Perhaps a matter of imagination TPCK in mathematics education Neil F. Grandgenett

Reading this chapter reminded me of two things. The first is how much I like reading quotes by Albert Einstein. Because this one is such a keeper I’m writing it here so I can review it without having the book on hand.

“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.”

I think this is important, in all content areas, and more importantly as we integrate content areas and collaborate with others to tackle problems or celebrations for the future. My hope would be that we include a place for imagination in our lessons and projects and that we integrate content areas for application.

The second thing, I was reminded of as I read this chapter is how much I dislike mathematics, probably because I never understood it. My learning style is so nonlinear. When the author asked for a definition of mathematics I actually got it right. Understanding that mathematics is the study of patterns and interacting with them was an understanding that I didn’t come to until I was teaching Investigations in my classroom. Seeing the whole picture, seeing patterns and how they can be used was never an understanding or a strategy that was used in my mathematical learning (or not learning) experiences.

The philosophical debate about the use of technologies such as calculators when students may not know their basic-facts is one I’ve heard many times before. The reply that using technology inappropriately or too often may cause misconceptions and bad habits is one that can be applied to other content areas as well. Literacy teachers may feel that relying on spell check may cause issues with spelling, science teachers may take issue with data collecting and displaying technologies. Again the theme seems to run through all of these chapters that as educators we need to make informed choices about our content, students and technologies as we design learning experiences TPCK. This leads into the section that I thought was the most important nugget of this chapter. The author related that tessellation artist, M. C. Escher, was not successful in mathematics courses but his artwork is now uses to illustrate mathematical concepts. Technology can make for a more inclusive classroom reaching students with different learning styles, genders, races, and backgrounds. “The computers’ flexibility with instructional scaffolding, alternative representations, screen displays, audio languages, assessment. and teacher feedback makes reaching a wider range of students increasingly more possible as computers become more pervasive and ubiquitous.”

I took a podcasting class, online, last spring and saw the use of this tool as a method for providing instructional scaffolding. Several participants in the class were math teachers. They were taking the class so that they could make instructional podcasts for their students. Students would be able to review a lesson, step-by-step, as often as


needed. I thought this was great and I think this would have been great for a student such as I was.

I do think that there is a place for technology in mathematics. Maybe as it is just a matter of imagination.