Working with a mixed-level class is the reality of almost every adult numeracy and HSE math teacher. One strategy that can really help teachers and students is using  push (extension) and support questions. By preparing questions to help dial down the problem, teachers can help make sure the core problem is accessible to all students. And by preparing questions to dial up the problem, teachers can keep faster students engaged in going further/deeper into a problem. Push and Support questions can provide a low floor and a high ceiling for a central problem, allowing students to work on the same problems, but at their own pace. When push and support questions are prepared beforehand, teachers can put them on a sheet and cut out slips of paper. That way, as they inquire into student thinking, teachers can drop a question for students need a little help or are ready to take the problem further.

To learn more about using and writing push and support questions:

• Push and Support Cards: A Bridge to Advanced Mathematics for the Multi-level Adult Education Classroom Curriculum Guide by Patricia Helmuth
• A Strategy for Teaching in a Multi-Level Classroom – Push and Support Cards by Eric Appleton – I recommend starting here, since this article discusses push and support cards in the context of adult education classrooms.
• Using Push and Support Cards for Differentiation (Brown, Mackiewicz-Wolfe, and Tily)

We are working on developing Push and Support Questions for problems and activities on CollectEdNY, Framework Posts and Math Memos. Here are a few examples of problems that have push and support questions:

• Paycheck Problem (MathMemos)
• Painted Cube (MathMemos)
• The Commission Problem (from Unit 2 of the CUNY HSE Math Curriculum Framework)
• The Bacteria Problem (Frameworks Posts), dealing with exponential growth
• Accurately Weighing Pennies (CUNY Framework Posts)
• Fixing the Furnace (CUNY Framework Posts)

As you use any of the math problems on this website, if you create your own push and support questions (and are willing to share them with other teachers), please let us know in the comment box below.

Other strategies for working with mixed-level math students:

• Notice/Wonder
• Choosing problems that allow for a wide variety of solution methods and problem-solving strategies (MathMemos and Developing Problem-Solving Strategies in the Mixed HSE-level Math Class)