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Putting conceptions in their place: using analogy to cue and strengthen scientifically correct
conceptions

Anne Nelmes
Ph.D. Student, Loughborough University

Paper presented at the British Educational Research Association Annual Conference, University of Manchester, 16-18 September 2004

This part of the research was funded by a Best Practice Research Scholarship

Abstract

Pupils come to physics lessons with some scientifically wrong ideas, sometimes referred to as misconceptions but often just misplaced conceptions; correct in some contexts but not in others.

Analogy has long been used to aid understanding of scientific concepts, both in and out of the classroom. Rather than trying to overtly change the misconception into the scientific conception, it may be as, or more, effective and certainly less time consuming to cue the right idea using analogy on a very low key level, without the pupils even realising that an analogy has been used. The idea of cueing correct ideas comes from work done by diSessa and others on p-prims (phenomenological primitives). These are small knowledge units which are cued to an active state to explain phenomena.

It is hoped the correct p-prim will be cued by use of the analogy and, if cued repeatedly, will strengthen.

In this research two groups (12-13 year-olds) are compared; an experimental group and a control group. Both groups are given a pre-test on the conception concerned where they have to decide how much sense two statements make; the correct scientific explanation and a common misconception. The groups then proceed with their work on the topic until the relevant point is reached. Before actually doing the experiment or having the correct explanation given to them, the experimental group are given a low-key analogy (usually as an aside to the lesson). The ‘sense’ questions are given again to both groups. It could be argued that some of the pupils would see the analogy as an analogy rather than it just unconsciously cueing their thought processes and so they are asked why they change their ideas if, indeed, they do.

The results are interesting. Generally, there is an increase in the sense of the scientific explanation for the experimental group even though they do not know why they have changed their minds or become more sure of that explanation. Rather than the control group staying approximately the same as on their pre-test, they have generally shown a decrease in the sense of the scientific explanation. This is worrying as all this group have done since the pre-test is other work on the topic so it seems as if this may confuse them. For example, just prior to the absorption/radiation topic, the pupils look at conductors and insulators of heat. These being opposites (good conductors are poor insulators) may strengthen their conviction that good radiators are poor absorbers).

The conclusions drawn from this work include the following:

This is obviously not a complete answer but if correct p-prims can be cued, then pupils may be helped to put their own conceptions in the right context.

Introduction – work leading to the present research

Consider the idea that objects require an unbalanced or net force to keep them moving at a constant velocity. This is a common student misconception and many such misconceptions are extremely difficult to change. They are particularly rife in physics, as pupils have had multiple experiences with the subject matter before ever having had a single, formal physics lesson. They have had 11 or more years in which to build up a myriad of conceptions, be they right or wrong, based on everyday experiences. A task of teachers is to assist pupils to understand scientific conceptions; a task that is both difficult and potentially rewarding. One method that has been used is ‘bridging analogies’.

It is easier to understand a close analogy than a distant one. Pupils may not be willing to accept straight away that A is analogous to C but, by introducing B, they may agree that A and B are analogous as are B and C. Thus, they may become more confident in the analogous relationship between A and C. The anchor-bridge-target model aims to start where the student is and finish where the scientist is having crossed the chasm using conceptual bridges usually going from the very concrete to the rather abstract.

I have researched the use of bridging analogies in several physics topics for 12-13 year olds and have found them to be potentially effective at improving retention of correct concepts.

The present research is to analyse the bridging analogy process using phenomenological primitives (p-prims). These are the very basic notions that people hold which have arisen from their interaction with the world. When faced with having to explain a phenomenon, p-prims are ‘cued to an active state’ depending on the context. Whether they remain active depends on the subsequent chain of mental events.

Phenomenological primitives (p-prims)

Work has been done on naïve theories, for instance McCloskey (1983) stated "people develop on the basis of everyday experience remarkably well articulated theories of motion", very similar to the impetus theory which was an accepted theory in the Middle Ages. However, diSessa believes that, although uniform results are sometimes obtained, mostly there is not the systematicity of a scientific theory (diSessa, 1993). Individuals are not systematic in their ideas and views differ between people. Even potentially promising candidates like the impetus theory are too limited in context. Beliefs are a little more successful in explaining naive physics but not convincingly so. Not even at the level of concepts is there a basic set of ideas.

diSessa (1993) concentrated on part of physics knowledge that he denotes as sense-of-mechanism. This is concerned with interaction with the physical world and allows us to predict and explain events.

His particular view, he called ‘knowledge in pieces’ and the knowledge elements that go to make up the sense-of-mechanism construction he called p-prims. When explaining a phenomenon, p-prims are cued to an active state. Which p-prims are cued depends on the context and whether they remain active depends on the subsequent chain of mental events.

We each have many hundreds or thousands of p-prims that can be cued quite readily. They can be thought of as ‘primitive’ in that they need no further explanation and they are ‘phenomenological’ in that they are based on our direct experience of the world. They probably arise from simple abstractions of a familiar event. Similar events are then ‘explained’ by the p-prim.

DiSessa (1993, 1996) has given several characteristics of p-prims and these are summarised below.

P-prims are:

Some of these characteristics will now be explained and/or expanded upon.

P-prims are difficult to articulate since they originate at a much more basic level than language. The level proposed is visual or kinaesthetic. This is maybe why pupils learn much through experiment with the proviso that they are guided to observe relevant features and pick up the right clues; in other words, to cue the correct p-prims. Unguided experiments are likely to strengthen already strong and possibly incorrect p-prims.

In changing from novice to expert, diSessa suggested that some p-prims become used more and some used less. With novices, the p-prims have different priorities but there are usually none with comparatively very high priority. He proposed that, during the novice to expert change, some p-prims are greatly reduced and some greatly increased resulting in more structure round central high priority p-prims. New p-prims may develop and old ones are probably never completely extinguished but some may take on new functions, e.g. they may come to cue some formal knowledge or procedure (diSessa, 1993, Sherin, 1999).

P-prims form a level beneath concepts and, until learning has taken place, it is unlikely that there will be enough strong p-prims in the same area to link together to form anything resembling a concept.

Since p-prims are so diverse, it is difficult to provide exemplars of them. However, some are more central and important than others. One such is Ohm’s p-prim. This is where effect, resistance and effort are linked:

This can apply to many situations, e.g. pushing harder against a weight to increase motion and increasing current through a resistor by increasing the potential difference. The latter is the origin of the name for this p-prim.

A change in direction of attention shows the fluidity of p-prims. A slight alteration in perspective may change the p-prim cued, sometimes seemingly with no problem to the observer who may see no conflict in the inconsistencies present. This is another indication that p-prims do not coalesce to form concepts, beliefs or theories since, if they did, surely the inconsistencies would be apparent and thus cause conflict.

As for the last characteristic in the summary, it is possible that sometimes p-prims do come together to form relatively stable arrangements that give so-called intuitive theories such as the ‘impetus’ theory described by, for example, McCloskey (1983).

diSessa points out that deep conceptual learning is unlikely to occur unless there is extended, cumulative and systematic experience with a concept (1996). A short lesson aimed at conceptual change of an idea is obviously not going to be sufficient. The lessons planned for this research are short and so I can hope for no more than to scratch the surface. However, if I can, through the use of bridging analogies, cause more relevant p-prims to be cued, then I can count it as a success.

P-prims are not the only knowledge type, argues diSessa (2002). There are also co-ordination classes which are much bigger and more complex than p-prims. They probably include p-prims and, unlike p-prims, can be considered as a model of at least one type of concept. They may not be present as such in naïve thought. Their function is to enable one to extract and use information about the world. diSessa identifies two main categories of co-ordination class comprising readout strategies (methods of extracting information) and the causal net (possible inferences from the information). As diSessa (2002) points out, "the development of a co-ordination class is an extended and complex affair". The present research is concerned with the cueing of p-prims using analogy rather than with the development of full-blown concepts and so I will leave the discussion of co-ordination classes at this point, being aware that they exist but also that they are beyond the scope of this study.

Methodology

One of the questions being asked in this research was ‘do p-prims account for any success in this bridging analogy method or does the introduction of analogy cause more conscious thought processes?’. In order to address this, it was necessary to use analogy at a low-key level so the pupils were not told an analogy was being used. If doing this was successful and the pupils did not know why they have decided on the correct idea, it may be safe to assume that the analogy had unconsciously cued the right p-prim. If the pupils were aware that it was the analogy which had made them decide on the correct idea, then it is probably due to more conscious thought rather than cueing of p-prims. However, if the wrong idea was chosen, then the analogy had not worked, either as a p-prim cuer or as a conscious thought promoter.

A comparison was made between pupils that had been taught using a short bridging analogy approach to the target problem (without being told that they are analogies) and those who had gone straight to the problem. The bridging analogies were based on known or postulated p-prims. For the problem, the pupils were asked to read two alternative explanations of, or statements about, a phenomenon. They gave each a ‘sense’ rating (1-5) and also decided which statement or explanation was the more likely to be correct.

The results were analysed using t-tests to see if the findings are statistically significant. The sample size for each group was only small (a maximum of 24) but, by aggregating the results for the different topics, this was effectively increased. The experimental and control groups were swapped for each topic to reduce the effect of intrinsic differences between the classes.

There was a question for both groups to ask about their thinking for the answers they have given, designed to try to identify any thought processes the pupils had during the lesson. This helped to reveal whether using analogy in this low-key way causes conscious or unconscious thought processes.

Research seems to have looked only at the topic of forces, where the use of bridging analogies has been beneficial, but this research included other topics as well.

Misconceptions, scientific conceptions, p-prims and analogies

This section outlines the misconception considered for each topic, together with a possible p-prim for the misconception. The correct scientific conception is then given together with the probable p-prim. Finally for each topic are the analogies to be used.

Heat 1 (conduction)

Misconception Metals feel colder than many other items because they are naturally at a lower temperature.

Possible p-prim for misconception Could there be a context-dependent meta p-prim, ‘objects have their own temperature dependent on the material they are made from (so long as they are not near any perceived heat source)’? This would be got from sensory data when very young – it feels cold so it is cold.

Scientific conception Metals feel colder than many other items because they are good conductors and take away heat from your body rapidly leaving your hand feeling cold.

P-prim needed to be cued for scientific conception This may be a type of ‘equilibration’ p-prim (diSessa, 1993). Objects (including metals) may start off at different temperatures but they will come to be the same temperature (before a person becomes involved). When a person is introduced into the situation, the pupils will need to know that:

They will then be able to understand that metals feel cold because the heat from a person’s hand is conducted away quickly. This means that the basic problem is that we need to cue the ‘same temperature’ idea rather than the ‘feels cold so it is’ idea.

Analogies used

1. If I push down on side A of this see-saw and then let go, what happens?

2. When the water is poured, where does it end up (higher or lower)?

3. What is different about pouring treacle?

4. What happens to a cup of tea if you leave it in a room for several hours (what temperature does it reach)?

Heat 2 Radiation/Absorption

Misconception Black surfaces are good absorbers of heat so they must be poor radiators of heat.

Possible p-prim for misconception This could be the idea that, if something is good at doing one thing then it must be bad at doing the opposite. This may be emphasised by ‘good conductors are bad insulators’.

Scientific conception Black surfaces are good absorbers of heat and good radiators of heat.

P-prim needed to be cued for scientific conception If something is good at one thing, it can be good at the opposite.

Analogies used

1. ‘People who do well in a subject are good at taking in information and good at giving it out again’.

2. ‘In a netball team, players are good at throwing a ball and good at catching it’.

Light 1 Reflection

Misconception Light goes onto a surface of an object and stays there to light it up.

Possible p-prim for misconception Seeing needs illumination to ‘light up’ objects’. We cannot see in the dark but we can see in the light so the important factor must be the light.

Scientific conception Light goes to a surface and is reflected (more accurately described as scattered) and some enters into our eyes.

P-prim needed to be cued for scientific conception I doubt that reflection is a central, strong p-prim but could it have been encompassed into the p-prim system by the age of 12? Bouncing is a p-prim (diSessa, 1993)

Analogies used

1. ‘What happens when we drop a bouncy ball?’

2. ‘What happens when we hit a snooker ball against the cushion (side of the snooker table)?’

Light 2 Filters

Misconception Colour filters add colour to white light.

Possible p-prim for misconception Change implies doing something positive, adding something’ OR adding something, i.e. the coloured plastic, necessarily means adding colour or, in other words, you cannot take away something by adding something.

Scientific conception Colour filters absorb colours and let only certain ones through.

P-prim needed to be cued for scientific conception This could be a ‘separation (in this case, filtering)’ p-prim.

Analogies used

1. ‘Remember doing a filtration experiment in chemistry. Watch the mixture being filtered. The solid is caught in the filter paper and not allowed to go through but the water can.’

2. ‘This time the solid is not at the bottom of the beaker but spread about in the water. However, when filtered, the solid is again caught in the filter paper and not allowed to go through but the water can.’

Forces 1 Reaction Force

Misconception If objects are stationary, then no forces or only one force acts on them.

Possible p-prim for misconception This may be the ‘supporting’ p-prim (diSessa, 1993). Since inanimate objects are not seen as being able to provide force, the table is merely seen as being in the way.

Scientific conception Stationary objects have balanced forces acting on them.

P-prim needed to be cued for scientific conception Perhaps this is a type of ‘springiness’ p-prim. A spring can push back on you so the table is acting like the spring and pushing back on the book.

Analogies used

1. ‘Push down on a spring. What do you notice (e.g. does the spring squash and does the spring push back on you?)’

2. ‘Balance a book on the spring. What do you notice?’

3. ‘Look at the book on ruler. What do you notice?’

Forces 2 Stretching Springs

Misconception Springs that are identical, except for length, will stretch by the same amount when loaded equally.

Possible p-prim for misconception This may be the ‘Ohms’ p-prim (diSessa, 1993). The factors involved in stretching would be weight, stiffness of spring and extension. The pupils know that pulling harder or a bigger weight extends a spring more and also that extension depends on the stiffness of the spring. Perhaps, if this idea is cued then pupils do not see that the extension could also depend on original length.

OR

It could be the ‘force as mover’ p-prim (diSessa, 1993). Greater force is needed to move more massive objects and in this case, the longer spring is more massive so it will need more force to extend it by the same length or the same force certainly will not double the extension.

Scientific conception Extension is proportional to original length.

P-prim needed to be cued for scientific conception Perhaps a sort of ‘more things present, more things affected’ p-prim is required here.

Analogies used

1. ‘A teacher tells a line of five children, who are queuing up in the playground to be quiet. They all ‘feel’ the same effect of her voice.

If there were ten children in the line they would still all ‘feel’ the same effect of her voice (so long as they can all hear her).

Discuss limitations of this and come to the conclusion that some things can have the same effect if there are only a few people or if there were lots of people. Be aware of, but do not discuss with the pupils at this time, the possible complications caused if springs in parallel were being considered where a different p-prim would have to be cued such as a ‘sharing a job reduces the amount of work each person needs to do’’.

2. ‘Hang a weight on a spring. Are the coils at the top and at the bottom stretched apart or just those at the bottom? Point out that the weight is having an effect on all the coils rather than just the bottom coils but do not discuss how much effect as this is giving the answer to the target question.’

3. ‘Hang two springs end to end and then hang the same weight on the end of the bottom spring. Do the coils on both springs stretch or just the coils of the bottom spring. These springs should be identical with each other but different from the first spring used so the pupils do not see that two springs extend twice as much as one spring.’

Results and analysis of research of individual research topics

Heat 1 (conduction)

Table 1 To show the ‘sense’ ratings and the percentage of pupils giving the correct answer for the experimental and control groups pre- and post-test (heat 1)

heat 1

experimental

 

control

 

ave. sense S

ave. sense M

% S

 

ave. sense S

ave. sense M

% S

pre-test

2.76

3.67

38.1

2.15

3.96

13.6

post-test

3.29

3.62

38.1

2.30

4.04

9.1

 

 

 

 

Key S is the scientific answer/explanation
M is the misconception

There was an increase in the average ‘sense’ score of the scientific answer for the experimental group together with a decrease in the misconception answer. For the control group there was also an increase for the scientific answer but only a small one. There was a very slight increase for the control group’s misconception answer.

In this topic, the pupils could have worked out the correct answer if they had put together the previous work that they had done. This probably explains the slight increase for the control group’s ‘sense’ rating for the scientific answer.

There was not much change in the answer the pupils thought was correct between pre-test and post-test for either group.

Heat 2 Radiation/Absorption

Table 2 To show the ‘sense’ ratings and the percentage of pupils giving the correct answer for the experimental and control groups pre- and post-test (heat 2)

heat 2

experimental

 

control

 

ave. sense S

ave. sense M

% S

 

ave. sense S

ave. sense M

% S

pre-test

3.13

2.67

58.3

3.32

2.82

59.1

post-test

3.42

2.77

62.5

2.82

3.05

45.5

 

 

 

 

 

There was a slight increase in the average ‘sense’ score for the misconception answer for the experimental group but a much greater increase for their scientific answer. The results for the control group showed a substantial drop for the scientific answer together with a corresponding increase for the misconception answer. This topic was difficult to work out the correct answer based on the previous work. It seems as though, having seen the absorption experiment, the control group become more sure that good absorbers are poor radiators. Their replies as to why they had given the answers that they had included the following:

M is a more likely explanation because it is the opposite and absorbing and radiation are opposites.

Other replies were similar in nature without actually emphasizing the word ‘opposite’. None of the replies from the experimental group mentioned the analogy directly although several used the word ‘you’ as in:

I think this because when you are good at something, radiating, you are usually good at the other, absorbing heat.

This use of a personal pronoun possibly indicates a subconscious link with the analogy meaning that the p-prim has been cued without conscious thought.

The sense ratings are a possible indication of the relative strength of the p-prim concerned.

4% more chose the correct answer for the experimental group between the pre-test and the post-test compared with a 14% decrease for the control group.

Light 1 Reflection

Table 3 To show the ‘sense’ ratings and the percentage of pupils giving the correct answer for the experimental and control groups pre- and post-test (light 1)

light 1

 

experimental

control

 

ave. sense S

ave. sense M

% S

ave. sense S

ave. sense M

% S

pre-test

4.18

2.23

90.9

4.50

2.00

90.5

post-test

4.36

2.05

90.9

4.14

2.18

76.2

 

 

 

 

As expected, a slight rise occurred for the experimental group’s sense rating of the scientific explanation together with a small drop for the misconception explanation. Also, there was an increase for the control group’s misconception answer sense rating with a drop in their scientific answer. This is surprising as, for this topic, the control group had had no further relevant teaching since the pre-test, it being the beginning of the topic.

With the experimental group, there was no change in the percentage who chose the correct answer but there was a drop of 14% for the control group.

Light 2 Filters

Table 4 To show the ‘sense’ ratings and the percentage of pupils giving the correct answer for the experimental and control groups pre- and post-test (light 2)

light 2

 

experimental

control

 

S

ave. sense M

% S

ave. sense S

ave. sense M

% S

pre-test

1.90

3.38

14.3

2.32

3.45

18.2

post-test

3.38

2.71

71.4

3.09

3.45

45.5

 

 

 

 

There was a pleasing increase in the experimental group’s scientific answer but this should be weighed against an increase in the control group’s scientific answer. The increase for the experimental group was, however, greater than that for the control group (1.44 as opposed to 0.77).The increase for the control group is to be expected as they saw the experiment showing that a colour filter blocks the passage of the other colours of the spectrum. In fact, it is surprising how many still adhered to the misconception that colour filters add colour to white light having seen the demonstration and video clip. The control’s group sense of the misconception answer remained constant while there was a good decline in the experimental group’s sense of the misconception answer.

There was a substantial increase in the percentage choosing the correct answer for the experimental group (57%) compared with an increase of 27% for the control group.

Forces 1 Book on table

Table 5 To show the ‘sense’ ratings and the percentage of pupils giving the correct answer for the experimental and control groups pre- and post-test (forces 1)

forces 1

 

experimental

control

 

ave. sense S

ave. sense M

% S

ave. sense S

ave. sense M

% S

pre-test

3.05

4.24

35.0

2.68

3.70

25.0

post-test

2.14

4.05

20.0

2.82

3.73

35.0

 

 

 

 

This was unusual and did not follow the usual pattern. Rather than an increase for the sense for the scientific answer, there was a decrease (for the experimental group).

Forces 2 Stretching

The final topic was on stretching and did not ask for sense ratings.

forces 2

 

experimental

control

 

% S

% S

pre-test

42.9

31.6

post-test

61.9

21.1

 

 

 

 

As can be seen from table, there is an increase (19%) in those choosing the correct answer from pre-test to post-test for the experimental group together with a decrease for the control group (11%). This followed the pattern of the first four topics.

Discussion of results

The first four topics show a cumulative effect in sense ratings as shown in the following graph.

The probability that these results happened by chance were calculated using a 1 tailed t-test for correlated data. p = 0.0035; this is statistically significant at < 0.01. The probability that these results happened by chance using a 1-tailed t-test for non-correlated data for the individual pupils’ results was 0.0026; statistically significant at < 0.01.

The first four and the final topic show a similar cumulative effect when the percentage of pupils choosing the correct answer is considered.

Average percentage choosing correct answer for first four and last topics

Experimental pre-test 48.9%

Control pre-test 42.6%

Experimental post-test 65.0%

Control post-test 39.5%

The results show that this is a relatively successful method for cueing the correct p-prims for these topics. However, the results for the ‘book on table’ topic show that the low key use of the bridging analogy plainly did not work for this topic. It is thought that the reason for this is because of the deeply entrenched idea that inanimate objects such as a table cannot produce forces and merely block the way.. This supporting or blocking p-prim totally eclipses any attempt at trying to cue alternative p-prims. A longer approach is indicated for this sort of problem.

Conclusion

This research has drawn together the work on analogy and p-prims and has shown that, for some topics, correct p-prims are more likely to be cued if a low-key analogy is used. Pupils subconsciously connect the analogy with the p-prim. It should again be emphasised that the link is subconscious and not overt as is shown by their answers to questions such as ‘why do you think this?’ where any reference to the analogy was missing. Low-key analogy does not always work. In topics where there are already deeply held beliefs such as the ‘book on the table’ problem, it is more difficult to steer pupils towards the correct idea using this simple method.

It is expected that using analogy in a less low-key manner may give better results as the link is then made explicit. This is, however, time-consuming as the use of analogy itself can cause problems. One of these is that analogies, by their very nature, are not perfect and at some point break down.

This increases the time needed considerably since the analogies used and their limitations must be discussed with the pupils, reducing time available for other work. For certain topics it may be more productive to use the low-key analogy method to encourage pupils to be thinking along the right lines before going into scientific explanations.

References

diSessa, A. A. (1993) ‘Towards an Epistemology of Physics’, Cognition and Instruction, 10(2&3): 165-255.

diSessa, A. A. (1996), ‘What do "just plain folk" know about physics?’ in D. R. Olson & N. Torrance (Eds.), Handbook of Education and Human Development: New Models of Learning, Teaching, and Schooling, Oxford: Blackwell Publishers, Ltd.

diSessa, A. A. (2002). ‘Why "Conceptual Ecology" is a Good Idea’ in M. Limón & L. Mason (Eds.), Reconsidering Conceptual Change: Issues in Theory and Practice (pp. 29-60). Dortrecht: Kluwer.

McCloskey, M. (1983). ‘Naive theories of motions’, in D. Gentner & A. Stevens (Eds.), Mental Models (pp. 289-324). Hillsdale, NJ: Lawrence Erlbaum.

Sherin, B. (1999) ‘Commonsense Clarified: Intuitive Knowledge and its Role in Physics Expertise’, NARST Annual Meeting.

 

I am looking for science teachers (key stage 3) to teach and comment on one or more analogy lessons.

If you would like to help me in my research, please send me an email at: a_nelmes@hotmail.com

This document was added to the Education-line database on 22 October 2004