Relational Understanding and Growth Mind-sets
In her talk, Professor Carol Dweck examines the mind-sets of young people. She describes a problem whereby children are born as curious and (as Sir Ken Robinson would say) divergent thinkers but as they pass through the education system this inquisitiveness and open-thinking is thwarted. She blames this on children having a “fixed mind-set” rather than a “growth mind-set” due to the educational system. The latter is advantageous to learning and excelling through exploration and she believes that this mind-set should be taught in schools in order for students to excel. Skemp on the other hand, looks at Mathematics in the classroom in terms of relational vs. instrumental understanding. Rather than improving student’s ability to achieve through changing student’s thought processes, he instead believes that it is the way in which the subject is taught which is the determining factor. Skemp’s ideas link with Dan Meyer’s talk, instrumental understanding can be demonstrated by the textbook example that Dan used, while relational understanding would happen through the deconstruction of the exam question and the way in which students have to know what is going on rather than just relying on the way in which the textbook sets out the question and the previous examples and questions.
Skemp explains how instrumental teaching of maths is demonstrated by the way in which topics are taught completely separately leading to the detriment of student’s knowledge, due to basic ideas for understanding one topic often facilitating the learning of other topics. My own learning at secondary school was certainly instrumental and I blame this in part to a lot of my subject audit being highlighted in red. I can remember the words, I can remember sitting in the lesson, but I have forgotten the methods, processes and how it all fits together. I wasn’t aware before starting this course of the way in which Mathematics has such a large cross-over between topics and it’s true relational nature. At school, each lesson taught you how to answer a certain type of question and that’s the method you would use if it came up in the exam. We were never taught the complexity and overlapping way in which maths works, which Jo Boaler advocates.
Despite Skemp outlining the way in which the educational system as it stands makes it difficult for teachers to teach in a way that is relational, he doesn’t suggest how or even if the educational model could or should be changed. In addition to this, I also find the idea that Dweck puts forward, that praising children’s ability is destructive, a tricky notion. On the one hand, I understand what she is saying in the sense that children may become complacent if they think that they are ‘an expert’ at a subject but at the same time I personally have found that praising ability does have benefits particularly regarding behaviour. In addition to this, I personally find that if I am praised for my ability then I will work harder to sustain this positive label. But is this because I have a growth mid-set? Or are there other factors at play here, such as gender, personality, confidence or other?…