This blog is a long time coming as I’ve been using this method for ages, and have mentioned it in my previous blog about SLOP (Shed Loads Of Practice) calculation sheets. I’ve been trying to get my students to present calculations in a way that truly shows how they got to an answer. Initially, this was just out of habit on my part: “I always show my working so my students should too.” But I realised that students didn’t really know what ‘show your working’ really entailed. So I started to use a simple mnemonic to outline what steps students should include to ‘show their working’ and I explicitly teach each of these steps over the course of the year and expect their calculations to be set out in this way. The basic outline is this:
I always prefer a mnemonic to have relevance to the topic, so I will frequently say “You need to set calculations out like this EVERY time”.
Students begin by writing out the relevant equation for their problem. At this stage, you can decide whether or not you want your students to rearrange before substituting (Matthew Benyohai has an excellent blog on the debate around this). AQA seemingly prefer the practice of substitution prior to rearranging (which is not my personal preference), but this is what I get my students to do.
My students then write out the values that they have in the question, along with their units, writing them all in the form SYMBOL = VALUE UNITS. At this stage, the units should be converted if necessary (and we’d do lots of practice of this throughout the year).
The values then get entered into the correct position within the equation. At this stage, if necessary, rearrangement with the substituted numbers would happen as is the AQA preference. Again, I’d explicitly teach this and do lots of practice.
That would lead us to our result. I’ve chosen to have the (Y)units as a separate step to emphasise its importance. One of my classes prefer this step to be called ‘Your units’ as they didn’t appreciate spelling units with a Y.
I then use this method in all worked and faded examples:
As I see it, the benefits are: a reduction in extraneous cognitive load (by automating the procedural knowledge of how to perform a calculation), a chance of gaining extra marks by being clear in your answer, a chance (as a teacher) to see exactly where students are slipping up.
Issues I’ve found are: students writing an “=” sign after each of the letters of EVERY (creating confusion about what the equation is), the initial additional cognitive load in understanding the system and why we do it, the system being a little too rigid when it comes to calculations with multiple steps.
I know a lot of people have already started using it, so I’d love to hear how they’re getting on. Below is an example I had to hand of a student in a foundation tier class using the system (after just a few lessons of having seen it). I wouldn’t enforce them writing out the full words for EVERY but this was useful for these students to begin with. Equally, over time, the support of writing the mnemonic can be removed too.
Let me know if you have any improvements or comments, I’m on twitter @TChillimamp