In chapter 8, Boaler proposes that students developed very different mathematical identities; she proposes that the contrasting learning and teaching experiences of the students led to differences in knowledge and beliefs about mathematics. The students enrolled at Amber Hill developed a static procedural knowledge of mathematics, where they learned the rules and algorithms to successful navigate particular problems and mathematical concepts. The students at Phoenix Park, however, through a problem oriented approach, viewed math as a tool and were quite capable of connecting it with the real world. Students at Phoenix Park became efficient problem solvers where as students at Amber Hill had difficulty problem solvers when presented with real life situations.
I believe in fostering automaticity. Automaticity is the ability to effortlessly complete tasks with low interference of other simultaneous activities and without conscious thought throughout the step-by-step process. Mastery of the material reduces the demand on the working memory and allows for higher order thinking. Repetition of math skills leads to the development of automaticity of the particular skills. Automaticity is achieved when a mathematics task can be completed almost effortlessly. The student does not have to think about individual steps and can carry out the task of solving the problem rather than focussing on the details of the basic skills required.
I see no reason that precision and drilled teaching methods need to go together altogether. Students need precision with terms, notation and skills. This does not mean that our students’ education should omit open and creative exploration. Quite the opposite, our students must rely on the accurate use of language, skills, symbols and diagrams that allows them to freely explore their ideas that are fabricated by these essential communicative tools.
In Dan Brown’s novel The DaVinci Code, the author introduces readers to the ‘divine proportion, providing the reader with a romantic vision of the potential of mathematics. The golden ratio is shown to exist throughout nature. When flower seeds grow in spirals, the spirals in seashells, pinecones, etc. I question critics who say that our classrooms should give children a sense of the nature of mathematics and that it is critical in preventing the low achievement. I do agree it is important but is it the gospel for educating our youth. They cite indices that students know what English literature and science are because they engage in bona fide aspects of the subjects in our schools.
Why should mathematics be so different?
Do we expect a student to become a successful writer if he or she does not learn the basics of grammar, aspects of writing? Will a science teacher be successful in completing a simple physics or chemistry lab if the student does not have the basic mathematics skills to interpret the data? Do we sacrifice one for the other? Is there any point in making our students successful at conceptualising how to solve a problem if we do not foster the skills to implement their ideas?
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