Microcourse 1: Designing Mathematical Tasks
The design of a mathematical task strongly influences how students think about mathematics. Some tasks encourage students to apply procedures, while others invite students to explore ideas, apply strategies, and explain their reasoning.
In this module, participants analyze a task from their lesson or curriculum and identify ways to strengthen opportunities for reasoning and discussion. Participants may work with a task from a published curriculum or a task they have designed themselves. Teachers anticipate how students might explore the task and what mathematical ideas may emerge during problem solving. Participants then implement the task in their classroom and observe how students approach the mathematics during problem solving.
Topics Covered
- characteristics of rich mathematical tasks
- anticipating student strategies
- identifying misconceptions
- teacher questions that reveal student thinking
- observing student reasoning during problem solving
- supporting student exploration of mathematical ideas
Guiding Questions
- What makes a mathematics task worth discussing?
- How does the design of a task influence how students approach a problem?
- What strategies might students use to solve this task?
- What misconceptions might appear?
- What mathematical ideas might students discover while solving this task?
- What questions might help students explain their thinking?
Key Terms
Mathematical Task
A problem or activity designed to engage students in exploring mathematical ideas.
Student Strategy
An approach or method students use to solve a problem.
Mathematical Reasoning
The process of explaining and justifying mathematical thinking.
Misconception
An incorrect or incomplete understanding of a mathematical idea.
Anticipating Student Thinking
Predicting how students might approach a task before teaching the lesson.
Mathematical Exploration
When students investigate a mathematical idea, apply strategies, and make sense of relationships while solving a task.