The illustration below demonstrates the idea of designing instruction that targets all students and still caters for those with difficulties or special needs. So for example, instead of planning a lesson that is mainly based on written tasks, one can plan for the same lesson with a strong oral component that will allow time and space for those with writing skills difficulty to explore ideas verbally first. All students benefit as ideas get clarified in class discussion before going down on paper. The National Center on Universal Design for Learning advocates, explains and shares research related to universal access design applied to instruction.

Thinking about differentiation in terms of universal access lesson design, here are some ideas specific for Mathematics. While you consider scaffolding for English Language Learners, you will see that activities also support and are delivered for the whole classroom.

### Anticipation Guides

Common Core and AERO Standards in Math now emphasise students ability to read complex mathematical text and develop arguments for their reasoning. There are many implicit ideas in textbook writing for example, that have to be decoded and digested by the students. Anticipation guides are developed around a few statements that are true or false, based on main concepts and also misconceptions. Students are given the opportunity to react and discuss those statements before reading a mathematical text. After the reading, they are required to justify with evidence whether the statements are really true or false, through continued discussion with peers. This strategy supports ELL students as it focuses on clarifying terminology as well conceptual meanings.

### Flexible Grouping

Having different ways of grouping and organising class activities also help students with difficulties as well as the whole class. Stir the Class is a strategy that allows two rounds of discussion on each topic in different small groups, allowing for a mix of ideas and thinking process time. It can be a great strategy to be used with anticipation guides, for example. Traffic Lights, by its turn, uses the color analogy to help students indicate whether they have difficulty or an explain a problem or topic. This helps the teacher to quickly see who needs more support and also helps organize peer tutoring.

### Explicit Instruction

You have probably heard about the “curse of knowledge” . The Edutopia article “The Teacher Curse No One Wants to Talk About” describes this “curse”: *” a strong base of content knowledge makes us blind to the lengthy process of acquiring it….As a result, we end up assuming that our lesson’s content is easy, clear, and straightforward. We assume that connections are apparent and will be made effortlessly”. *Explicit instruction is an attempt to make thinking visible, allowing students to grasp the hard and implicit thinking process that goes into any subject area, particularly in Math problem solving.

There are several ways to make instruction more explicit. One way is to “think aloud” during problem solving, showing not a straightforward solution, but the actual struggle one goes about when encountering the problem for the first time. Other ways involve graphic organizers that show connections between concepts, examples, non-examples, definitions. The non examples are particularly interesting, because they are usually not shown or mentioned, remaining implicit. Students can be assigned to find those out and keep them visible in graphic format.

### Descriptive Feedback

Descriptive feedback has already been described in the blog post Feedback & Differentiation: How do They Connect. Giving good descriptive feedback is a skills to be developed, and it is equally useful for all students.

### Sources

- Universal Design for Learning – CCSS for Math
- Common Core Standards and Differentiated Instruction
- Anticipation Guides: reading for Math Understanding
- Stir-The-Class: Math Journeys
- Formative Assessment / Peer Tutoring
- Explicit Instruction in Math
- Descriptive Feedback
- Learning Profile Cards
- Learning Profile Quick Surveys
- Math RAFT Writing
- Quadratics RAFT