AS a mathematics teacher, it will be interesting to see what concrete impacts the recently concluded seminar on the mathematics teaching practices of Singapore will have on Jamaica’s policy and pedagogical landscape. Singapore maths is touted as being transformational and able to deliver breakthroughs in learning outcomes in a subject that many students struggle to master.
As Singapore math is practised, it embeds the findings of American psychologist Jerome Bruner, who argued that a learner passes through three phases: the concrete, the pictorial, and the abstract. Singapore maths spends a lot of time in ensuring that problems are cast in the appropriate stages for a suitably long enough time so that the structures of the problem are well-understood. Once achieved, it is then and only then that the problems are projected in the abstract or symbolic dimension. Benefits, in principle, the core benefits I believe that can be drawn from this approach to pedagogy, are threefold.
First, there is a reduction in the expansiveness of the math curriculum — it is no longer about being a Jack or a Jill of all things mathematical. Rather, it is about knowing fewer things, but knowing them extremely well. I believe reducing the cognitive overhang, the knowledge burden that students must bear as they go through a course of learning can only augur well for improved retention and performance on the core skills of mathematical reasoning and its expression in quantitative problem-solving.
Second, the Singapore math model not only relies on a trimmed-down curriculum, but it forces students, or better, exposes students to the multi-dimensionality of problem representation, and gives them cognitive elasticity in solving problems by reframing same in an appropriate dimension; whether concrete, pictorial, or symbolic. Just changing the way we think about the problem can provide insight into the problem. We must recognise that the ability to reason spatially (ie, concretely) impacts on the ability to reason symbolically. It is this modal disconnection that impoverishes students’ ability to engage in rich problem-solving — an inability to see a problem in multiple modes.
Third, in unpacking Singapore math, teachers, through collaboration or through extended engagement with fewer content, are able to deepen reflection and improve ‘delivery’ of the content. Less is more — not only for the students, but for the teachers. This is also a boon for teachers who are not specialists in the subject as they will be better able to concentrate their cognitive resources in understanding a narrower domain of knowledge, while improving the opportunity to more efficaciously teach the content with clarity and confidence.
Caveat academic achievement — like mathematical problem-solving — is equally multidimensional in character. One should not be quick to conclude the easy, causal relationship between delivering Singapore math and facilitating high student achievement. There are cultural considerations that should be applied to put a brake on such easy inferences.
Students do well for a variety of reasons: strong parental involvement; high personal and family aspirations; strong school leadership; student resilience; and self-discipline. In other words, good schools which provide a positive environment for high achievement, and which are supported both by a student who desires to do well and works accordingly, along with a family environment that agrees on and complements those aspirations and goals, all aid in preparing a foundation for strong academic achievement. Any attempt, therefore, to deliver a new culture of math without the prerequisites for success will fall victim to the old proverb of putting ‘new wine into old wineskins’.
Fuente: Jamaica Observer