Category Archives: B. PCK

TPACK in a 6-week online course

I already heard about TPACK in my very first ETEC course. I still find the concept quite clear, well explained, and helpful. Obviously, it is not enough to talk about technology. Technology use is “context-bound”, as Mishra (2008) notes. Thus, the theory of TCK resp. TPACK helps to focus on the fact that any use of educational technology has to be planned in relation to the content and to the pedagogy that the teacher aims for. This also has implications for the organization of professional development workshops.

So while the concept seems quite clear, I will now try to verify it by applying it to my own teaching. I just taught a 6-week online course on project management. Thirteen adults with various health care professional background participated. Their workload was around 15 hours per week. The course was organized within our learning management system Moodle.

Now let’s use TPCK as analytic lens: My content knowledge (CK) on this subject is fair – I know the basic of project management in theory and practice. My pedagogical knowledge (PK) as a university teacher is somewhat limited; for this course, we chose a constructivist approach, using the concept of Etivities by Gilly Salmon (Salmon, 2007) and elements from the Community of Inquiry (Garrison, 2007) and from collaborative and situated learning. My technological knowledge (TK) regarding Moodle is good.

My TPK told me that there exists some functionality in Moodle that support our pedagogical approach, including message forums, badges, online-based tests and peer feedback, so I used these. My PCK told me that to teach project management, the best is to have the students do a real project. As this was not possible within the available six online weeks, I decided to let them first work on a fictive case and then develop a project plan for an own, real project. I also used reflections to activate previous experiences and to derive lessons-learned for future projects. My TPCK, finally, brought this all together in a well-structured, collaborative learning environment based on Etivities. Overall, the course worked quite well, the students were satisfied and learned, in my point of view, some important basics of project management.

So summarizing, I think TPACK is a helpful lens that covers important aspect in planning and conducting teaching. Yet I am not sure that I got new insights while analyzing my course using TPCK. I am curious to know whether you find I missed important points, or how you feel that TPCK can be applied while preparing a course.

Elske

References:

Garrison, D. R. (2007). Online community of inquiry review: Social, cognitive, and teaching presence issues. Journal of Asynchronous Learning Networks, 11(1), 61-72.

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

Salmon, G. (2013). E-tivities – The key to active online learning. New York: Routledge.

Teaching Multiplication – Grade 3

Reflecting on the PCK model and the TPCK model, I think that our individual curriculum documents do a great job at breaking down the content (subject) knowledge. For instance, our Math curriculum has a list of outcomes at each level, descriptions of what each outcome means,  suggested assessments, manipulatives that can support the outcomes, success criteria, etc. The second part, pedagogical knowledge, is not so black and white. As Shulman (1987) suggests, it doesn’t matter how much the teacher understands the outcomes they need to be able to foster understanding of them in such a way that is accessible to all learners.

Teaching Multiplication

Many students come into my class with their time’s tables memorized (or somewhat memorized). When teaching multiplication, though, I do not want them just to be able to regurgitate their multiplication facts, but instead, understand that multiplication is counting equal groups (repeated addition) and learn strategies to multiply larger numbers using mental Math. When students grasp this concept, it helps them when applying it in their real life. The following break down is done over several weeks.

Prior-Knowledge

I always start a multiplication unit after an addition unit, and before even uttering the words ‘times tables’ or ‘multiplication’ I activate prior knowledge by looking at skip counting. We practice counting up by different numbers and then look at how many times we counted.

E.g. 7, 14, 21, 28. How many times did we count by 7? So, 4 groups of 7 equal 28.

Looking at Concrete Materials

Next, we will look at how we can represent this counting using manipulative and pictures. Students first use different types of manips to create equal groups and then practice various counting strategies on their own. I formatively assess how students are counting. The ones who are still counting by 1’s, I know need more time and support with these activities. After they have mastered using manips they can start to draw simple representations of equal groups and show how they count them.

After, we move onto word problems where students solve problems using the strategies above. When addressing these problems students are expected to answer by drawing a representation of the numbers in the form of a picture, and write a concluding statement, i.e., 7 equal groups of 4 is 28.

Looking at the Abstract

Once they have mastered this, we add an extra element by  representing problems with a number sentence i.e. 7 + 7 + 7 +7 = 28 and 7 x 4 = 28.

Practice and Reinforcement

When students reach this point where they can look at multiplication abstractly is when I would introduce quick warm-ups where students are practicing their recall.

The last skills I teach students are different ways to solve multiplication problems by applying different written and mental strategies other than using the traditional algorithm. For instance, we look at partitioning numbers first by looking at small numbers and 2 by 1 multiplication and then move to larger numbers and 2 by 2 multiplication.

Example: 12 x 4

10 x 4 = 40

2 x 4 = 8

40 + 8 = 48

This type of teaching, allows we to do ongoing assessments and easily differentiate for students who ate struggling as well as those who are excelling. Furthermore, by introdcuing a wide range of strategies allows students to find one they can identify with.

PCK

Many of my students struggle with fractions, in particular converting mixed numbers to improper fractions; it is such an abstract concept that they have a hard time understanding it and there is more than one step so that also confuses them. One of the first things that I do is activate prior knowledge; sometimes students have lots of knowledge with fractions (and other content) but they just don’t know it. Once I know where my students are at, I plan accordingly and try to differentiate for my students (this is important as many of my students have learning disabilities). One of the most important things that I do is explain everything slowly, step-by-step, using LOTS of visuals. By explaining everything with step-by-step and going at a steady pace with my instruction, it can help with misconceptions and allows my learners to not panic. Mishra & Koehler (2006) state that transformation in teaching occurs when “the teacher interprets the subject matter and finds different ways to represent it and make it accessible to learners… which is at the heart of PCK.” I use games and fun websites such as Khan Academy to enhance my lessons. (If you have not already checked out this website, I highly recommend it; it is fantastic!). I also use Pinterest as other educators share fantastic resources. I have gone to numerous math workshops which gives me a deeper understanding about math and how to teach it effectively. These workshops also contain numerous resources and fun manipulatives. I bring in technology for many of my lessons but math in particular because my students and students in general, have a fear of math and technology decreases that fear; “these new technologies have changed the nature of the classroom” (Mishra & Koehler, 1023). By combining games and technology it creates an engaging and fun environment for students to learn about something that they once feared and corrects those misconceptions. As an educator, it is my job to make sure that I find any resources necessary to make sure that my students learn about what I am teaching and incorporating “analogies, illustrations, examples, explanations and demonstrations” so that these concepts are “accessible and comprehensible” and there is no better way to do this than technology.

In previous posts, we have all discussed the myriad of reasons why some teachers do not utilize technology in their classrooms but “good teaching requires an understanding of how technology relates to the pedagogy and content” (1025) and “knowledge of technology becomes an important aspect of overall teacher knowledge,” it becomes a part of our pedagogy which is important to appreciate.

References:

https://www.khanacademy.org/

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