Your typical maths class has an enormous range of capabilities. Different students, know different things. Add to that, different students have different levels of literacy skills, energy and enthusiasm.
Rich tasks are designed to be accessible to all students, but the reality is that accessibility can mean different things from one student to the next. Even well designed rich tasks will just be the starting point and it's then over to the teacher to communicate that task and help all students to get started.
So what can that mean in practice? Here are three strategies for helping all students get started on rich tasks, no matter their level of readiness.
1. Lower the floor
Given rich tasks can be taken in different directions, it's up to you exactly where you get started. Lowering the floor is all about increasing a task's accessibility for all students. Consider what minimum information students will need to know so they can get started independently and what will pique their interest. Focus the beginning of the task around this, before then presenting the main challenge.
With the Postal Routes problem, for example, you need to know what the postman is trying to do, i.e.:
A postman is on his daily delivery round. He arrives at a block of houses, with mail to deliver to each one. The postman can choose to take any route. But, he has limited time so can't go over the same path twice.
You also need to know what it looks like when a route works and doesn't work:
Other ways to lower the floor, include:
demonstrating a game,
giving examples and non-examples of a concept or idea,
getting students familiar with a new tool, or
removing some of the problem's constraints (which can be introduced later as students rise to the challenge).
2. Build curiosity
Your own curiosity will drive the curiosity of your students. So first, do the task yourself. Figure out what you like about it and what hooks you in. Then, share this enthusiasm with your students.
I really like the Step Numbers problem, but the first time I ran it in a workshop I didn't sell it. Mid-way through the task, a teacher said they couldn't see the point of doing it. Since then and as an entry to the problem, I've made a point of sharing my love of patterns and the mysteries numbers hold. The task itself hasn't changed, but the motivation for doing it has.
Side note: if you're not that interested in a task, perhaps it's not the best one for you to run with your students. There's a world of maths out there, choose something you enjoy!
3. Follow up one-on-one
Even when you've used a low entry point and after you've 'sold' the task to students, in all likelihood, there will be some students in the room who are still struggling to get started. With these students, it helps to follow up one-on-one or in a small group.
Sometimes, all that will be needed is to re-explain what's already been said, before then getting students to state the task in their own words. At other times, more guidance will be needed. This could involve working with the students as they get started or introducing some constraints until they are comfortable looking at the problem more openly.
For the Jumping Frogs problem, for example, you might go through a couple of trials together of trying to swap the frogs around and during this, emphasise what moves are allowed and not allowed. Or you might simplify the problem so that it involves two frogs per side instead of three.
Have you used these strategies with tasks? What have you noticed? And are there any other strategies that you've found to be successful?