At the heart of the following approach to teaching calculations in chemistry is the belief that setting all working out clearly and systematically leads to a greater chance of success (we’ll come to the evidence supporting this in a minute). This is not an original thought – my teachers said something similar to me when I was at school way back when. The emphasis here, however, tends to be on what the student should do. It may be implicit that this advice also applies to the teacher, but, as we know from mark schemes, implicit doesn’t always cut the mustard. So, let’s be explicit instead.
Distributed Cognition
In the last few years, my appreciation for Cognitive Load Theory has increased massively, in part thanks to NSW Government’s fantastic resources and Oliver Lovell’s excellent Sweller’s Cognitive Load Theory in Action. Similarly, following Oliver Caviglioli and David Rodger-Goodwin on Twitter has opened my eyes to the concept of External Memory. This has lead me to doing some investigating of my own.
In the mid to late 80s, and in part prompted by the publication of the English translation of Lev Vygotsky’s Mind in Society, Edwin Hutchins began considering seriously the idea of distributed cognition (see Rogers 1997), which highlighted the roles the body, technology, society, culture and time can play in cognitive processes (Hutchins 2000). Hutchins writes specifically of three kinds of distributed cognition, the most relevant to us being when ‘the operation of the cognitive system involves coordination between internal and external (material or environmental) structure’ (ibid, p1).
Not long after Hutchens started working on distributed cognition in earnest, Douglas Norman wrote Things That Make Us Smarter, which considered the ‘cognitive artefacts that allow human beings to overcome the limitations of human memory and conscious reasoning’ (Norman 2018). Unsurprisingly, these included writing [as a side note, it was Norman who coined the term ‘user experience’].
Towards the end of the 90s, Andy Clark and David Chalmers introduced the concept of ‘The Extended Mind’ into philosophy. Like Hutchins, they argued that the environment (anything beyond the boundary of ‘skin and skull’) played an active role in cognitive processes.
The work of Hutchins, Norman and others eventually led to research examining areas such as ‘distributed working memory resources during problem-solving’ (Cary & Carlsen 2001) and ‘the relations between external representations and working memory’ (Zhang & Wang 2009) with the latter testing the hypothesis that ‘external representations help problem-solving by augmenting the limited capacity-working memory’.
Norman co-created the Nielsen Norman Group, a user experience research and consulting firm. In 2018, they published an article by Raluca Budiu on ‘Working Memory and External Memory’ that argued that ‘when tasks are too hard, users should be able to offload some of the working-memory burden to user-interface features that can serve as an external memory’. While the article focuses on websites and user interfaces, its guiding principles offer some useful insights concerning student learning, particularly regarding using ‘external memory’ to reduce the load on our working memory. To quote the article at length:
‘Definition: Human working memory can be conceptualized as a buffer or scratchpad in which the mind deposits information relevant to the current task.
The working-memory buffer has limited capacity — think of it as an egg carton with a small number of slots. If a task requires too much information to be kept in the working memory, we need to free up some of the occupied slots to make space for that information. What is removed from working memory can, in fact, still be needed to finish the task, and we may end up working harder to recover that data; as a result, we may take longer to do the task or make mistakes. In our addition example, we may end up dumping out a carry or digit from one of the original numbers, and produce the wrong answer…
…It’s easy to say: “limit the working-memory burden”, but certain tasks are naturally more complex than others. How can we help users get around their working-memory limitations? In our original addition example, we cannot change the task; addition is what it is. But we can make it easier — by providing pen and paper, so people can write down the numbers and the intermediate products in the task without having to store them in the working memory. The paper acts as a physical scratchpad, a “fake” working memory.
Definition: External memory refers to any tool or UI feature that allows users to explicitly save and access information needed during a task.’
I think distributed cognition provides many fruitful opportunities for students, including guidance on that magical, almost mythical, beast ‘exam technique’. But the focus here is on what it means to my practice when teaching reacting mass calculations.
Teaching GCSE quantitative chemistry?
I’ll start by saying that I’ve laid out my work as follows for a number of years, i.e., before I was aware of the research above. However, my reading and switching from a mixture of PowerPoint and whiteboard to first a visualiser and iPad, and supplementing these with mini-whiteboards (MWBs), has refined my practice considerably. Using a visualiser/iPad has helped slow my teaching down and placed greater emphasis on my talking through why I’m doing what I’m doing. In other words, modelling cognitive and metacognitive strategies (Kistner et al. 2010 and Ellis et al. 2013).
Mapping our progress through a significant chunk of quantitative chemistry in
Combined Science.
Time is initially spent on relative atomic mass and relative formula mass with lots of worked examples and student practice using MWBs followed by worksheets. The concept of the mole and Avodagro’s number comes next followed by the relationship between mass, Mr and moles. Something I stress is the unit of Mr: g/mol as we have one of our calculation equations right there – Mr = mass/moles. Again, more MWB work is followed by worksheets.
Next comes molar ratios, which we spend a reasonable amount of time practising. We’re now at a point to combine nearly all our learning in reacting masses calculation. This is how I write out and talk through EVERY reacting mass calculation I do. We’ll take the following question as an example.
- I write the reaction equation out even if it’s given in the question so that I have space across the page.
- I write the molar ratios above the reaction, emphasising the fact that they’re ratios.
- I write mass, Mr, moles, Mr and mass down the side.
- I write the mass of what we’re given underneath its formula and a ‘?’ underneath what we’re trying to find out. This includes highlighting the information in the question that matches these markings (the colour deliberately matches too).
- I write the Mr of the substance we know the mass of and then work out moles, writing divide and equals in the blue list. By far the most common mistake students make is to multiply the Mr by the molar ratio at this point. By talking through what I’m doing, by getting them to do parts of the full calculation on their MWBs later followed by class work, I hope to weed this problem out (I never do it completely – some will return to type at a later date).
- Now we draw an arrow from the moles of what we know to what we’re trying to determine (the purpose of our ? is (hopefully) now made clear) and annotate the two relevant molar ratios from which we determine the number of moles of the unknown.
- We now write the Mr of the unknown, taking care to IGNORE its molar ratio as we’ve already considered this before working out the final mass.
- Our mathematical journey to the final answer is clearly laid out and visible for further inspection (e.g. checking).
I model a number of these calculations. After a short while, students ‘help’ me through each step using their MWBs before practising some on their own while still able to discuss their thinking with their partner. Using MWBs at this stage means their work is still clearly visible to me as I walk around the room, making it easier to monitor, and help with, their difficulties. Finally, we consolidate our learning with worksheets. This doesn’t all happen in one lesson.
While we’re working through this area of the course, nearly students will adopt a literal version of my approach. Those that really begin to master things will adapt it. When it comes to the exams, their work may ‘look’ significantly different. That’s absolutely fine as long as their accuracy levels are high. However, some will take a different tack too early and start to make mistakes quite quickly. Having a clear and visible method like the one described allows us to get back on course quicker than might otherwise have been the case.
To finish, this approach provides a wonderful opportunity to demonstrate the conservation of mass in a reaction mathematically.
Afterthoughts
I’m constantly reflecting on my teaching practice, and I know I need to improve distributed practice of the above as it’s easy for students to go from secure to floundering very quickly. But I am, at least, usually able to remind them that they were able to do it and that makes moving forward much easier.
Finally, I employ the general approach described above all the way to y13 and redox titrations…
… but I’ll leave discussing further that to another time.
Photo by Terry Vlisidis on Unsplash
