The purpose of this blog is to further illustrate and elaborate on the RaPID model and the five principles that underlie it:
Wherever possible, blog posts will include classroom resources or examples. If you haven’t taken the course, you’ll still find valuable ideas in the blog, but some of the ideas and terms would likely make more sense after Unit 1. Note that you can access the course by clicking on the “Math Minds” link on the top right of this page. You may also be interested in checking out some of our publications, which you can access here.
For those who have taken the course, the following brief summary may be helpful. We’ll start with the principles: Mathematical structure (P1) motivates and sustains each of the other principles and practices. A growth mindset (P2) is a necessary condition for bringing it to life. Here, growth mindset is much more than telling learners they could succeed if only they would try hard enough; it’s about showing them that they are capable of learning sophisticated mathematics at or beyond grade level. Effective teaching is essential to ensuring they do so.
For learning to take place, it’s important to attend to the limits of working memory (P3) without fragmenting content to the point that necessary contrasts (P4) and associations (P5) are lost. This is a highly sophisticated art—and one that we argue should be a shared responsibility between a teacher and a quality resource, particularly when it comes to raveling mathematical content.
RaPID practices are based on these principles. Raveling refers to both the long-term structuring of mathematical content, both within and between grades (R-a) as well as to the immediate structuring of ideas in a particular lesson (R-b). Prompting draws heavily from variation theory, which we’ll have much to say about. It involves offering appropriate contrasts and juxtapositions (P-a) and engaging learners in making relevant distinctions and associations (P-b). Interpreting is about asking questions that offer windows into understanding (I-a) and attending to each learner’s response (I-b). Deciding is about using that information to inform the unfolding of a lesson (D-a)—in a way that allows all students to continue engaging together (D-b).
These principles and practices form the organizing framework for both the course and the blog.