Teachers of middle school classrooms who are aiming to help students develop deep contextual understandings of mathematical concepts face several dilemmas. Some of the dilemmas come from having to reconcile demands of a curriculum that has specific notions about the mathematical ideas with more colloquial understandings that are present in the media and which many students already bring to their classrooms.
It is important for the teacher to understand their students' ideas and ways of thinking, helping to make these visible to the students. They then can provide mediating experiences which help students to make meaningful connections between their own ideas, the mathematical ideas and everyday usage and contexts. Students can begin to see the diversity of perspectives in using mathematical concepts and can distinguish between the validity of each.
By clicking on the menu at the top of this page you can explore what some of the research tells us about student reasoning and their cognitive frameworks or capacity at various ages in relationship to particular mathematical concepts. This then becomes a useful springboard for thinking how best to mediate the experiences of the students in the classroom as you aim to develop their critical numeracy.