Journal articles: 'Learning multiplication'

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Grabauskienė, Vaiva, and Oksana Mockaitytė-Rastenienė. "AN EXPRESSION OF MATHEMATICAL CONNECTIONS IN MULTIPLICATION-RELATED THINKING IN THIRD AND FOURTH GRADES OF PRIMARY SCHOOL." ŠVIETIMAS: POLITIKA, VADYBA, KOKYBĖ / EDUCATION POLICY, MANAGEMENT AND QUALITY 11, no. 1 (August 25, 2019): 9–29. http://dx.doi.org/10.48127/spvk-epmq/19.11.09.

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Mathematical comprehension is closely related to a cognition of mathematical connections. A multiplication is a mathematical operation characterized by complex mathematical connections. Students are early introduced with the multiplication. Therefore, in primary school, not so developed cognition of mathematical connections may become a reason for difficulties in Maths. A functionality of concept is based on a view to a multiplication. The analysis scientific literature revealed that a thinking of multiplication can be either additive or multiplicative. Additionally, the multiplication learning has a variety of additive and multiplicative explanations. Because they use different specificity of visualization, the models are not equally suitable for teaching children about different properties of multiplication. Based on research, in Math classes, students are only introduced with few of the models, not covering a whole variety of them. In the research, a paper and pencil type of survey consisted of 157 participants from 3rd and 4th Grades, eight different classes from four different schools. The students had to fill the table explaining multiplication of 5 x 12 in a form of writing and drawing. The quantitative analysis of results has showed that in Grades 3 to 4, the additive view to multiplication is much more prevalent, in comparison to the multiplicative reasoning. The array model is used often but not in an extensive way. The students do not know other types of multiplicative type models. In conclusion, the results showed that students of Grades 3rd and 4th knew not enough about the mathematical connections. Therefore, teachers should pay more attention to teaching students various ways of visualizing, for children, to obtain a comprehensive understanding of the multiplication process. Acknowledgement. This work was supported by a grant (No. 09.2.1-ESFA-K-728-01-0040) from the ESFA. Keywords: additive reasoning, multiplication learning, multiplicative reasoning, primary mathematics education.

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Chang, Kuo-En, Yao-Ting Sung, Yu-Lung Chen, and Long-Hua Huang. "Learning multiplication through computer-assisted learning activities." Computers in Human Behavior 24, no. 6 (September 2008): 2904–16. http://dx.doi.org/10.1016/j.chb.2008.04.015.

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Caron, Thomas A. "Learning Multiplication: The Easy Way." Clearing House: A Journal of Educational Strategies, Issues and Ideas 80, no. 6 (July 2007): 278–82. http://dx.doi.org/10.3200/tchs.80.6.278-282.

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Schmitt, Michael. "On the Complexity of Computing and Learning with Multiplicative Neural Networks." Neural Computation 14, no. 2 (February 1, 2002): 241–301. http://dx.doi.org/10.1162/08997660252741121.

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In a great variety of neuron models, neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks that contain units that multiply their inputs instead of summing them and thus allow inputs to interact nonlinearly. The class of multiplicative neural networks comprises such widely known and well-studied network types as higher-order networks and product unit networks. We investigate the complexity of computing and learning for multiplicative neural networks. In particular, we derive upper and lower bounds on the Vapnik-Chervonenkis (VC) dimension and the pseudo-dimension for various types of networks with multiplicative units. As the most general case, we consider feedforward networks consisting of product and sigmoidal units, showing that their pseudo-dimension is bounded from above by a polynomial with the same order of magnitude as the currently best-known bound for purely sigmoidal networks. Moreover, we show that this bound holds even when the unit type, product or sigmoidal, may be learned. Crucial for these results are calculations of solution set components bounds for new network classes. As to lower bounds, we construct product unit networks of fixed depth with super-linear VC dimension. For sigmoidal networks of higher order, we establish polynomial bounds that, in contrast to previous results, do not involve any restriction of the network order. We further consider various classes of higher-order units, also known as sigma-pi units, that are characterized by connectivity constraints. In terms of these, we derive some asymptotically tight bounds. Multiplication plays an important role in both neural modeling of biological behavior and computing and learning with artificial neural networks. We briefly survey research in biology and in applications where multiplication is considered an essential computational element. The results we present here provide new tools for assessing the impact of multiplication on the computational power and the learning capabilities of neural networks.

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Emelo, Randy. "Group mentoring: rapid multiplication of learning." Industrial and Commercial Training 43, no. 3 (April 19, 2011): 136–45. http://dx.doi.org/10.1108/00197851111123587.

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Meyer, Ruth A., and James E. Riley. "Multiplication Games." Arithmetic Teacher 33, no. 8 (April 1986): 22–25. http://dx.doi.org/10.5951/at.33.8.0022.

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Drill and practice are essential for the learning and retention of basic multiplication facts. Nonetheles, if drill becomes repetitive and uninteresting, the time spent on it becomes less effective. Games, such as those described in this article, can be used not only to bring interest and excitement into drilling the basic multiplication facts but also to help children to learn some problem-solving strategies. These games would fit well into any classroom ituation and would provide variety for those students who become bored with regular classroom routines.

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Denham, André R. "Strategy Instruction and Maintenance of Basic Multiplication Facts through Digital Game Play." International Journal of Game-Based Learning 3, no. 2 (April 2013): 36–54. http://dx.doi.org/10.4018/ijgbl.2013040103.

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Formative instruction on multiplication primarily focuses on rote memorization. This leads to factual fluency, but also develops a narrow view of multiplication and hinders the development of conceptual understanding. Theory and research recommend the concurrent development of conceptual understanding and factual fluency during the initial stages of learning about multiplication. Woodward (2006) conducted a field study to investigate this instructional approach and found a significant difference between those who received instruction on multiplicative properties and timed-drills of multiplication facts on a conceptual measure than those who only spent time on timed drills. This study investigated the efficacy of integrating the same approach within a digital game. There was a significant decrease between pre- and post- measures of participants timed retrieval of multiplication facts, but no differences were found between conditions on pre- and post-measures of conceptual understanding. These findings indicate that special attention must be paid to intrinsic integration of instructional content in order to address conceptual understanding through digital game play.

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De Los Santos, Estella. "Helping a Student with Learning Disabilities Memorize Multiplication Facts." International Journal for Innovation Education and Research 7, no. 7 (July 31, 2019): 133–46. http://dx.doi.org/10.31686/ijier.vol7.iss7.1590.

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Abstract A sixth grade student’s ability to memorize multiplication facts was investigated. The overall goal of the work was to improve the student’s understanding and knowledge of basic multiplication facts (0-10) for the zeroes, to fives. There were 66 facts, for example 4 x 6 = 24. The student had been taught multiplication concepts in her elementary years and she did have a basic understand of the meaning of multiplication facts as shown on a pretest. She understood that 4 x 6 is a representation of four sets of six or 6 + 6 + 6 + 6 = 24. The student’s previous knowledge and history were used to develop an individualized education plan to help her have a better understanding of the concept and to memorize basic multiplication facts. The interventions were concrete, semi-concrete, and abstract models of instruction. A pretest was given prior to the sessions and a posttest was given after the sessions. The number of sessions was determined based on the student’s ability to learn the concepts. The student was successful at memorizing multiplication facts for the zeroes through fives. The next study will be to help the student achieve automaticity of the multiplication facts.

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Kaufmann, Odd Tore. "Students´ reasoning on multiplication in primary school classroom context." Journal of Research in Mathematics Education 8, no. 1 (February 24, 2019): 6. http://dx.doi.org/10.17583/redimat.2019.2822.

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This article investigates how students in third grade discuss and reason on multiplication when they first encounter that concept in the classroom context. By analysing the data from 24 classrooms focused on teaching and learning multiplication, the article aims at contributing to the research and conceptualisations about students´ reasoning and strategy use in multiplication. The analysis shows that some of the features within previous research are helpful in characterizing the students´ reasoning about multiplication. However, the data material also reveals new aspects of students´ reasoning multiplication in classroom settings. One aspect is how students reason about different characteristics of multiplication, and reason about the concept of multiplication in a more general way. They put it in a broader context by going beyond the actual example in which the activity takes place. The students have moved away from the actual example, shifting their attention towards a focus on mathematical relationships. Another aspect is how a strong emphasis on using addition when they work with multiplication, by for instance that some students may begin to use different sub-totals, can cause tensions in the discussions between the teacher and students. Results are discussed in relation to previous studies of students´ multiplicative reasoning and implications for practice are elaborated upon.

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Abrahamson, Dor, and Christian Cigan. "A Design for Ratio and Proportion Instruction." Mathematics Teaching in the Middle School 8, no. 9 (May 2003): 493–501. http://dx.doi.org/10.5951/mtms.8.9.0493.

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This article describes a method for teaching ratio and proportion in a fifthgrade classroom. Our unit design creates and follows a learning path that begins with revisiting multiplication as repeated addition. It then explores patterns in the multiplication table and moves to the concept of rate as a single column out of the multiplication table. Next, students discuss ratio as two linked rate columns, or a ratio table, then look at two rows out of a ratio table, or a proportion quartet. As a fifth-grade introduction to ratio and proportion, this unit focuses on integer cases, that is, situations in which the question mark in a:b = c:? is an integer. This emphasis fosters multiplicative reasoning in a developmentally appropriate numerical environment.

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De Los Santos, Estella. "Helping a Student with Learning Disabilities Develop Automaticity with Multiplication Facts." International Journal for Innovation Education and Research 8, no. 7 (July 1, 2020): 106–22. http://dx.doi.org/10.31686/ijier.vol8.iss7.2459.

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An eighth-grade student, was able to memorize multiplication facts (0 to 10) for the zeroes to fives with 100% accuracy. In a previous study [1] the student used skip counting and her hands to recall all the facts for the ones to fives. The overall goal of the current study was to improve the student’s automaticity of multiplication facts (0-10) for the ones through fives, such as 4 x 6 = 24. The student had been taught multiplication concepts in her elementary years and she did have a basic understanding of the meaning of multiplication facts as shown in the previous study. She understood that 4 x 6 is a representation of four sets of six or 6 + 6 + 6 + 6 = 24. The student had used skip counting and flash cards with illustrations of the multiplication facts to memorize the multiplication facts. In the current study a multiple baseline design was used to measure the acquisition of fluency of multiplication facts over time. The student was able to develop automaticity with 80% accuracy by giving the solution within 3 seconds for all of the facts (0-10) for the ones through fives.

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Wati, Indah Kartika, Destiniar Destiniar, and Nyiayu Fahriza Fuadiah. "Didactic Anticipation of Two Matrix Multiplication Learning." JIPM (Jurnal Ilmiah Pendidikan Matematika) 9, no. 1 (September 14, 2020): 1. http://dx.doi.org/10.25273/jipm.v9i1.5904.

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This study aims to create a didactic design in an effort to overcome the learning obstacle through DDR (Didactical Design Research) in learning multiplication of two matrices through prospective, meta-pedadidactic, and retrospective analysis stages. Data collection using the following techniques: 1) observation, namely observing learning activities, analyzing teaching materials and learning implementation plans used by teachers in classroom learning; 2) tests in the form of diagnostic tests for students to determine the learning obstacle, prerequisite ability tests, and final identification tests; 3) interviews with mathematics subject teachers by asking questions that lead to student difficulties and teacher difficulties in delivering mathematics learning material; and 4) instructional videos in the learning process. The data were analyzed to find a learning obstacle and based on these findings, a was prepared Hypothetical Learning Trajectory (HLT)which was outlined in a hypothetical didactic design. The didactic design that has been designed is implemented to test as well as validate HLT. The results of the instructional video recordings were analyzed in the meta-pedadactic stage. The didactic design of the two matrix multiplication material contains didactic anticipation that can be an alternative for the teacher when facing situations and responses that may occur.

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Yuniasih, N., R. E. N. Putri, C. I. R. Nita, and Y. Findawati. "DOMI KALI: Elementary school multiplication learning media." Journal of Physics: Conference Series 1402 (December 2019): 077084. http://dx.doi.org/10.1088/1742-6596/1402/7/077084.

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Hendriana, Heris, Rully Charitas Indra Prahmana, and Wahyu Hidayat. "THE INNOVATION OF LEARNING TRAJECTORY ON MULTIPLICATION OPERATIONS FOR RURAL AREA STUDENTS IN INDONESIA." Journal on Mathematics Education 10, no. 3 (August 25, 2019): 397–408. http://dx.doi.org/10.22342/jme.10.3.9257.397-408.

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The rural area's student difficulties in learning the concept of number operation had been documented by several studies, especially for the case of multiplication. The teacher typically introduces the multiplication concepts using the formula without involving the concept itself. Furthermore, this study aims to design learning trajectory on multiplication operations in the Mathematics of GASING (Math GASING) by focusing more on the concept itself than the formula and by starting from the informal to a formal level of teaching. Design research used as the research method to solve this problem consisting of three phases, namely preliminary design, teaching experiment, and retrospective analysis. The research results show that the Math GASING has a real contribution for students to understanding and mastering in the concept of the multiplication operations. This research also explains the strategy and the model discovered by students in learning multiplication that the students used as a basic concept of multiplication. Finally, the students were able to understand the concept of multiplication more easily, and they showed interest in using this learning trajectory.

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Wicaksono, Agung. "PENERAPAN PENDEKATAN PEMBELAJARAN OPEN ENDED UNTUK MENINGKATAKAN PEMAHAMAN SISWA KELAS V AL ANKABUT SDIT AL FAHMI PALU PADA MATERI OPERASI HITUNG BILANGAN BULAT." IBTIDAI'Y DATOKARAMA: JURNAL PENDIDIKAN DASAR 2, no. 1 (June 30, 2021): 25–36. http://dx.doi.org/10.24239/ibtidaiy.vol2.iss1.24.

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The background of this research is that generally students understand the concept of multiplication and division of integers by memorizing. Basically, the memorization method will be appropriate if you memorize it, you know and understand what you have memorized. So that students do not just memorize alone. However, students really understand what they have memorized, and the teacher in providing material on multiplication and division of integers is only glued to the textbook but does not use other solutions that are easier for students to understand. To improve students' understanding of the operations of multiplication and division of integers, learning uses an Open-Ended approach that designs a solution and answer in the operation of multiplication and division of integers with more than one solution and answer. The main objective of this research is to find out how big the Open-Ended learning approach is in improving the understanding of fifth grade students of Al Ankabut SDIT Al Fahmi on the operations of multiplication and division of integers. In this study, the researcher conducted classroom action research with six students as research subjects who were selected based on their ability level, consisting of six students, namely two students with low abilities, two students with moderate abilities, and two students with high abilities. The process of collecting data was done through tests, observations, interviews and field notes. The action was carried out four times, namely Action (1) was learning about all the elements in multiplication using Open-Ended learning through a structural approach. Action (2) is learning about integer multiplication operations with the application of Open-Ended learning through a structural approach. Action (3) is learning about all the elements in the division using Open-Ended learning through a structural approach. Action (4) is learning about the operation of dividing integers by applying Open-Ended learning through a structural approach. The results show that learning with an Open-Ended approach can improve the understanding of fifth grade students at Al Ankabut SDIT Al Fahmi Palu in the operations of multiplication and division of integers.

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Nurkholidah, Nurkholidah. "Application of Team Assisted Individualization Cooperative Learning to Improve Mathematics Learning Multiplication Material." Social, Humanities, and Educational Studies (SHEs): Conference Series 3, no. 3 (November 15, 2020): 62. http://dx.doi.org/10.20961/shes.v3i3.45698.

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<pre>The purpose of this study was to improve the multiplication material learning Mathematics. This study uses the Team Assisted Individualized Cooperative learning model, namely by grouping students into several groups, each of which contains smart children and less intelligent children. Each group worked on the multiplication questions given by the teacher, children who were good at guiding children who were less intelligent (peer tutors). The results of the study using this learning model showed encouraging results for children who previously had many who were incomplete by using this learning model many children who value above KKM.</pre>

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Thai, Liong Kon, and Mohd Hanafi Mohd Yasin. "Magic Finger Teaching Method in Learning Multiplication Facts among Deaf Students." Journal of Education and Learning 5, no. 3 (April 21, 2016): 40. http://dx.doi.org/10.5539/jel.v5n3p40.

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Deaf students face problems in mastering multiplication facts. This study aims to identify the effectiveness of Magic Finger Teaching Method (MFTM) and students’ perception towards MFTM. The research employs a quasi experimental with non-equivalent pre-test and post-test control group design. Pre-test, post-test and questionnaires were used. As many as 70 deaf students from three special education primary schools in Selangor and Federal Territory were gathered as research respondent. Data were analyzed by using descriptive and inferential statistics of t-test. Findings from the t-test analysis showed that MFTM has a significant effect on multiplication facts achievement among deaf students whereas conventional teaching method does not given a significant effect on multiplication facts achievement among them. The findings from questionnaires found that the deaf students have high level of perception towards MFTM in the dimensions of interest, self-confidence, persistence and motivation in learning multiplication facts. The findings serves as an implication towards students, parents, teachers, Special Education Division and Malaysia Education Ministry in terms of awareness, involvement, planning and implementation in the context of diversifying of multiplication facts teaching method, and the suitability of supporting materials in teaching and learning multiplication facts.

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Christensen, Evelyn B., and Stephen M. Christensen. "Quick Reads: A Handy Multiplication Mystery." Mathematics Teaching in the Middle School 17, no. 1 (August 2011): 14–15. http://dx.doi.org/10.5951/mathteacmiddscho.17.1.0014.

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We had just finished a Thanksgiving meal last year, and several family members were relaxing on the front porch. I sat on the swing next to my eight-year-old niece. “What interesting things have you been learning in school recently?” I asked. She told me that she had been learning her multiplication tables. As a former math teacher and elementary teacher, I was pleased that she considered learning math to be interesting.

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Cai, Jingyong, Masashi Takemoto, Yuming Qiu, and Hironori Nakajo. "Trigonometric Inference Providing Learning in Deep Neural Networks." Applied Sciences 11, no. 15 (July 21, 2021): 6704. http://dx.doi.org/10.3390/app11156704.

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Despite being heavily used in the training of deep neural networks (DNNs), multipliers are resource-intensive and insufficient in many different scenarios. Previous discoveries have revealed the superiority when activation functions, such as the sigmoid, are calculated by shift-and-add operations, although they fail to remove multiplications in training altogether. In this paper, we propose an innovative approach that can convert all multiplications in the forward and backward inferences of DNNs into shift-and-add operations. Because the model parameters and backpropagated errors of a large DNN model are typically clustered around zero, these values can be approximated by their sine values. Multiplications between the weights and error signals are transferred to multiplications of their sine values, which are replaceable with simpler operations with the help of the product to sum formula. In addition, a rectified sine activation function is utilized for further converting layer inputs into sine values. In this way, the original multiplication-intensive operations can be computed through simple add-and-shift operations. This trigonometric approximation method provides an efficient training and inference alternative for devices with insufficient hardware multipliers. Experimental results demonstrate that this method is able to obtain a performance close to that of classical training algorithms. The approach we propose sheds new light on future hardware customization research for machine learning.

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Suandi, Rahmawati. "LEARNING DESIGN OPERATION MULTIPLICATION ALGEBRA USING WATER CONTEXT, OIL AND STONE STUDENTS CLASS V." Jurnal Daya Matematis 6, no. 3 (February 28, 2019): 236. http://dx.doi.org/10.26858/jds.v6i3.8522.

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The purpose of this study resulted in the learning path of students of algebraic multiplication materials by using water, oil and stone that evolved from informal to formal forms. The method used is a research design consisting of three stages, namely preliminary, design experiment and retrospective analysis. A series of lessons are designed and developed based on conjectures from the learning process and PMRI approach. This research was conducted in SMP N 5 Palembang involving 30 students of class VII. Learning Trajectory (LT) obtained includes three activities that are activities 1. Introduce the objects around that can be used in learning algebraic multiplication such as oil, stone and water, 2 Finding the Concept of Multiplication Algebra and 3. Solving problems related to daily life. The results of the experimental learning show that a series of activities that have been done helps to improve students' understanding of algebraic multiplication learning

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Suwariyasa, Made. "The Analysis of Students’ Ability of Decimal Numeral Multiplication of the Fifth Grade Students." Journal of Psychology and Instructions 1, no. 1 (March 1, 2017): 36. http://dx.doi.org/10.23887/jpai.v1i1.9629.

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This study aimed to (1) describing Learning multiplication of decimal fractions in V grade,(2) The students' ability in completing the multiplication of decimal fractions, (3) The constraints which were faced by students in completing the multiplication of decimal fractions and the solutions to overcome those obstacles. The type of this study was descriptive quantitative and qualitative research. The subjects of this study were the fifth grade students of SD Negeri 2 Penarukan, consisted of 20 students and teachers in V class. The object of this study were (1) Learning multiplication decimal fraction in V grade, (2) The students' ability in completing the multiplication of decimal fractions, (3) The constraints which were faced by students in completing the multiplication of decimal fractions and the solutions to overcome those obstacles. The observation, test, interview, and documentation were used to collect the data. The data were analyzed using descriptive quantitative and qualitative approach. The results showed (1) Learning multiplication decimal fractions was categorized good with a value of 84 , (2) the average test results in classical 59.9 with low category with the highest indicators is to solve everyday problems which involves multiplication of various fractions 55.25% and the lowest indicator is determining the results of multiplication operations of various fractional 88.5 %, (3) The constraints faced by students are: forget the concept of decimal fractions multiplication operations, forget to put coma at the end of the answer and students are still confusein completing the essay task. The solution to overcome those constraints aregiving students a lot of exercises regarding the multiplication of decimal fractions. So that students are better trained and familiar with the particular multiplication exercises.

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Wood, Donna K., Alan R. Frank, and David P. Wacker. "TEACHING MULTIPLICATION FACTS TO STUDENTS WITH LEARNING DISABILITIES." Journal of Applied Behavior Analysis 31, no. 3 (September 1998): 323–38. http://dx.doi.org/10.1901/jaba.1998.31-323.

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Andriyani and M. Maulana. "Cubaritme in the trajectory learning of multiplication concept." Journal of Physics: Conference Series 1188 (March 2019): 012049. http://dx.doi.org/10.1088/1742-6596/1188/1/012049.

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Mattingly, Judith C., and Deborah A. Bott. "Teaching Multiplication Facts to Students with Learning Problems." Exceptional Children 56, no. 5 (February 1990): 438–49. http://dx.doi.org/10.1177/001440299005600507.

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Williams, Dawn M., and Belva C. Collins. "Teaching Multiplication Facts to Students with Learning Disabilities." Journal of Learning Disabilities 27, no. 9 (November 1994): 589–97. http://dx.doi.org/10.1177/002221949402700908.

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Gil, Maria Luiza Evangelista, and Luciana Figueiredo Lacanallo Arrais. "A MULTIPLICAÇÃO E O ENSINO: UM ESTUDO A PARTIR DAS PROPOSIÇÕES DE DAVYDOV." COLLOQUIUM HUMANARUM 18, no. 1 (July 5, 2021): 77–85. http://dx.doi.org/10.5747/ch.2021.v18.h510.

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The objective of this article to discuss the process of teaching multiplication, having as principles the assumptions of the Historical-Cultural Theory -THC. Mathematics is present in our daily life and allows us tocommunicate, solve problems and promote social relations. This proves the importance and need for the appropriation of the concepts involved in the aritmetic operations is essential, especially multiplication. Therefore, through a bibliographical research, studies were made on Vygostki, Davydov, Moura Rosa, Galdino and other contemporary authors linked to this same perspective, the search for understanding principles that help us teach multiplication in the early years of schooling. We found that teaching needs to go beyond empirical aspects towards the development of theoretical thinking, being indispensable the execution of tasks and actions that make the student enter into study activity and understand the concept. The research shows that the theme needsmore investigated in order to have more propositions and referrals to ensure the learning of the multiplicative concept.

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Fernandes, Mimik, Farida F, Yanti Fitria, Ahmad Fauzan, and Nelvyarni Nelvyarni. "IMPROVEMENT OF LEARNING OUTCOMES IN RESULT USING REALISTIC MATHEMATIC EDUCATION APPROACH IN BASIC SCHOOL." Unes Journal of Education Scienties 2, no. 2 (November 30, 2018): 157. http://dx.doi.org/10.31933/ujes.2.2.157-165.2018.

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Based on experience and reflection multiplication of fractions learning at fifth class SDN 33 VII Koto Padang Pariaman district. Student learning outcomes is still low and the learning undertaken by teachers arenot using realistic problem to beginning of learning. So the author through this research trying to improve student learning outcomes in subjects multiplication of fractions. The purpose of this study was to describe the planning, implementation and learning outcomes. This research is action research (class action research), this study used a qualitative and quantitative approach. Learning is used by using the realistic mathematics education approach. After doing research hence an increase in student learning outcomes in multiplication of fractions lesson using realistic mathematics education approach. It can be seen, both from the ability of teachers in designing learning from 83% up to 94%, implementation of learning increased 94% from 77%, and learning outcomes increased to 86,87 from 74,04.

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Mardiyani, Anisa, Yusuf Suryana, and Winarti Dwi Febriani. "Improve Student Learning Outcomes in Multiplication Learning Mixed Fractions Using Teams Games Tournament (TGT) Model." Social, Humanities, and Educational Studies (SHEs): Conference Series 4, no. 1 (February 22, 2021): 34. http://dx.doi.org/10.20961/shes.v4i1.48563.

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The problem in this study was the low student learning outcomes in mathematics learning the subject of multiplication of mixed fractions in class V. The purpose of this study was to see an increase in student learning outcomes in learning mixed fraction multiplication using the TGT learning model in class V SDN 2 Cigembor, Ciamis District, Regency. Ciamis. The population in the study were 30 grade students of SDN 2 Cigembor. The method used in this research is Classroom Action Research Methods (PTK) according to Kemmis and Mc. Taggart which consists of four stages: planning, implementing, observing, reflecting. This research was conducted in two cycles. The instruments used in this study were evaluation instruments, teacher performance instruments, and student activity instruments. Based on the results of the evaluation test data from cycle I to cycle II, it shows that in the first cycle the average student learning outcomes were 74.40 and learning completeness was 57%, while in the second cycle the average student learning outcomes were 79.83 and completeness learn by 87%. Based on the results of the research, it can be concluded that the use of the TGT learning model can improve student learning outcomes in the multiplication of mixed fractions in class V SDN 2 Cigembor, Ciamis District, Ciamis Regency, Academic Year 2019/2020.

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Setiadi, Nanang. "The Use of Realistic Mathematics Education (RME) to Help Indonesian 5th-Grade Students to Learn Multiplication and Division." Southeast Asian Mathematics Education Journal 10, no. 1 (September 30, 2020): 41–53. http://dx.doi.org/10.46517/seamej.v10i1.98.

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Abstract This paper discusses the use of Realistic Mathematics Education (RME) as an alternative approach to enhance Indonesian 5th-grade students’ ability in multiplication and division. It presents the analysis of Indonesian 5th-grade students’ difficulties in applying stacking method for multiplication and division. Furthermore, it describes a mathematics teaching learning practice to stimulate students constructing their strategies, mathematical models and number sense in solving mathematical problems that involve multiplication and division. The teaching learning practice aims to apply RME for helping students develop their multiplication and division ability.Findings shows that stacking methods for multiplication and division are difficult for the students. The main students’ problem in multiplication and division stacking methods is in reapplying the steps of the methods. The steps taken to improve the learning process by implementing RME are: (1) analyze in detail the difficulties of students in multiplication and division stacking methods, (2) provide contexts of mathematical problems that can stimulate students to think mathematically, (3) hold a class mathematics congress, and (4) conduct a test to measure students’ achievement. Based on the students’ achievement, there has been several improvements. After RME, there were more students whose grades passed the Minimum Mastery Criteria. Moreover, there was a student who got 100. Then, the average test was higher. Meanwhile, there were only 3 children whose grades were 0. Thus, the application of RME has helped the 5th-grade students to improve their ability in multiplication and division.

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Dotan, Dror, and Naama Friedmann. "Reducing interference improves the memorization of multiplication facts in case of hypersensitivity to interference." Journal of Numerical Cognition 5, no. 3 (December 20, 2019): 400–430. http://dx.doi.org/10.5964/jnc.v5i3.203.

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Hypersensitivity to interference (HYSTI) is a situation in which a person has a severe difficulty in memorizing verbal items that are similar to each other. This may result in induced dyscalculia: HYSTI was shown to correlate with a difficulty in learning the multiplication table, presumably because the multiplication table, which is memorized verbally, has much similarity between the items ("six times seven equals forty two", "six times eight equals forty eight", etc.). Here, we show causal evidence that HYSTI disrupts the memorization of multiplication facts. We report DL, a woman with HYSTI who had extremely poor knowledge of the multiplication table. To examine whether her multiplication difficulty resulted from HYSTI, we tested whether she could learn multiplication facts when interference was reduced. In a series of merely 12 short sessions over a period of 4 weeks, DL rehearsed 16 multiplication facts – four facts per week. When the 4 facts in a given week were similar to each other, DL’s learning was poor. Conversely, when the 4 facts in a given week were dissimilar from each other, DL learned them quickly and easily. The effect of similarity was observed during the training period and persisted at least two months after the end of training. These results provide the first causal evidence that HYSTI impairs the learning or retrieval of arithmetic facts. From a pedagogical perspective, our findings may call for re-considering how multiplication facts should be taught in elementary school.

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Zulfitria, Zulfitria. "UPAYA MENINGKATKAN HAFALAN PERKALIAN MATEMATIKA DENGAN MENGGUNAKAN METODE BERNYANYI PADA SISWA KELAS 2 SD DI MUHAMMADIYAH 12 PAMULANG BANTEN." Instruksional 1, no. 1 (September 16, 2019): 17. http://dx.doi.org/10.24853/instruksional.1.1.17-24.

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Mathematics is one of the most frightening learning for students, the real ability of social teaching is low. One way to improve students' multiplication skills by memorizing multiplication using the singing method.Research to find out how to learn mathematics in multiplication learning through memorizing methods by singing at Muhammadiyah Elementary School 12 Pamulang-Banten. The subject of the study was the second grade students of Al-Farisi class from August to September 2018.The research results obtained from each cycle have expressions from each cycle. This can be done by using the method of memorizing multiplication more pleasant and making it easier for students to remember it. Student students learn the assignments given by the teacher.

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Zhang, Zhidong. "Assessment of Matrix Multiplication Learning with a Rule-Based Analytical Model–A Bayesian Network Representation." International Education Studies 9, no. 12 (November 28, 2016): 182. http://dx.doi.org/10.5539/ies.v9n12p182.

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This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model, comprising of 2 layers of explanatory variables-Matrix Multiplication, Performance and Semantic Explanations; and one layer of evidential variables containing 9 evidential variables-was developed. With the simulating data, 9 students’ Performance and Semantic Explanation evidences were recorded. The results indicated that the hierarchical Bayesian assessment effectively traced and recorded students’ learning trajectories; and assessed students’ learning dynamically and diagnostically.

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Purwasih, Ratni, Indah Puspita Sari, and Ratna Sariningsih. "CUISENAIRE LEARNING MEDIA FOR ADDING, SUBTRACTING, MULTIPLYING, AND DIVIDING INTEGERS." MaPan 9, no. 1 (June 30, 2021): 167. http://dx.doi.org/10.24252/mapan.2021v9n1a11.

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This study aims to describe the manufacture and use of Cuisenaire rod learning media for understanding the concepts of addition, subtraction, multiplication, and division of integers for elementary school students. The research method used is literature study, which is a series of activities related to the methods of collecting library data, reading and recording, and processing research materials. This research uses a qualitative approach. Data sources and research results in library research in the form of a description. Data sources are bibliographic or come from various literature, including books, journals, newspapers, personal documents, etc. The research results are that the utilization of Cuisenaire rod media is more optimized on learning in elementary schools, especially in addition, subtraction, multiplication, and division of integers because Cuisenaire rod media can help understand and can concrete the concept of numbers. In addition, it can be used as reference material for research on learning addition, subtraction, multiplication, and division of integers by utilizing different learning media.

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Salsabila, Silvy Yulistia, Geri Syahril Sidik, and Rizki Hadiwijaya Zulkarnaen. "Analysis of Basic Students Learning Difficulties in Multiple Materials." Social, Humanities, and Educational Studies (SHEs): Conference Series 4, no. 1 (February 22, 2021): 14. http://dx.doi.org/10.20961/shes.v4i1.48560.

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This study aims to obtain an overview of learning difficulties. This research was conducted in third class of SDN 2 Cintaraja. The research method used is descriptive qualitative. The data collection technique was carried out in two ways, namely by giving story questions and interviews. The story questions used in this study were three questions which refer to four characteristics of student learning difficulties according to Jamaris in 2014 (weakness in counting, difficulty in transferring knowledge, understanding of mathematical language, difficulty in visual operations) regarding the multiplication. The results showed that there were still many students who had learning difficulties in this multiplication material, of the six students who were sampled all of them were only able to master one characteristic of the four characteristics of learning difficulties, namely in terms of understanding the language of mathematics, while the other three learning difficulties had not able to be mastered by them, namely in terms of calculating weaknesses, difficulties in transferring data, and difficulties in visual operations of the multiplication material.

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Anjarsari, Agnes Fitri. "MODEL KOOPERATIF TIPE TPS TERHADAP HASIL BELAJAR KONSEP PERKALIAN BILANGAN CACAH MATEMATIKA ANAK TUNARUNGU." JPI (Jurnal Pendidikan Inklusi) 1, no. 1 (April 23, 2018): 1. http://dx.doi.org/10.26740/inklusi.v1n1.p1-18.

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One of the deaf students disorders in mathematics lesson was their understanding toward the material of the concept of multiplication of numbers count mathematics so that it had less good impact to learning mathematics result. Based on the problem, this research applied cooperative learning of Think Pair Share (TPS) type with the purpose to analyze the influence of cooperative model of TPS type toward learning the concept of multiplication of numbers count mathematics result to hearing impairment students before and after going treatment.The approach used was quantitative with pre-experiment kind and the design was one group pretest-posttest design. The data was collected by test method, observation, and documentation.The results of data analysis, shows that the use of implementation influence of cooperative learning model of Think Pair Share (TPS) type approach significantly to learning the concept of multiplication of numbers count mathematics result to deaf students in SLB-B Dharma Wanita Sidoarjo.Keywords:Think Pair Share (TPS), learning mathematics result, Deaf

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Dussawal, Wahed, Muhammad Ihdal Husnayain, Muchlisin Muchlisin, and Wulida Arina Najwa. "Desain Pembelajaran Matematika Berbasis PMRI Pada Materi Perkalian Siswa Kelas 2 Sekolah Dasar." EduBasic Journal: Jurnal Pendidikan Dasar 1, no. 1 (April 15, 2019): 28–36. http://dx.doi.org/10.17509/ebj.v1i1.26178.

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Mathematics is one of the subjects studied by students from elementary school to university level. Therefore, mathematics becomes one of the scientific foundations at the basic level. There are some errors that are most often found in learning mathematics in the early grades of elementary school. One of them is related to understanding symbols, place values, process errors and mistakes in doing calculations. The problem is caused because the learning model provided by the teacher is still abstract. The purpose of this research is to provide alternatives learning option with to the design of realistic mathematics education learning or learning based on real life on multiplication material. This writing uses the study of literature from various scientific sources related to the problem. It is hoped that educators can apply mathematical learning models based on the Indonesian Realistic Mathematics Approach (PMRI) or RME (Realistic Mathematics Educatio) non multiplication material by using learning designs based on students' real lives or learning designs. The article shows that there is potential for PMRI design to be used to improve the multiplication ability of elementary school students.

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De Los Santos, Estella P. "Helping a Student with Learning Disabilities Memorize Multiplication Facts." International Journal of Technology and Inclusive Education 8, no. 2 (December 30, 2019): 1484–91. http://dx.doi.org/10.20533/ijtie.2047.0533.2019.0182.

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Huang, Jianyi, and Li Chao. "Specific Intervention for Multiplication Skill with Learning-Disabled Students." Psychological Reports 84, no. 2 (April 1999): 662. http://dx.doi.org/10.2466/pr0.1999.84.2.662.

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A multiple baseline design was used to assess the intervention of individual tutoring to help two learning-disabled students (15 and 16 years old) improve their multiplication of 1 -digit numbers over nine days of 10-min. instruction. Observation or visual analysis indicated 40 to 50% improvement after the intervention, and a nonparametric test of randomization showed that the students' improvement was retained during the 2-wk. follow-up.

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Greene, Gary. "Mnemonic Multiplication Fact Instruction for Students With Learning Disabilities." Learning Disabilities Research and Practice 14, no. 3 (June 1999): 141–48. http://dx.doi.org/10.1207/sldrp1403_2.

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Flores, Margaret M., Vanessa M. Hinton, and Kelly B. Schweck. "Teaching Multiplication with Regrouping to Students with Learning Disabilities." Learning Disabilities Research & Practice 29, no. 4 (October 28, 2014): 171–83. http://dx.doi.org/10.1111/ldrp.12043.

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Roscoe, Matt B. "Using TileFarm to Support Emerging Multiplication." Mathematics Teacher: Learning and Teaching PK-12 114, no. 7 (July 2021): 518–27. http://dx.doi.org/10.5951/mtlt.2020.0250.

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Symmetric dot patterns are a particularly powerful object for investigation, providing opportunities for foundational learning across PK–5. We found that second-grade students naturally used repeated addends to count symmetric dot patterns created using the new software TileFarm.

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A. Supovitz, Jonathan, Caroline B. Ebby, Janine T. Remillard, and Robert Nathenson. "Experimental Impacts of Learning Trajectory–Oriented Formative Assessment on Student Problem-Solving Accuracy and Strategy Sophistication." Journal for Research in Mathematics Education 52, no. 4 (July 2021): 444–75. http://dx.doi.org/10.5951/jresematheduc-2021-0032.

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In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory–oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students’ multiplicative reasoning involves improvements in both problem-solving accuracy and sophistication of strategies used to solve problems, we designed an assessment instrument to measure both dimensions of student learning. The instrument was used to measure the impact of the Ongoing Assessment Project (OGAP), which develops teachers’ capacity to regularly assess student thinking in relation to a learning progression to develop instructional responses that are based on evidence of student thinking. The results showed significant impacts of OGAP on both students’ problem-solving accuracy and the sophistication of their strategy. The findings suggest that capturing both dimensions of students’ multiplicative reasoning offers important information for researchers and program designers who seek to understand different dimensions of student mathematics performance.

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van der Ven, Sanne H. G., Marthe Straatemeier, Brenda R. J. Jansen, Sharon Klinkenberg, and Han L. J. van der Maas. "Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems." Learning and Individual Differences 43 (October 2015): 48–62. http://dx.doi.org/10.1016/j.lindif.2015.08.013.

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Marhayati, Marhayati, and Nuril Huda. "Mendeteksi Pemahaman Konsep Perkalian Mahasiswa Calon Guru Madrasah Ibtidaiyah Melalui Problem Posing." Madrasah 12, no. 1 (January 7, 2020): 63–73. http://dx.doi.org/10.18860/mad.v12i1.7864.

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This study aims to determine the understanding of the mathematical multiplication concept of Islamic Elementary School prospective teachers. This study applied a descriptive qualitative method. The research subjects were 33 students of Islamic Elementary Teacher Education Department at the Islamic State University of Maulana Malik Ibrahim Malang. Submission of mathematics questions is the learning strategy used in the Pembelajaran Matematika course. The results of data analysis showed that there were three categories: (1) understanding the concept of multiplication (33.3%); (2) understanding the concept of pseudo multiplication (18.2%); (3) not understanding the concept of multiplication (48.5%).

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Behrend, Jean L. "Learning-Disabled Students Make Sense of Mathematics." Teaching Children Mathematics 9, no. 5 (January 2003): 269–73. http://dx.doi.org/10.5951/tcm.9.5.0269.

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Cal loved mathematics word problems. He delighted in new types of problems, exclaiming, “This is fun!” when a problem was presented. At the end of third grade, he successfully solved word problems involving addition, subtraction, multiplication, division, multiple steps, and extraneous information.

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Theeracheep, Siraphob, and Jaruloj Chongstitvatana. "Multiplication of medium-density matrices using TensorFlow on multicore CPUs." Tehnički glasnik 13, no. 4 (December 11, 2019): 286–90. http://dx.doi.org/10.31803/tg-20191104183930.

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Matrix multiplication is an essential part of many applications, such as linear algebra, image processing and machine learning. One platform used in such applications is TensorFlow, which is a machine learning library whose structure is based on dataflow programming paradigm. In this work, a method for multiplication of medium-density matrices on multicore CPUs using TensorFlow platform is proposed. This method, called tbt_matmul, utilizes TensorFlow built-in methods tf.matmul and tf.sparse_matmul. By partitioning each input matrix into four smaller sub-matrices, called tiles, and applying an appropriate multiplication method to each pair depending on their density, the proposed method outperforms the built-in methods for matrices of medium density and matrices of significantly uneven distribution of non-zeros.

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Zhao, Yang, Fengyu Qian, Faquir Jain, and Lei Wang. "Quantum-Dot Transistor Based Multi-Bit Multiplier Unit for In-Memory Computing." International Journal of High Speed Electronics and Systems 29, no. 01n04 (March 2020): 2040007. http://dx.doi.org/10.1142/s0129156420400078.

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In-memory computing is an emerging technique to fulfill the fast growing demand for high-performance data processing. This technique provides fast processing and high throughput by accessing data stored in the memory array rather than dealing with complicated operation and data movement on hard drive. For data processing, the most important computation is dot product, which is also the core computation for applications such as deep learning neuron networks, machine learning, etc. As multiplication is the key function in dot product, it is critical to improve its performance and achieve faster memory processing. In this paper, we present a design with the ability to perform in-memory multi-bit multiplications. The proposed design is implemented by using quantum-dot transistors, which enable multi-bit computations in the memory cell. Experimental results demonstrate that the proposed design provides reliable in-memory multi-bit multiplications with high density and high energy efficiency. Statistical analysis is performed using Monte Carlo simulations to investigate the process variations and error effects.

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Jayanti, Yunita Desi Dwi. "Implementasi Media Corong Berhitung Dalam Pembelajaran Matematika (Perkalian) Kelas II di SD Negeri 3 Gesikan Tulungagung." JURNAL INOVASI PENDIDIKAN DAN PEMBELAJARAN SEKOLAH DASAR 3, no. 2 (January 10, 2020): 1. http://dx.doi.org/10.24036/jippsd.v3i2.107401.

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The purpose of this research study is the application of counting funnel media to make it easier for students to understand multiplication lessons. This research is descriptive qualitative research by describing all the results of there search. Data collection techniques used by researchers are observation, interviews, and documentation. The subjects of this study were grade II SDN 3 Gesikan with the number of students as many as 35. The results of the study, namely the implementation of counting funnel media in mathematics learning (multiplication) in class II, had been well implemented. this media can help teachers and students in the process of learning mathematics especially multiplication lessons. The teacher's steps to apply are appropriate. During the use of media students pay attention, besides that students also understand what is conveyed by the teacher easily. The conclusion that the implementation of funnel media counting has been done well and smoothly. This media has helped the teacher to deliver the material and students to understand the material. This media is good to use mathematics learning especially multiplication material. in a simple way can lure students to pay attention to student focus.

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Drake, Jill Mizell, and Angela T. Barlow. "Assessing Students' Levels of Understanding Multiplication through Problem Writing." Teaching Children Mathematics 14, no. 5 (December 2007): 272–77. http://dx.doi.org/10.5951/tcm.14.5.0272.

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Assessing student learning is a very important part of teaching. As teachers, we are continually searching for assessments that give us valid information about what our students are learning. Occasionally, the assessments we use can surprise us with the results they yield.

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Miller, Sarah J., George H. Noell, Meredith T. Harris, Elise B. McIver, and Jessica P. Alvarez. "Assessing the Effects of Instructional Set Size on Learning." Assessment for Effective Intervention 46, no. 1 (January 28, 2019): 14–26. http://dx.doi.org/10.1177/1534508418825304.

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Research evaluating the variables that influence learning has devoted inadequate attention to the influence of the amount of new material presented at one time. The current study evaluated the impact of varying instructional set size (ISS) on the rate at which elementary school students mastered multiplication facts while receiving constant time delay (CTD) instruction. Instructional time was equated across conditions. Instruction was provided for an ISS of five and 20 using CTD instruction for multiplication facts. ISS 20 was more efficient for two out of the three participants. This suggests a much larger efficient ISS than previous research. The implications of this finding for the importance of the instructional method in attempting to identify an efficient ISS, as well as the study’s connection to prior research, in this area are discussed.

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Journal articles on the topic 'Learning multiplication'

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