Category Archives: Science

The p-prim path to enlightenment…?

The Duke of Wellington was once asked how he defeated Napoleon. He replied: “Napoleon’s plans were made of wire. Mine were made of little bits of string.”

In other words, Napoleon crafted his plans so thay they had a steely, sinewy strength that carried them to completion. Wellington conceded that his plans were more ramshackle, hand-to-mouth affairs. The difference was that if one of of Napoleon’s schemes broke or miscarried, it proved impossible to repair. When Wellington’s plans went awry, he would merely knot two loose bits of string together and carry on regardless.

I believe Andrea diSessa (1988) would argue that much of our knowledge, certainly emergent knowledge, is in the form of “little bits of string” rather than being organised efficiently into grand, coherent schemas.

For example, every human being has a set of conceptions about how the material world works that can be called intuitive physics. If a ball is thrown up in the air, most people can make an accurate prediction about what happens next. But what is the best description of the way in which intuitive physics is organised?

diSessa identifies two possibilities:

The first is an example of what I call “theory theories” and holds that it is productive to think of spontaneously acquired knowledge about the physical world as a theory of roughly the same quality, though differing in content from Newtonian or other theories of the mechanical world [ . . .]

My own view is that . . . intuitive physics is a fragmented collection of ideas, loosely connected and reinforcing, having none of the commitment or systematicity that one attributes to theories.


diSessa calls these fragmented ideas phenomenological primitives, or p-prims for short.

David Hammer (1996) expands on diSessa’s ideas by considering how students explain the Earth’s seasons.

Many students wrongly assume that the Earth is closer to the Sun during summer. Hammer argues that they are relying, not on a misconception about how the elliptical nature of the Earth’s orbit affects the seasons, but rather on a p-prim that closer = stronger.

The p-prims perspective does not attribute a knowledge structure concerning closeness of the earth and sun; it attributes a knowledge structure concerning proximity and intensity, Moreover, the p-prim closer means stronger is not incorrect.


diSessa and Hammer both argue that a misconceptions perspective assumes the existence of a stable cognitive structure where, in fact, there is none. Students may not have thought about the issue previously, and are in the process of framing thoughts and concepts in response to a question or problem. In short, p-prims may well be a better description of evanescent, emergent knowledge.

Hammer points out that the difference between the two perspectives has practical relevance to instruction. Closer means stronger is a p-prim that is correct in a wide range of contexts and is not one we should wish to eliminate.

The art of teaching therefore becomes one of refining rather than replacing students’ ideas. We need to work with students’ existing ideas and knowledge — piecemeal, inarticulate and applied-in-the-wrong-context as they may be.

Let’s get busy with those little bits of conceptual string. After all, what else have we got to work with?



diSessa, A. (1988). “Knowledge in Pieces”. In Forman, G. and Pufall, P., eds, Constructivism in the Computer Age, New Jersey: Lawrence Erlbaum Publishers

Hammer, D. (1996). “Misconceptions or p-prims” J. Learn Sci 5 97


Filed under Education, Philosophy, Physics, Science

Learning Is For The Birds

​Well versed in the expanses
that stretch from earth to stars,
we get lost in the space
from earth up to our skull.

Wislawa Szymborska, To My Friends

What do we mean by learning? To tell the truth, even as a teacher of twenty-five years experience, I am not sure. 

Professor Robert Coe has suggested that learning happens when people have to think hard. In a similar vein, Daniel Willingham contends that knowledge is the residue of thought. Siegfried Engelmann proposes that learning is the capacity to generalise to new examples from previous examples. I have also heard learning defined as a change in the long term memory.

One thing is certain, learning involves some sort of change in the learner’s brain. But what is acknowledged less often is that it doesn’t just happen in human brains.

Contrary to standard social science assumptions, learning is not some pinnacle of evolution attained only recently by humans. All but the simplest animals learn . . . [And some animals execute] complicated sequences of arithmetic, logic, and data storage and retrieval.
— Steven Pinker, How The Mind Works (1997), p.184

An example recounted by Pinker is that of some species of migratory birds that fly thousands of miles at night and use the constellations to find North. Humans do this too when we find the Pole Star.

But with birds it’s surely just instinct, right?

Wrong. This knowledge cannot be genetically “hardwired” into birds as it would soon become obsolete. Currently, a star known as Polaris just happens to be (nearly) directly above the Earth’s North Pole, so that as the Earth rotates on its axis, this star appears to stand still in the sky while the other stars travel on slow circular paths. But it was not always thus.

The Earth’s axis wobbles slowly over a period of twenty six thousand years. This effect is called the precession of the equinoxes. The North Star will change over time, and oftentimes there won’t be star bright enough to see with the naked eye at the North Celestial Pole for there to be “North Star” — just as currently there is no “South Star”.But there will be one in the future, at least temporarily, as the South Celestial Pole describes its slow precessional dance.

Over evolutionary time, a genetically hardwired instinct that pointed birds towards any current North Star or South Star would soon lead them astray in a mere few thousand years or so.

So what do the birds do?

[T]he birds have responded by evolving a special algorithm for learning where the celestial pole is in the night sky. It all happens while they are still in the nest and cannot fly. The nestlings gaze up at the night sky for hours, watching the slow rotation of the constellations. They find the point around which the stars appear to move, and record its position with respect to several nearby constellations. [p.186]

And so there we have it: the ability to learn confers an evolutionary advantage, amongst many others.


Filed under Philosophy, Science

Practicals Make Perfect

The physical environment provides continuous and usually unambiguous feedback to the learner who is trying to learn physical operations, but does not respond to the learning attempts for cognitive operations.

Engelmann, Siegfried; Carnine, Douglas. Theory of Instruction: Principles and Applications (Kindle Locations 1319-1320). NIFDI Press. Kindle Edition.

Into The Dustbin Of Pedagogy?

Helen Rogerson asks: “Should we bin [science] practicals?” and then answers emphatically: “No. We should get better at them.”

I wholeheartedly concur with her last statement, but must confess that I find it hard to articulate why I feel practical science is such a vital component of science education.

The research base in favour of practical science is not as clear cut as one would wish, as Helen points out in her blog.

New-kid-on-the-blog Adam Boxer has even written a series of blog posts with the provocative title “Teaching Practical Skills: Are We Wasting Our Time?“. He writes:

[T]his then raises the question of “what about the kids who are never going to see a pipette dropper again once they’ve left school?” I don’t have a great answer to that. Even though all knowledge is valuable, it comes with an opportunity cost. The time I spend inculcating knowledge of pipette droppers is time I am not spending consolidating knowledge of the conservation of matter or evolution or any other “Big Idea.” [ . . . ] But if you’ve thought about those things, and you and your department conclude that we do need to teach students how to use a balance or clamp stand or Bunsen burner, then there is no other way to do it – bring out the practical! Not because anyone told you to, but because it is the right thing for your students.

Broadly positive, yes. But am I alone in wishing for a firmer foundation on which to base the plaintive mewling of every single science department in the country, as they argue for a major (or growing) share of ever-shrinking resources?


The Wrong Rabbit Hole

Image result for rabbit hole

I think a more substantive case can indeed be made, but it may depend on the recognition that we, as a community of science teachers and education professionals, have gone down the wrong rabbit hole.

By that, I think that we have all drunk too deep of the “formal investigation” well, especially at KS3 and earlier. All too often, the hands-on practical aspect plays second- or even third- or fourth-fiddle to the abstract formalism of manipulating variables and the vacuous “evaluation” of data sets too small for sound statistical processing.


So, Which Is The Right Rabbit Hole?

The key to doing science practicals “better” is, I think, to see them as opportunities for students to get clear and unambiguous feedback about cognitive operations from the physical environment.

To build adequate communications, we design operations or routines that do what the physical operations do. The test of a routine’s adequacy is this: Can any observed outcome be totally explained in terms of the overt behaviours the learner produces? If the answer is “Yes,” the cognitive routine is designed so that adequate feedback is possible. To design the routine in this way, however, we must convert thinking into doing.

Engelmann, Siegfried; Carnine, Douglas. Theory of Instruction: Principles and Applications (Kindle Locations 1349-1352). NIFDI Press. Kindle Edition.


Angle of Incidence = Angle of Reflection: Take One

It’s a deceptively simple piece of science knowledge, isn’t it? Surely it’s more or less self-evident to most people…

How would you teach this? Many teachers (including me) would default to the following sequence as if on autopilot:

  1. Challenge students to identify the angle of incidence as the independent variable and the angle of reflection as the dependent variable.
  2. Explain what the “normal line” is and how all angles must be measured with reference to it.
  3. Get out the rayboxes and protractors. Students carry out the practical and record their results in a table.
  4. Students draw a graph of their results.
  5. All agree that the straight line graph produced provides definitive evidence that the angle of reflection always equals the angle of incidence, within the limits of experimental error.


I’m sure that practising science teachers will agree that Stage 5 is hopelessly optimistic at both KS3 and KS4 (and even at KS5, I’m sorry to say!). There will be groups who (a) cannot read a protractor; (b) have used the normal line as a reference for measuring one angle but the surface of the mirror as a reference for the other; and (c) every possible variation of the above.

The point, however, is that this procedure has not allowed clear and unambiguous feedback on a cognitive operation ( i = r) from the physical environment. In fact, in our attempt to be rigorous using the “formal-investigation-paradigm” we have diluted the feedback from the physical environment. I think that some of our current practice dilutes real-world feedback down to homeopathic levels.

Sadly, I believe that some students will be more rather than less confused after carrying out this practical.


Angle of Incidence = Angle of Reflection: Take Two

How might Engelmann handle this?

He suggests placing a small mirror on the wall and drawing a chalk circle on the ground as shown:


Theory of Instruction (Kindle Location 8686)

Initially, the mirror is covered. The challenge is to figure out where to stand in order to see the reflection of an object.


Note that the verification comes after the learner has carried out the steps. This point is important. The verification is a contingency, so that the verification functions in the same way that a successful outcome functions when the learner is engaged in a physical operation, such as throwing a ball at a target. Unless the routine places emphasis on the steps that lead to the verification, the routine will be weak. [ . . . ]

If the routine is designed so the learner must take certain steps and figure out the answer before receiving verification of the answer, the routine works like a physical operation. The outcome depends on the successful performance of certain steps.

Engelmann, Siegfried; Carnine, Douglas. Theory of Instruction: Principles and Applications (Kindle Locations 8699-8709). NIFDI Press. Kindle Edition.

Do I want to abandon all science investigations? Of course not: they have their place, especially for older students at GCSE and A-level.

But I would suggest that designing practical activities in such a way that more of them use the physical environment to provide clear and unambiguous feedback on cognitive ideas is a useful maxim for science teachers.

Of course, it is easier to say than to do. But it is something I intend to work on. I hope that some of my science teaching colleagues might be persuaded to do likewise.

A ten-million year program in which your planet Earth and its people formed the matrix of an organic computer. I gather that the mice did arrange for you humans to conduct some primitively staged experiments on them just to check how much you’d really learned, to give you the odd prod in the right direction, you know the sort of thing: suddenly running down the maze the wrong way; eating the wrong bit of cheese; or suddenly dropping dead of myxomatosis.

Douglas Adams, The Hitch-Hiker’s Guide To The Galaxy, Fit the Fourth


Filed under Direct Instruction, Education, Science, Siegfried Engelmann

Songs In The Key Of Energy

​The fact narrated must correspond to something in me to be credible or intelligible. We as we read must become Greeks, Romans, Turks, priest and king, martyr and executioner, must fasten these images to some reality in our secret experience, or we shall learn nothing rightly.

–Ralph Waldo Emerson, “History”

The autumn term is always the longest term: that long drag from the wan sunlight of September to the bleak darkness of December. This is the term that tests both the mettle and the soul of a teacher. At the end of it, many of us have cause to echo the gloom of Francisco’s lines from Hamlet — “’tis bitter cold, and I am sick at heart.”

But even when it seems like it’s all over, it’s still not over. 

The heavy hand of collective-responsibility roulette has tapped me on the shoulder. It’s my turn to write the scheme of work and resources for the next term. I am to write the energy module for the new GCSE Science course. And it must be done, dusted and finished over the Christmas break. The Christmas break.

And the surprising and unexpected truth is . . . I actually think I’m going to like doing it! Yes, really.

Strange to say, I have always enjoyed writing schemes of work. To my mind, it’s a bit like fantasy teaching instead of fantasy football. I move lesson objectives and resources hither and thither where others shift premier league strikers and goalkeepers.

Some aspects of the Science curriculum are abtruse and hard to communicate. Undoubtedly, some of the things we narrate do not always correspond closely enough to something which is already in students to be either credible or intelligible to them. The images and concepts must be fastened to some reality in their “secret experience” for them to learn rightly.

And what can we do to help them? Simply this: make sure that students get as much hands-on practical work as possible. Of course, it goes without saying (I hope!) that it should go hand-in-glove with coherent and thorough explanations of the theoretical underpinnings of scientific understanding.

One without the other is not enough.

Physics: it’s remarkably similar to Maths. But there’s a point to Physics

Let us hope that our students (in the words of R. A. Lafferty) never see a bird fly by without hearing the stuff gurgling in its stomach.


Filed under Education, Physics, Science

The Care And Feeding Of Ripple Tanks (Part One)

And so they’re back — ripple tanks, that is. And a Required Practical to boot!

They were a staple of Physics teaching when I started my career, but somehow they fell into an undeserved desuetude. I know many fine teachers and excellent technicians who have never used one in anger, which is a real pity, since they are a great teaching tool.

So I present here my eclectic mix of ripple tanks: what you really need to know.

The Basics: “Look at the shadows, honey, look at the shadows!”

A ripple tank is simply a container with a transparent base. The idea is to put water in the container and make waves or ripples in the water. A light source is positioned above the water so that a screen underneath the transparent tank is illuminated. The crests and troughs act as converging and diverging lenses and produce a pattern of light and dark lines on the screen which enables us to observe wave behaviour more easily.

Remember: look at the pattern of shadows on the floor or bench top, not the ripple tank itself.

If doing this as a demo, sight lines will usually be a bitch for your class. If you have an old fashioned OHP, just put the tank on top of it and project the shadow pattern on to a wall or screen. Alternatively, experiment with positioning the light source underneath the tank and projecting the pattern on to the ceiling.

“Water, Electricity, Children and Darkness: What Could Possibly Go Wrong?”

The ripple tank works best in subdued lighting conditions. Make sure that walkways are free of bags and other trip hazards. If you want students to complete other work during this time, giving them desk lamps (e.g. the ones used by biologists for microscopes) can be useful, and can actually create a nice atmosphere.

Have some towels ready to mop up any water spills.

Most ripple tanks use a low voltage (12V) bulb and vibration generator (0-3 V) to minimise any electrical hazards involved. Be vigilant when plugging in the low voltage supply to the mains and ensure that the mains cable stays dry.

Fill ‘Er Up!

Have a large plastic beaker handy to fill and drain the ripple tank in situ. Don’t try to fill a ripple tank direct from the tap and carry a filled ripple tank through a “live” classroom — unless you want to risk a Mr Bean-type episode. (But you may need to add more water if demonstrating refraction — just enough to cover the plastic or glass sheet used to change the depth.)

In general, less is more. The ripple tank will be more effective with a very shallow 2-3 mm of water rather than a “deep pan” 2-3 cm.

Use the depth of water as a “spirit level” to get the ripple tank horizontal. Adjust the tank so that the depth of water is uniform. (If this seems low tech, remember that it is likely that ancient Egyptians used a similar technique to ensure a level platform for pyramid building!)

It’s also helpful to try and eliminate surface tension by adding a tiny amount of washing up liquid. I dip the end of a thin wire in a small beaker of detergent and mix thoroughly.

And so it begins…

Before switching on the vibration generator etc., I find it helpful to show what a few simple manually-created waves look like using the tank. Using a dropping pipette to create a few random splashes can be eye catching, and then showing how to create circular and straight wavefronts by tapping rhythmically using  the corner of a ruler and then a straight edge.


Filed under Physics, Science

It’s Not All Relative: Five Things That Einstein Never Said

We have all done it, haven’t we? Each and every one of us has, at some point, appropriated (or misappropriated) a quotation from a great thinker or writer to lend a spurious profundity to our own footling little thoughts.

While it may be well-nigh irresistible to wrap ourselves in the borrowed robes of literary or scientific genius, the temptation is fraught with dangers. To spare both our own blushes and those of our unsuspecting audience, it’s a good idea to check whether the Great Person actually said what they are reputed to have said.

For one reason and another, the life, career and reputation of Albert Einstein makes him an especially tempting target for spurious attributions.

This is my eclectic list of five things that Einstein did NOT say, and yet seem to be quoted and requoted again and again, especially in an educational context.

It is a melancholy truth that these particular memes will most likely be circulating on the internet until the last router rusts away to nothingness. However, on the principle that it better to light a candle than complain about the dark, I present this list (although, given their preternatural persistence, a flamethrower might be more appropriate).

Watch out, any one of them may well be coming to a CPD near you sometime soon…

Nein-stein No. 1

Everyone is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.

This, according to Quote Investigator [QI 1], was first attributed to Einstein as recently as 2004. The original allegory about animals attending a school and being judged against inflexible criteria, can be traced back to physicist Amos E. Dolbear who published it under a pseudonym in 1898.

Nein-stein No. 2

Everything is energy and that’s all there is to it. Match the frequency of the reality you want and you cannot help but get that reality. It can be no other way. This is not philosophy. This is physics.

Philosophy this gem certainly isn’t. Sadly, it bears no relation to any recognisable form of Physics either. (“Pass the bag labeled ‘New Age Quantum Claptrap’ please, Alice.”)

The original form of this quotation was penned by special effects artist Darryl Anka in 1998 — forty years after Einstein had shuffled off this mortal coil (or, at least, had become significantly less ordered).

Incidentally, Anka never attempted to attribute this thought to Einstein. In fact, he claimed that it had been obtained via “trans-dimensional channelling” from an extraterrestrial entity named “Bashar”. [QI 2]

Nein-stein No. 3

Two things inspire me to awe: the starry heavens and the moral universe within.

A beautiful quote, but Einstein? Naaaah. From Immanuel Kant’s Critique of Practical Reason (1788), actually. Highbrow enough for ya? [Ref 1]

Nein-stein No. 4

The definition of insanity is doing the same thing over and over and expecting different results.

Not Einstein. Not Benjamin Franklin. Not Rita Mae Brown either. The earliest instance tracked down by Wikiquote was from a Narcotics Anonymous publication from 1981.

Nein-stein No. 5

Two things are infinite: the universe and human stupidity. Actually, I’m not sure about the universe.

Einstein may or may not have said this, but the only evidence we have is from the works of therapist Frederick S. Perls, who credited the quote to a “great astronomer” in a book published in 1947. In later works, Perls specifically named Einstein as the originator of the quote which was said during a personal meeting with Perls. However, Perls did present different versions of the statement over the years. [QI 3]


Filed under Humour, Physics, Science

The Renaming of Parts; or, Energy is the New Orange


A PC approach to energy?

Neil Atkin recently wrote a fascinating post about the “New” approach for teaching the concept of energy to secondary school students, and provides some interesting commentary and some very useful links: go read!

I first came across the work of Ogborn and Boohan, on which much of the “New Approach” is based, in the 1990s. I remember embracing it enthusiastically. However, I subsequently returned to the more “traditional” kinetic-chemical-heat-potential-light-sound “naming of parts” model, mostly because many of the resources favoured by our students followed the older convention.

And so it has remained for a number of years, so I was all set to give the “New Approach” a proper rubbishing (as might be gleaned from my selection of the Gary Larson cartoon above) as a specious form of PC — physical correctness as opposed to political correctness, perhaps.

But as I read more about the “New Approach”, I gradually came to the conclusion that it is conceptually sound. More importantly, I think it follows one of the basic principles suggested by Engelmann and Carnine:

[I]f we are to understand how to communicate a particular bit of knowledge . . . we must understand the essential features of the particular concept that we are attempting to convey. Only if we understand what it is and how it differs from related concepts can we design a communication that effectively conveys the concept to the learner.
The Theory Of Instruction, location 296

In other words, I think the “New Approach” is a more accurate representation of the physics of energy, and less likely to lead to misconceptions and false inferences.

Energy Is The New Orange


Read Dr Dav’s excellent blog post from 2013 for a clear summary of the arguments in favour of the New Approach, as well as Robin Millar’s excellent paper on the topic.

Rise of the Enoji

One of the suggestions made in the IOP’s Energy 11-14 is to use ideograms or icons to represent different energy stores.


By analogy with the ubiquitous ’emojis’ I suggest that we should call these energy icons Enojis. Who knows, it could just catch on…


Filed under IoP Energy "Newspeak", Physics, Science