810 words - 4 pages

My Mathematics Philosophy

How did you get that answer? Why? Can you get the same answer another way? These are important questions for all math educators to ask. I believe that encouraging autonomy is one of the most important things that a teacher can do. According to Piaget, the aim of education must be to develop the child's autonomy, which is indissociably social, moral, and intellectual (Kamii, 21). Without autonomous learners, our classrooms would be made up of memorization of formulas and procedures, which is detrimental and can short circuit learning (Reynolds, 25). Educators have a great impact on children, not only for the year they have the children in class, but ...view middle of the document...

Manipulatives can be important tools in helping students to think and reason in more meaningful ways. By giving students concrete ways to compare and operate on quantities, manipulatives can contribute to the development of well-grounded, interconnected understandings of mathematical ideas (Stein, Bovalino, 356).

I will use various hands- on activities in my classroom. My students will come to an understanding of mathematics and learn to be autonomous. I will have my students do activities that encourage understanding and autonomy. For example, "Six Inch Ruler" would encourage autonomy because the students must come up with their own ways of measuring. Maybe they measure every inch of something with their ruler, or maybe they can come up with an algebraic equation, which will give them the answer. Through activities like these, my students will be where I want them to be.

In my classroom, I will do quick draws or spot the dot every day before math. This will help them think in units. Counting does not encourage construction of units since it is a sequential activity. Students' capacity to reason about quantities and their relationships is a major factor influencing their ability to think about physical situations and solve problems (Reynolds, 11,15).

Representations show how children see numbers. If a teacher can see how the child is mentally seeing the number, she can more effectively guide him. As stated in NCTM (136), representations allow students to...

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