Monthly Archives: January 2017

In Shulman’s article “Knowledge and Teaching: Foundations of the New Reform,” he describes how both management of students and management of ideas are necessary components of guides of good practice.  He also says that teachers themselves have difficulty in articulating and explaining what they know and how they know it.  These two points stuck out to me in particular as they emphasize the interconnectedness of the different components of PCK and TPACK.  Individually, each of the components provides a fragment of the image of teaching and learning, but it is only through a collective approach that true teaching occurs.  An individual with strong content knowledge but poor pedagogical knowledge likely would not be truly effective at achieving learning goals in the classroom, nor would an individual with weak content knowledge and strong management skills.  The balance is what I feel develops over time as university students become professionals and new professionals become more experienced in the profession.  Unfortunately, it would seem that for teachers who struggle to find this balance, burnout caused by needing to compensate for gaps in pedagogical or content knowledge can be more likely.

When I teach students about fractions, I spend time developing understandings with physical manipulatives (e.g. coloured cubes, fraction magnets, egg cartons and marbles, fraction pizzas) and digital simulations in Smart Notebook or on the iPad, and then move into the more abstract concepts of the written algebra.  This comes to mind as an example of PCK (or TPACK depending on the strategies on a particular day) as it includes knowledge of the actual mathematics of fractions, what they represent, common errors when working with them, and real-world applications, while also accounting for pedagogical strategies of how best to help specific students learn the concept.  I have found that while students initially struggle with the abstract concept of fractions, when they are able to see and manipulate conditions, they are better able to develop an understanding of fractions and their mechanics, and then subsequently be able to apply this knowledge in further learning.  Someone with a strictly mathematical knowledge base would not likely be able to select the most effective activities for the learning needs of particular students, and someone with a weak understanding of fractions would not likely be able to provide a wide range of learning opportunities and manage student questions and strategies.

In situations where a teacher needs to teach unfamiliar or uncomfortable topics, what strategies can be used to help them continue to provide effective learning experiences?  How can more experienced colleagues support new teachers in developing the skills and knowledge necessary to find the balance without burning out in the process?

While the specific terminology PCK and TPACK are novel to myself, the concepts themselves are not. The fusion of content knowledge and pedagogy are vital to any teacher’s success. Schulman argues that the teacher is responsible for taking what they know and preparing it for effective instruction. This process involves the following aspects: comprehension, transformation, instruction, evaluation, reflection, and new comprehension. Teaching is a complicated process that involves knowing concepts and conveying them to students in hopes that they too obtain this understanding. Shchulman states this can occur through “talking, showing, enacting, or otherwise representing ideas.” In summary, an effective educator needs to have both a mastery of the content itself, as well as the ability to convey that information to students through transformation of that knowledge and instruction.

In terms of an example of PCK lesson of mine, we are currently introducing the concepts of significant figures, precision, and accuracy in Physics 11. Students often have difficulty differentiating the ideas of precision and accuracy and further, applying significant figures to real world data. Following discussion of these topics, students then complete a mini lab where they use lab equipment (such as meter sticks, rulers, calipers, tape measures and various graduated cylinders) and apply those concepts to practical measurements. They are faced with four problems that involve measurement and calculations that will assist them later in the course.

References:

Shulman, L.S. (1987). Knowledge and teaching. The foundations of a new reform. Harvard Educational Review, 57(1)1-23.

While pedagogical knowledge and content knowledge continue to be different concepts by definition (with pedagogical knowledge addressing the “how” of our teaching, and content knowledge addressing “what” we are teaching), it is interesting to me that these concepts would have been treated as separate entities, not that long ago (Shulman, 1986; Mishra & Koehler, 2006), rather than interconnected as I believe they are seen today. In the past, the “how” was through an imparting of knowledge from teacher to learner. Children’s minds were to be filled and knowledge was transferred through lectures and independent work assignments. Today, through research and technology, we realize that students do not learn well in these environments. In addition to this, the content that we once deemed important has changed as well, and will continue to evolve as the world changes with the development of new technologies and as we learn from our current world structures and experiences.

The concepts of pedagogical and content knowledge are not new, but the way they are addressed in our society and our classrooms today has changed (or at least is in the process of changing) to support the increased importance and value of digital technology and related multiliteracies/new media literacies. This brings into question “how” we are using technology in our classrooms today, as well as what programs or skills we are teaching through it. Are we enhancing learning? As Mishra and Koehler (2006) point out, “Merely introducing technology to the educational process is not enough” (p. 1018) and both the “how” of teachers’ application of technology and the “what” that technology will look like play important roles in our classrooms today. As Mishra and Koehler (2006) discuss, it is now the “how” of educational technology’s integration into our curriculum and teaching practice that must be addressed.

Today, I feel that much of our teaching is moving away from imparting “teacher” content knowledge and towards instead teaching students skills so that they can investigate and research to find their own knowledge. While this might sound like we are beginning to shift our focus back to “pedagogical knowledge,” I would argue that today pedagogical knowledge incorporates concept knowledge (and in some classrooms, technology knowledge – we’re getting there…) in so well, that they blend together quite naturally. Students construct knowledge best by doing, not by listening, so by allowing students to be creators of their own content knowledge (to a certain extent – teachers, of course, continue to play an important role), we are allowing them the choice and flexibility to learn more freely, with fewer restraints. For example, for a science unit on the human body, my students and I explored, together as a class, the digestive system, which included some textbook reading (read and discussed together as a class, not individually), a look at x-rays of human intestines (belonging to a colleague of mine who recently retired and passed on a set of old x-rays to me – the kids love them!), student diagrams/models, and so on. Once we have done one body system together, students are sent out to research and become “experts” on one other body system that they will be able to share with their peers. The teaching that is done to support this is around the “how” to research effectively, which resources would be appropriate, how to reference works, and so on. There is some “what” (content) mixed in as students are taught to ask inquiry-style questions to get their research going; however, it is not a delivering of knowledge of the actual scientific content I want students to come away with – that part they have to do themselves. Ultimately, students create projects that fulfill criteria that we designed together before beginning the project. Students are required to create initial questions they have about their system, then attempt to answer those questions through their research. They are required to use at least one book source and one online source, to include pictures, keyterms and definitions, and eventually to share their knowledge in small groups with others in their class. Each student ultimately learns about each system, but in the process, they have interacted with the content themselves, collaborated with peers, problem solved and actively participated in their own learning and then in the teaching of others. In this way, the students become creators of their own knowledge and the information being learned becomes more accessible to learners in the classroom.

References:

Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017-1054.

Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4 -14.