Archive > Reform Math - The Idea

What is Reform Math?

The term itself is more a shorthand than a description, and it is now used in a great many ways, especially by those who are opposed to what they think it is. Another term is Standards-based mathematics, referring to the NCTM Standards, originally published in 1989 and revised in 2000. Many prefer the term teaching for understanding.

Whatever the term, the underlying idea is that people who learn mathematics by making sense of it rather than simply accepting it will learn it better, like it more and be better able to use it outside of, and beyond, school.

The idea was articulated a century or so ago by John Dewey, who taught that way and described his students’ responses. More formal research has been taking place since the 1940’s.

Some people associate reform mathematics teaching with constructivist learning. Constructivism is a theory of learning and not a theory of teaching. Generally, it means, whatever the situation, whether you are working on something or listening to someone else, the mind makes sense of information based on what it already knows, adding on to knowledge or refining it. This theory does not suggest that there is a right way to teach. [For a longer description of the differences between the two sides of the Math Wars, see Reform Mathematics vs. The Basics: Understanding the Conflict and Dealing with It]

Teaching math so that the learner develops both fluency and understanding entails a teacher carefully using problems, activities, and discussion to help the learner develop correct and meaningful knowledge. That’s the ideal for which all of the “Standards-based curricula” (also known as the NSF curricula) are reaching. There are roughly five such curricula at each level – elementary, middle and high. [For details, see The NSF-Sponsored Curriculum Projects]

Such teaching means that the teacher needs to understand what students get and what they don’t. The teacher needs to calibrate challenges accordingly. Too much time spent bouncing around ideas results in a loss of sense of direction, and too little results in a loss of the students’ drive to make sense of it for themselves.

When teachers plan instruction for both skill and understanding, the rewards are great. This means that teachers must have a sufficient mathematical background to be clear about the goals for instruction and know what it takes for students to develop the skills and understanding that they need. Many local teachers will testify to this, and research results consistently show that when teachers focus on developing students’ fluency and understanding, student fare better. [Further references can be found at Research Supporting NCTM-Standards-Based Mathematics Education Reform]


Setting the Record Straight

A certain number of misapprehensions recur regularly in conversations, radio talk shows, newspaper articles and op-eds and even on-line. We will attempt to set the record straight for those that are brought to our attention.



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