Reduce. Reuse. Recycle. Instructions for building a mathematical house?
Reduce. Reuse. Recycle. These are the instructions for minimising our impact on the planet but they seem to be key to increasing students grasp on mathematics. Willingham suggests that we should reduce the topics covered each year to increase the amount of conceptual understanding. This is echoed by Salman Khan in his TED Talk when he suggest that getting 80% is considered acceptable in the current educational system. Would you feel comfortable living in a house with only 80% of the foundations? What topics should we remove though?
The idea of reducing the amount covered would encourage the conceptual understanding, what Skemp calls relational understanding, however we need to not forget that in many cases the instrumental, or factual, understanding is just as important. Willingham suggests that by reusing the same analogies for topics allows both of these to be ingrained more quickly. The Singapore bar method seems to capture humans’ natural abilities to link space and numbers. This idea of relational understanding allows for us to put our knowledge in to the context of previous knowledge and where we are able to go. Khan shows us a great example of this with his idea of progressing through topics that lead to the next and open doors to the future. We can see why the maths we learn now is important in the future. However does Khan do enough in his videos and questions to truly pass on and test relational understanding or are we simply testing students instrumental abilities?
Khans idea of allowing students to flip the classroom and have students learn at home and do questions at school seems ideal however is it really the best way. Do students miss out on the chance for a discussion and therefore challenge their understanding in a profound way? What happens if someone doesn’t watch the video they are going to start missing some important information?
My greatest fear is that while Khan is admirable in his attempts to allow for the future, current students are already building on shaky foundations. Students who are learning will already have missed understanding in previous years are likely to be those already disinterested in maths. Would you expect them to cover topics they already think they know? This idea of pushing onwards and upwards is reminiscent of Ken Robinson discussing the factory schools where the “bad eggs” are kicked out at the end and stamped with “not to standard”. How can we address this for students already at school?
Perhaps by encouraging schools to embrace the growth mindset expounded by Carol Dweck we can encourage students to fill those gaps themselves. This would most definitely be a wonderful use of the Khan Academy especially if we could link the ideas to the teacher.desmos.com website then students would be able to apply the maths they have just learnt.
Reduce. Reuse. Recycle. Is this the only catchphrase we should apply to maths?