As Mathematics teachers we are often confined to teach to a prescribed curriculum. We feel pressured to prepare students, as well as we can, for their final year of secondary schooling. In Victoria, this is known as the Victorian Certificate of Education (VCE). It is administered by the Victorian Curriculum and Assessment Authority (VCAA).
We hope that beyond school, students will be able to apply their mathematical skills, to a wide range of situations. However, we send a big message that the most important skill is being able to reproduce skills in an exam. And then it is OK to promptly forget these skills.
In the real world, we know that correctly using mathematical algorithms, is only a part of the process. Will students be able to define variables, recognize constraints, seek out relevant data, synthesize results, draw valid conclusions, etc?
Consider the 2 clusters of dots in the diagram above. Can you identify the parts of your mathematics curriculum, that would be needed to find which set of dots is the most closely clustered together? Could your students?
I sometimes wish for more curriculum freedom so that I can allow my students to practice being real Mathematicians! Then I would freely use worksheets like 12 Clusters. And maybe, students would love Mathematics as a sexy, new subject?
Images from cafepress.