Productive struggle seeks to engage students in challenging learning opportunities designed to promote thinking about important mathematics concepts. Productive struggle causes students to explore as they develop strategies and their own thinking about the use of mathematics to investigate a question.

The ultimate goal of productive struggle is to encourage students to make meaning of mathematical content for themselves.

Making explicit connections helps reinforce earlier learning and builds a strong foundation for future understanding.

Explicit connections enable students to routinely ask themselves questions that constitute mature mathematical learning habits: how is this like something I already know, how is this related to other ideas or techniques that I have studied before, and what kinds of problems can I solve with this?

Deliberate practice requires students to think about the approach they are using to solve the problems, why they are choosing that particular approach, and how the approach must be adapted for appropriate use in a new context or problem.

Often these require students to stretch their learning and to apply it in a new way.