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The general consensus of large-scale studies that compare traditional mathematics with reform mathematics is that students in both curricula learn basic skills to about the same level as measured by traditional standardized tests, but the reform mathematics students do better on tasks requiring conceptual understanding and problem solving. [3]
[20] The Panel effectively called for an end to the Math Wars, concluding that research showed "conceptual understanding, computational and procedural fluency, and problem-solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided."
Reform texts emphasize written and verbal communication, working in cooperative groups, and making connections between concepts and between representations. One of principles of reform mathematics is social equity. [5] In contrast, "traditional" textbooks emphasize procedural mathematics and provide step-by-step examples with skill-building ...
Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations. They contrast with most homework and exam problems in science and engineering that typically require ...
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]
Procedural knowledge (i.e., knowledge-how) is different from descriptive knowledge (i.e., knowledge-that) in that it can be directly applied to a task. [2] [4] For instance, the procedural knowledge one uses to solve problems differs from the declarative knowledge one possesses about problem solving because this knowledge is formed by doing.
Another thing to address is the importance of teaching and promoting multiple solution processes. Procedural fluency is often times taught without an emphasis on conceptual and applicable comprehension. This leaves students with a gap between their mathematical understanding and their realistic problem solving skills.
A concept definition is similar to the usual notion of a definition in mathematics, with the distinction that it is personal to an individual: "a personal concept definition can differ from a formal concept definition, the latter being a concept definition which is accepted by the mathematical community at large." [1]