This document discusses constructivism and problem-solving approaches to learning mathematics. It first defines constructivism as the view that students actively construct their own knowledge based on their existing experiences. It then discusses key aspects of constructivist learning like students developing their own understandings and comparing new information to existing knowledge. The document also outlines the four phases of a constructivist approach to mathematics learning and how teachers can implement it by starting with students' existing knowledge. It concludes with an example of a constructivist-inspired dialogue between a student and teacher about problem solving in mathematics.