Mylène has some interesting musings in her post Who knew there were so many weak definitions of “series circuit”?

This is the sort of misunderstanding that is hard to discover with clicker questions or multiple-guess tests. Even standard design questions might not reveal it.

I think that there is a way to uncover (and maybe correct) this sort of misunderstanding in a peer-instruction context, and I think I might try it in the applied circuits course (assuming I get to teach it). During the first week, I’d draw schematics of resistors connected in series and in parallel on the board, and ask the class to identify which one is series and which parallel, just with voice response. I expect that essentially everyone would get that right. Then I’d pass out index cards and ask everyone to write a definition of a series circuit on one side of the card, without discussion. After a couple of minutes, I’d have them compare definitions with a couple of neighbors, discuss for a couple of minutes any differences in definitions, then write a revised definition on the other side of the card. I’d then collect the cards, draw a few at random, and discuss the (revised) definitions with the whole class.

I’ve never used that approach to instruction before, but it seems to be a good one for checking fundamental concepts, but only if there is a high probability that students will get it wrong on the first attempt. I’ll have to look for opportunities to use it in my bioinformatics class this quarter.

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Interesting ideas. To clarify, my students will consistently differentiate series from parallel circuits, if given only those options. Where it falls down is if they have to pick out series and parallel components in a series-parallel circuit. For example, the circuit we were discussing in class the day I wrote my post was a voltage-divider-biased class A amp. We treat the biasing resistors as if they’re in series, when clearly they’re not. It was this situation of “acting” like things were in series while trying to justify why that was a reasonable (but technically incorrect) approximation that yielded all of the confusion.

Some options: have them write definitions for series and parallel “circuits”, and then see which definitions can be generalized to series and parallel “components.” Try giving a circuits where R1 is in series with the parallel combination of R2//R3 — have them test their definitions to determine if anything can be considered to be in series. Try giving a circuit where R1 is in series with the parallel combination R2//R3, followed by a series R4 (sorry, no time to make up drawing this morning — let me know if this is unclear). Which ideas define R1 and R4 as being in series, and which ones don’t? Try giving a wheatstone bridge with a high-impedance load (voltmeter?) across the bridge. Do the definitions differ in their implications of which components are in series or in parallel? (By my definition, a loaded wheatstone bridge has nothing in series nor in parallel, except to consider the entire bridge circuit in series with the power supply). An even simpler example is a simple, two component, series circuit. Connect a voltmeter across one component. We don’t normally consider the voltmeter to change the component relationships, but of course it does. This is now neither a series nor a parallel circuit. Or consider a single component connected to a single power supply. Series or parallel? A strong set of definitions will conclude that it is both, exhibiting all the characteristics of both, and that this is not a contradiction. Another useful exercise is to draw two resistors connected at one end, then draw ground symbols at the unconnected ends. Series or parallel? This can motivate a conversation about whether we need to know where the power supply will be connected before we can discern whether things are in series or parallel. Finally, another useful exercise is to have students apply the Thevenin theorem to simple circuits. This process requires students to “disconnect” a component, which can change the series/parallel relationships. It also requires students to imagine replacing any voltage sources with 0 ohm resistors (my preferred explanation, rather than telling them to “short out the supply”) and replace current sources with opens, which also change the relationships, and forces students to tangle with the idea that the series or parallel relationship between two components is not only influenced by those two components, but also by what is around them.

Try giving them a circuit for which they can not quickly discern the purpose, nor estimate any voltages currents (a simple BJT amp is a good example, if they haven’t analyzed them in the past). Ask them what is in series and what is in parallel.

A big booby-trap in this mental process is that students have a strong tendency to conclude that things are either in series, or in parallel. In other words, if a circuit (or collection of components) fails the series test, they will assume that it passes the parallel test, without checking.

Comment by Mylène — 2012 October 13 @ 08:40 |

So the problem is not that students don’t understand series and parallel, but that they can’t generalize these concepts to more complicated situations where a part of the circuit can be usefully modeled as series or parallel connections. The “big booby-trap” at the end of your comment is their not realizing that sometimes a part of circuit

cannotbe usefully modeled as series or parallel.Some of your illustrative examples will be very useful for homing in on a good definition. A pedagogical question is when to give them the examples. Before they try to define the concept? After their first attempt but before their second attempt? During whole-class discussion? As homework?

We have rather limited class time (35 hours to get through everything, including any assessments), so I want the time in class to be used efficiently. (Lab time is another 30 hours, but I think lab time is too precious to spend on concepts that don’t need access to equipment.)

How much time are these concepts worth? What fraction of the class needs to have really internalized the concepts before we move on to other concepts? I have a history of pitching my classes to the top third of the class, so that they really learn stuff. The next third can usually keep up if they work at it, and I often lose a number of students from the bottom third. This slow, careful building of the definition of series seems more aimed at the middle and bottom of the class and is likely to bore the top students after the first few minutes.

The bioengineering students I’ve encountered before (in senior design project classes) span a huge range of abilities, from ones who were publishing excellent first-author papers as undergrads (and filing IP with the university) to ones who seemed incapable of even simple engineering homework. If this course is going to work for most of the bioengineering students, at least as well as the standard circuits class, I don’t want to lose too many at either the top or the bottom end. I don’t feel I need to reach everyone, since some attrition from engineering majors to other majors is acceptable, but I am trying to make this course be one that attracts students into bioelectronics, rather than serving as a barrier to keep them out (as the current circuits course does).

Comment by gasstationwithoutpumps — 2012 October 13 @ 12:53 |