Subtraction From a Historical Perspective

Abstract

The algorithms used for subtraction vary. In the United States, three different algorithms were used almost equally until the 1940s: the equal additions, the decomposition, and the Austrian method. After William Brownell modified the decomposition algorithm, the use of other algorithms was practically eliminated in mathematics textbooks. Today, some texts introduce the equal additions algorithm, but the decomposition is still the predominant algorithm. This article reviews the historical use of each of the three algorithms in the United States, discusses the modification to the decomposition algorithm, and gives a brief overview of the current status of subtraction algorithms.Although the algorithms used to teach subtraction changed very little before the 1940s, there were significant changes after the 1940s. The algorithms developed and used then have had a major impact on the way subtraction is taught today. This article is a review of the historical development of subtraction algorithms used in the United States.

Numbers as a cognitive and social technology: on the nature of conventional number sequences used in economic systems

“…For a brief review of the historical development of subtraction algorithms used in the US since colonial times, seeRoss and Pratt- Cotter (2000). For a brief review of the historical development of subtraction algorithms used in the US since colonial times, seeRoss and Pratt- Cotter (2000).…”

“…3The standard algorithm has been taught in US schools since the 1940s. For a brief review of the historical development of subtraction algorithms used in the US since colonial times, see Ross and Pratt-Cotter (2000). See Smith (1925: 97–101) for a brief history of subtraction algorithms in Europe since Fibonacci (1202).…”

Αλγοριθμικές Διαδικασίες Ως Κύρια Μαθηματική Γνώση

“…75-48 = 37, αφού, μέσω του δανεισμού, αφαιρείται μια δεκάδα από τον μειωτέο και ακολούθως προστίθεται από λάθος ακόμη μία, ως επίδραση του ευρωπαϊκού τρόπου εκτέλεσης της αφαίρεσης). Πάντως μέχρι και τη δεκαετία του 1930 στην Αμερική, σοβούσε μια αντιπαράθεση μεταξύ των εκπαιδευτικών, όσον αφορά σε ποιον αλγόριθμο της αφαίρεσης θα έπρεπε να υιοθετήσουν τα σχολεία της Πρωτοβάθμιας Εκπαίδευσης (Ross & Pratt-Cotter, 2000). Μάλιστα, είχαν διεξαχθεί και πολλές σχετικές έρευνες και μελέτες.…”

“…Η χρήση του όρου «δανεισμός», προφανώς, δεν είναι δόκιμη, καθώς τίποτε δεν επιστρέφεται(Ross & Pratt-Cotter, 2000). Ο δανεισμός συνεπάγεται (προϋποθέτει, σωστότερα) επιστροφή «προϊόντος»…”