Chapter 8 - Developing identities

Mathematical empowerment. What a loaded phrase from chapter 8. What does it mean to be “mathematically empowered”? Boaler suggests that the students at Phoenix Park were mathematically empowered because they were flexible in their approach to mathematics, because they were prepared to take what they had learned and adapt it to new situations. The flexibility in their thinking and approach to mathematics was reliant on two key features, one being that students believed the math they were learning was adaptable, that it had many uses and could be applied in numerous situations and secondly it relied on students ability to adapt and change the math methods, to think mathematically. These students do not see any separation between the mathematics they are learning at school and the mathematics they are using in real life, they feel that they have knowledge and skills that are of use to them, as opposed to being in a possession of fragmented and disconnected ideas about mathematics, much like the Amber Hill students.

Who we are as teachers will determine who our students become as learners and users of mathematics. If we provide them with challenges and aim to have them construct meaning for themselves then our students are likely to develop this sense of “empowerment” that Boaler describes in the Phoenix Park students. On the contrary, if we provide our students with set procedures and methods, rules that they must follow without having a true understanding of the mathematics behind “the rules” then we are likely to produce students of a similar calibre of those at Amber Hill. Students who are led to believe that they will do well in mathematics if they “follow the rules” but who find that in the real world they are not prepared to think about and make sense of problems of a mathematical nature, students who have a false sense of security that has been provided by cuing systems, rules and practice.

I know that I would like to prepare my students to face “the real world” of mathematics; I would like them to approach problems with the certainty that they are capable of arriving at a solution through their own thinking (without having to rely on long forgotten rules). I would like my students to believe in themselves as learners and users of mathematics but I would also like them to believe in the mathematics. In constructing their own knowledge, taking time to investigate and make sense, taking time to understand, time to see why “the rules” work without just practicing rules. I believe students can become more skilled in their use of school mathematics, whether it is for school use of real world use. How can I achieve this? How can I ensure that my students are not just becoming passive users of mathematics, that they are not simply “playing the game” or “following the rules” much like the students at Amber Hill? I think that even at a young age students can assume some of the responsibility for the construction of knowledge, knowledge that is built through hands on investigations rather than worksheets or text book questions that follow a chalk and talk session directed by the teacher. Can we really expect young students to grasp some of mathematical concepts at a symbolic level when they have not had enough time to experiment with it at a concrete level? We see from Boaler’s work that it didn’t work at Amber Hill, so it is likely to fail our own students as well.

Like the teachers at Amber Hill and Phoenix Park I too have my student’s best interest at heart when I plan my mathematics lessons. The challenge now is to combine best interest with best practice, to use instructional methods that allow students to construct knowledge and apply knowledge, in the classroom and in the real world.