What place does Mastery Learning have in school mathematics? August 12, 2012Posted by Editor21C in Engaging Learning Environments, Primary Education, Secondary Education.
Tags: curriculum, learning theories, mathematics education, parenting, tutoring services
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It was hard to decide at first if the article on Kumon was an infomercial (SMH, Saturday 2nd June, p.7, Difficult to pigeonhole, but teaching method has a loyal following) or an attempt to present a balanced report. While most of the adults interviewed in the article were Kumon instructors, there was no reason to doubt that they have the interests of their students as their first priority. Yet the article seemed to muddy the waters for parents seeking advice about this and other similar programs.
Through the intrusion of the internet, parents are presented with a large array of offers to help their children and there are many similar digital versions of Kumon available to choose from. So in the interests of clarifying some of the confusion that was created by the article, I make the following comments in relation to research on mathematics teaching and learning.
Firstly, Kumon and other mastery programs do help some students. These students improve their skill knowledge and their scores on tests and examinations. They are called mastery programs because they are based on a behaviourist philosophy which is often linked to training. Behaviourism assumes all children can learn if the journey of learning is broken into small steps. The student progresses by mastering each step through intensive repetition and drill. In the early days, students who could not master the small steps were labelled ‘slow learners’. Not all students are able to cope with the intensive practice and become disengaged, and various programs in order to address this have included systems of rewards.
Another assumption of behaviourism is that during the intensive practice to master a skill the student will come to an understanding of the underlying concept. Now for some students this in fact happens, and I am sure the bright young girl in the photo in the SMH article is probably one of these. However, there is no guarantee and in fact, research has shown that in a large number of cases the conceptual understanding does not happen. In some of these cases, within a short period of time after the drill and practice ends, then so does the students’ mastery.
It was the failure of behaviourism to concentrate upon students’ thinking and understanding rather than focus on skill proficiency that led to other theories of learning such as the cognitive science approach or the socio-cultural approach. These theories have sought to build more complex and inclusive models and have been greatly influenced by the developments in brain research and social and cultural research. They also have a far greater track record in producing, at a much faster rate, students who understand the underlying concepts.
The concentration upon thinking and conceptual understanding is often driven by the need for students to be able to apply their learning to novel and unique challenges and environments and not to mere test situations.
So to conclude, revision and practice and proficiency with mathematical procedures is important but should be accompanied by experiences that develop deep thinking and conceptual understanding. Mastery learning programs can help with the first but have a poor track record with the second. It is up to parents and teachers to decide if a child will benefit from a short term exposure to such mastery programs.
Allan White is Associate Professor in Mathematics Education at the University of Western Sydney, Australia. He teaches in UWS’s Master of Teaching (Secondary) teacher education program, and is an internationally recognised researcher into mathematics education, teaching and learning. He also posted a popular earlier post on 21st Century Learning titled NSW Secondary mathematics teachers battered by a ‘perfect storm’.