Widespread practice and understanding of mathematics needs to better reflect existing research.
Many academics, researchers, teachers, groups and organisations have been working tirelessly for years to develop mathematics teaching. They have produced thorough evidence that supports a pedagogical change towards encouraging 'mathematical thinking'. Despite this, public understanding and widespread school practice still lags behind, based on little other evidence than 'the way we have always done it'. The most important development for the next 10 - 15 years should be addressing that reality and putting the results of existing research in to practice.
Martin Little commented
The biggest aspect of this is changing the perspective of what mathematics is. All the research talks about the need for developing mathematical processes but the emphasis of the curriculum is doing mechanical things that can be best done by machines. The public's view of what is a good mathematician is that it is somebody who can calculate. Therefore we continue to educate children in being able to do calculations a lot of which they would use a machine to do for them once they left school (that is any they can't do in their head). Somehow children are being lazy if they use a machine to do calculation. We are allowed to use machines for all sorts of other things but not calculating
The content of the curriculum still reflects the needs of a society that has gone, We need to get more people out there explaining what mathematics is and what it needs to be. This has to infiltrate the thinking of politicians.
David M commented
Thanks for this. How should this problem be addressed?