Posts Tagged ‘teaching’

Off the trail

Posted: December 1, 2013 in The root of the matter
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“…mathematics teaching which possesses an ecological sensibility also provokes an awakening for that which is yet unknown. This kind of awareness re-cognizes mathematical environments, mathematics, teaching and learning to be coemergent events, events that can only be brought forth as they occur moment-to-moment.”


As the first four months of term come to a close, I find myself more open and accepting of mathematics than I have ever felt in my twenty six years of life.  This class has been so interesting and unique: I admit that I expected to be given full lesson examples and ‘real world training’ like so many of my other teacher education courses. This never happened, and I am so very thankful and appreciative I was given a different experience. Jennifer’s job is to push us to think about how we, as future educators, are going to teach our students; why we will teach certain concepts, and how our perspective affects our students. Our goal should not be to become a replica of Jennifer and teach her activities (for that is robotic); our goal should be to take the knowledge we all acquired during our 4 months together and connect it to our individual teaching philosophies and then create holistic teaching activities that are meaningful, connected, and leave our students wanting more. This is one of my goals.




In this chapter, the reader is offered glimpses into Jennifer’s mathematics classroom. We see that the students are constructing their own Koch snowflake and identifying interesting patterns that they observe throughout this process. The student examples given in the text are all unique, but also share something in common: each child can write what they are observing using mathematical language and symbols. They start by finding a pattern-some choose sides, others shapes, and others corners. Then, the students describe what is happening to their pattern as more layers are added. Finally, the students revisit their snowflakes later in the year and express snowflake growth with use of symbols and knowledge of number operations.

The idea of guided exploration really appeals to me. The students were all given the same task (observe a pattern and write down what was happening to that pattern), but were allowed to come up with different patterns (corners, triangles, sides) that they could express using mathematical language and symbols.  This allows for creative thinking to emerge, and at the same time, gives the teacher an idea of where each student’s mathematical understanding lies. Furthermore, confidence in mathematical abilities increases due to the exploratory nature of this activity: each student was able to express their pattern in a number of ways, and prove their pattern using language and numbers.

I think it is important to remember that math can be fun and meaningful at the same time! I am sure Jennifer’s students had a great time looking through a magnifying glass to count out their pattern, then making predictions about their pattern’s growth (SCIENCE!) By intertwining mathematics to other subject areas, we are reinforcing this idea that math is everywhere, and we need to embrace it.