Perhaps a matter of imagination; TPCK in mathematics education

After reading this chapter I wish I could start my mathematical education all over again in a classroom guided by a teacher with strong TPCK.

Expectations of mathematics teachers today are much different than they were 50 years, and the reason for this is technology. Technology has caused increased awareness of the depth, usefulness and beauty of mathematics.

Consider fractals found in “real-world phenomena” (p.147) that allow us to learn about the world in ways we “never could before” (ibid).  Study of fractals at this time in history is driven by technology. Another topic mentioned is tessellations, whose creator (interestingly) was unsuccessful learning most traditional mathematics. Also explained are the different goals of continuous mathematics and discreet mathematics with examples of how they have been expanded through technology.  

Some advantages of a mathematics teacher with strong TPCK are the abilities to: be spontaneous, make visible connections, establish real-life contexts, and answer the question “why do we need to know that” (p. 156) before the question ever arises. Other qualities needed are cultural sensitivity and “demonstrated caring that encourages students to take intellectual chances” (p. 162). 

It isn’t possible for teachers to learn the infinite number of combinations where TPCK could come together.  Instead, teachers must learn to “imagine ‘possibilities’ and develop an open mind for using a variety of approaches and strategies with their students” (p.151).  Mathematics teachers with TPCK have the opportunity to create “powerful analogies, illustrations, examples, explanations, and demonstrations to make the subject accessible and comprehensible” (p. 152) as Shulman describes about PCK.

The qualities described above are similar to the qualities I am learning through mentors and in-depth study to work with children with severe autism. Everyday I must imagine “possibilities” and be open minded to use (and create) a variety of approaches and strategies with my students.  Because of what I’m learning in this class I will have more to offer students in technology and mathematics.