*by Guillermo Bautista Jr. *

In this post, I am going to use quadratic functions as a context to explain TPACK. The purpose of this post is to clarify ideas about the relationships among content knowledge, pedagogical knowledge, technology knowledge and all their possible combinations.

**Content Knowledge** (CK) is the knowledge about the subject matter. For example, if the topic in mathematics is quadratic functions, a teacher with deep content knowledge should know about its definition, properties, and applications. The teacher should also know how to represent the quadratic function verbally, numerically, algebraically, and graphically and should know how to solve and identify the roots of quadratic functions using different representations.

**Pedagogical Knowledge** (PK) is the teacher’s knowledge in the methods and processes of learning. In teaching quadratic functions, teacher should know that students would be able to make deeper connections if mathematical concepts are represented in different ways.

**Pedagogical Content Knowledge** (PCK) is the combination of the content and pedagogy. A teacher with a deep pedagogical content knowledge should know that quadratic functions should be taught in different representations namely numerically, verbally, graphically, and algebraically.

**Technology Knowledge** (TK) is the teacher’s knowledge about the tools that can be used to teach quadratic functions. The teacher should be aware that there are graphing software and computer algebra systems that can be used to teach the said topic.

**Technological Content Knowledge** (TCK) is the teacher’s knowledge about how technology and content influence each other. The teacher should know about the advantages of some software over the others in a particular context. The teacher should be aware that even though graphical representations can explain functions, they do not capture the entirety of the function. For instance, a graph shown in a window, no matter how large, is only a portion of the function.

**Technological Pedagogical Knowledge** (TPK) is the teacher’s knowledge that learning can change depending on the technology used. During the time when blackboard was the only visual to teach graph, drawing graphs are the highlights of the lesson. Now that graphs can be constructed instantly students should be able to know the effects of parameters among graphs.

**The Technological and Pedagogical Content Knowledge** (TPACK) is the teachers’ ability to combine the knowledge above to deliver effective teaching.

Reference

M. (2012, September 24). TPACK Explained. Retrieved May 30, 2017, from http://matt-koehler.com/tpack2/tpack-explained/