# What is a worthwhile mathematical task?

## What is a worthwhile mathematical task?

Worthwhile mathematical tasks are those that do not separate mathematical thinking from mathematical concepts or skills, that capture students’ curiosity, and that invite students to speculate and to pursue their hunches.

A mathematical task has been defined as a single problem or a set of problems that focuses student attention on a mathematical idea (Stein et al., 1996). The type of task used in the classroom has an influence on the level of students‟ engagement (Hiebert and Wearne, 1993; Smith et al., 2000).

#### What characteristics of a task make it worthwhile or effective in the mathematics classroom?

The National Council of Teachers of Mathematics (NCTM) has defined worthwhile mathematical tasks as those that:

• Are based on sound and significant mathematics.
• Use knowledge of students’ understandings, interests, and experiences.
• Develop students’ mathematical understandings and skills.

What are some metaphors for teaching?

1. A teacher is a gardener.
2. A teacher is a coach.
3. A teacher is a juggler.
4. A teacher is a firefighter.
5. A teacher is a dictator.
6. A teacher is a chairperson.
7. A teacher is a sculptor.
8. A teacher is a big hug.

What makes a high quality math task?

Has multiple entry points. Allows for different strategies for finding solutions. Makes connections between mathematical concepts, between concepts and procedures, or between concepts, procedures, and application. Prompts cognitive effort.

## How do you implement productive struggle?

Here are some best practices for embracing productive struggle in the classroom:

1. Call on students who may not have the correct answer.
2. Give students informative feedback.
3. Praise students for perseverance in problem solving, not for being smart.
4. Display work that shows creative problem solving, not the highest scores.

### How do I make math tasks rich?

Offer a format that makes them accessible to all learners. Invite students to wrestle with a problem. Contain multiple solution pathways. Encourage use of multiple representations.

#### What are open ended math tasks?

An open ended math question (which is known as an open ended math problem or open ended math task) is a real world math situation presented to students in a word problem format where there is more than one solution, approach, and representation.