Multiplication Research Papers - Academia.edu (original) (raw)

Middle-Grades students should have opportunities to experiment actively with situations that model probability, including “making hypotheses, testing conjectures, and refining their theories on the basis of new information” (NCTM 1989,... more

Middle-Grades students should have opportunities to experiment actively with situations that model probability, including “making hypotheses, testing conjectures, and refining their theories on the basis of new information” (NCTM 1989, 111). These experiences should include a discussion of theoretical probabilities, where appropriate, and the use of correct mathematical terminology and expressions.

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students’ construction of fraction composition schemes. A fraction composition scheme... more

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students’ construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in relation to the whole. Students’ whole number multiplicative concepts were found to be critical constructive resources for students’ fraction composition schemes. Specifically, the interiorization of two levels of units, a particular multiplicative concept, was found to be necessary for the construction of a unit fraction composition scheme, while the interiorization of three levels of units was necessary for the construction of a general fraction composition scheme. These findings contribute to previous research on students’ construction of fraction multiplication that has emphasized partitioning and conceptualizing quantitative units. Implications of the findings for teaching are considered.

ABSTRACT. The middle-grades mathematics related to multiplicative structures has under-gone careful scrutiny over the past decade. Researchers have identified the types of reason-ings involved; the difficulties students have with the... more

ABSTRACT. The middle-grades mathematics related to multiplicative structures has under-gone careful scrutiny over the past decade. Researchers have identified the types of reason-ings involved; the difficulties students have with the concepts and why these difficulties might ...

The Simple Tesla algorithm is the art of multiplying by adding. We can use this method to calculate the product of any number with true precision. It has indisputable applications in various areas, such as polynomials, complex numbers,... more

The Simple Tesla algorithm is the art of multiplying by adding.
We can use this method to calculate the product of any number with true precision. It has indisputable applications in various areas, such as polynomials, complex numbers, binary numbers and many more.
Basically, multiplication is an act of repeated sums, and true to this concept is how this algorithm is developed.

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Multiplication algorithms have a crucial role with occuring of approximately 10% in operating systems such as Windows, Linux, Mac OS, IOS, DOS and etc. Furthermore, these types of algorithms which are related with multiplication have to... more

Multiplication algorithms have a crucial role with occuring of approximately 10% in operating systems such as Windows, Linux, Mac OS, IOS, DOS and etc. Furthermore, these types of algorithms which are related with multiplication have to make an efficient impact on speed of CPU. Nevertheless, a lot of investigators have been making research on both improvement and optimising of methods to make a huge stride on increasing efficiency of processor’s speed. In this article, a new multiplication algorithm going to be introduced with basis on the cooperation of pascal triangle and also given specific examples about the other basic multiplication algorithms which are, Karatsuba and Nikhilam. However, results of pascal multiplication algorithm with respect to a factor of complexity analysis have been evaluated and compared to complexity of Karatsuba and classical multiplication.

'Magic' is one of the Romanian strawberry cultivars widely grown in recent years, mainly due to its high yields and excellent flavor. Therefore, micropropagation of large quantities of planting material from this cv. is at high demand. In... more

'Magic' is one of the Romanian strawberry cultivars widely grown in recent years, mainly due to its high yields and excellent flavor. Therefore, micropropagation of large quantities of planting material from this cv. is at high demand. In order to test the ability of cv. 'Magic' for large scale micropropagation, meristem-derived plantlets were cultured on solid Murashige and Skoog medium supplemented with N 6-benzyladenine and indole-acetic acid. The number of shoots formed per meristem-derived plantlet varied largely in successive subcultures, with an average multiplication rate during the first three subcultures of 5.44, 17.05 and 21.5, respectively. The length of micropropagated shoots (revealing their vigour) was found to be strongly dependent on their number. Almost all the developed shoots were vigorous enough for further multiplication by subculturing them on fresh MS medium every four weeks.

The goals of this study were to investigate whether children's use of two arithmetic shortcuts based on the understanding of the operations of multiplication and division could be increased and to examine how children's evaluations of the... more

The goals of this study were to investigate whether children's use of two arithmetic shortcuts based on the understanding of the operations of multiplication and division could be increased and to examine how children's evaluations of the shortcuts interacted with the brief task aimed at promoting shortcut use. Grade 6, 7, and 8 students solved two sets of inversion (e.g., d × e ÷ e) and associativity (e.g., d × e ÷ f) problems. Children with a good understanding of the relation between multiplication and division can use conceptually-based shortcuts to solve both types of problems. Students were also given a brief task demonstrating the inversion shortcut (the answer is the first number and no calculations are required) and the associativity shortcut (dividing first and then multiplying) and were asked to compare each shortcut to a left-to-right procedure (i.e., multiplying and then dividing). Half the participants were given the demonstration task between the problem sets and the other half after the sets. Inversion and associativity shortcut use increased by Grade 8 and improved across problem sets for both the Demonstration Middle and Demonstration Last groups. The demonstration task successfully promoted subsequent shortcut use but the participants who positively evaluated the shortcuts compared to the left-to-right procedure in the demonstration task had greater subsequent shortcut use. Conceptually-based shortcut use on multiplication and division problems was increased using a brief demonstration task but children's subsequent use of shortcuts depended on their evaluations of the shortcuts. Crown

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations – meet,... more

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations – meet, multiplication, and fuzzy equality – and a unit element. They open the door to an alternative development of fuzzy (many-valued) logic with the basic connective