When the process of learning in arithmetic is conceived to be the mere acquisition of isolated, independent facts, the process of teaching becomes that of administering drill.Math educator William Brownell wrote this in...
And yet his words feel like they could have been written today to describe how drill and kill, algorithmic instruction continues to hold an indelible grip over math classrooms all over the world.
Traditional education and its legacy of sit and get, do as your told and get the right answer quickly distracts us with its infatuation with behavioral mathematics.
Good math teachers concern themselves with helping children make sense of math for themselves.
Good math teachers understand that we no longer believe that human beings acquire knowledge by internalization, reinforcement and conditioning.
Good math teachers understand the superiority of Jean Piaget's Constructivism. In her book Young Children Reinvent Arithmetic, Constance Kamii explains:
Piaget's theory provides the most convincing scientific explanation of how children acquire number concepts. It states, in essence, that logic-mathematical knowledge, including number and arithmetic, is constructed (created) by each child from within, in interaction with the environment. In other words, logic-mathematical knowledge is not acquired directly from the environment by internalization.Behavioural mathematics is malpractice for at least two reasons:
Firstly, behavioural mathematics places an exorbitant emphasis on time, and secondly, it convinces kids that product is infinitely more important than process. Both are poisonous pills for any classroom set on intellectual exploration.
Mad Minutes! and its emphasis on time is counter-productive for creating a classroom climate built on real learning. Alfie Kohn explains:
Teachers who want to encourage intellectual growth give students time to be confused and create a climate where it's perfectly acceptable to fall on your face.A classroom determined to help kids find "right answers" are one's that oddly enough place more emphasis on process than product. Ted Sizer writes:
Good schools promote displays of incompetence (strange as that may sound) in order to help students find their way to competence.Traditional instruction does not sell learning as a process; rather it teaches kids that math is really about being fast and right. And the best way for kids to achieve this kind of mindless math mimicry is to memorize at the cost of real learning.