What Makes a Good Task?
Post 1 of 5 in the Series ‘Orchestrating Math Discussions’
This blog series is inspired by the book 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein as well as our own classroom experiences.
What Makes a Good Math Task?
Math is more than numbers and equations—it’s problem solving and critical thinking. The problem solving tasks we select impact the degree to which students use critical thinking, build understanding, and develop math concepts. Good tasks have the following characteristics:
Clear Purpose: A good task serves a clear purpose, which is to advance students toward a learning goal. First, we must identify the goal, and then we can choose the task. For example, Ms. Reames, a second grade teacher, noticed her students relying on objects and drawings when representing addition and subtraction situations. Ms. Reames wanted to advance her students toward more sophisticated representations like numbers or equations. Therefore, Ms. Reames identified the following goal and task:
High Interest: A good math task centers around a relevant and interesting context. Ms. Reames created a problem around a jumping contest after observing her students having jumping contests during recess. When students are interested in the context of the task, they are invested in their work and more likely to remain engaged in the mathematics. While the previous example is a word problem, a task can also be an engaging math puzzle, game, or activity. Here are some sites that contain high interest tasks:
- Tools4NCTeachers: Each grade-specific page provides ‘Instructional and Assessment Tasks’ aligned to North Carolina math standards.
- 1-2 NIM: Dan Finkel, Founder of Math For Love, explains how and why to play the game of NIM.
- Card Tricks: Students discover the math behind card tricks performed by Peter Liljedahl, author of Building Thinking Classrooms.
- Open Middle. As their website states, these are challenging problems and puzzles worth solving.
Opportunities for Problem-Solving: A good math task provides opportunities for students to solve authentic problems. When students are faced with rich problem-solving opportunities, they use reasoning and sense making. They analyze information, draw conclusions, and make connections between concepts and to their own prior knowledge. When given such opportunities, students often develop their own strategies rather than apply memorized procedures.
Promote Productive Struggle: A good math task provides an appropriate level of challenge. Tasks that do not have the appropriate level of struggle, can lead to boredom, frustration, or behavior problems. Finding the right balance encourages growth, builds confidence, and empowers students to see themselves as mathematicians. Tasks should allow students to try different solution paths, make and learn from mistakes, and eventually arrive at a solution.
Access for All Learners: A good math task allows for multiple starting points and strategies. This enables all students to work with the task in ways that make sense to them. For example, one of Ms. Reames’ students represented the jumping contest task with drawings while another recorded equations.
Student 1’s Work
Student 2’s Work
Does a Good Task Ensure a Great Lesson?
Although selecting an appropriate task based on the learning goal is a great start, it does not ensure a successful lesson. Engaging in a productive mathematics discussion after grappling with the task is a key to success!
In this blog series, we will examine five practices for orchestrating productive mathematics discussions:
Stay tuned for the next post where we will be anticipating student thinking to prepare for a productive mathematics discussion.
Want to learn more? Discover the differences between low and high cognitive demand tasks in the NC2ML briefs The Role of Mathematical Tasks, K-2, and The Role of Mathematical Tasks, 3-5.