Math Models for Understanding

The National Council of Teachers of Mathematics (NCTM) has called for a shift in emphasis in grades K–12

• away from a curriculum dominated by the memorization of isolated facts and procedures and proficiency with paper-and-pencil skills and
• toward one which emphasizes conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving.

To accomplish this shift, the NCTM urges teachers to differentiate the math curriculum with manipulatives, allowing greater access to the curriculum by all learners:

• learners at the concrete stage of development,
• learners whose first oral language is not English, and
• learners whose best Intelligence is not Linguistic, rather Spatial and/or Bodily-kinesthetic.

The NCTM also recommends the use of manipulatives because they

• allow students to readily think in pictures rather than in only words,
• invite greater engagement, and hence, less negative avoidance behavior, and
• serve as a medium for understanding and communicating math concepts, skills, and problem solving.

It’s time to DO the math!