CHAPTER 1
Using Pedagogical Content Knowledge to Plan to Overcome Misconceptions
Pedagogical content knowledge is rather a mouthful to say. It might be thought of as the millefeuille of educational thought, in that it is known yet remains unfamiliar. The cake of a thousand leaves is reminiscent of the many interleaved layers of understanding that a teacher has: of the content being learned, how the learning tends to happen, the strategies it is best to employ, the knowledge and learning needs of their students. Pedagogical content knowledge was developed by Lee Shulman (1986, 1987) and is a blend of subject knowledge, pedagogical knowledge and knowledge of the context in which learning takes place. It is all of these things and more; describing it as a âblendâ does not really do it justice. Although the individual elements are important in themselves, it is in combination that they become as potent as when the Ghostbusters crossed their proton beams.
At first glance, pedagogical content knowledge appears to be âjargoneeringâ, but the name is a useful one in terms of giving us a focus on how the content is to be transmitted so that it is learned. It is our pedagogical content knowledge that differentiates us, as teachers, from our equivalent non-teaching specialists (scientists, writers, mathematicians, economists); it is our pedagogical content knowledge that compels us to organise the transmission of knowledge in the way that we do. It is our own pedagogical content knowledge that we must employ in our planning, and it is the studentsâ pedagogical content knowledge that we must seek to spot in lessons so that we can speed up its acquisition.
My first, and only, formal experience of pedagogical content knowledge came early on in my career. (I say formal but, in reality, it was only as formal as a cramped science prep room can possibly be.) It involved a dear colleague, Mark Lovatt, passing me a folder with Ros Driverâs Eliciting Childrenâs Ideas in Science inside and being told, âRead this. Itâs great for planning lessons!â It was great; it still is great.
Sadly, I do not think I am alone in not having had any real training or discussion about how our subjects are learned. We tend to focus therefore on what we do as teachers â getting hung up on strategies, methods, teacher actions and any feedback we receive on our teaching. We call this teaching & learning: excited colleagues produce teaching & learning bulletins; we attend training in teaching & learning; we build teaching & learning toolkits; we speak of teaching & learning cycles; go on jollies to teaching & learning conferences; ruminate over teaching & learning development plans; we adhere to teaching & learning policies. And all the time we do this, pedagogical content knowledge is under our noses â ignored. What is pedagogical content knowledge? Let me tell you, dear colleague ⌠pedagogical content knowledge is the very ampersand between teaching & learning.
The ampersand
The great potential for formalising our use of pedagogical content knowledge is that we can move from using it instinctively and inconsistently to being able to plan with it systematically. Perhaps most importantly, it helps us to become more aware of what learning might look like in the classroom, sensitising us to misconceptions when they arise and turning them into teachable moments.
Pedagogical content knowledge most commonly manifests as one of four interacting forms:
- Knowing how to represent knowledge so that it can be learned. This is context dependent, with teachersâ prior understanding of their class(es) being a key part of how they go about representing this knowledge.
- Knowing how to organise or sequence knowledge so that it can be learned. We have to understand how the knowledge is connected to other knowledge and other concepts. This must involve planning on a macro and micro scale so that the overarching idea and the interrelated details underneath become clearly connected.
- Knowing which concepts and ideas are difficult to learn and, subsequently, how to help students learn them. This includes knowledge of likely student misconceptions.
- Knowing which knowledge is important. This includes threshold concepts.
We can also add to this our knowledge of the (ever changing) curriculum and the assessment of the subject.
To be clear, the content of this book, and not just this chapter, is dedicated to understanding our pedagogical content knowledge. The next two chapters detail how we can understand the teaching of our subjects better, and the last three look at the more generic pedagogical content knowledge of the processes of how to teach and how we learn.
Planning to tackle misconceptions
What are misconceptions?
Carnegiea gigantea, the Saguaro cactus (a native of the south-western United States) is the stereotypical flora of our cartoon childhood; it is the version of cactus that marked the barren landscape through which Wile E. Coyote chased the Road Runner. Although they are surprisingly shallow rooted for a plant of that size, their rooting system is well adapted, with roots wrapping around rocks to provide anchorage. They are also incredibly robust plants. It is no surprise that Wile E. generally comes off second best when he runs into one. The Saguaro cactus itself has no awareness of how silly its choice of home is or even of how it has changed the climatic and edaphic features of the Mojave Desert.
Similarly, student misconceptions are generally shrouded in a haze of blissful unawareness of their folly or illogic. Like the cactus, they too are anchored to rocks, this time of âknowingâ, and like the cactus, these misconceptions can be extremely hardy. Additionally, misconceptions â like the effect the cactus has on Wile E. when he comes into close contact with one â also have the capacity to taint any ideas that come into contact with them. The cactus belongs in its habitat. Likewise, there can be many logical reasons for misconceptions to exist. The idea itself may be wrong but the reasoning behind it can be as right as rain.
The problem with misconceptions
Misconceptions can have a strong grounding in our studentsâ everyday experiences. They can lie in their use of day-to-day language or in partially formed ideas that have persisted because they havenât yet been challenged. In some cases, students have actually seen the phenomena with their own eyes! And seeing, as we know, often results in believing. The word âbeliefâ tells us that our studentsâ misconceptions can be deeply held to the point of feeling as if they are unquestionable. The importance of this is brought to bear by Nuthall (2007: 156): students âevaluate [each] new experience, and what the experience implies, against their prior knowledge and beliefsâ. Here, he is saying that students use their prior experiences and what they know to interpret and make sense of any new ideas being presented. If this âknowledgeâ is actually incorrect, then the students will not make the correct interpretation of this information and learning wonât happen. This mode...