Reactivating Memories from a Mathematical Task over a Period of Sleep

Sleep, especially slow-wave sleep (SWS), has been found to facilitate memory consolidation for many types of learning. Mathematical learning, however, has seldom been examined in this context. Solving multiplication problems involves multiple steps before problems can be mastered or answers memorized, and thus it can depend on both skill learning and fact learning. Here we aimed to test the hypothesis that memory reactivation during sleep contributes to multiplication learning. To do so, we used a technique known as targeted memory reactivation (TMR), or the pairing of newly learned information with specific stimuli that are later presented during sleep. With TMR, specific memories can be reactivated over a period of sleep without disrupting ongoing sleep. We applied TMR during an afternoon nap to reactivate half of the multiplication problems that had previously been practiced. Results showed no effect of TMR on response time or accuracy of multiplication problem solving. Because these results were unexpected, we also used a variation of this paradigm to examine results in subjects who remained awake. Comparisons between the wake and sleep groups showed no difference in response time or accuracy in either the initial test or the final test. Although neither TMR nor sleep differentially influenced multiplication performance, correlational analysis provided some clues about mathematical problem solving and sleep. On the basis of these findings, even though they did not provide convincing support for our hypotheses, we suggest future experiments that could help produce a better understanding of the relevance of sleep and memory reactivation for this type of learning.

Content and Problem Analysis in Turkish and Singaporean Mathematics Textbooks: The Case of Multiplying Fractions

In this study, Turkish and Singaporean textbooks were compared in terms of teaching content for multiplying fractions, a subject that most students have difficulty in understanding. The study analyzed the 6th-grade mathematics textbook published by the Turkish Ministry of National Education and its Singaporean counterpart. While the Singaporean textbook covered all meanings of multiplying fractions, the Turkish textbook did not include the operator meaning of multiplying fractions. Compared to the Turkish textbook, the Singaporean textbook included more solution strategies. The number line model was not used in the textbooks of either country, and only one representation format was used to model a fraction multiplication problem. The Singaporean textbook included more fraction multiplication problems than did the Turkish textbook. Many problems in both textbooks were of a one-step fashion and required numerical answers.

Optimal sequence for chain matrix multiplication using evolutionary algorithm

The Chain Matrix Multiplication Problem (CMMP) is an optimization problem that helps to find the optimal way of parenthesization for Chain Matrix Multiplication (CMM). This problem arises in various scientific applications such as in electronics, robotics, mathematical programing, and cryptography. For CMMP the researchers have proposed various techniques such as dynamic approach, arithmetic approach, and sequential multiplication. However, these techniques are deficient for providing optimal results for CMMP in terms of computational time and significant amount of scalar multiplication. In this article, we proposed a new model to minimize the Chain Matrix Multiplication (CMM) operations based on group counseling optimizer (GCO). Our experimental results and their analysis show that the proposed GCO model has achieved significant reduction of time with efficient speed when compared with sequential chain matrix multiplication approach. The proposed model provides good performance and reduces the multiplication operations varying from 45% to 96% when compared with sequential multiplication. Moreover, we evaluate our results with the best known dynamic programing and arithmetic multiplication approaches, which clearly demonstrate that proposed model outperforms in terms of computational time and space complexity.

Application of deep learning and cloud data platform in college teaching quality evaluation

In this paper, the author introduces the theory of fuzzy mathematics into the evaluation of higher education. By determining the set of evaluation factors and comments, the author constructs the relevant mathematical model and processes the data, thus turning the evaluation problem into the multiplication problem of the fuzzy matrix. Deep learning is a very active branch of machine learning research in recent years. By increasing the depth and breadth of the model, i.e. increasing the number of operations from the input end to the output end and the number of channels of the model, the scale of parameters of the model is increased, so that the model has the ability to express complex functions. It is appropriate to use deep learning in teaching quality evaluation. The simulation results show that the deep learning model is very effective in dealing with data diversity and extracting complex implicit rules. It can effectively model experts’ professional knowledge and experience. Deep neural network has powerful expressive ability, and can effectively extract the deep-seated laws affecting the teaching quality. It can be used as an assistant technology for the evaluation of teaching quality in Colleges.

Pengaruh Penggunaan Jarimatika Terhadap Kemampuan Berhitung Perkalian Peserta Didik Kelas IV Sekolah Dasar

This study aims to determine the effect of the Jarimatika method on the ability of multiplication in fourth grade of elementary school students. This research focused on the use of Jarimatika to assist students in solving numeracy multiplication problem questions. This is based on factual condition where students have not been able to work on the number multiplication and also the monotonous learning methods implemented made learning mathematics feels difficult. This research employed an experimental method with a quasi experimental design in the form of nonequivalent control group design. The experimental group treated by Jarimatika, while the control group used the conventional methods of expository, question and answer and rote method. Data collection techniques in this study used tests. Research data are presented using descriptive statistical data analysis techniques. The research shows that there is an increase in the average of pretest and posttest score of the experimental group. Based on the t-test results obtained, the t obtained value of 6.966 is greater than t table of 2,056 (6,966 2,056) and a significance value of 0,000 is less than 0.05 (0,000 0.05) at a significance level of 5%. Based on the results of the t test, it showed a significant influence on the use of Jarimatika on multiplication learning outcomes in forth grade students of elementary schools.

TRANS MODEL MATHEMATICS EDUCATION (T2ME) UNTUK MENINGKATKAN KETERAMPILAN OPERASI HITUNG PERKALIAN BERBANTUAN TEKNIK SUBATSAGA DI SEKOLAH DASAR

This research is conducted to produce a product that can organize learning well and can ease problem solving in learning especially mathematics. The resulting product is the development of learning models and create an easy techniques as a solution to complete multiplication in Elementary School (SD). This is motivated by the low ability to solve various multiplication problem that occurred in the 4th grade in Elementary School (SD). This data was obtained based on observation and interviews conducted with teacher’s classroom at some public Elementary Schools in Purwakarta district. In one of the public Elementary Schools it was found that only 25% of students were able control multiplication. Based on the problems, the research method use is Research and Development (R&D) Borg and Gall. Product design that will be developed and applied that is model of learning model of mathematics education model (T2ME) and technique of SuBatSaGa multiplication. Our Product design developed has been approved by the experts. The experts in this research that is lecturer of mathematics. Keywords: multiplication, Trans Model Mathematics Education (T2ME), SuBatSaGa technique.

Impact of ageing on problem size and proactive interference in arithmetic facts solving

Arithmetic facts (AFs) are required when solving problems such as “3 × 4” and refer to calculations for which the correct answer is retrieved from memory. Currently, two important effects that modulate the performance in AFs have been highlighted: the problem size effect and the proactive interference effect. The aim of this study is to investigate possible age-related changes of the problem size effect and the proactive interference effect in AF solving. To this end, the performance of young and older adults was compared in a multiplication production task. Furthermore, an independent measure of proactive interference was assessed to further define the architecture underlying this effect in multiplication solving. The results indicate that both young and older adults were sensitive to the effects of interference and of the problem size. That is, both interference and problem size affected performance negatively: the time needed to solve a multiplication problem increases as the level of interference and the size of the problem increase. Regarding the effect of ageing, the problem size effect remains constant with age, indicating a preserved AF network in older adults. Interestingly, sensitivity to proactive interference in multiplication solving was less pronounced in older than in younger adults suggesting that part of the proactive interference has been overcome with age.