Mistakes and Speed in Mathematics
This week's online class focused on what might be considered the relationship between pedagogical practice of mathematics and pedagogical ethics. The focus here is not necessarily on what teachers teach (I.e. content) but on how teachers teach (I.e. methodology). In a series of videos Jo Boaler and other academics argue for a more enlightened approach to the way teachers instruct classes on mathematics. Two premises in particular are put forward, they are, roughly, "mistakes should be viewed as an opportunity to grow and develop our understanding" and "being fast at mathematics is not a necessary condition for being good at mathematics." I will expand on these two positions respectively.
In my opinion the claim that mistakes should be viewed as an opportunity to grow and develop our understanding is a sound principle for any academic setting. This kind of attitude towards learning demonstrates a determination for improvement. Significantly, teachers plays an important role of instilling this kind of attitude in their classrooms. This is achieved by creating an environment that does not punish or ridicule mistakes but rather inspects and ameliorates them. Such integrity in the classroom can only be achieved if the instructor is able to foster welcoming and open mentality. Approaching mistakes as an opportunity as oppose to a catastrophe is no easy feat and will require a psychological shift in the mindset of both teacher and student.
The other premise presented in this week's module states that being fast at mathematics is not a necessary condition for being good at mathematics. As argued in the previous paragraph, instilling this kind of mentality in the classroom is largely dependent on the pedagogical approach an instructor adopts. Traditionally, being fast at something was often associated with being competent at something. However, according to new research espoused by Jo Boaler and others, being fast at mathematics is not a necessary conditions for being good at mathematics. The term "good" here demarcates competence and understanding. Boaler and others argue that deeper thinking requires time and patience. Furthermore, it is an indicator of an extensively holistic understanding of a broader framework. It follows that students requiring extended time to analyze a given problem is not necessarily an indicator that they can not grasp the solution. Rather, time should not be a major factor when it comes to the intellectual engagement with a particular problem. It is the engagement itself that is important and the learning development that it galvanizes.
In closing, I believe that both of the aforementioned premises seem to be sound principles for teachers to adopt in their classrooms, and not only for the teaching of mathematics. Allowing students to explore their mistakes without the fear of sanction and allotting them sufficient time to process their thoughts are ideals worthy of a virtuous pedagogical practice.
In my opinion the claim that mistakes should be viewed as an opportunity to grow and develop our understanding is a sound principle for any academic setting. This kind of attitude towards learning demonstrates a determination for improvement. Significantly, teachers plays an important role of instilling this kind of attitude in their classrooms. This is achieved by creating an environment that does not punish or ridicule mistakes but rather inspects and ameliorates them. Such integrity in the classroom can only be achieved if the instructor is able to foster welcoming and open mentality. Approaching mistakes as an opportunity as oppose to a catastrophe is no easy feat and will require a psychological shift in the mindset of both teacher and student.
The other premise presented in this week's module states that being fast at mathematics is not a necessary condition for being good at mathematics. As argued in the previous paragraph, instilling this kind of mentality in the classroom is largely dependent on the pedagogical approach an instructor adopts. Traditionally, being fast at something was often associated with being competent at something. However, according to new research espoused by Jo Boaler and others, being fast at mathematics is not a necessary conditions for being good at mathematics. The term "good" here demarcates competence and understanding. Boaler and others argue that deeper thinking requires time and patience. Furthermore, it is an indicator of an extensively holistic understanding of a broader framework. It follows that students requiring extended time to analyze a given problem is not necessarily an indicator that they can not grasp the solution. Rather, time should not be a major factor when it comes to the intellectual engagement with a particular problem. It is the engagement itself that is important and the learning development that it galvanizes.
In closing, I believe that both of the aforementioned premises seem to be sound principles for teachers to adopt in their classrooms, and not only for the teaching of mathematics. Allowing students to explore their mistakes without the fear of sanction and allotting them sufficient time to process their thoughts are ideals worthy of a virtuous pedagogical practice.
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