Category Archives: Science

The Life and Death of Stars

Stars, so far as we understand them today, are not “alive”.

Now and again we saw a binary and a third star approach one another so closely that one or other of the group reached out a filament of its substance toward its partner. Straining our supernatural vision, we saw these filaments break and condense into planets. And we were awed by the infinitesimal size and the rarity of these seeds of life among the lifeless host of the stars. But the stars themselves gave an irresistible impression of vitality. Strange that the movements of these merely physical things, these mere fire-balls, whirling and traveling according to the geometrical laws of their minutest particles, should seem so vital, so questing.

Olaf Stapledon, Star Maker (1937)

Star Maker Cover

And yet, it still makes sense to speak of a star being “born”, “living” and even “dying”.

We have moved on from Stapledon’s poetic description of the formation of planets from a filament of star-stuff gravitationally teased-out by a near-miss between passing celestial orbs. This was known as the “Tidal Hypothesis” and was first put forward by Sir James Jeans in 1917. It implied that planets circling stars would be an incredibly rare occurrence.

Today, it would seem that the reverse is true: modern astronomy tells us that planets almost inevitably form as a nebula collapses to form a star. It appears that stars with planetary systems are the norm, rather than the exception.

Be that as it may, the purpose of this post is to share a way of teaching the “life cycle” of a star that I have found useful, and that many students seem to appreciate. It uses the old trick of using analogy to “couch abstract concepts in concrete terms” (Steven Pinker’s phrase).

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I find it humbling to consider that currently there are no black dwarf stars anywhere in the observable universe, simply because the universe isn’t old enough. The universe is merely 13.7 billion years old. Not until the universe is some 70 000 times its current age (about 1015 years old) will enough time have elapsed for even our oldest white dwarfs to have cooled to become a black dwarf. If we take the entire current age of the universe to be one second past midnight on a single 24-hour day, then the first black dwarfs will come into existence at 8 pm in the evening…

And finally, although to the best of our knowledge, stars are in no meaningful sense “alive”, I cannot help but close with a few words from Stapledon’s riotous and romantic imaginative tour de force that is yet threaded through with the disciplined sinews of Stapledon’s understanding of the science of his day:

Stars are best regarded as living organisms, but organisms which are physiologically and psychologically of a very peculiar kind. The outer and middle layers of a mature star apparently consist of “tissues” woven of currents of incandescent gases. These gaseous tissues live and maintain the stellar consciousness by intercepting part of the immense flood of energy that wells from the congested and furiously active interior of the star. The innermost of the vital layers must be a kind of digestive apparatus which transmutes the crude radiation into forms required for the maintenance of the star’s life. Outside this digestive area lies some sort of coordinating layer, which may be thought of as the star’s brain. The outermost layers, including the corona, respond to the excessively faint stimuli of the star’s cosmical environment, to light from neighbouring stars, to cosmic rays, to the impact of meteors, to tidal stresses caused by the gravitational influence of planets or of other stars. These influences could not, of course, produce any clear impression but for a strange tissue of gaseous sense organs, which discriminate between them in respect of quality and direction, and transmit information to the correlating “brain” layer.

Olaf Stapledon, Star Maker (1937)

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Teaching Magnification Using the Singapore Bar Model

He was particularly indignant against the almost universal use of the word idea in the sense of notion or opinion, when it is clear that idea can only signify something of which an image can be formed in the mind. We may have an idea or image of a mountain, a tree, a building; but we cannot surely have an idea or image of an argument or proposition.

— Boswell’s Life of Johnson

The Singapore Bar Model is a neat bit of maths pedagogy that has great potential in Science education. Ben Rogers wrote an excellent post about it here. Contrary to Samuel Johnson’s view, the Bar Model does attempt to present an argument or proposition as an image; and in my opinion, does so in a way that really advances students’ understanding.

Background

The Bar Model was developed in Singapore in the 1980s and is the middle step in the intensely-focused concrete-pictorial-abstract progression model that many hold instrumental in catapulting Singapore to the top of the TIMSS and PISA mathematical rankings.

Essentially, the Bar Model attempts to use pictorial representations as a stepping-stone between concrete and abstract mathematical reasoning. The aim is that the cognitive processes encouraged by the pictorial Bar Models are congruent with (or at least, have some similarities to) the cognitive processes needed when students move on to abstract mathematical reasoning.

Applying the Bar Model to a GCSE lesson on Magnification

I was using the standard I-AM formula triangle with some GCSE students who were, frankly, struggling.

Image from https://owlcation.com/stem/light-and-electron-microscopy

Although most science teachers use formula triangles, they are increasingly recognised as being problematic. Formula triangles are a cognitive dead end because they are a replacement for algebra, rather than a stepping stone that models more advanced algebraic manipulations.

Having recently read about the Bar Model, I decided to try to present the magnification problem pictorially.

“The actual size is 0.1 mm and the image size is 0.5 mm. What is the magnification?” was shown as:

Screen Shot 2018-03-18 at 11.35.05

From this diagram, students were able to state that the magnification was x 5 without using the formula triangle (and without recourse to a calculator!)

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Magnification question.

The above question was presented as:

Screen Shot 2018-03-18 at 12.02.57

 

Note that the 1:1 correspondence between the number of boxes and the amount of magnification no longer applies. However, students were still able to intuitively grasp that 100/0.008 would give the magnification of x12500 — although they did need a calculator for this one. (Confession: so did I!)

More impressively, questions such as “The actual length of a cell structure is 3 micrometres. The magnification is 1500. Calculate the image size” could be answered correctly when presented in the Bar Model format like this:

Screen Shot 2018-03-18 at 12.22.21

Students could correctly calculate the image size as 4500 micrometres without recourse to the dreaded I-AM formula triangle. Sadly however, the conversion of micrometres to millimetres still defeated them.

But this led me to think: could the Bar Model be adapted to aid students in unit conversion? I’m sure it could, but I haven’t thought that one through yet…

However, I hope other teachers apply the Bar Model to magnification problems and let me know if it does help students as much as I think it does.

 

 

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Corinne’s Shibboleth and Embodied Cognition

You can watch a bird fly by and not even hear the stuff gurgling in its stomach. How can you be so dead?

— R. A. Lafferty, Through Other Eyes

In modern usage, a shibboleth is a custom, tradition or speech pattern that can be used to distinguish one group of people from another.

The literal meaning of the original Hebrew word shibbólet is an ear of corn. However, in about 1200 BCE, the word was used by the victorious Gileadites to identify the defeated Ephraimites as they attempted to cross the river Jordan. The Ephraimites could not pronounce the “sh” sound and thus said “sibboleth” instead of “shibboleth”.

As the King James Bible puts it:

And the Gileadites took the passages of Jordan before the Ephraimites: and it was so, that when those Ephraimites which were escaped said, Let me go over; that the men of Gilead said unto him, Art thou an Ephraimite? If he said, Nay; Then said they unto him, Say now Shibboleth: and he said Sibboleth: for he could not frame to pronounce it right.

Judges 12:5-6

The same story is featured in the irresistible (but slightly weird) Brick Testament through the more prosaic medium of Lego:

Shibboleth

Sadly, the story did not end well for the Ephraimites:

Then they took him, and slew him at the passages of Jordan: and there fell at that time of the Ephraimites forty and two thousand.

This leads us to Corinne’s Shibboleth: a question which, according to Dray and Manogoue 2002, can help us separate physicists from mathematicians, but with fewer deleterious effects for both parties than the original shibboleth.
Corinne’s Shibboleth

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Mathematicians answer mainly B. Physicists answer mainly A.

This is because (according to Dray and Manogoue) mathematicians “view functions as maps, taking a given input to a prescribed output. The symbols are just placeholders, with no significance.” However, physicists “view functions as physical quantities. T is the temperature here; it’s a function of location, not of any arbitrary labels used to describe the location.”

Redish and Kuo 2015 comment further on this

[P]hysicists tend to answer that T(r,θ)=kr2 because they interpret x2+ y2 physically as the square of the distance from the origin. If r and θ are the polar coordinates corresponding to the rectangular coordinates x and y, the physicists’ answer yields the same value for the temperature at the same physical point in both representations. In other words, physicists assign meaning to the variables x, y, r, and θ — the geometry of the physical situation relating the variables to one another.

Mathematicians, on the other hand, may regard x, y, r, and θ as dummy variables denoting two arbitrary independent variables. The variables (r, θ) or (x, y) do not have any meaning constraining their relationship.

I agree with the argument put forward by Redish and Kuo that the foundation for understanding Physics is embodied cognition; in other words, that meaning is grounded in our physical experience.

Equations are not always enough. To use R. A Lafferty’s picturesque phraseology, ideally physicists should be able to hear “the stuff gurgling” in the stomach of the universe as it flies by….

Dray, T. & Manogoue, C. (2002). Vector calculus bridge project website, http://www.math.oregonstate.edu/bridge/ideas/functions

Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5-6), 561-590.

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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.

[p.50]

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.

[p.103]

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?

REFERENCES

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

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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.

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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:

engelmannreflection

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.

engelmannreflection2

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

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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.

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