Knowledge in Pieces

One part of my job is “helping students understand that they leave each class with Swiss cheese knowledge – it looks solid but it is full of holes.” That’s #4 of Hoyle’s Top Ten, an insightful list that I regularly revisit.

I was reminded of the Swiss cheese analogy today while reading “A Friendly Introduction to Knowledge in Pieces: Modeling Types of Knowledge and Their Roles in Learning” by Andrea DiSessa. I was cued into this article having read a different article related to Ionization Energy – more on that in a moment – and that’s how going down the rabbit hole works.

The article is aimed at math educators but it also provides some interesting examples in physics; since the Knowledge in Pieces (KiP) framework began in physics education. KiP attempts to bridge the gap between theorizing about how conceptual change and the actual practice of learners as they work their way through a problem. KiP assumes that learning is a complex and messy process, taking place over multiple scales and timeframes. It’s also one of the few frameworks that considers the value of what others might consider folk-science intuitive thinking, because such ‘primary’ approaches are unlikely to be easily discarded and for good reason. Instead of just labeling such an approach a ‘misconception’, why not leverage it to good use by providing more examples and varying contexts?

Several things that jumped out at me: KiP assumes that naïve knowledge is both conceptually rich and productive. This doesn’t mean it gets things right all the time – there are many examples of intuition leading one astray especially when encountering non-intuitive ideas in science. There are plenty of examples in physics and chemistry, which has led to increased use of concept inventories in introductory classes at the college level. The richness of this naïve knowledge means that it is interconnected with many other intuitive experiences, hence context matters. DiSessa emphasizes the point that as students experience conceptual change as they learn, there are also contextual changes. This is why we often think a student has learned the right concept when they demonstrate it in one context, and then be flabbergasted when they fail to apply similar reasoning in another context moments later.

One of the broad intuitions that students (and even instructors) have is some notion of balance. Things sorta balance out, somehow. Here’s an example that shows up in general chemistry: Students can easily tell me that a cation is smaller in size than its neutral atom. When asked to explain why, they will reason thus – when an electron is removed from an atom, the number of protons remains the same but the number of electrons has decreased by one. Hence the positive charge of the nucleus is now spread out over fewer electrons so it can attract them more strongly, pulling them closer to the nucleus, and thus reducing the size of the cation.

Now, if you read the explanation too quickly, you might nod your head in agreement. While I’d like to think I haven’t consciously used this explanation, it makes me wonder how careful I am when I’m helping students formulate the argument. Most of the argument works except the part where the student invokes the principle of balance – with one less electron, things need to balance out so the nucleus attracts the remaining electrons more strongly. (What actually happens is that the electron-electron repulsion is reduced.) I was reminded of this example reading a paper on student misconceptions related to Ionization Energy by Daniel Tan and co-workers (Intl. J. Sci. Educ. 2008, 30, 263-283). To counter the misleading intuition, the paper actually provides an excellent counter-example: the bonfire! I’ll quote the paper.

To challenge the common notion that the nucleus gives out an amount of force or attraction to be shared by the electrons, teachers need to emphasise the basic Coulombic principles. A possible analogy to teach the nuclear attraction for an electron is to say that it is similar to the heat one receives from a bonfire—this is dependent on how big the bonfire is, the distance one is away from the bonfire, and whether one is blocked (screened/shielded) from the bonfire, but is independent of how many people are present at the same distance away from the bonfire. This analogy may prevent students from thinking that electrons share the attraction from the nucleus. However, it does not take into account the equal and mutual attraction of the nucleus and the electron, as well as the repulsion between electrons, so these have to be highlighted.

I think I need to start using this example in class to help counter the misconception that I’m sure many of my students would fall back on. A graphic illustrating said bonfire would probably help too! I’ve started showing the picture of a large thumb (with a crown) to remind the students that the octet rule is a rule-of-thumb! Otherwise, they invoke it as the explanation for all manner of things. They have knowledge in pieces, like Swiss cheese, but today I’m reminded of how much of my knowledge is also in pieces especially as I’m learning new things during my sabbatical.