192 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ Easy Multiplication from Left to Right and Al Khwarizmi Method: Hypothesis Testing Against Median Values Endro Tri Susdarwono Ilmu Komunikasi, Universitas Peradaban Email : midas999saniscara@gmail.com Abstract This study aims to provide an overview of easy multiplication using the left-to-right method and also the right-to-left method (Al Khwarizmi Method). Furthermore, the easy multiplication method from left to right and also from the right to left method was tested to determine the level of ease in its application to the two multiplication methods. The method used in this research is experimental. While the approach in this study used is quantitative. The quantitative approach used includes hypothesis testing on the median value. The conclusion of this study is that the median value of the posttest scores for easy multiplication from left to right and easy multiplication from right to left are indeed the same. Because the median is also an average value, it can also be concluded that the average number of easy multiplication posttest scores from left to right and easy multiplication posttest scores from right to left are the same. As an implication, the two easy multiplication techniques are able to produce the same level of convenience. Keywords: median value, multiplication from left to right, multiplication method Al Khwarizmi INTRODUCTION Human life cannot be separated from mathematics, almost everything in this world is related to a very important science known as mathematics. Mathematics is an important tool in various fields of science, including engineering, medical, natural sciences, and even social sciences need it as an analytical tool such as economics and psychology. In the original language, mathematics is known as Latin Regina Scientiarum, while in German it is known as konigin der wissenchaften, these two terms are interpreted as words that are related to science (Alisah and Dharmawan, 2007). Even Carl Friedrich Gauss explicitly says that mathematics is the queen of science (Suwarsih, 2018). Learning mathematics is especially touching in terms of how teachers are able to help students understand mathematics, and provide encouragement for students to apply the use of mathematics when solving problems of daily life. Teachers must create conditions for students to be able to enjoy learning mathematics. Mathematics learning itself is defined as a learning experience process that is given to students by involving a series of planned activities so that students gain competence regarding the mathematical materials provided (Purwanti, 2015). The teaching process in learning mathematics will be more mailto:midas999saniscara@gmail.com 193 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ successful and organized if it is directed to the structure and concepts of the mathematics subject being taught (Anwary, 2017; Bito, 2014). At the elementary school level, multiplication operation material is given. This material is very demanding how every teacher is able to instill the concept of multiplication as a whole, so teachers must have their own strategy or method by adjusting to the conditions that exist in students and their environment. The stages of learning activities in elementary schools should also pay attention to what is described by Bruner, namely: 1) enactive (concrete), 2) iconic (semi-concrete), and 3) symbolic/abstract (Youtube, 2021). Regarding the multiplication concept applied in class V, in general it is actually a continuation of the material from integers that was previously taught in class IV including addition and subtraction of integers (Wahyuningtyas & Ladamay, 2016). The introduction to multiplication arithmetic operations has actually been found in class II, although it is still very basic (Sulistiawati, 2014). So that students should be able to apply the multiplication concept to other higher-level materials in grades IV, V, and VI. However, it can be seen that in fact students in class V which incidentally belongs to the high class, there are even students who have not memorized the basic multiplication so that doing multiplication of two or more numbers has difficulty (Lelawarna, 2017). The situation that occurs is presumably because the initial learning provided is not contextual, in the sense that there is no association of problems with the real-life context that students live in their daily lives (Raharjo et al., 2009). Whereas multiplication is a basic thing that requires absolute mastery because it serves to lead students to understand the next material and to deepen the material across fields of study (Oktafiani et al., 2018). The right strategy is needed in making students able to master and understand correctly number operations. This learning strategy must be able to touch the stages of concrete, semi-concrete to abstract (Suwarto, 2017). The concept of number operations such as addition, standard multiplication taught in schools is generally calculated from right to left. The concept in this method teaches that the units are multiplied first and then the tens and so on. This is actually reasonable because the arithmetic technique was discovered by one of the most famous Persian Arab scientists, Muhammad bin Musa al-Khwarizmi. Because of his great service, Al-Khwarizmi was nicknamed the Father of Algebra (Arryawan, 2011). There is nothing wrong with counting from right to left as taught in schools whose origin is the Al Khwarizmi Method. But, actually for those of us who are used to writing from left to right, Al Khwarizmi's method, can be modified into a calculation from left to right. The advantage is that because we write Latin letters from left to right and also count in the same way, namely from left to right, we don't have to guess how many digits we have to provide so that the paper we need is enough. 194 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ This study aims to provide an overview of easy multiplication with the left- to-right method and also the right-to-left method. Furthermore, from easy multiplication with 2 methods, testing is carried out to determine the level of ease in its application to the two multiplication methods. RESEARCH METHOD The research method is a natural way to obtain data with specific uses and purposes (Lestari & Yudhanegara, 2012). In this study the method used is experimental. While the approach in this study used is quantitative. The quantitative approach used includes hypothesis testing on the median value. Research design Research design is the whole of planning to answer research questions and anticipate some difficulties that may arise during the research process. This is important because research design is a strategy to get the data needed for hypothesis testing or to answer research questions, and as a tool to control variables that influence research (Sugiyono, 2010). The paradigm in research is illustrated as follows: Figure 1. Research Design Information: X = the treatment given (independent variable) O = posttest (observed dependent variable) The sampling technique used for this design is purposive sampling. Purposive sampling is a sampling technique with certain considerations. The consideration in taking the sampling is that the research is intended specifically to examine the fifth grade elementary school students in Pemalang Regency. Data Analysis Technique X O Easy Multiplication Method from Left to Right Posttest to measure students' knowledge ability X O Easy Multiplication Method from Right to Left Posttest to measure students' knowledge ability 195 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ This study seeks to ensure the similarity of the median value of two or more populations from the sample, this is done through hypothesis testing of the median value (median test). The median or also called the middle value is the middle value of a series of data that has been arranged regularly, i.e. in order from the smallest value to the largest value or vice versa. By calculating the median value in a data series, the distribution of the data is divided into two equal parts, i.e. half is below the median value and the other half is above the median value. To determine the median value, it must first be determined by applying a formula. 𝑃 = 𝑁 + 1 2 Where P is the location of the median and N is the amount of data. Besides being intended to determine the similarity of the population from which the sample originates, hypothesis testing on the median is also carried out to determine whether or not the difference in the median value of two or more populations is significant. In this case, the null hypothesis states that the two populations from which the sample originates have the same median value. While the alternative hypothesis states the opposite, that is, the two populations from the sample have different median values. Previously, the median value derived from the combined sample distribution or the combined median value needed to be calculated first. Furthermore, from each group, the frequency of values that lie at or above the combined median value and the frequency of values that lie below it must also be calculated. If n1 and n2 are the number of observations in the two sample groups, we can use the 2 x 2 table as follows: Table 1. Table 2 x 2 for Hypothesis Testing on the Median Value Value Frequency Sample Group I Sample Group II Total Above the combined median value A B a + b Below the combined median value C D c + d Total a + c = n1 b + d = n2 n1 + n2 = n If the null hypothesis is proven, the two populations from which the sample originates have the same median value. Thus, this situation can also be interpreted that half of the frequency value of each sample group will lie below it and the other half above it. Based on the appearance of the table, it can be symbolically stated that: a = c = 0,50 n1 b = d = 0,50 n2 Then, the sum of n1 plus n2 is greater than 20 and the expected frequency in a cell is at least 5, the test by means of a chi-square distribution is applied. The formula to find out the value is: 196 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ 𝑥2 = 𝑛 𝑥 [(𝑎 𝑥 𝑑) − (𝑏 𝑥 𝑐) − ( 𝑛 2 )] 2 ( 𝑎 + 𝑏) 𝑥 (𝑐 + 𝑑) 𝑥 (𝑎 + 𝑐) 𝑥 (𝑏 + 𝑑) Where x2 is the chi-square value, a is the frequency of values above the combined median value of sample group I, b is the value above the combined median value of sample group II, c is the frequency of values above the combined median value of sample group I, and d is the frequency values below the combined median of the sample groups. RESULTS AND DISCUSSION The following are the differences in the easy multiplication method from right to left and from left to right which are used as treatments. Suppose we want to calculate 234 x 567? Figure 2. Multiplication from Left to Right and Multiplication from Right to Left the Long Way What is described above is the calculation of the long way, without saving. This method can be taught to children who are not yet proficient in multiplication. 197 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ The advantage of the long way for children is that mistakes tend to be easier to see. It's easy to check where the fault is. The drawback of course requires a longer paper The two ways above: the multiplication of left right or left right, both are true and have their respective advantages. Of course, because it produces answers that are both correct, both methods can be used. Two ways that seem to be opposite from left to right and from right to left when placed in a row form a symmetrical rung of the ladder, which results in both correct answers. After discussing the long way of calculating multiplication both from right to left and from left to right, now we discuss the short way. To calculate multiplication in a short way using the school method (from right to left), the method is to multiply the rightmost number by the rightmost number, if the result is tens of units, the tens are written down and stored for later added to the units of multiplication of the numbers on the left. For multiplication from left to right, just reverse it. First, multiply the leftmost number by the leftmost number, if the result is tens of units. The tens are written, the units are stored to be added to the tens of multiplication numbers to the right. The Short way Figure 3. Multiplication from Left to Right and Multiplication from Right to Left the Short Way The steps are described below: • Multiplication from Left to Right 5 x 2 = 10 The number 1 is written on the left, the number 0 is stored 5 x 3 = 15 1 plus deposit 0, the amount = 1 is written to the right, the number 5 is stored. 5 x 4 = 20 2 plus deposit 5, sum = 7 is written. 198 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ The number 0 is also written because there are no more numbers on the right. If necessary, attach a dot or a 0 below the leftmost number to form a ladder. Do the multiplication for 6 in the same way. And so on and then the ladder are added up. • Multiplication from Right to Left 7 x 4 = 28 The number 8 is written to the right of the number 2 is stored. 7 x 3 = 21 1 plus deposit 2, the amount = 3 is written to the left, the number 2 is stored. 7 x 2 = 14 4 plus deposit 2, sum = 6 is written. If necessary, attach a dot or a 0 below the rightmost number to form a ladder. Do the multiplication for 6 in the same way. And so on and then the ladder are added up. The following is an example of student work Figure 4. Example of Student Work Results Multiplication from Right to Left in a Short Way 199 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ Figure 5. Example of Student Work Results Multiplication from Left to Right in a Short Way The following table contains the posttest scores of students, these scores were obtained by giving tests to both groups after receiving treatment or treatment according to the material above. Table 2. Posttest Scores Student Name for Each Group Easy Multiplication Post-test Score From Left to Right From Right to Left Student 1 82 80 Student 2 84 83 Student 3 83 84 Student 4 86 86 Student 5 82 87 Student 6 93 88 Student 7 91 90 Student 8 89 87 Student 9 92 94 Student 10 93 95 If we want to know whether or not the median value of the easy multiplication posttest from left to right and from right to left, we can determine it through the hypothesis testing step. The test procedures that must be applied to determine the truth of the allegation are: Formulating the null hypothesis and alternative hypothesis, in this experimental study, the null hypothesis essentially states that the median value of the total posttest scores for easy multiplication from left to right and from right to left is the same. While the alternative hypothesis states that the median value of the number of posttest scores of easy multiplication from left to right and from right to left is not the same. Thus, the formula for the null hypothesis and the alternative hypothesis are: 200 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ H0 : Md value of easy multiplication post-test from left to right = Md value of easy multiplication post-test from right to left H1 : Md value of easy multiplication post-test from left to right ≠ Md value of easy multiplication post-test from right to left Md value of easy multiplication post-test from right to left Determining a certain level of significance, for the context of this study, the significance level is determined at 5% or 0.05. If the applied significance level is 5% and the degree of freedom is 1, the chi-square value in the distribution table is 3.841. Formulating the test criteria, the test criteria applied in this experimental research is that the null hypothesis is accepted if 𝑥2 ≤ 3,841 While the null hypothesis is rejected if 𝑥2 > 3,841 Calculating the chi-square value, before the chi-square value is calculated, the data regarding the easy multiplication posttest scores from left to right and from right to left must be sorted first so that the combined median value can be known. The order of posttest scores is not sorted by easy multiplication from left to right or easy multiplication from right to left, but rather a combination of the two. After sorting from the smallest to the largest number, then the order of the values is as follows: Table 3. Order of Easy Multiplication Posttest Values From Left to Right and From Right to Left Order 1 2 3 4 5 6 7 8 9 10 Score 80 82 82 83 83 84 84 86 86 87 Order 11 12 13 14 15 16 17 18 19 20 Score 87 88 89 90 91 92 93 93 94 95 Then, the location and the median value must be found. The location of the median in the data series is: 𝑃 = 𝑁 + 1 2 𝑃 = 20 + 1 2 = 10,50 The median location based on the above calculation is 10.50. This means that the value is between the 10th and 11th data sequences. In the array of values, the 10th and 11th data values are 87. Next, a 2 x 2 table must be arranged to show the frequency of values that are above and below the combined median value. 201 Mathematics Education Journals Vol. 5 No. 2 August 2021 ISSN : 2579-5724 ISSN : 2579-5260 (Online) http://ejournal.umm.ac.id/index.php/MEJ Table 4. Frequency of Values Above and Below the Combined Median Value Value Frequency Easy Multiplication Post-test Score from Left to Right Easy Multiplication Post-test Score from Right to Left Total Above or at the combined median value 5 6 11 Below the combined median value 5 4 9 Total 10 10 20 The next step is to calculate the chi-square value. In this experimental study, the magnitude of the chi-squared value is: 𝑥2 = 𝑛 𝑥 [(𝑎 𝑥 𝑑) − (𝑏 𝑥 𝑐) − ( 𝑛 2 )] 2 ( 𝑎 + 𝑏) 𝑥 (𝑐 + 𝑑) 𝑥 (𝑎 + 𝑐) 𝑥 (𝑏 + 𝑑) 𝑥2 = 20 𝑥 [(5 𝑥 4) − (6 𝑥 5) − ( 20 2 )] 2 ( 5 + 6) 𝑥 (5 + 4) 𝑥 (5 + 5) 𝑥 (6 + 4) = 8000 9900 = 0,81 Formulating the final conclusion, the conclusion is formulated by comparing the chi-square value in the distribution table with the chi-square calculation results and then aligning it with the applicable test criteria. From the calculations that have been done, the chi-squared value is 0.81. This value is much smaller than the chi- square value in the table of 3.841. Based on the testing criteria applied in this experimental study, if the chi-square value of the calculation result is less than the chi-square value in the distribution table, the null hypothesis is accepted. CONCLUSION In this experimental research, the null hypothesis is accepted. 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