Manipulatives can be used as concrete representations of mathematical ideas. To learn mathematics from manipulatives, what must students perceive?

Manipulatives can be used as concrete representations of mathematical ideas. To learn mathematics from manipulatives, what must students perceive?

• A. The color of the manipulatives
• B. The size of the manipulatives
• C. Relationships Between Manipulatives and Other Forms of Mathematical Expressions
• D. That manipulatives are decorative

Answer: (C)

Making connections between concrete manipulatives and the ways we record math in symbols and language is what learning with these tools is all about. To learn mathematics from manipulatives, students must perceive the relationships between the physical pieces and other forms of mathematical expressions—numbers, operations, symbols, and sentences that express the same idea. Think of how a group of blocks can stand for a number, and how combining blocks represents addition. The same quantity can be shown as a numeral, spoken words, or a written equation. By noticing how the manipulatives map to those other forms, a student can reason with the concrete model and then transfer that understanding to abstract notation. Color, size, or whether the pieces are pretty or plain don’t carry mathematical meaning by themselves; they’re just features of the objects. What matters is recognizing and using the relationships the manipulatives have to numbers and operations, so the learner can generalize beyond the concrete setup to other representations and problems.

Making connections between concrete manipulatives and the ways we record math in symbols and language is what learning with these tools is all about. To learn mathematics from manipulatives, students must perceive the relationships between the physical pieces and other forms of mathematical expressions—numbers, operations, symbols, and sentences that express the same idea.

Think of how a group of blocks can stand for a number, and how combining blocks represents addition. The same quantity can be shown as a numeral, spoken words, or a written equation. By noticing how the manipulatives map to those other forms, a student can reason with the concrete model and then transfer that understanding to abstract notation.

Color, size, or whether the pieces are pretty or plain don’t carry mathematical meaning by themselves; they’re just features of the objects. What matters is recognizing and using the relationships the manipulatives have to numbers and operations, so the learner can generalize beyond the concrete setup to other representations and problems.