What This Means for Instruction

Here are some tips to help educators planning instruction in representation:

• Accept students' varied and alternative ways for representing mathematical ideas.
• Give students opportunities to show their thinking in an organized way. Model multiple representations for students and provide them with opportunities to think about and discuss the advantages and disadvantages of each way of thinking.
• Use the same materials to represent different mathematical ideas over time to lessen the amount of time it takes to introduce a topic and to help students make connections between topics (Grouws & Cebulla, 2000).
• Do not limit manipulatives to the introduction of topics; provide students with plenty of opportunities for hands-on practice (Grouws & Cebulla, 2000).
• Follow these guidelines for using representational tools with students:
1. Students should construct meaning for representational tools.
2. Representational Tools must be used for a purpose.
3. Representational Tools should be used to record, communicate and think about mathematics (Hiebert et al., 1997).