However, there are flaws with teaching this way. The first is the time constraint. In public schools, this method of teaching would not work in any way. Warrington had actually been teaching fractions to these students for FIVE months, which, in a public school, is the time given to teach MANY different topics. Second, the issue arises, what if that one student hadn't had those thoughts, and nobody had thought that 4 and 2/5 divided by 1/3 is 13 and 1/15 was wrong? Would Warrington give them the correct answer, or would she let them go on thinking the way they were? Third, what about those who just don't have the ability to think about mathematics in this way. For some, math just does not ever click. And last, Warrington said that "children can and do invent ways to do sophisticated mathematics," but sometimes those ways are just plain wrong. Take Benny for an example. He had many ways of doing math, but only some of them were actually logical and correct. Warrington's method of teaching is a wonderful way of letting children discover the world of mathematics, but it would really only work in a private school institution, and never in a public school with the curriculum they have to cover.
Monday, February 15, 2010
MthEd 117 Blog #5
In Mary Ann Warrington's paper, "How Children Think about Division with Fractions", she gives examples from her class of students at the Atrium School in Watertown, MA, to illustrate the fact that children can develop their own mathematical formulas and ideas when you give them the opportunity to discuss them within the classroom. Warrington believes strongly that "children construct knowledge on the basis of what they already know," and that the best way to teach them is to let them teach themselves through discussion in the classroom. Warrington does not even tell her class the correct answers, but lets them guide themselves to discovering the concepts themselves. The greatest example she gives is when she asked the class what 4 and 2/5 divided by 1/3 was. Many believed that it was 13 and 1/15, but one student disagreed and brought up the idea of 13 and 1/5. As Warrington states: "This response was not only logical and mathematically correct but also a shining example of the autonomy that children develop when encouraged to think for themselves." Giving children the opportunity to think this much and develop their own mathematical ideas and theories can be quite a wonderful way to allow children to explore the world of mathematics.