Category Archives: B. PCK

Shulman (1986) differentiates between content knowledge and pedagogical content knowledge (PCK).  It is true the teacher must be an expert in the content she wishes to teach but at the same time must also be an expert in how to teach that content.  This is where Shulman (1986) suggests PCK is, “…the most useful form of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations…” (p. 9).  The ideas he speaks of are the content, the concepts, the specific learning outcomes outlined in the curriculum guides.  It is essentially not enough to know the stuff, but to know how to help students know that stuff that you know so well.

An example of PCK I have used in the past that has anecdotally worked well for me is the topic of blood types and blood transfusions, hence the title of this post :).

Blood types and transfusions shows up in the biology 30s Manitoba curriculum under the circulatory system.  It is a challenge for students to understand how we have 4 different blood types, and why getting certain red blood cells (RBCs) can be beneficial to a patient and why others can be catastrophic.  In order to help illustrate these ideas I have used the analogy of donuts. I did not come up with this analogy, simply found it online and borrowed it like any teachers with the best of intentions at heart.

Basically the analogy goes that RBCs are like donuts, some have A sprinkles, some have B sprinkles, some have A and B sprinkles and some have no sprinkles.  Sprinkles are analogous to antigens found poking out on the surface of these RBCs that help identify the type of they are either A, B, AB, or O.  The Rh sprinkle is tacked on after when students are comfortable with the A, B, AB, and O.

Then comes the challenging part of identifying correct versus wrong blood transfusions where students often get lost.  Here the presence of antibodies is explained and the Blood Typing Came from Nobleprize.org (https://www.nobelprize.org/educational/medicine/bloodtypinggame/) is used to help gamify transfusions and help the development of the concept in an engaging way.  I suppose this is where I use technology and essentially  I am using TPACK at this point in the lesson.

I enjoy teaching this lesson as I get to talk about donuts and the game is fun to play.

Thanks,

Vibhu

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

Blood Typing Game. (Nobleprize.org). Retrieved from: https://www.nobelprize.org/educational/medicine/bloodtypinggame/

In Schulman’s reflections we see the recent development of a distinction between knowledge and pedagogy. The idea of teacher competence has shifted towards competence with pedagogy rather than the historical view of teachers as the holders and disseminators of knowledge.  With the emphasis  on classroom management, organizational skills,  assignment creation and questioning formats, planning and assessment strategies Schulman proposes that an important piece is missing. We should be asking  questions about how the content of the lessons is taught. The important questions of where teacher explanations come from, how decisions about teaching are made, how to represent content, how to question students and how to deal with problems of misunderstanding are integral to sound practice. He proposes that by asking these questions we can begin to build information that can address gaps in these areas.  Content deserves as much attention as the elements of teaching process.

He disseminates this further, breaking down knowledge into 3 components: content knowledge, pedagogical content knowledge and curricular knowledge, all of which should be robust for education to be rich and for an optimal teaching and learning environment.

In my own classroom I am currently teaching the concept of time to grade 2 students. When teaching this concept, the background knowledge in skip counting by 5’s and well as previous understanding on time to the hour both on analog and digital clocks is helpful. It can be a difficult concept for some students because the numbers on the clock 1-12 also correspond with skip counting by 5’s all the way from 0-60. The hour is 60 minutes, there are 5 minutes between each number on the clock. So, there are a lot of competing mathematical ideas for young children to simultaneously understand. In addition, there are several different names for time. There is 6:30 and half-past 6:00. There are 6:45 and a quarter to 7:00. In addition, with a heavy reliance on telling time digitally, for example on a mobile device, many parents are not discussing time or telling time using an analog clock at home. Yet, it is still in our  curriculum.

When I teach time I usually have the children construct a model of their own clock with paper and this is a scaffold for them as we begin to explore the concept. In grade 2 the curriculum asks for us to explore 15 minutes on the clock, so 6:15, 6:30, and 6:45.  I begin by reviewing time by the hour and having a discussion with the students about why it is helpful or important to learn to tell the time. We brainstorm ideas and discuss this. Then we begin to map out different important times within the day at school, nutrition break, lunch, recess, etc. On idea I have been reflecting on lately is the fact that time is viewed different within different cultures, and I would like to explore this more fully as I am only teaching from my perspective of linear time. Some cultures believe in circular time.  This brings me back to PCK.  Just because an educator has knowledge of something does not mean it will fit within the structures of our school. Time is limited and decisions need to be made based on many factors.

Digitally I use an interactive clock on the smart board to practice telling time, and I also have children engaged in time games which helps solidify understandings in a fun way. Telling time is a skill that can be taught in school, but for it to be useful the students need to “need” to use it in real ways in their lives. So I introduce the concept, allow them to try using it in school and hopefully in grade 3 and so on they will continue to grow in their understandings and ‘need” to be able to tell the time.

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

Pedagogic Content knowledge is an area of and Technological Pedagogical Content Knowledge are significant theories in the teaching profession.  As we all have experienced at some point in our academic studies, great researchers do not always equate to great teachers.  As a teacher, it’s not just about knowing content, but being able to convey information in a way that it understood by the audience (i.e. students) in the classroom.  As far as educational technologies is concerned, teachers that employ ePCK, integrate technology in a way that maximizes students learning (Koelher et al, 2006).

When approaching a lesson the technology employed should never be chosen first, then the content and knowledge.  Teachers should decide what the end goal or competency is that they want their students to have, and then investigate if there are way to weave technology into them mix.  As Koelher et al (2006) states, technology should be used in a way that enhances the lesson.  Something to be mindful of as teachers, is to not focus too heavily on all areas of TPACK at the same time.  Koelher et al (2006) mentions that students can feel overwhelmed when their teachers focus too heavily on developing their content and technological knowledge all at once.

I recently did a class activity where I sent the students an excel file with data on the times when the ocean was at high tide and low tide. We had spent some times prior discussing the phases of the moon and the gravitational influence on the ocean water.  Then they investigated how the times changed different times of the year in different regions of the world. They choose a country and researched how the changing phases of the moon, seasons and orbit impacted that particular country certain times of the year.

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

In Shulman’s “Knowledge and Teaching: Foundations of New Reform” (1987), he provides readers with an analogy that implies that our subject matter is a vehicle that will “service other goals” (p. 7). He continues to assert that at the secondary level, “subject matter is a nearly universal vehicle for instruction” (p.7).  Near the end of his paper, he provides us with the example of the talented English teacher with two degrees, who lacked grammatical confidence.  When teaching topics that were not in her wheelhouse, she transformed into a “didactic” pedagogue, lacking confidence and displaying anxiety.

I would be lying if I never felt like a didactic pedagogue, early on in my career!  When I started out, I taught a lot of Junior Science, which meant  teaching Biology and Chemistry, two subjects that I did not have beyond a first year level of instruction. The lack of knowledge base, shook me to my core; I am certain that my lack of confidence was obvious to my students, as well. In time, I grew more comfortable with the material, but never above the level that I was teaching. Thankfully, in the last twelve years, I have solely been teaching Mathematics and Physics, but being thrown a junior science is a possibility, every year. <insert wheezing sounds>

What I have learned in my time at the wheel, is that it is OK to not know everything, but it is important to know enough.  And without question, it sure helps to have a solid grasp of at least one year above what you are teaching. Preparing students for their next course is very difficult, when you personally do not understand the material in the next level up!  So to answer my question, these days, I feel like I am driving a pretty solid BMW, although stick me with Junior Science and hello 1977 Ford Pinto.

***

One strategy that I have only recently used, is to teach/review algebra with my FPC Math 10 (academic math) class, having the students sit in pairs of their choosing. Each pair has a table top whiteboard (London Drugs sometimes clears them out…), marker and eraser.  I review the basic “moves” and reinforce opposite operations and remind them that the order of the “moves” is important (“Reverse BEDMAS”, usually helps them remember).  Then, we do a series of increasingly difficult algebraic problems, WITHOUT variables. For example, rearrange “2 + 3= 5” for 3.  My approach is to reinforce that “if it works on the numbers, it will work on the letters.”  The students work in pairs and flash me their answers.  When students are struggling, I send other students to help, that have already shown me their work. The goal is to increase student interactions— Vygotskian social learning!  During which time, I am discussing proper notation (where to put the = sign, working vertically, using fraction bars for division, etc.). What I am finding is that is is a huge confidence boost for my low folks, because they can find their own mistakes (clearly, 3 doesn’t equal 5/2, for example). When we leap into the variables, I can then attach the more abstract algebra to the concrete algebra.  Practically right away, we can then start throwing our symbols across the equal sign, completing multiple steps simultaneously.

I chose this as my example because it exemplifies how important it is to have a knowledge base beyond your subject material. Being a physics teacher, I know how important it is to be comfortable with symbolic manipulation.  My colleagues without the physics, tend to not prioritize symbolic manipulation prior to substitution. What they don’t seem to understand, is that it is far more efficient to rearrange before substituting and it is critical to do so from Physics 12 onward.

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Shulman, L.S. (1987). Knowledge and teaching. The foundations of a new reform. Harvard Educational Review, 57(1)1-23. Retrieved from chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://gse.buffalo.edu/fas/yerrick/UBScience/UB_Science_Education_Goes_to_School/21C_Literature_files/shulman,%201987.pdf

One aspect that struck me about PCK and TPACK is that, in certain ways, it does help to identify the qualities that make a good educator and a good educational plan.  By connecting the conceptual, pedagogical, and technological knowledge a teacher has, it provides a guide to thinking about teaching.  Shulman develops this further in a discussion about what he terms “aspects of pedagogical reasoning and action” (1987).  Still salient currently, Shulman breaks down pedagogical thinking into various aspects that, in sequence, help to formulate the process of teaching, from personal comprehension of the topic to selecting and delivering lessons and activities to the assessment of student work.  Many of what Shulman lists can still be considered relevant in teaching although the fluency in technology must now be considered.  This point is made more evident by Shulman qualifying his “Aspects of Pedagogical Reasoning” section by claiming his presumption that the teacher is starting with some form of “text” only, with no consideration for other mediums of knowledge.

My own personal experience with TPACK (although I did not think about it in such terms) came in a Science & Technology 11 course in which I did a unit on bridge building.  Throughout the design of the unit I went through the various stages that Shulman discussed, from comprehension (understanding trusses and force distribution), to transformation (planning lessons and designing activities), to instruction (lessons), and evaluation (assessing their final bridge projects).

Interestingly, discussing teaching as a set of pedagogical skills helps to identify something as intangible as “good teaching”.  Certainly knowledge in the pedagogical, conceptual, and technological areas is needed, but effective teaching comes from an educator’s ability to meld the knowledges together and not only develop lessons, but to deliver them well.  This intangibility is acknowledged by Shulman later when he warns that an overly technical approach to teaching robs it of its human quality, stating that “we must achieve standards without standardization” (Shulman, 1987).  This is an important consideration when discussing technology integration as technology (currently, anyway) is not yet able to operate with as much flexibility and adaptability as a human can.  Thus, the T in TPACK becomes ever more crucial as educators and administrators continue to make decisions on which technologies to use in the classroom.

References:

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

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.