An approach to density in decimal numbers: A study with pre-service teachers / Un acercamiento a la densidad en los números decimales: un estudio con profesores en formación

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with the same mathematical content and question intent) were formulated differently and administered to a probability sample of 1647 students (grade 8). All the achievement tests were anchored via a set of common items. Students’ answers, equated and then analysed using the Rasch model, confirmed that different formulations affect students’ performances and thus the psychometric functionality of items, with discernible differences according to gender. In particular, we explored students’ sensitivity to the effect of a typical misconception about multiplication with decimal numbers (often called “multiplication makes bigger”) and tested the hypothesis that girls are more prone than boys to be negatively affected by misconception.

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How Informal Out-of-School Mathematics Can Help Students Make Sense of Formal In-School Mathematics: The Case of Multiplying by Decimal Numbers

Mathematical Thinking and Learning ◽

10.1207/s15327833mtl0704_3 ◽

2005 ◽

Vol 7 (4) ◽

pp. 313-344 ◽

Cited By ~ 19

Author(s):

Cinzia Bonotto

Keyword(s):

School Mathematics ◽

Decimal Numbers ◽

Out Of School

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Decimal Hardware Multiplier

Encyclopedia of Information Science and Technology, Fourth Edition ◽

10.4018/978-1-5225-2255-3.ch400 ◽

2018 ◽

pp. 4607-4618

Author(s):

Mário Pereira Vestias

Keyword(s):

Number System ◽

Floating Point ◽

Binary Number ◽

Correct Result ◽

Fundamental Operation ◽

Floating Point Arithmetic ◽

Decimal Arithmetic ◽

Decimal Numbers ◽

Decimal Multiplication ◽

Point Arithmetic

IEEE-754 2008 has extended the standard with decimal floating point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal Multiplication is a fundamental operation utilized in many algorithms and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This article focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

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Decimal Hardware Multiplier

Advanced Methodologies and Technologies in Artificial Intelligence, Computer Simulation, and Human-Computer Interaction - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-5225-7368-5.ch054 ◽

2019 ◽

pp. 722-736

Author(s):

Mário Pereira Vestias

Keyword(s):

Number System ◽

Floating Point ◽

Binary Number ◽

Correct Result ◽

Fundamental Operation ◽

Floating Point Arithmetic ◽

Decimal Arithmetic ◽

Decimal Numbers ◽

Decimal Multiplication ◽

Point Arithmetic

IEEE-754 2008 has extended the standard with decimal floating-point arithmetic. Human-centric applications, like financial and commercial, depend on decimal arithmetic since the results must match exactly those obtained by human calculations without being subject to errors caused by decimal to binary conversions. Decimal multiplication is a fundamental operation utilized in many algorithms, and it is referred in the standard IEEE-754 2008. Decimal multiplication has an inherent difficulty associated with the representation of decimal numbers using a binary number system. Both bit and digit carries, as well as invalid results, must be considered in decimal multiplication in order to produce the correct result. This chapter focuses on algorithms for hardware implementation of decimal multiplication. Both decimal fixed-point and floating-point multiplication are described, including iterative and parallel solutions.

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On the decimal numbers basen

International Journal of Mathematical Education in Science and Technology ◽

10.1080/00207390500064031 ◽

2005 ◽

Vol 36 (6) ◽

pp. 601-605

Author(s):

K.-K. Poon * ◽

K.-W. Yeung ◽

W.-C. Shiu

Keyword(s):

Decimal Numbers

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Understanding Decimal Numbers: A Foundation for Correct Calculations

International Journal of Nursing Education Scholarship ◽

10.2202/1548-923x.1439 ◽

2008 ◽

Vol 5 (1) ◽

pp. 1-15 ◽

Cited By ~ 10

Author(s):

Robyn U Pierce ◽

Vicki A Steinle ◽

Kaye C Stacey ◽

Wanty Widjaja

Keyword(s):

Decimal Numbers

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A Study of the Process of Transformation with Special Emphasis on Its Application to the Division of Decimal Numbers

Mathematics Teacher ◽

10.5951/mt.40.7.0345 ◽

1947 ◽

Vol 40 (7) ◽

pp. 345-354

Author(s):

Louis E. Ulrich

Keyword(s):

Mathematics Teacher ◽

Decimal Numbers

Recently several interesting articles on the division of decimal numbers appeared in The Mathematics Teacher,1 and in various other professional publications referred to in this paper. When a subject is thus widely discussed, it points to a healthy quest on the part of teachers to get at the root of the matter.

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