The Harmful Effects of Algorithms in Grades 1–4 is a research paper published in the NCTM 1998 Yearbook and written by Constance Kamii and Ann Dominick. It argues that children should not be taught through traditional mathematics methods in elementary school, and should instead be guided to construct their own mathematical reasoning.
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The paper's data is derived from a sample of 46 low-performing, low-socioeconomic status 1st graders, divided into control and experimental groups – the experimental group was found to perform better on word problems at the conclusion of the school year.
Textbook curricula such as Investigations in Number, Data, and Space which were inspired by the NCTM standards fully carry out the recommendation of not only omitting instruction of traditional computation methods, but instructing teachers in the teacher guides to not permit students to use such methods as regrouping, adding and dividing the number of items to compute an average, or multiplying length by width by height to compute volume, even if learned outside the class from home.
Such texts are often supplemented by districts such as Bellevue School District with other texts even though the teacher guide states that the book needs no supplement, and the supplements generally provide instruction in methods specifically recommended by Investigations to be removed from the curriculum such as using "R" to indicate a remainder.
Citation
"The Harmful Effects of Algorithms in Grades 1–4," in Lorna J. Morrow and Margaret J. Kenney, eds., The Teaching and Learning of Algorithms in School Mathematics, 1998 Yearbook (Reston, Va.: National Council of Teachers of Mathematics, 1998), pp. 130–40; and Constance Kamii, Young Children Continue to Reinvent Arithmetic, 3rd Grade (New York: Teachers College Press, 1994), pp. 33–48.