Follow the yellow brick road?…. Or discover something new?
In the video, Jo Boaler explains how teachers are stuck in a cycle where they teach their students the way they were taught when they were students which means that there has been no real progression in maths classrooms. Boaler advocates students choosing their own ideas and developing their own thinking and combining this with standard mathematical methods. This is in stark contrast to Syed’s idea of high quality practice and the underlying idea of Khan Academy whereby students practice and reproduce maths questions and problems with little opportunity to adapt or apply methods in a way that’s interesting for them. Boaler believes problem solving enables students to see the more creative side of maths, which is something that Ken Robinson would encourage, and that using visual aids helps to bring maths alive for students. In the video you could see that the student were working in small groups; something the likes of Dan Meyer would encourage.
The idea that maths can be approached by a variety of ways and you will still arrive at the same answer is something I had not thought of much prior to the course. However through our skft sheets where we are encouraged to show multiples methods and multiple representations of problems I have had my eyes opened to the way in which it is possible to arrive at the same conclusion whatever path you choose to take. I think this needs to be said more explicitly in classrooms in order for students to be less scared of making mistakes reducing the stigma which Robinson outlines.
The article I read by Kirshner, Sweller and Clark was in stark contrast to Jo Boaler’s ideas as they were extremely cautious of the idea of discovery or inquiry-based learning. They looked at the way in which students who are given little instruction, are less likely to store the knowledge they have “discovered” in their long-term memory. Therefore they would argue that the type of learning that Boaler is describing is lacking in instruction which gives learners explicit guidance on how to process information in a way that will allow them to retain it in their long-term memory. A particularly interesting fact they mentioned was that all information which is stored in the working memory and not rehearsed is lost within 30 seconds. Suddenly Khan Academy is becoming more a more appealing, useful tool! The article goes on to look at constructivism; a theory which states people construct their own understanding of the world through experiencing things and reflecting on these experiences when learning. This reminds me of Lockharte’s article where he believes students need to stop being deprived from “doing maths”. However Kirshner, Sweller and Clark argue that when a student or learner is given the complete information (more instruction) a more accurate representation emerges.
I was extremely surprised that they stated that problem-solving can occur without any learning. Furthermore, unguided environments can be detrimental for novice learners who lack proper schemas to integrate new information with their previous knowledge. This is not something which had previously occurred to me and as a result I think we as teachers need to weigh up the pros and cons of a discovery or enquiry learning environment. We must ensure that when we are implementing such a teaching style that our learners are receiving at least some guidance to maximise their learning, in order to reduce misconceptions and incomplete knowledge.