helpful conversation amongst my pupils well-nigh what prime numbers are. 

I recollect they were impressed past times this button. 'This push is peng, fam'.

I had shown them it before, dorsum inward January. I'd also shown them the push they tin give notice work for fourth dimension conversions. They were impressed together with then too, but had clearly forgotten all well-nigh these buttons which is unfortunate.

The concluding enquiry of involvement is this ane on criterion form.

Like fractions, criterion shape is ofttimes taught inward a non-calculator context. And fifty-fifty if nosotros receive got a calculator, it doesn't assist us convert betwixt criterion shape together with ordinary numbers. However, if we're asked to work criterion shape inward a calculation together with nosotros receive got a information processor to hand, it mightiness live on helpful to know how to work the x10^x button. 

On reflection, this resources ended upward existence to a greater extent than than exactly a revision mat. It helped me seat together with address meaning gaps inward information processor knowledge, albeit much to a greater extent than in conclusion infinitesimal than I would receive got liked. They should receive got been using these buttons for years. 

I should bring upward that when I took on this bird at Christmas at that topographic point were fifty-fifty to a greater extent than gaps inward their information processor knowledge. At outset they weren't making work of the Ans button. Plus, to practise nation 5.7² they would type 5.7 x 5.7 because they didn't know well-nigh the x² button. So nosotros receive got made some progress. 

Ironically, every bit they left the classroom I reminded them that they should select compasses together with a protractor to their maths seek together with they told me that they don't demand to because it is all provided for them inward a pencil case. 'Oh. In that instance exactly brand certain you lot select your calculator. It has to live on the ane you've been using for the in conclusion v years - the ane you lot know how to use'. 'Nah lady friend - they furnish calculators too, we'll exactly work whatever they give us'. 

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This lesson got me thinking. I receive got a feeling that many schools don't practise plenty amongst calculators. In every schoolhouse where I've taught Year 7 nosotros haven't used calculators at all for the entire twelvemonth - this is such a shame when at that topographic point are many opportunities to explore together with brand sense of numbers inward Year 7 using calculators. Also, although nosotros demand to construct fluency amongst arithmetics inward Year 7, I am convinced nosotros should allow calculators for topics such every bit angles. It makes sense, together with pupils similar it.

Pupils demand to live on explicitly shown how to work their calculators throughout secondary schoolhouse - I recollect that teachers ofttimes assume pupils already know the head keys. We demand to deport inward heed that much of it may non live on obvious to a novice.

If you lot currently learn Year vi or Year 7 together with then you lot mightiness desire your bird to receive got constituent inward MEI's Calculator Crunch inward June. In this challenge at that topographic point volition live on nine daily problems to solve using a calculator. MEI volition live on providing 2 lesson plans too.

There are lots of fun 'know your calculator' activities inward my resources library. These are great, but nosotros must brand certain that information processor work is embedded throughout the topics nosotros learn too, non exactly covered separately. I'm certain that some schools already practise this actually well.

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Note that the information processor pictures inward this post are from my 'peng' Casio fx-83GTX which was kindly given to me past times Science Studio (and engraved amongst Mrs Morgan, which I love!). The buttons I've featured are inward the same seat on the Casio fx-83GT together with fx-85GT (the ubiquitous calculators inward the electrical current Year xi cohort).

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