This is part 2 in the AFL in Science symposium. Read the rest of the series:
Part 1: Introduction by Adam Boxer
Part 3: Do they really get it, or are they just giving me the correct answer? by Niki Kaiser
Part 4: Validity of formative assessment by Deep Ghataura
Part 5: Measuring and improving the quality of science writing in schools by Ben Rogers
Part 6: Planning for effective assessment in science by Matt Perks
Since I read Christine Counsell’s blog on the need for subject-specific approaches I have been thinking about the nature of “school science knowledge” (SSK). I think it’s important to call it “school science knowledge” as there are problems in taking science as practised by working scientists and transferring it straight into the classroom, and I think it’s possible that similar problems might exist in doing the same with its epistemology.
I’ve had many conversations like the one Adam has described with his SLT member. Or rather, conversations that started off similar, but instead of challenging the comments I’ve said “ok then”, and then gone off and performed what I now view as contortions, corruptions of my teaching of SSK, in order to please observers, and to do a good job because I’ve naively thought they knew what they were talking about. I’ve written up lists of ostensibly hierarchical success criteria so that pupils know how to improve their work. I’ve given pupils frequent extended writing tasks so that they will have something meaningful to improve on. I’ve created lessons around a hinge question so as to make sure I’ve got a hinge question in my lesson.
If I’m going to challenge my seniors, I like to be prepared. In this essay I have attempted to begin to describe SSK, in order that I, and others, may successfully challenge blithe exhortations to do something in our teaching that is just not appropriate. I’m indebted to many writers and tweeters, acknowledged at the end of the article.
Four characteristics of SSK
- SSK has a vertical, explanatory structure
At the nodes are propositions:
- Principles or descriptions of explanatory entities. “F=ma”; “temperature is a measure of the average kinetic energy of particles in a material”
- Elaborations: specific but general implications of a principle such as “An object under an accelerating force in a resistive medium will reach a terminal velocity”
- Exemplar phenomena such as “the force on a passenger during a crash is high because the time for deceleration to 0 is short”, or the graph showing the motion of an object reaching terminal velocity.
- Procedures, e.g. for calculating the force during a crash. Procedures can be a set of steps but are often best represented by exemplars or “worked examples”.
The links are explanatory relations. Certain fundamental principles and entities explain many exemplar phenomena and procedures.
The propositions are very numerous, I would suggest perhaps more numerous than in many other subjects.
Neither the propositions, nor their relations, are the subject of debate. They are accepted as objective and true.
What are the implications of this for our teaching? I suggest a few. We should carefully consider what the “knowledge-maps” are like for SSK, and teach with explicit regard to them. Several writers suggest sharing the organisation of this knowledge with pupils. We should explicitly teach, and assess for learning, and respond to correct, understanding of the relationships as well as the propositions. I do not make the assertion that teaching should always begin with the fundamental principles, as there are problems with this model.
- SSK contains declarative elements
Both the propositions and the relationships between them have significant declarative elements.
Thus we wish to teach pupils so they know-that “force = mass x acceleration” and to know-that “this is ultimately the reason for crumple zones in cars.”
2.i. The declarative knowledge is often counter-intuitive
In SSK, pupils are not just learning new explanations for observable phenomena. In order to become an expert in SSK one must successfully overcome many misconceptions, many of them biologically primary. For example, the misconception that a force is needed to keep an object moving is very deeply held and is probably evolutionary in origin as humans did not evolve in a frictionless environment.
What are the implications for our teaching? First, there needs to be a great deal more research on misconceptions in SSK and Geary’s work, as Adam Boxer has called for. In the meantime, I believe that scripted explanations and being explicit about what the common misconceptions are, and why they might be held, would be a good start. Mary Whitehouse at the University of York has done important work on diagnostic questions in school science. R. Driver et al “Making Sense of Secondary Science” is a great resource for finding misconceptions in order to make them explicit. I hope one day to compile a bank of demonstrations to help overcome misconceptions, such as weighing an inflated balloon to prove that air has mass.
2.ii. The declarative knowledge both comprises and depends on exemplars
While there are an infinite number of phenomena that can be explained using the fundamental principles and entities, a more limited number are included in SSK, as exemplars. Exemplars are often an idealised situation so that the illustration is optimal. Thus we are told we can “ignore air resistance”, for example. Some exemplars are demonstrations or experiments, such as the reactions of the alkali metals with water. Exemplars perform several functions:
- They may be considered to be worth knowing in their own right
- They may be part of the “canon” of SSK – “You can’t NOT do the alkali metals…”
- They may offer a concrete illustration of an abstract principle, allowing pupils to build their schema around an abstract principle
- They may contain certain features that other inferences from a principle share, and thus facilitate pupils’ recognising underlying features in future problems.
2.iii. The declarative knowledge comprises a vast number of possible inferences
Inferences are manifestations of a principle. Exemplars are in the class of inferences but they are a subset since they are chosen for one or more of the values listed above. A non-exemplary inference might just be more obscure, or a less idealised situation. Examiners are fond of these non-exemplary inferences as they are believed to test true understanding of a principle or principles rather than slavish regurgitation of an exemplar. Recognising that a principle should apply in a certain situation is known as “recognising underlying structures” and is what we have called “apply to new situations” in the past. The possible inferences that could attend a knowledge-map are perhaps infinite or at least very numerous in some cases. Below is an example of a non-exemplary inference in an exam question from the new AQA Trilogy specimen exam paper: 
The question is intended to test recognition of terminal velocity. Pupils are likely to have studied an exemplar with a falling object but not with a swimmer, at least until such a question is released, after which it will most likely be studied as a secondary exemplar.
What are the implications for school science? Well, we should recognise our exemplars and treat them with appropriate veneration and reservation. Exemplars are part of the institution of science education and for good reason – but wherever we can we should seek to widen pupil knowledge using other, more obscure or more messy, inferences as secondary exemplars. We should provide plenty of opportunities for our pupils to practise thinking with the declarative knowledge, and feedback on the tasks so that pupils can learn the correct ways of thinking with the knowledge.
- A large part of SSK is procedural, usually formal-procedural
In SSK we have a lot of problem-solving, through calculations, drawing diagrams, and a few other processes and algorithms such as punnet squares. I’ve used the term formal-procedural to indicate that these procedures usually have only one or a small number of correct ways to be carried out. If you ask me to write an essay on X or draw a picture of Y, there are several ways I could go about those tasks that would bring me success. However, if you ask me to solve this problem, again from the new AQA Trilogy specimen paper:
then there is really only one way to do it successfully.
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. Some philosophers have claimed that procedural knowledge is simply a subset of declarative knowledge, but I agree with Winch that procedural knowledge is a combination of declarative and tacit knowledge, which I shall return to in later posts.
What are the implications for school science? We should seek to make every step in a procedure explicit and teach it. We should give plenty of opportunities for practice so that procedures can become automated in order to free up working memory. We should give feedback on whether each step is being performed correctly so that pupils can learn the correct procedure. This feedback must, by definition, be unique to the particular procedure in question and cannot be generalised.
- SSK offers definitive answers to certain sorts of questions
One of the most damaging things to happen to school science is the attempt to foist upon it inappropriate styles of questions, activities, and feedback models. To avoid this we must ask, what types of question are appropriate and valuable, and what types of answers and therefore feedback should we seek and give?
With SSK, we seek to explain, describe, predict, calculate, and demonstrate.
The answers to questions in science are almost always wrong or right. Thus rubrics are seldom appropriate, whereas model answers are.
In this regard SSK is similar to mathematics, but there is an important difference to note. In mathematics one can take almost any topic and write questions of increasing levels of difficulty, to a great many levels. In science this is only sometimes possible, and in many areas there are only a few levels of difficulty available without drawing other knowledge in. Thus “progress” must often happen through accumulation of more declarative knowledge, or correcting a misconception, rather than an ascent through a hierarchy of difficulty.
We can therefore argue that when “assessing SSK for learning” we are looking at and giving feedback on:
- Pupils’ representation of correct conceptions/declarative knowledge
- Pupils’ knowledge of specific exemplars
- Pupils’ ability to make valid inferences from declarative knowledge and exemplars to related areas
- Pupils’ ability to relate different items of declarative knowledge to each other
- Pupils’ memory of the correct procedure to be followed
- Pupils’ application of the correct procedure
AfL in SSK must be geared to the above but it must be specifically tailored to the exact pupil failing. The above cannot be generalised when looking at individual performance. If a pupil is failing to “relate different items of declarative knowledge” when discussing magnetism, their feedback cannot be “improve relation of different items of declarative knowledge” in a general sense. We must explicitly point out which knowledge is missing in this case so as to develop student understanding of this particular area. Assessment, and feedback, must always be about specific knowledge. Only when we place knowledge at the centre of our practice can we reap the full benefit of AfL in Science.
Chi, M., Feltovic, P., Glaser, R., “Categorisation and Representation of Physics Problems by Experts and Novices” (2010), Cognitive Science
Coffey J., Hammer, D., Levin, D., and Grant, T.,: “The Missing Disciplinary Substance of Formative Assessment” (2011), Journal of Research in Science Teaching
Geary, D.: “Reflections of Evolution and Culture in Children’s Cognition” (1995), American Psychologist
Reif, F.: “Applying Cognitive Science to Education” (2008), London: MIT Press
Wheelahan, L.: “Why Knowledge Matters in Curriculum” (2010), London: Routledge
Winch, C.: “Curriculum Design and Epistemic Ascent” (2013), Journal of Philosophy of Education
And conversations with the following people on Twitter:
Adam Boxer (@adamboxer1)
Christine Counsell (@Counsell_C)
Tim van der Zee (Research_Tim)
Deep Ghataura (@DSGhataura)
Gareth Sturdy (@stickyphysics)
Niki Kaiser (@chemDrK)
 Hierarchical in difficulty
 Wheelahan (2010) ch.2
 Reif (2008) p.145
 The specification and arrangement of this map could well be debated and I do not present it as definitive, but rather as illustrative.
 Although there may be incommensurability between the subjects. What counts as a proposition in languages, for example? Does each word of vocabulary?
 At the frontiers of PSK? they are of course the subject of debate and change, but not in SSK except in a few rare instances.
 Reif (2008) p.160
 Coffey et al (2011) p.21
 Winch (2013) p.139
 Geary ((1995)
 See Chi et al (2010)
 Though a perfectly good answer could be given referring to respiration.
 This is one reason teachers pounce so on past paper questions. They act as exemplars to help facilitate recognising underlying features in future questions.