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This article by Dr Niki Kaiser was originally posted on the Kaye Chem Notebook. I wanted to share it with you in the context of ‘future-ready education’. It is no longer enough to teach knowledge, even if that is sufficient to pass an exam. To succeed in the future, our students need a deep and intuitive understanding of their subject. Few writers address this with either the clarity or the practical teaching background Niki does.

One of the topics I most like to teach in chemistry is ionization energies: explaining their relative magnitudes, and outlining the consequent evidence for a shell structure in atoms. Students must draw on a range of fundamental ideas to master the new concepts that I introduce to them and, although they tend to struggle at first, they eventually “get it”, and the joy that they feel is tangible. I treasure these moments.

I’ve always enjoyed teaching Chemistry topics that require a solid conceptual understanding. I enjoy the planning process: thinking through how I’m going to explain things, constructing questions that will tease out the information I need. And there is huge potential for observing “lightbulb moments”.

What’s a concept?

I always thought I understood what a concept was: it’s something you understand, and once you’ve understood it, you can’t “un-understand” it. And how do you know you’ve understood it? Because you can apply it within any context, familiar or not.

So I was pretty clear about the role of a teacher: to support pupils in breaking through that barrier in understanding. Subsequent, higher-level ideas and application would therefore almost look after themselves, because pupils now understood the underlying concepts, and they wouldn’t forget them. So:

• A concept is something you understand, and once you’ve understood it, you can apply this understanding to unfamiliar contexts

Threshold Concepts: portals to a point of no return?

I was therefore really drawn to the idea of Threshold Concepts when I first read about them. They have been described as “portals to a transformed way of thinking”. They’re troublesome, but once mastered they are “probably irreversible”.

I see the mastery of Threshold Concepts as akin to lightbulb moments. We’ve all had the experience of struggling to get our heads around a tricky idea, when suddenly it “clicks”, and a whole range of linked ideas that we had previously been struggling with also fall into place.

For example, one of the first Threshold Concepts I identified was the idea that particles in a liquid are held together by forces of attraction, and that these must be overcome before a liquid can evaporate. You can’t understand ideas about changes of state or variation in Boiling Temperatures without an appreciation of this core idea.

Talanquer (2014) distinguishes between Threshold Concepts and “Big Ideas.

Whilst Big Ideas generate answers to questions or help you to make predictions in a range of contexts, they are not transformative. Threshold Concepts are distinctive because they transform your way of thinking, and induce profound conceptual change.

But they are challenging, because you first need to dismantle your existing ideas and build new ones. In fact, he argues that you don’t “cross” a Conceptual Threshold but instead you build it, without knowing when you’ll actually reach the summit! So:

• Threshold Concepts are troublesome ideas that act as portals to a new or transformed way of thinking.

Permanance

It can be tricky to identify truly transformative threshold concepts because, as experts, we are likely to have forgotten our naive understanding (and misunderstanding) of the world around us. But misconceptions literature can be a good place to start.

I am not going to discuss theories for conceptual change here, but Adam Boxer’s blog has a good summary of the research in this area, and it lead me to some research by Shtulman (2012), who argues that misconceptions are suppressed, rather than erased. For example, as Chemist, I can tell you that air contains matter but deep down, I probably believe nothing is there (which is more intuitive, and which I believed for a long time, before being corrected in my Science lessons). In fact, those naive ideas that we’ve held longest, and which we gained earlier, appear to be harder to replace than domains of knowledge encountered later in life.

This is one reason I started to look at spaced practice for reviewing/ retrieval of concepts once I’d taught them. I found pupils needed reminding of concepts they’d previously (apparently) understood. This liminal path to conceptual understanding, with apparent steps backwards as well as forwards, is described by Glynis Cousin:

The idea that learners enter into a liminal state in their attempts to grasp certain concepts in their subjects presents a powerful way of remembering that learning is both affective and cognitive and that it involves identity shifts which can entail troublesome, unsafe journeys. Often students construct their own conditions of safety through the practice of mimicry.

So:

• Threshold Concepts are, by definition, transformative. But conceptual change may not be permanent and, in many cases, may be preceded by mimicry rather than true understanding.   

Mimicry

As I’ve read more about Threshold Concepts, misconceptions and conceptual understanding,  and as I’ve observed responses from my own classes, I have been persuaded that mimicry often precedes mastery of concepts. Pupils might give the correct answers to conceptual questions without really knowing why their answers are right, and sometimes this is simply because the path to mastery can be challenging, so pupils can seek “refuge” in mimicry.

I believe that this liminal state can be valuable, as long as we support pupils to “let go” of their naive ideas and the perceived security of mimicry. We can give pupils time for tricky concepts to settle if we revisit them, and re-examine the underlying ideas from different angles.

The thing is, as a firm believer in the use of formative assessment to inform feedback and planning, but this makes me question what exactly it is I should be assessing, and how I should do it. How do I know if students have truly understood a particular concept, and they’re not just well-practised in giving the correct answer? And even if I am sure they’ve properly mastered a particular concept, how can I be sure that this shift in their understanding is permanent?

This is why thoughtful assessment is so important. Students might give you the correct answer to a conceptual question, but are they also able to explain their reasoning? Or had they just learned (or guessed) the answer? If you ask the question in a different way, are they secure enough in their understanding to still answer it correctly? If the langauge you use is more straightforward or more complex? If you expect them to interpret a diagram to uncover conceptual understanding? I am now careful never to assume pupils understand something just because they’ve given me the “correct” answer to a question! So:

• Mimicry can precede mastery of a concept, so we should support pupils to review and question their understanding. We shouldn’t assume that correct answers to a particular question reflects true, deep understanding. 

Transfer

At the start of this post, I stated that a concept is something you understand, and once you’ve understood it, you can apply this understanding to unfamiliar contexts. However, I have encountered convincing arguments that this might not be quite so straightforward either. In her post, Rosalind reminds us how, as soon as exemplar questions from an exam board are published, teachers will download them to give to pupils. Teachers and pupils will practise past exam questions over and over again because they believe (probably rightly) that it will improve their mark in the final exam. This is perhaps recognition (albeit unconscious) that, although it is possible to understand something in one context and then apply it to another (“transfer”), it’s actually very difficult to do this, and few can do it successfully without scaffolding and practice.

Without getting any deeper into the transfer debate, I prefer to take a pragmatic approach as a teacher: it’s easier to apply concepts to new situations if you practice applying them to new situations as many times as possible! So:

• Transfer is tricky and it needs practice. It’s best if you practise applying concepts to a range of contexts.                   

Procedural Knowledge

Rosalind’s blog also helped me to clarify my thoughts with her description of procedural knowledge. I used to think that once you’d gained a good understanding of something, this would automatically enable you to apply it to a range of contexts. But I now believe pupils need support to apply even firm understanding to novel contexts.                

For example, to work out the ionic formula of a particular compound, you need to work out the charge on the ions that make up the compound, and then use these charges to determine the formula. Easy and straightforward, right?

Well yes- it is for me. And by the time I ask my pupils to do this, they have all the knowledge and skills required to complete this relatively simple task. But many of them flounder for a while if I don’t lead them through the process first. As Rosalind says

Procedural knowledge in SSK often has many steps, many of them often invisible to us as teachers as we have automated them as we have become experts…. I agree with Winch that procedural knowledge is a combination of declarative and tacit knowledge…

And my ionic formula example is a case in point. When I said “you need to work out the charge on the ions that make up the compound, then use these charges to determine the formula” my actual thought process is more complex, as explained in the next section. So:

• Pupils need to make connections between related variables, but this requires a degree of tacit knowledge, which might not be immediately evident to pupils.

The complexity of straightforward procedures

Let’s take magnesium sulphate as an example. For the first step in my simple process “you need to work out the charge on the ions that make up the compound” my thinking would be something like:

• There are two ions that I need to take into account
• One of those is positive, and one negative
• I know that magnesium is an element, and it’s a metal, so it’s likely to be the positive one. Which group is it in? Ah yes, group 2. So it’s mostly like to lose electrons and form a positive ion.
• Okay, so it loses 2 electrons. This means its ion will have a charge of +2. It’ll form Mg²⁺.
• Now, I know that sulphate is a compound ion that’s made up of sulphur and oxygen. It has a negative charge.
• I know the formula and charge for sulphate is SO₄^2-. I know this because I learned it off-by-heart when I was doing my GCSEs over 20 years ago, and it’s held up there in my brain alongside all the (latin) lyrics to Carmina Burana, which I was forced to learn at the age of 8 for a performance at the Albert Hall. They are still there now!

Even in my more elaborate description, each step is fairly straightforward, but some are tacit and others are now completely automatic. This isn’t the case for the pupils I teach. They will have done all the individual processes associated with each step many times before we come to do this. Yet, in general, they don’t put them together easily.

If I had a whole lesson available to me just to help the class do this particular procedure, I might scaffold their thinking with skilful questioning, to work out the method themselves. But again, I am a pragmatist, and I have limited time, so I go for efficiency. This process is a pretty minor step that will help pave the way to more interesting and difficult ideas, and I actually don’t want to dwell too long on it. So I demonstrate how to do this with a series of “fading” worked examples, and talk through my reasoning as I do it. For example, it’s obvious to me that Na will form a positive ion and Cl will form a negative ion without even thinking about it, but I make sure I think aloud about why this happens. So:

• You need to identify your own tacit assumptions in procedures that you teach, and teach them explicitly.

Language and Automaticity

So even something that is relatively “straightforward” (like the determination of an ionic formula) involves

• specific scientific language
• conceptual understanding and application of that concept
• some maths and procedural knowledge
• certain key pieces of information that are committed to memory, but can be easily retrieved.

We can think of memory as having two components: working memory (WM) and longterm memory (LTM). WM can only hold a small amount of information at any time (Cowan, 2010) and we use both WM and LTM to solve problems in Science. Memorisation, familiarity with key langauge and automation of key procedures can free up WM so students are able to carry out more complex processing (Hartman, 2015), so we need to employ a range of strategies to free up WM and aid conceptual understanding. This might include making tacit ideas explicit, increasing familiarity with key language, and helping pupils to develop automaticity in core processes. So:

• Familiarity with key language, alongside automation of certain processes, helps pupils to access more complex ideas.

And… Threshold Concepts?

The problem with procedures, such as determining an ionic formula, is that you can concentrate so much on the procedure that you forget the underlying concepts. Last year, I determined the most pervasive misconceptions (and potential Threshold Concepts) for this topic with my groups, and I now take these into account, even when I teach something like this that is almost “recipe-like”.

So before I begin any worked examples for determining formulae, I remind the class of the underlying, tricky concepts we’d encountered in previous lessons. I re-state that the ionic formula of a compound is just the ratio of the millions of oppositely charge ions within it. I also emphasise that “ionic bonding” outlines a process where atoms lose and gain electrons to form charged ions, and are then attracted to any oppositely charged particle that is close enough, forming a 3-D lattice, not an “ionic molecule“.

This means that, once we’ve mastered this procedure, it will still be grounded in the models and concepts we’ve already encountered, and my pupils will be able to make connections between ideas, concepts and procedures more easily. So:

• Don’t get lost in the “recipe-like” nature of procedural examples and forget the underlying concepts.

Assessment

If what students learn were predictable, there would be no need for assessment (William, 2010). In this post, I’ve stated that:

• A concept is something you understand, and once you’re understood it, you can apply this understanding to unfamiliar contexts.
• Threshold Concepts are troublesome ideas that act as portals to a new or transformed way of thinking.
• Threshold Concepts are, by definition, transformative. But conceptual change may not be permanent, and in any case may be preceded by mimicry rather than true understanding.
• Mimicry can precede mastery of a concept, but so we should support pupils to review and question their understanding. This raises the question of how we assess true understanding vs surface mimicry of the correct answers to questions.
• Transfer is tricky and it needs practice. It’s best if you practise applying concepts to a range of contexts.    
• Pupils need to make connections between related variables, but this requires a degree of tacit knowledge, which might not be immediately evident to pupils.
• You need to identify your own tacit assumptions in procedures that you teach, and teach them explicitly.
• Familiarity with key language, alongside automation of certain processes, helps pupils to access more complex ideas.
• Don’t get lost in the “recipe-like” nature of procedural examples and forget the underlying concepts.

But the impact of formative assessment is strongly dependent on the quality of the questions asked, and how this is embedded into practice (William 2011) and, as I said before, I have begun to question what exactly I should be assessing, and how I should be doing it. How do I know if students have truly understood a particular concept, and they’re not just well-practised in giving the correct answer? And even if I am sure they’ve properly mastered a particular concept, how can I be sure that this shift in their understanding is permanent?

The central business of teaching is about creating changes in the minds of students – in what students know and believe and how they think.  The ability to create change means that, in some way, teachers need to be constantly reading the minds of students.  Are their minds focused?  What are they understanding, or not understanding?  What do they really think?…unless you know what has changed in the minds, skills and attitudes of your students, you cannot really know how effective you have been (Nuthall, 2007)

So when I teach a particular topic, I try to find out what the associated misconceptions are, identify what the “sticking points” (or threshold concepts) might be, and use these to shape my teaching from start. I address them explicitly, and assess them specifically. I try to support pupils through liminal periods of uncertainty, encouraging patience and resilience, and helping them to view this lack of certainty as an important part of the learning process. I try to assess understanding in a number of different ways, using a range of questions with varied langauge and potential red herrings.

I also ask myself which procedures will need to be automatic, what key language will help pupils to access more complex understanding, and which aspects need to be memorized.

I’m still unsure whether shifts in conceptual understanding are permanent, and I don’t always know how to distinguish between mimicry and mastery. I also don’t know how important all of this is in the scheme of things…. However, I do think that “getting it” is different to “giving the correct answer”, and I will continue to drill down below the surface in any formative assessment I do.