Study+of+Individual+Child

// A Mathematics Learning Profile of an Individual Child // A student’s mathematical reasoning and understanding is crucial to their development of mathematical concepts. Students need to be supplied with inquiry-based tasks often throughout the school year to exercise their knowledge of problem solving strategies while experimenting with new ones. The benefit of inquiry-based tasks is for students to receive opportunities to apply what they learned in instruction and formulate new methods to solving problems. Inquiry based tasks are important to implement because it allows teachers to gain insight about the way in which students think, with the strategies they are secure and insecure about as well as the big ideas conveyed throughout the problem. I chose to create the Mathematical Learning Profile on the same student that I work with for most of my reports and assessments, Aidan. He is in kindergarten and has average math abilities, but often has trouble finishing his work. The task I chose to do with Aidan was an extension of a lesson that I gave on addition. The lesson I created with Ms. Kamm followed the curriculum and was appropriate for their mathematical ability. The lesson began with a clear mini-lesson, which was executed using the Smart Board to demonstrate guided practice by rolling dice to form an addition sentence. During guided practice, Aidan participated by showing his understanding of addition sentences on the Smart Board. This was a small assessment that I gave Aidan to test his ability of the concept during a large group lesson. He was very successful when rolling the dice and creating an addition sentence. When Aidan finished his sentence, I asked him to explain how he got the answer so quickly. He explained that there are many strategies that Ms. Kamm taught him but this time he just used the visual of the dice as his tool to solving the problem. Students then moved into two 15-minute rounds of “math to self” and “math with a partner.” These activities served as another assessment for me to gain a better understanding of their problem solving strategies. During “math to self,” I asked Aidan how he solved the problem and he stated: “My brain knows everything, my mom gives me practice so that all my friends think I’m the genius of the class.” But when I asked the class about ways to solve problems they developed very mature and sophisticated answers. I thought this was interesting because when I asked Aidan about his problem solving strategy independently he answered very abstractly as opposed to the mature reasoning he gave me during guided practice. These answers included, counting on from a given number, using the example (5+5=10) and knowing that one less is 9 when solving the problem 4+5. This lesson was very hands-on and helped me gain a better understanding of Aidan’s mathematical ability. Inquiry based tasks are essential elements to mathematical instruction as students develop reasoning skills, problem solving strategies, and an understanding of mathematical big ideas through them. Just as the problem provoked students to think critically over methods of solving and explanations for doing so, it also fostered the mathematical idea of addition and its applications to problem solving. Aidan was a prime example of demonstrating the understanding of the big idea as he used a variety of techniques in solving the problems. He was able to create an addition sentence using dice, and explain how he got his answer. Overall, inquiry based tasks, an understanding and development of the child’s mathematical profile and conveying of a big mathematical idea are all components of meaningful mathematics instruction.