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.

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