According to James Hiebert and Patricia Lefevre, “The development of conceptual knowledge [can be] achieved by the construction of relationships between pieces of information . . . For example, Jane (age nine) understood multi-digit subtraction for the first time when she recognized the connection between the algorithm she had memorized and her knowledge of the positional value of each digit” (Hiebert & Lefevre, 1986, p. 4). Jane’s ability to carry out the calculations without understanding why they work illustrates her procedural knowledge.
For an illustration of the connection that should exist between procedural and conceptual knowledge, see Hung-Hsi Wu’s paper Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education.
Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1–27). Hillsdale, NJ: Erlbaum.
Wu, H. (fall, 1999). Basic skills versus conceptual understanding: A bogus dichotomy in mathematics education. American Educator 23 (3): 14–19, 50–52.
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