Worthwhile Tasks

The tasks we choose and the way in which we implement them have a big impact on student understanding and mathematical progress. Are the tasks you choose ones that invite students to wonder and explore? Are they talk-worthy? Do they require students to reason about relationships and use prior knowledge?

Below are some tips and resources to help your students get the most out of the lessons you choose every day.

Meredith's Must-Know Info

According to NCTM, a worthwhile task is “a project, question, problem, construction, application, or exercise that engages students to reason about mathematical ideas, make connections, solve problems, and develop mathematical skills.” (NCTM 1991, pp. 24–25) When we take into consideration the range of learners in our class and our drive to provide equitable learning opportunities for all of them, a worthwhile task also must provide a structure that engages all learners. It’s not just about being worthwhile for some students, but instead making sure everyone in the class is invited to high- quality tasks.

So when considering the quality of the task you are choosing, try asking these questions. (You may not be able to answer yes to all of these, but if you are answering yes to the majority of them, you likely have a worthwhile task.)

  • Can students to reason about ideas or are they simply required to call on a memorized procedure?
  • Are there deep mathematical ideas to talk about?
  • Are there multiple entry points for your range of learners?
  • Are there multiple solution paths?
  • Does the task require a high level of cognitive demand? (See cognitive demand chart linked in resources.)
  • Does it promote making connections?
  • Does it engage students in exploring big mathematical ideas.
  • Does it offer opportunities to engage in productive struggle?
  • Can I use the task as a tool for understanding student thinking?

It’s also important to recognize that choosing the task is only the first step. The way in which we implement it can arguably have more impact than the task itself. So we must also consider:

  • Are we implementing the task in a worthwhile way?
  • Are students engaging in the task in a worthwhile way?

Here are four tips for keeping the implementation of the task worthwhile.

  1. Anticipate the range of ideas. Doing the math ourselves before teaching is really important in making sure we are prepared for the range of ideas that will be presented by our students. Especially when the tasks are complex. If we go into the lesson blind, we will not be able to flexibly adjust in the moment when our learners need support or extension.
  2. Choose scaffolding that doesn’t remove the “heavy lifting” of thought from the students. Can you offer a manipulative, change of number, or create a connection to prior knowledge to help students get on track? Try to avoid step-by-step direct instruction as the default scaffolding; when we do that, we are removing the opportunity for students to engage in reasoning. And we become the ones actually doing the math. Without intention, this results in teaching a learned helplessness… students will just sit there long enough for us to give them the steps if that’s the pattern we establish.
  3. Consider your questions. The way we question students can have a big impact on students’ reasoning skills. Consider if your questions are focused on a student answer or if your questions are drilling down to an answer or step that you have in mind. We call this focused or funneled questioning. Focused questions better promote reasoning skills in students and help students to develop resilience in problem-solving, while funneled questions stifle students’ mathematical thinking and build habits of looking to the teacher for all the answers instead of relying on mathematical intuition. Start moving towards focused questioning patterns by asking questions like,
    • “Where did you decide to start?”
    • “What do you know about our work from this week that would help you with this problem?”
    • “How do you know that would make sense?”
    • “Would there be another possible answer? Why or why not?”
    • “How do you know that answer is correct?” Questions like this honor the student and their thoughts. They also give us evidence of student thinking in order to reveal misconceptions or gaps in understanding.
  4. Conclude the task with a class discussion. Talking about the task is an important way to keep it worthwhile. Sharing solutions, making connections to others’ ideas, and troubleshooting mistakes together can help students to connect the mathematical dots. It also shows a value to student ideas and gives students opportunities to engage in the mathematical standards of math practice like MP3: Critiquing the reasoning of others, MP7: Look for and make use of structure, and MP8: Look for and express regularity in repeated reasoning.

Videos

Rich Learning with Dan Finkel, Part 1: Introduction

This is part 1 of an excellent PD series released by Dan Finkel and the Math 4 Love team. In this introduction, Dan begins discussing why teaching with rich tasks can transform student learning.

Rich Learning with Dan Finkel, Part 2: Lighting Student Curiosity

In part 2 of this four part series, Dan explores how to launch a task by hooking students and igniting their curiosity.

Rich Learning with Dan Finkel, Part 3: Productive Struggle

In the third part of this series, Dan engages us in thinking about how we can keep students in a place of productive struggle with appropriate scaffolding.

Rich Learning with Dan Finkel, Part 4: Student Ownership

The final part of this series teaches viewers how to help students take ownership of their ideas. It explores ways for teachers to use student ideas to promote further understanding of the whole class.

Lesson Support

youcubed

Jo Boaler’s Stanford University site full of great tasks. Jo and her team have developed tasks set up by grade level that include mindset boosting videos and lessons called the “Week of Inspirational Math” series. You can also find tasks by grade level and topic on the site. All are engaging and most definitely worthwhile. You and your students will have a lot of fun with these tasks.

Grades K-12

Illustrative Mathematics

IM has had a lot of growth over the past few years, developing a full high school and middle school curricula, and they are now writing a full curriculum for elementary school mathematics which will surely be as fantastic as their lessons for upper grades. While the full curriculum are available for purchase only, lucky for us, their original free tasks are still found at the link above. Tasks are organized by grade and standard and all are most certainly worthwhile.

Grades K-12

Estimation180

Estimation tasks for every day of the year! In helping students to boost abilities to reason and think about reasonable answers, estimation is a key skill. This site will help you to make sure you are nurturing estimation throughout your year, no matter your grade level, and you and your students will have fun with it along the way!

Grades K-12

Tools4NCTeachers

Written by educators across North Carolina, Tools4NCTeachers is a database of lessons organized by clusters of standards. Though it is not intended as a full curriculum, there are plenty of high-quality resources here to get you started.

Grades K-8

Graham Fletcher's 3-Act Tasks

If you haven't tried out 3 Act Tasks, they are a great structure for getting students interested in solving a complex, inquiry-based, (and usually pretty fun!) task. First developed by Dan Meyer, Graham has pioneered the development of elementary tasks. You'll find a great bank of them on his site. For pointers in implementing a 3-Act Task, see Dan Meyer's site, linked in additional research.

Grades K-7

NRich

NRich is a site from the University of Cambridge dedicated to providing quality math instruction to all learners. In addition to loads of tasks and games for students, you will also find quality PD and research on this site.

Grades K-12

Open Middle

Often the tasks on this site have multiple solutions (ie. what we refer to as open-ended), but the emphasis here is on multiple solution paths which creates an "open middle" and invites our range of learners to the mathematics. You can search by grade and domain of standards.

Grades K-12

Achieve the Core

This website includes several tasks per grade, but the most notable resource on this site is their coherence map. By navigating with the map, you can select a standard of focus and then see the concepts/ standards that come before the selected standard and come after. When considering your range of learners and how to support them with appropriate scaffolding, this can be a powerful tool. Tasks on this site are linked in the Coherence Map and you can also search by grade.

Grades K-12

Additional Research

Designing and Implementing Worthwhile Tasks

M. Lynn Breyfogle and Lauren E. Williams

Through a case study example from a fourth grade class, authors discuss the creation and implementation of worthwhile tasks.

Cognitive Demand Task Analysis Guide

Stein, Smith, Henningsen, & Silver

This cognitive demand chart explains the different levels of cognitive demand required for various types of tasks and is useful in task analysis. I recommend starting with some team conversations about upcoming tasks... which level of demand are the tasks that you've planned? What is your evidence? Is there a way to modify the task to increase cognitive demand?

The Three Acts of a Mathematical Story

Dan Meyer

Originator of 3-Act Tasks, Dan Meyer, explains the structure of this lesson protocol with easy to follow examples and videos. Upper grade teachers, you will also find upper level 3-Act Tasks linked here.

Rich Tasks and Contexts

Jennifer Piggott

NRich gives an extensive definition of rich tasks in this article. There are also links to additional professional development resources from NRich.