Chapter 7 TPCK in Mathematics

The quote by Albert Einstein, “Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand,” (145) makes reference to the real world. This correlates with the reason for the use of technology in our school systems, for it to provide students with real life experiences that cannot be found in textbooks.
I do agree with the statement found on page 146. I spend too much time worrying over “what” type of technology to use, instead of focusing on “how” to use the technology. This is my wicked problem! When I was in High School we were taught how to solve mathematical problems, then we were allowed to use a calculator to check the answers. Now High School students use the calculators to solve the math problems, but do not know how to work through the computation process. Is this a wicked problem that our society will have to address when these students enter the work force?
Hurrah for the idea of limiting the mathematical concepts that will be taught in grades K-8. This will provide me with the opportunity to cover standards more effectively. At the first grade level, the students need many opportunities for practicing these concepts. Our math program, Investigations, requires many math concepts to be taught throughout the school year. With so many math concepts to teach there is not enough practice time or time spend on any one of these concepts in order for students to achieve mastery level.
Chapter 7 provides positive reasons to integrate technology into mathematical instructions. Technology can be used to help educators create lesson plans that are engaging, imaginative, and will meet the needs of diverse learning styles.
What I have learned from this chapter is that the mathematical framework needs to include students’ prior knowledge and understanding, builds and organizes factual knowledge, and uses a meta-cognitive approach to help students learn new math concepts. In order to provide successful mathematical instructions, this framework needs to be integrated with technology that can engage students in real world experiences.