Prompt 4: Mathematical Thinking and Expression

            I have not seen a lot of math being practiced in my placement. I have observed a couple of mini activities that dealt with counting, but I have not seen them sit down for a math lesson or discussion. A couple math materials I have observed include:

• ·         Number line:  The number line helps students communicate different ways to add and subtract within the number line.
• ·         Number cards with pictures (1-10): This relates to the communicating and connecting processes. The classroom has cards with numbers 1-10 written on them. Underneath the number, each picture has the correct amount of objects. In the morning the teacher points the pointer at the numbers and asks the students to say which number he/she is touching. This allows students to practice their communication with numbers. They can also make a connection between the number and how many objects that number represents in the picture below it.
• ·         Number charts: One time I observed my students create their own number chart. They were given a bag of skittles and asked to separate them by color. They were then asked to count how many were in each color and fill in a chart with the correct marks. This type of activity uses the representing process. The children were able to represent the information by writing it down on a chart. The Bullard text says, “Children might use fingers, make tallies, create diagrams, produce graphs, make maps, or draw pictures to represent their knowledge.”
• ·         Different colored animals: These different colored animals can be used for counting, creating different patterns, or to practice grouping.
• ·         Counting books: Some of these books represent good problem solving situations that the students have to figure out together. The Bullard text describes the steps to problem solving as, “understanding the problem, making a plan for solving the problem, implementing the plan, and reflecting to see if the solution works or the answer makes sense.” A lot of these books are set up to take students through the steps of problem solving.  
• ·         Calendar:  The calendar uses the connecting process. The children connect that the date (the 17^th) is defined by the amount 17 that they use while counting. It also helps to show them how each day that goes by adds 1 more onto the last number. This works with their addition skills or subtraction skills depending on questions the teacher may ask them.

I have seen a lot of my students use the reasoning process to solve certain problems while they play. On occasion when I am playing with the students, I ask them why they are doing the things they do. Most of the children give me their reasons as to why and how they solve different problems. The teacher is also very good at asking questions to understand the students thinking processes. I have also seen different forms of communication with math between my students. When a lot of my children are asked “how much” questions, they usually hold the answer up on their fingers. The Bullard text says that children may communicate verbally or nonverbally.

The idea of number instinct is something that is hard-wired into our brain. The Carey article says, “Human beings, even if they live in remote cultures with no formal math education, have a general grasp of quantities as well, anthropologists have found.” Number instinct is something we do on a daily basis and it goes unrecognized. For example, let’s say someone is offered two different bowls that both have strawberries in them. One of the bowls is going to have more strawberries than the other. Of course, most people wouldn’t sit there and count out how many strawberries are in each bowl. Instead, our number instinct gives us the ability to know which bowl has more without counting.

Although I have not experienced a lot of math in my classroom, I have witnessed an activity where the teacher was building on the student’s idea of number instinct. My teacher would lay out 2 different piles of rubber animals. She would then ask the students to decide which pile has more or less without counting them. Sometimes she would line them up, while other times she would just put them into 2 different piles. I believe the best way to do an activity like this would be to do it with one child at a time. It could also be used as a good assessment tool to see where their knowledge of number instinct is.