Complex Mathematical Thinking

As teachers we have to begin to think like children. Many times since as adults we have mastered the idea of numbers and counting it can be hard to understand the struggles children are having in math. Richardson does a good job explaining this by stating, “When they count, they must ignore the physical properties of what they are counting. Number can’t be seen. Number is an idea. We are often unaware of just how complex an idea is until we see very young children work to figure out number concepts.” It is therefore important to remember that we have to understand the struggles children may face in learning mathematics. Four of the things Richardson talked about in his article are inclusion, one-to-one correspondence, conservation of number, and number sense and relationships. From my experiences in teacher education classes at MSU I have a good understanding of one-to-one correspondence and conservation of number. The two ideas that I was unaware of were inclusion and number sense and relationships. I will discuss these two ideas separately.

Inclusion: Before reading this article I had never thought of the idea the children would only bring you the 3rd object they counted rather than bringing all three objects. When someone says “Bring me three oranges” they mean to include all of the oranges that were counted to get up to the number three. I have never seen a child do this but would like to see a child before they have a grasp on inclusion.

Number sense and relationships: Richardson stated “Children need lots of practice before counting becomes a genuinely meaningful and useful tool.” These experiences and practice need to be meaningful experiences and not for any old reason. “Given meaningful counting experiences, children will develop a strong sense of number and number relationships as they simultaneously develop facility with counting.” I feel that he gave good examples of how to create meaningful experiences by counting children in the bus line, the number of people in each group, etc.

Overall I really enjoyed this article and learned a little more about children’s mathematical thinking.

I read the Woleck (2001) piece for the jigsaw reading. In the article he stated, “Drawing emerges as a powerful medium for discovering and expressing meaning; for the young child, drawing brings ideas to the surface.” I really think this quote allows teachers to see how drawing can be useful in a mathematical context. The drawings can be used for children to work through their thinking process but can also be used to help explain their ideas to the whole class. Drawings can become a way for mathematics to become more static and less complex.