The multiplication table

Two experiments were conducted in order to determine the nature of the difficulties encountered by learning disabled (LD) adolescents in the resolution of multiplication problems ( a b, where a and b vary between 2 and 9). A response production task (Experiment 1) revealed that the incorrect responses generally belonged to the table of one of the two operands, and that the order of difficulty of the problems was the same for the LDs as for normal children, adolescents, and educated adults as reported in the literature. This result suggests that the difficulties are not solely due to memory problems. Experiment 2 tested the hypothesis that these difficulties were caused by a problem in inhibiting the incorrect responses from a set of possible responses. Subjects completed a multiple response task in which the correct response was presented along with three distractors. The level of interference between the correct response and the distractors was varied by manipulating the nature of the distractors (Null Interference, NI: numbers that did not belong to the multiplication table; Weak Interference, WI: numbers belonging to other tables than those of a and b; Strong Interference, SI: numbers belonging to the tables of either a or b). The SI condition resulted in a higher level of errors than the NI and WI conditions and there was no difference between these latter two conditions. This result suggests that the main difficulty encountered by LD subjects is associated with inefficient inhibition of incorrect responses. Thus, the mobilisation of inhibitory processes seems to be an important stage in the development of multiplication skills.

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Multiplication Table

Wolfram Demonstrations Project ◽

10.3840/07000320 ◽

2007 ◽

Keyword(s):

Multiplication Table

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74 MULTIPLICATION TABLE AND BEAU AT BATH

10.7560/733145-076 ◽

1959 ◽

pp. 154-155

Keyword(s):

Multiplication Table

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Chapter 4

Adventures of Huckleberry Finn ◽

10.1093/owc/9780199536559.003.0007 ◽

2008 ◽

Author(s):

Mark Twain

Keyword(s):

Multiplication Table

Well, three or four months run along, and it was well into the winter, now. I had been to school most all the time, and could spell, and read, and write just a little, and could say the multiplication table up to six times...

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On Nilpotent Products of Cyclic Groups. II

Canadian Journal of Mathematics ◽

10.4153/cjm-1961-045-2 ◽

1961 ◽

Vol 13 ◽

pp. 557-568 ◽

Cited By ~ 8

Author(s):

Ruth Rebekka Struik

Keyword(s):

Normal Subgroup ◽

Finite Number ◽

Free Product ◽

Multiplication Table ◽

Unique Representation ◽

Cyclic Groups ◽

Positive Integers

In a previous paper (18), G = F/Fn was studied for F a free product of a finite number of cyclic groups, and Fn the normal subgroup generated by commutators of weight n. In that paper the following cases were completely treated:(a) F a free product of cyclic groups of order pαi, p a prime, αi positive integers, and n = 4, 5, … , p + 1.(b) F a free product of cyclic groups of order 2αi, and n = 4.In this paper, the following case is completely treated:(c) F a free product of cyclic groups of order pαi p a prime, αi positive integers, and n = p + 2.(Note that n = 2 is well known, and n — 3 was studied by Golovin (2).) By ‘'completely treated” is meant: a unique representation of elements of the group is given, and the order of the group is indicated. In the case of n = 4, a multiplication table was given.

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On Nilpotent Products of Cyclic Groups

Canadian Journal of Mathematics ◽

10.4153/cjm-1960-039-x ◽

1960 ◽

Vol 12 ◽

pp. 447-462 ◽

Cited By ~ 15

Author(s):

Ruth Rebekka Struik

Keyword(s):

Abelian Group ◽

Direct Product ◽

Finite Abelian Group ◽

Nilpotent Groups ◽

Multiplication Table ◽

Direct Products ◽

Free Products ◽

Cyclic Groups ◽

Special Cases ◽

Product Of Groups

In this paper G = F/Fn is studied for F a free product of a finite number of cyclic groups, and Fn the normal subgroup generated by commutators of weight n. The case of n = 4 is completely treated (F/F2 is well known; F/F3 is completely treated in (2)); special cases of n > 4 are studied; a partial conjecture is offered in regard to the unsolved cases. For n = 4 a multiplication table and other properties are given.The problem arose from Golovin's work on nilpotent products ((1), (2), (3)) which are of interest because they are generalizations of the free and direct product of groups: all nilpotent groups are factor groups of nilpotent products in the same sense that all groups are factor groups of free products, and all Abelian groups are factor groups of direct products. In particular (as is well known) every finite Abelian group is a direct product of cyclic groups. Hence it becomes of interest to investigate nilpotent products of finite cyclic groups.

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Charles Todd, 1869-1957

Biographical Memoirs of Fellows of the Royal Society ◽

10.1098/rsbm.1958.0022 ◽

1958 ◽

Vol 4 ◽

pp. 281-290

Keyword(s):

Multiplication Table ◽

Poor Health ◽

Small Farmers ◽

The Family ◽

Principal Parts ◽

Three Sisters

Charles Todd died at Croydon on 22 September 1957, seventeen years after he had retired from active work. He was born on 17 September 1869 at Carleton, a small village near Carlisle. His father, Jonas Todd, was clerk and steward of the Cumberland and Westmorland asylum; his mother was born Grace Barker. His forbears on both sides of the family had been small farmers in that district as far back as records can be traced. Charles was the eldest of the family: he had three sisters, two of whom died young. He had poor health as a boy and did not attend school regularly till he was 12. For a time before that he attended a dame school in Carlisle ‘where the education consisted in the daily repetition of the multiplication table, the dates of the kings of England and the principal parts of the Latin verbs’.

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