• School Mathematics
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• v.11 no.4
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• pp.745-771
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• 2009

To acquire the hints of the development of children's multiplication strategies, this study tried to find the differences between the students who learned multiplication and the students who didn't. And we also tried to explore their acquired computational resources. As a result, we confirm that there is a certain direction on the development of children's multiplication strategies according to their grades and the level of acquirement of mathematical knowledge. Moreover, we comprehend that commutative law is an important part of the strategies on two-digit multiplication and that acquisition of the computational resources must precede the learning of multiplication strategies. In the end part, this article proposes a new taxonomy of strategies for multiplication. To support our proposal, we integrated the prior researches with our findings.

• The Mathematical Education
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• v.47 no.4
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• pp.405-419
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• 2008

The purpose of this study is to find oui the effects of teaching mathematical concepts by designing and applying teaching and learning programs that takes into consideration the students' strong intelligence, through the teaching and learning strategies based on the multiple intelligences theory. For this study, developmental and experimental research was conducted. In the developmental research part of the study, teaching and learning programs for teaching the concept of multiplication were designed and the activities based on the multiple intelligences were chosen. On the other hand, in the experimental research part, the data acquired from the application of nonequivalent control group pretest-posttest design in the actual classes was processed and analyzed. The results above indicate that the teaching and learning program based on the multiple intelligences theory improved the students' overall understanding of mathematical concepts by providing various types of activities. In addition, this program helped students to increase their confidence and generate a positive attitude towards learning math.

• Research in Mathematical Education
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• v.24 no.1
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• pp.1-27
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• 2021

For elementary school children, learning the standard multiplication algorithm with accuracy, clarity, consistency, and efficiency is a daunting task. Nonetheless, what should be our expectation in procedural fluency, for example, in finding the product of 25 and 37 among fifth grade students? Collectively, has the mathematics education community emphasized the value of conceptual understanding to the detriment of procedural fluency? In addition to examining these questions, we survey multiplication algorithms throughout history and in textbooks and reconceptualize the standard multiplication algorithm by using a new tool called the Multiplication Aid Template.

• The Mathematical Education
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• v.53 no.1
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• pp.57-73
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• 2014

This study investigated the connections of mathematical thinking of students at the second, fourth, and sixth grades with regard to multiplication, fraction, and proportion, all of which have multiplicative structures. A paper-and-pencil test and subsequent interviews were conducted. The results showed that mathematical thinking including vertical thinking and relational thinking was commonly involved in multiplication, fraction, and proportion. On one hand, the insufficient understanding of preceding concepts had negative impact on learning subsequent concepts. On the other hand, learning the succeeding concepts helped students solve the problems related to the preceding concepts. By analyzing the connections between the preceding concepts and the succeeding concepts, this study provides instructional implications of teaching multiplication, fraction, and proportion.

• Education of Primary School Mathematics
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• v.22 no.4
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• pp.281-294
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• 2019

The purpose of this study is to analyze errors and treatment behavior during the course of mathematics learning of academic achievement by applying reflective activities in the second semester of the third year of elementary school. The study participants are students from two classes, 21 from the third-grade S elementary school in Seoul and 20 from the comparative class. In the case of the experiment group, the multiplication unit was reconstructed into a mathematics class that applied reflective activities. They were pre-post-test to examine the changes in students' mathematics performance, and mathematical communication was recorded and analyzed for the focus group to analyze the patterns of learners' error handling in the reflective activities. In addition, they recorded and analyzed students' activities and conversations for error type and error handling. As a result of the study, the student's mathematics achievement was increased using reflective activities. When learning double digit multiplication, the error types varied. It was also confirmed that the reflective activities helped learners reflect on the multiplication algorithm and analyze the error-ridden calculations to reflect on and deal with their errors.

• Journal of the Korea Society of Computer and Information
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• v.14 no.10
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• pp.233-240
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• 2009

In this paper we made the serious game learning multiplication table to be evolved. The serious game is to induce the interest of the learner. This program has an interaction form which reflects the intention of the user and using this program a learner to learn the multiplication table as teacher's location are training a program that are seen as the abata and came to be that learner is smart. A study ability to be evolved used an back propagation neural networks. But we improved a study speed using divided weight table concept. The engine is studied perfectly in 60~80 times training. The learning rate increase to various non-monotonic functional form not to do a mechanical rise. And the learning rate is similar with the study ability of the human.

• Journal of The Korean Association of Information Education
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• v.26 no.4
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• pp.285-293
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• 2022

The COVID-19 outbreak, which took longer than expected, caused considerable damage to students' basic academic ability in mathematics. In this paper, a multiplication table practice application that can help students improve their basic multiplication arithmetic skills has been developed based on a cloud-service. The performance of the application was improved by integrating the Flutter framework, Google Cloud, and Google Sheets. As a result of applying this application to 72 6th graders in elementary schools located in K Metropolitan City, for one week. students' spending time required for solving multiplication table problems was reduced by more than 28% compared to the initial period, while students' learning data was able to be accurately collected without errors. It is hoped that the development case conducted through the Flutter framework in this study can lead to the development of other educational learning applications.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.475-496
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• 2018

Although the multiplication of decimal fractions is expected to be easy for students to understand because of the similarity to natural numbers multiplication in computing methods, students show many errors in the multiplication of decimal fractions. This is a result of the instruction focused more on skill mastery than conceptual understanding. This study is a basic study for effectively developing a unit of multiplication of decimal fractions. For this purpose, we analyzed the curriculums' performance standards, significance in teaching-learning and evaluation, contents and methods for teaching multiplication of decimal fractions from the 7th curriculum to the revised curriculum of 2015 and the textbooks' activities and lessons. Further, we analyzed preceding studies and introductory books to suggest effective directions for developing teaching unit. As a result of the analysis, three implications were obtained: First, a meaningful instruction for estimation is needed. Second, it is necessary to present a visual model suitable for understanding the meaning of decimal multiplication. Third, the process of formalizing an algorithms for multiplying decimal fractions needs to be diversified.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.293-309
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• 2012

The algorithm of natural number multiplication is one of the basic topics of elementary school mathematics. Mastery of algorithm and understanding of the principles are important educational aims. In this paper we analyzed elementary school mathematics textbooks of South Korea, the United States, Singapore, Japan. As a result of analysis, we found out that there are much differences in the teaching of multiplication with three numbers, '${\times}10$', and '${\times}tens$'. We suggested some implication for the teaching of algorithm of natural number multiplication.

• Journal of IKEEE
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• v.24 no.3
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• pp.895-900
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• 2020

In this paper, BSPE replaced the existing multiplication algorithm that consumes a lot of power. Hardware resources are reduced by using a bit-serial multiplier, and variable integer data is used to reduce memory usage. In addition, MOA resource usage and power usage were reduced by applying LOA (Lower-part OR Approximation) to MOA (Multi Operand Adder) used to add partial sums. Therefore, compared to the existing MBS (Multiplication by Barrel Shifter), hardware resource reduction of 44% and power consumption of 42% were reduced. Also, we propose a hardware architecture design for BSPE Core.