Developing Students' Mathematical Habits of Mind

Far too many students can be classified as inexperienced problem-solvers who don’t know what to do when they don’t know what to do. These are the students who lack experiences in making sense of and solving problems, and in communicating and using precise, appropriate mathematics and mathematics language. They have never developed the overarching habits of a productive mathematical thinker.

In every math classroom, student expectations in mathematics include the development of conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning for use in solving authentic problems. Even so, many students when presented with a problem to which they don’t know the immediate answer continue to struggle and have not have developed effective strategies of the mind for mathematics. While most curricular materials have been aligned to address these student outcomes and challenges, teachers are often left to determine how to adjust their instructional practices accordingly.

This course has been designed to help teachers in the development of experienced student problem solvers who practice perseverance and automatically employ the mathematical habits of mind. Teachers will gain a better understanding of the many facets of problem-solving strategies students might employ, and also provide them with methods of instruction and assessments for use in supporting students in developing their problem-solving habits of mind.

Teachers will be immersed with resources and strategies which lead to the development of classroom experiences that will promote learning through problem-solving, making and using abstractions in their lessons, and applying mathematical theories with greater opportunities for developing student mathematical habits of mind.

This course is divided into the following modules:

  1. Understanding Problem Solving
  2. The Problem-Problem Solving Relationship
  3. The Problem Solving Classroom
  4. Problem Solving Strategies (Polya)
  5. Designing Lessons
  6. Assessing Problem Solving





Demonstrating Knowledge of Content and Pedagogy


Designing Coherent Instruction


Using Questioning and Discussion Techniques


Reflecting on Teaching