We have noticed significant improvements in the following area’s.
Experimenting and estimating results
As students have come to better understand the influence of their disposition they will be better equipped to self regulate their learning (including how they work mathematically).
The time spent exploring and understanding not only the different dispositions but how they fit into working mathematically and how working mathematically fits within the syllabus has been invaluable and no doubt a worthwhile learning experience. Whilst it was a learning experience it also enabled me to assess the influence of working mathematically with my students. From this learning I’ve developed working mathematically learning intentions and success criteria, checklists to monitor how and when students use these skills, and finally assessable rubrics to assess properly the outcomes linked to these skills.
The measure of success, though academically, is based on the content of what we teach rather than the way students work. Working Mathematically helps students problem solve and reason their strategies when learning. Whilst it doesn’t link directly to the content of learning how to add and subtract 4-6 digit numbers, it does allow the students a framework. The framework gives them the pathway to create mathematical hypotheses, solve their own problems by testing what went right or wrong, and reason and communicated that reason for why it did or didn’t work.