‘Fields, force, energy and potential’: alternative conceptions, analogies and learning

‘Fields, force, energy and potential’: alternative conceptions, analogies and learning Richard Gunstone (Centre for Science, Mathematics and Technology Education Monash University)

An outline - - - • Some examples of student perspectives on this section of the curriculum - - via a comparison of some aspects of context for “gravity” (!!) and “electricity” (!!) • The central issues with analogies for abstract ideas such as “potential difference”, “electricity” (!!), “field”,………… • Some of the more pervasive and significant Alternative Conceptions • And a short comment or two on other aspects you might think of keeping in mind

Some compare and contrast with ‘Gravity’ and ‘Electricity’ to explore student learning issues

CURRENT – *A “current” in all other contexts is the movement of a physical entity……. (remember the origins of this term being used in our physics context….) POWER – *Having control or authority or influence over others….. *Ability (to do), capacity (of doing), a particular physical or mental capacity… *x to the power 2, etc, etc, etc POTENTIAL – *Something that exists as a possibility, not a reality - - - So potential energy must refer to something that has the possibility of having energy, not something that has energy (e.g. IF that box falls off the shelf it will have energy [kinetic energy], but it does not at the moment and that’s why it is said to have “potential energy”)

IF you wish to link “potential” in the context of electric fields with “gravitational potential energy”, for example with objects dropped from the top of a given cliff, what will your description of the cliff and “gravitational potential energy” need to look like??

Another significant language issue – “voltage” Early this century, as part of a much broader investigation, Pam Mulhall, Brian McKittrick and I interviewed many physics textbook authors, including to probe their conceptual understandings of electricity. We wrote at the time (G, McK, M, 2003) that “[w]e regard ‘voltage’ as, at best, an unhelpful term to use in the study of DC electricity”, because • There is no clear agreed meaning for the term ‘voltage.’ • There are unresolved problems in the multiple and variable ways ‘voltage’ is used in some textbooks (e.g. is it concerned with ‘energy’ or ‘energy difference’? with energy ‘source’ or ‘sink’? …) and we noted that a number of iconic physics textbooks make no mention of ‘voltage’ anywhere in their indexes We hold that it is more helpful to consider ‘voltage’ as essentially a form of physics slang expression, derived from the word ‘volts’ and meaning ‘how many volts.’ Of course ‘volt’ is a different matter – and for many students problematic for no good reason……

Some examples of student perspectives on this section of the curriculum - - in summary Across the topics usually labeled ‘gravity, ‘electricity’, magnetism: • Some students do not see constructs such as “field” and “energy” as the same in each conceptual area of physics (or science…) • Many students have some confusion with the physics meanings and everyday meanings of words that are common to both (something that is not resolved by dismissing the everyday meaning, even though it very likely has the student suggest all is now fine) • These language/concept confusions are magnified by the occasional physics use of terms for which there is no commonly accepted meaning (e.g. voltage) • The above and the much more problematic matter of the complete abstractness of the concepts of electricity means that many (?most) students quickly come to “take refuge” in formulas to try to analyze electrical phenomena/situations – and to very often base their reasoning on a literal description of the “formula” or an incorrect causal analysis of it. • This is further compounded by the common student “failure” to relate macroscopic phenomena (the observable, either direct or via the black box of instruments) with the microscopic concepts that lead to the explanatory theory (eg field, potential difference…)

THE central issues with analogies for abstract ideas **Would you like to hear my “best analogy to use for electricity concepts”? NOT POSSIBLE!! There is NO “best analogy” for all matters electrical While some analogies are completely unhelpful (often because they are complicated and compromised by trying to explain what they cannot), most problems with analogies are about the USE of the analogy. • Be clear about ‘TARGET CONCEPT’ (what concept, SPECIFICALLY, is the analogy intended to help with (clear for both teacher and students) • Be clear about the ‘ANALOG CONCEPT’ (both Tr and Sts) • Be clear about the RELEVANT features of both Target and Analogy • MAP the similarities between the RELEVANT features in 3. • Be clear (both Tr and Sts)where the analogy breaks down, does ‘NOT WORK’ And #5 is THE most important issue in using analogies so that student understanding of the Target concept is actually enhanced

THE central issues with analogies for abstract ideas **Would you like to hear my “best analogy to use for electricity concepts”? NOT POSSIBLE!! There is NO “best analogy” for all matters electrical While some analogies are completely unhelpful (often because they are too complicated and compromised by trying to explain what they cannot), many problems with analogies are about the USE of the analogy. • Be clear about ‘TARGET CONCEPT’ (what concept, SPECIFICALLY, is the analogy intended to help with (clear for both teacher and students) • Be clear about the ‘ANALOG CONCEPT’ (both Tr and Sts) • Be clear about the RELEVANT features of both Target and Analogy • MAP the similarities between the RELEVANT features in 3. • Be clear (both Tr and Sts)where the analogy breaks down, does ‘NOT WORK’ And #5 is THE most important issue in using analogies so that student understanding of the Target concept is actually enhanced

Some of the more pervasive and significant Alternative Conceptions(many known to be held by physics undergraduates as well) • “Concept X in one area (say dynamics) is not the same as X in another (say electrical)” [X can be ‘energy’, electric potential in electrostatics or circuits] • “An electric field is the area around an electric charge” (and not what is in that area) (this is essentially taking “field” to have its everyday meaning) • “An electric field is a collection of charges.” • “Electric field and electric force are the same thing, and in the same direction” • “Field lines are the field” (fields only exist where the lines are) • “Field lines show the direction of motion of a [relevant thing] at that point in the field” • “Field lines can cross each other” • “Electric fields can only exist when there is moving charge” (and so, as there is no moving charge in an insulator there cannot be an electric field in an insulator) • “The explanations for the movement of charges [from dynamics] are not linked to the ideas of ‘action-at-a-distance’ and ‘field’ and ‘electrical force’ ” • “Electric current passes through a wire because there is more charge [meaning greater quantity of charge] at one end of the wire than at the other.”

Other matters you might think about --- the textbook Look carefully at the text books in these areas - - - Some statements from a 1st year undergrad text widely used around the turn of this century: **"Electrons will flow out of the negative terminal of the battery, through the resistance R and cumulate on the upper plate of the capacitor" (p 612) (Both this clear statement that any one electron will move around the totality of the circuit and the strong inference that the battery is the source of these electrons are repeated in various ways at a number of points, eg p 587 and in a number of end-of-chapter problems.) **Consistent confusion between charge as a physical quantity and charge as a particle, with no comment at any point about this duality of meaning. **Energy is explicitly described as "not a substance " and as "not having a definite location" (p 572). BUT - - then "Nevertheless it is often useful to think of [energy] as being stored in the electric field between the plates [of a capacitor]" (p 572) and this notion of energy as substance is then commonly used. (No justification other than "nevertheless it is often useful to think of" is given for this use of energy as substance.)

You might think about the textbook ---- because the author of that textbook MIGHT think ….. This author of Yrs 11 and 12 physics textbooks that were quite widely used in the Australian relevant state ~15 years ago is NO LONGER writing textbooks. **His/her own comments about ‘emf’, ‘potential difference’, ‘voltage’ included --I see voltage as being – I stress this word there – an indication [interviewee’s emphasis] of the energy that the charges have got --Emf and potential difference are sort of the old traditional ones there and we tend to use voltage as being more familiar to students cos they can relate better to that than the other two terms --I tell students that … we use the term emf and we’ve got potential difference there and voltage and I tend to tell them that you know, really all those things are sort of voltage if you want to use one sort of term, um, even though you know scientifically each of them on their own [has] got a more precise meaning **(no – he/she could not give us any sense of what these “more precise meanings” were) Yes - - - the book is as bad as these shorts extracts from our interview with him/her would suggest!!

Other matters you might think about --- Google When one of your students Googles “what is an electric field?” the first page of hits will likely include (because it DID include on Oct 10) [1] “Electric field - a region around a charged particle or object within which a force would be exerted on other charged particles or objects.” [2] “Electric field is defined as the electric force per unit charge” [3] “An electric field is a vector field that associates to each point in space the Coulomb force that would be experienced per unit of electric charge, by an infinitesimal test charge at that point” [5] “We can think of the forces between charges as something that comes from a property of space. That property is called the electric field.” [8] “Learn what an electric field is……..An electric field is the force that fills the space around every electric charge or group of charges. Electric fields are caused by electrical forces.” ……………….

‘Fields, force, energy and potential’: alternative conceptions, analogies and learning