Chapter 7
Perhaps a matter of imagination TPCK in mathematics education

For me personally, math has been very complex and logical, which frustrated me and made it difficult for me to understand and apply effectively. After reading this chapter, I have come away with a different perspective about how math attempts to make connections and define relationships among objects and natural phenomena.
In my classroom, I teach the basics; numeral recognition, patterns, counting, adding, subtraction, sorting, graphing, shapes, and the essential concepts that the children will begin to build understanding and higher level thinking skills from. When I began teaching I assumed that when children demonstrated one to one when counting objects, that they understood that whatever number they counted to was equivalent with the number of objects in front of them. I quickly learned that children could count objects, but did not fully understand that the number that have was directly related to the objects and this does not change until one object was added or taken away. This occurrence is similar to reciting the ABC’s without knowing what a “h” looks like. This hierarchical skill was not known to almost all of my students. So we uncovered this topic in depth and the children made connections from their new learning to other topics in the classroom like attendance and the lunch count, which is now done by the children. Another surprising thing that I learned when we started to explore addition was that most children had to count all the objects, they could not subitize numbers and add one group to another without counting the objects individually. We continue to subitize numbers and add groups, finding new and various ways to compute numbers making connections and using their prior knowledge to scaffold their learning to new heights.
From this chapter, I have learned that I must do more to incorporate technology into the math curriculum and to do this effectively and seamlessly. I know there are many resources on the Internet to provide games and activities to challenge children of all mathematical levels. I am familiar with the national museum of virtual manipulative which is a wonderful site that is interactive and covers many topics at different developmental levels.
I see my role in teaching children mathematics as a facilitator to explore topics and concepts, while providing direct instruction and the opportunity to encourage independent thinking, reflection, problem solving, communication, representation, questioning, connections, imagination, and observing patterns around us.
I now see math as a “discipline in which the imagination and logic of the human mind strive to structure the reality of our existence” (150). I look forward to teaching mathematics to young children with my new learning and to discover the possibilities when combining math and technology.