TPACK Ch 7 TPACK in Mathematics in Education

I found Neal Grandgenett's chapter much more readable than previous chapters. His use of Albert Einsteins quotes throughout were potentially a bit cliche but he pulled it off by elaborating on them and using more extended versions instead of t-shirt and poster sound-bites. I would like to read the Primer and Phillips book, Everything Einstein, 2003.

Technology integration questions are brought up throughout the chapter with the classic math calculator question as a springboard - When should students use a calculator when learning math? I believe this question can now be extended beyond calculators a more philosophical one about any technology that humans rely on for information, computation or decision guiding processes. What knowledge should reside in our biological brains compared to our silicon-based assistants (cell phones, computers, online accounts...)?

In Neal's discussion of what the study of mathematics really is, he notes how the "human" or creative element gives interest and beauty to the subject and how not considering the human element can reduce the spirit and depth of the subject.

Here is a distillation of the Qualities of a Math teacher with TPCK from Chapter 7:

They are:

• relative openness to experimentation
• will "try" technology based lessons on a regular and spontaneous basis with their students
• strive to be consistently "on-task" for the mathematical topic
• know "where" their students are conceptually, "what" they need to achieve the next step
• characteristically embrace the administrative capabilities of technology
  
• do their best to be caring teachers who are comfortable and optimistic for change

I found this chapter the most readable to date. It was full of rich examples and excellent suggestions for teachers of any subject