# Letters Teaching relativity to year olds Christina Astin SSR

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Teaching relativity to 10-year-olds               the Doppler shift, or the shifting times of
appearance of the moons of Jupiter, as
■ Christina Astin (SSR, 86(316), 34–35)
noted by Romer and used by him as
offers a very nice way of introducing the
evidence that light has a finite speed. But
idea of relative velocity to young pupils.
the ‘experiment’ is certainly not relativist-
In it, pupils walk along in a row past the
ic, because the velocities of ‘photons’ and
teacher, each speaking as they pass. First
‘observer’ add up in the usual Galilean
the teacher stands still, and then walks in
way (as above). This is like the way the
the same direction as the pupils, but more
Doppler shift works for sound, but not for
slowly. The time interval between pupils
light. In this case, the ratio of time inter-
passing the teacher increases, because the
vals for moving and stationary observer
relative velocity of pupils and teacher is
would be (1 + v/c), where v is the relative
now smaller. Very neat.
velocity and c is the speed of the signal. If
Unfortunately, Christina Astin presents           the signal is light (or radiowaves) this
this as an illustration of relativistic time      becomes γ (1 + v/c), where
dilation, which it certainly is not. There
are several obvious reasons why there is                           1
no parallel at all with time dilation. First,        γ =
1 − v2 /c2
the teacher can clearly choose to walk in
the opposite direction, increasing the            is indeed the relativistic time dilation, but
relative velocity and shortening the time         appears nowhere in the ratio of times in
interval between pupils speaking as they          Christina Astin’s ‘experiment’. For ideas
pass her. It seems likely that 10-year-olds       about how to introduce this, see Ogborn
might think of doing this, and be led to          and Whitehouse (2001), chapter 12. But
imagining relativistic time contraction too.      not for 10-year-olds!
Second, the ‘experiment’ has nothing to           In other words, you should disregard all
do with the invariance of the speed of            the talk about time, clocks, photons and
light with respect to motion of source or         the speed of signals in Christina Astin’s
To see this for sure, it is quite easy to write   note. All that talk is completely beside the
down expressions for the time interval            point. This does not detract from an
between pairs of pupils speaking as they          otherwise very simple, effective and
pass the teacher. If the teacher is at rest,      interesting idea about making the idea of
and the pupils walk at velocity u, with           relative velocity accessible to 10-year-olds.
distance x between them, the time interval        This is certainly a good first step on the
is just x/u. If the teacher walks in the          way to relativity. It just isn’t the step that
same direction as the pupils at velocity v,       Christina Astin hoped it was.
the time interval becomes x/(u – v).                                                 Jon Ogborn
Notice that the latter becomes x/(u + v) if             Emeritus Professor of Science Education,
the teacher walks in the opposite                   Institute of Education, University of London
direction, thus reducing the time interval.
Reference
Worse, if the teacher walks as at first but
now faster than the pupils, overtaking            Ogborn, J. and Whitehouse, M. (ed) (2001) Advancing
physics A2. Ch. 12. Bristol: Institute of Physics
them, the sequence in which they speak is          Publishing.
reversed! In the way Christina Astin
presents the ‘experiment’ one would have
Editors’ note
to regard this as time reversal.
This letter was received soon after the
Christina Astin wants the pupils to                article ‘Teaching relativity to 10-year-olds’
represent a stream of photons going past           was published. Christina Astin herself
an observer, having been emitted at equal          published a letter in the June edition (SSR,
time intervals by a clock. If so, the              86(317), 10) accepting some of the
‘experiment’ is about phenomena such as            comments which are included in this letter.

School Science Review, December 2005, 87(319)         11
Letters

Spouting confidently                            Therefore, if teachers ensure that their
piece of apparatus satisfies condition (1)
■ In his recent Science note ‘Spouting on’,
(or (2)) they can spout with confidence!
(SSR, 86(317), 13–14), Frank Harris
considers the well-known piece of               Readers who are interested are invited to
apparatus (comprising a vessel containing       contact the author for a detailed solution.
water and with holes drilled in it) used to                                       P. Glaister
demonstrate the principle that ‘pressure
increases with depth’. Having shown that         Department of Mathematics, University of
the horizontal distance travelled by the                                        Reading
water jets varies in such a way that the
maximum value is attained by a hole half-
way up, he concludes that to ensure the         ■ I remember that the spouting can
correct visual impression the apparatus         experiment has had a public airing before,
has to be ‘tweaked’, but does not specify       about 15 years ago, but it was possibly in
how this can be done, either qualitatively      Physics Education. I recall drawing a family
or quantitatively.                              of parabola-shaped curves, using a BBC
The simplest way this can be achieved is        computer (remember those?), to illustrate
by having the depth of water sufficiently       the expected path of the water spout from
small, or by ensuring the holes are             different levels. The same set could also
sufficiently far from the bottom, or a          be drawn by hand. I thought this pattern
combination of both. More specifically, if      of curves so interesting that I made my
the height of the water column is H and         own spouting bottle. This was a 1 gallon
the two holes are at heights ha, hb from the    (4.5 litre) plastic container in which I
bottom of the vessel, then the lower jet        drilled seven equal holes at equal vertical
will travel a larger horizontal distance        spacing (Figure 1). There was also a slight
than the higher one provided:                   horizontal spacing. This was to prevent
H < ha + hb                           (1)    each jet hitting those below.
water in
as shown in Figure 1, giving the desired
effect of demonstrating the ‘pressure
increases with depth’ principle. (Clearly, if
H is sufficiently small, or ha + hb is                    ‘overflow’
sufficiently large, then (1) will hold.)                maintaining
of water

ha
H
Figure 1 Arrangement of seven holes drilled to
make a spouting can.
hb
Figure 1
Then, when I came to show the ‘Wet the
teacher experiment’ (it was rare to have
Further, if the vessel is additionally placed   only my hands wet after completing any
on a block of wood of height d, then (1)        version of the spouting cans
now becomes:                                    demonstration), I placed the container on
H < ha + hb + d                       (2)    a box of about the same height so that the
In other words, if the vessel is placed on a    water could run into a large sink.
block of wood of sufficient height d, where:    The greatest practical difficulty is then
d > H – (ha + hb)                            keeping the water level constant as the
then the jets will show the desired effect.     water is flowing. I made an extra hole on
another side of the container, near the top

12   School Science Review, December 2005, 87(319)
Letters

surface tension or viscosity. In reality, both
influence the flow.
Due to surface tension, water will not
emerge from a small hole near the top.
About 10 mm depth is needed for a 3 mm
diameter hole. The slowest outflow (for a
slightly greater depth of water) clings to
the wall of the container. It is interesting
to try holes of a different size at the same
level to show that surface tension and
viscosity are significant. I have used
measurement of water-flow relative to
depth as an investigation for A-level
physics in the context of modelling the
Figure 2 Position of container for use          use of locks on canals. The context of
testing the validity of the spouting can
could be an interesting option.
and of larger diameter, to take an
overflow pipe. If the inflow is sufficient,     The cans sold by suppliers of school
spare water runs out of the overflow.           apparatus for this demonstration usually
have three outlets which are not just holes
This set-up indicates that at the level of
but tubes. Viscosity will have a greater
the base of the container, one of the
effect with a tube than with a hole of the
central jets has the greatest horizontal
same diameter (many will remember
range, but as the jets continue, the jet from
measuring viscosity using the flow
the lowest opening has the greatest
through a horizontal capillary tube).
horizontal range (Figure 2).
Finally, it is worth drawing attention to
There should be no need for ‘tweaking’
what I call the ‘Tom and Jerry’ version. If
the experiment although I have seen a
left to draw what they think we want to
textbook photograph where this had been
see, many students produce something
done. I assume this was to satisfy the
like Figure 3.
expected outcome, or the demands of
examiners.
Once students have grasped the basic idea
of increased pressure with depth, leading
to an expectation that the jet from the
lowest hole should emerge with the
greatest velocity as a consequence, they
can look into what really happens.
Without any mathematical treatment, I
Figure 3 A student (‘cartoon’) version of the
simply ask students to consider the fact        expected diagram.
that from a hole at the level of the top of
the water, the horizontal velocity is zero.
The water is just unable to emerge;             When I have seen this, I suggest that it
therefore the range is zero. Compare then       means that the water rushes out
a hole at the bottom. Although this jet has     horizontally, looks down to see that there
greatest horizontal velocity on emerging,       is nothing underneath, and then falls, and
its path is immediately downwards. This         the lowest jet rushes out faster so it travels
means the horizontal range from this level      further before looking down. The cat of
is zero. Therefore a jet from somewhere         the Tom and Jerry cartoons regularly ran
between top and bottom must have the            over the edge of a cliff, rooftop, etc., in the
greatest range at the base level.               same fashion.
The theory used to obtain the basic                                              Geoff Auty
parabolic curves takes no account of                      formerly at New College, Pontefract

School Science Review, December 2005, 87(319)     13
Letters

Continuing professional                            ■ Sufficient duration and intensity of CPD.
development (CPD)                                  It is universally recognised that the one-
day INSET course is totally useless
■ I was extremely interested in the article        (except perhaps for introducing a class-
on CPD by the White Rose University                room tool such as PowerPoint). Joyce
Consortium Team (SSR, 87(318), 105–111).           (1995) says it takes 30 hours to master a
They make a number of important points,            new teaching skill. In the bid we made
but I believe they have underemphasised            from a rival consortium to run the
one or two factors critical to effective           National Science Learning Centre we
CPD. I would like to offer more evidence           insisted that the minimum provision of
in support of their argument, and add two          any course would be a day, plus trial
points. I do this since, while the article has     period in school, plus a second day for
‘not attempted to carry out an exhaustive          reflection and feedback. Because of the
review of the literature’, I was able to do so a   cost of longer term CPD, this is not a story
couple of years ago, the results of which          that many heads want to hear, nor one
appear in Adey et al., 2004. This may              which is popular with the DfES. But I
appear as a bit of a puff, but I hope it will      would contend that the current fashion for
nevertheless offer some substance.                 one-day INSET is a total waste of money.
On the topic of ‘what counts as effective
■ What the CPD is introducing matters. I
CPD’, I would point to Guskey, 2000. His           might run a wonderful long and varied
five levels of evaluation extend somewhat          course on ‘Learning styles’; the teachers
the four bullet points of ‘what counts as
will love it, they’ll work together to assess
effective’ and include effects on the whole        their students, label them all, and the
school as well as on individual teachers           effect on students’ learning will be zero.
and students. While I personally would
Why? Because there are no such things as
hold out for ‘measurable effects on learners’      learning styles – at least not as stable
as the only real measure of effectiveness of       entities which are any use to teachers (see
CPD, I realise how difficult it is to assess       Adey, Fairbrother and Wiliam, 1999, and
this, and that it would be political suicide       Coffield et al., 2004). So the subject matter
for a CPD provider to promise it.                  of the CPD has to have established
The article makes the very important               validity.
point that effective CPD requires teachers         There is more, much more, that could be
to work in groups. It is almost vanishingly
said: it’s in our CPD book (2004).
difficult for a lone teacher to introduce
and maintain an innovatory pedagogy                                                 Philip Adey
without the tacit support and encourage-             Emeritus Professor of Cognition, Science and
ment of the department and senior                          Education, King’s College London, and
management team. For primary teachers                      proprietor of Developing Intelligence
such support may come from SMT or
References
science subject leaders, but also, in our
Adey, P., Fairbrother, R. and Wiliam, D. (1999) A
experience, from teachers in nearby
review of research on learning strategies and
schools struggling to introduce the same             learning styles. King’s College London.
innovation. ‘Collegiality’ is quoted as a
Adey, P., Hewitt, G., Hewitt, J. and Landau (2004) The
critical factor in almost every research             professional development of teachers: practice and
report on effective CPD – see, e.g. Stoll            theory. Kluwer Academic.
and Fink (1996) and Adey et al., 2004, page        Coffield, F., Moseley, D., Hall, E. and Ecclestone, K.
166, for many other references.                      (2004) Learning styles and pedagogy in post-16
The Shulman characterisation of the types            learning. Learning Skills and Research Centre.
of professional knowledge base which               Guskey, T. (2000) Evaluating professional
CPD may address is really useful, and the            development. Sage.
article does a good job in tying it in with        Joyce, B. (1995) Student achievement through staff
focuses of CPD episodes and approaches.              development. Longman.
Stoll, L. and Fink, D. (1996) Changing our schools.
There are two CPD factors which the
OUP.
article does not emphasise enough:

14   School Science Review, December 2005, 87(319)

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