Integrative Mathematics: Mathematical Concepts in Hadiths with the Theme of Uqiyah

ABSTRACT


INTRODUCTION
The progress of a civilization cannot be separated from the results of quality education carried out by its people.A good education not only hones and sharpens students' cognitive abilities but also develops several other aspects, one of which is attitude, character and morals [1]- [3].That is also regulated by The Law number 20 of 2003, which states that one of education's goals is to unleash the potential of students to become morally upright people who respect and revere God [4].Therefore, attitude and character become important aspects expected from an education.
Mathematics, as one of the sciences taught at school, has a role to train students in cognitive aspects, reasoning, and problemsolving [5]- [7].Because it introduces students' cognitive skills, math is often considered one of the fields that escape the responsibility of shaping students' attitudes, character, and morals [8], [9].At the same time, the means in shaping students' attitudes and morals are not limited by science because the goal of education must be carried out in every lesson [3], [10].Therefore, combining mathematics with aspects of attitude, character, and morals is essential.
Several efforts have been made to involve attitudinal and moral aspects in mathematics.One incorporates and connects these aspects in mathematics learning [11]- [13].If the element of introducing culture and customs in mathematics is integrated through ethnomathematics [14]- [16], the attitudinal and moral aspects in mathematics learning are integrated through Islamic integrated mathematics, known as integrative mathematics [3], [10], [11].
Integrative mathematics is seen as combining Islamic values with mathematics to produce a whole and inseparable unity [17], [18].Integrative mathematics is not only defined as the process of finding religious propositions for mathematics or the Islamization of mathematics.Still, it is defined as an effort for students to get closer to Allah SWT through mathematics [3], [19], [20].In addition, integrative mathematics also provides an opportunity for Muslims to repeat their glory days when Islamic values were incorporated into every mathematics lesson [21], [22].
Furthermore, efforts to introduce Islamic-integrated mathematics have begun to be loved.That is indicated by Islamicintegrated mathematics learning models at school and campus levels [3], [23].Another effort is shown by the Kompetisi Sains Madrasah (KSM) or Madrasah Science Competition at the school level, which is integrated with Islam [24].In addition, several studies have explored integrative mathematics in learning tools and Islamicintegrated math problems [12], [25]- [28].
Despite being the latest trend in education, integrative mathematics has not been fully realized.That is due to the lack of educators' ability to search for various literature on religious sources, understand their meaning, and the educators' inability to find Islamic values in harmony with mathematical concepts [19], [29].Therefore, there is a need for valid and reliable references on mathematical concepts integrated into Islamic values, especially those sourced from the Al-Quran and Hadith.
However, prior research has only examined fundamental ideas in mathematics, such as numbers, sets, and their operations.Furthermore, these studies are also dominated by Islamic sources derived from the Quran.Islamic sources also consist of hadiths, books of scholars, and the history of Islamic civilization.
As a civilization, Islam is not only present as a religion in society but as a way of life and perspective based on Islamic values [21], [22], [35].Historically, Islamic civilization has existed for around 1200 years.In its heyday for seven centuries [22], Islamic civilization has carved a new color in historical records.One of them is in the measurement field, which includes quantities and units.[22], [36].
History records that the quantities and units used in Islamic civilization include many things, ranging from length, area, weight, distance, and time [35].Islamic civilization inherited from Arab culture has its weight units, namely ratl, uqiyah, nish, nawat, and dirham.These units have coloured the activities of Arab society during the Islamic civilization [35]- [37].
Uqiyah is one of the units of weight used during the Islamic civilization.The use of uqiyah was not only limited to trading activities but also to daily activities [38].Uqiyah is used in several Islamic laws, such as payment of zakat, alms, and the Prophet's dowry to his wife [39]- [42].The use of the uqiyah unit in the life of the Prophet is written in the famous books of hadith [43], [44].
The explanation of the uqiyah seems to be dominated by fiqh, history and religious science.Meanwhile, the description from the perspective of mathematics is still minimal.Therefore, an in-depth study of the mathematics in the hadith about uqiyah is needed.
The researcher proposes to investigate the mathematical ideas in context with the description given in the introduction.contained in the uqiyah-themed traditions.So, the research theme used is Integrative Mathematics: Mathematical Concepts in Hadiths with the Theme of Uqiyah.

Hadith Reported by Ibnu Majah number 1876
"Ubaidullah ibn Sa'id reported to us and said: Sufyan narrated to us, he said: 'Amr ibn Yahya narrated to me, and it was also narrated from another route, and it was narrated to us by Muhammad ibn Al Mutsanna and Muhammad ibn Basysyar from 'Abdurrahman from Sufyan and Shu'bah and Malik from 'Amr ibn Yahya from his father from Abu Said that Rasulullah tells: "There is no zakah on less than five wasaqs of grain, no zakaah on less than five dhuds of camels, and no zakaah on less than five uqiyahs of silver."(Hadith Reported by An-Nasa'i number 2402).

Mass Units of the Arab Societies
Measurement includes many things, ranging from measuring length, weight, volume, distance, time, and others.Weight measurement is one of the measurements that has an essential role in people lives [45].In measuring weight, an agreed unit and the measuring instrument are needed.Generally, the measuring instrument used is a scale [36], [46].The Muslim community has studied the knowledge of weight measurement for hundreds of years.That is because weight measurement is related to the laws of Islam, such as zakat, marriage dowry, buying and selling, almsgiving and others [38], [47], [48].shown in Figure 1.[36].

Mass units often used in everyday life
The units of weight used by Arabs differ from those used by modern society.While international units of weight have a fixed multiple of each unit, Arab units have different multiples.The multiples of ratl, uqiyah, nish, nawat and dirham are different.
Here are the different levels of international weight units and Arabic weight units, as shown in Figure 2 [36], [45], [46].The difference between units on the scale of Arab society comes from several references.For example, the hadith narrated by Aisha R.A. about the Prophet's dowry to Siti Khadijah.The hadith, as narrated in Sunan Ibn Majah, explains the conversion of uqiyah units to nish, uqiyah units to dirham, and nish units to dirham.[43], [44].

METHODS
In this study, a literature review strategy is combined with a descriptive qualitative methodology.Hadith books, math books, integrative math books, books on the history of Islamic culture, journal articles, and conference papers were all employed in this study's literature review.The researcher then reviewed all the literature diligently and in detail [49], [50].
The data collection technique in this study uses secondary sources.That means the data obtained is not directly given to the researcher but is obtained through other intermediaries [51].literature on mathematics, mathematics in Islamic civilization, mathematics integrative article, and hadith books are examples of secondary data in these fields.The data collected in this research is presented descriptively in words, tables, and pictures.
The research procedure is carried out through four stages.(1) Determining the research theme, (2) Collecting data, (3) Conducting reviews, (4) Analyzing data, (5) Writing down the results of data analysis.These stages are a form of synthesis standard in literature studies [49].Hadith reported by Ibn Majah no.1876, provides several statements about uqiyah, nassy and dirham.These statements are formal sentences with mathematical equations, for example, U = uqiyah; N = nassy; D = dirham.Then, the following equations are formed.

One Uqiyah in Linear Equation
Then substitute ( 2) for ( 1), thus obtaining Equation ( 3) shows that one uqiyah is equivalent to 40 dirhams.Then, if equation ( 2) is multiplied by two in both segments and substituted into (3), we get ) Equation ( 4) shows that one nasy is equivalent to 20 dirhams.
Based on the mathematical equations in the hadith reported by Ibn Majah no.1876, the following conclusions are obtained: (1) The conversion of the value of uqiyah to nasy and dirham can be determined by solving the problems in the hadith using the concept of linear equations.

Concept of Equal Comparison
Hadith narrated by Darimi number 1572, presents the following statement."For every five uqiyah of silver, there are five dirhams of zakaah.If there is an excess, then one dirham is due on every forty dirhams.If it is less than five uqiyah, there is no zakaah due on it" (Hadith narrated by Darimi number 1572).
The first statement says that for every five uqiyah (200 dirhams), there are five dirhams of zakah.The second statement says that for every 40 dirhams, there is a zakat of 1 dirham.The first and second statements can be written in fraction form, with the ratio of the amount of wealth to the zakat that must be paid is

Concept of Function
The concept of function can be formed from hadith narrated by Darimi number 1572.The previous concept explains that the ratio of wealth to the zakat that must be paid is 40: 1.If  represents the amount of wealth in dirhams and  represents the zakat that must be paid, the comparison formula will be obtained.It can be seen that the value of x depends on the value of y.Mathematically, it can be said that x is a function in y or  = () [20].In this case it is denoted by () = Suppose the amount of wealth is 1000 dirhams, then the amount of zakat that must be paid is  = (1000) = So, the amount of zakaah must be paid with an asset of 1000 dirhams is 25.

The Concept of Linear Equations from Two Points
Another mathematical concept that can be formed from hadith narrated by Darimi number 1572 is the concept of linear equation from two points.The first provision mentions, "For every five uqiyah (200 dirhams) there is zakaah of 5 dirhams, and for every 40 dirhams there is zakaah of 1 dirham".
The statement can be written in consecutive pairs (200,5) and (40,1).The existence of two coordinates in this hadith seems to imply that to make a particular line, at least two different coordinate points are required.If only one coordinate point is mentioned, for example (200,5), then a line cannot be formed [20], [52].
Suppose ( 1 ,  1 ) and ( 2 ,  2 ) are two different coordinates, then the line through these two coordinates will have an equation Then, it can be formed into a new equation, namely.
In a simple form, it can be expressed as The equation  =  +  is known as the general form of a line equation.The  is called the gradient (slope) of the line, and  is called a constant.Then, the existence of the three conditions in hadith narrated by Darimi number 1572 forms the equation  = 1/40, with the gradient () formed is

The Class of Elementary School
The concept of linear equations related to uqiyah and dirham can be applied in mathematics.Suppose the teacher gives the problem "two meters + 300 centimeters = ... decimeters".In that case, the teacher can modify it to "If it is known that one uqiyah is equivalent to one nasy, and one nasy is equivalent to 40 dirhams.Then the value of two uqiyah + two nasy = ... dirham".
This concept not only involves students' ability to be able to operate and convert units.But it also introduces directly to students that other units were used during the Islamic civilization so that the application of Islamic integrated mathematics is also shown through the problems given.

The Class of Junior High School
At the junior high school, comparison is taught when students enter the seventh grade.Comparison is the process of comparing the values of two similar quantities.Comparison is usually expressed in fraction form.Often, teachers use the concepts of speed, discharge, and construction time as a context for problems in comparison.
Using Islamic-integrated math, teachers can use uqiyah as a context to explain the concept of comparison.Usually, teachers give

96 Vol. 1 ,
to indicate an amount include milligrams, West Science Islamic Studies  No. 01, October 2023, pp.93-101 grams, ounces, kilograms and tons.As for the units of weight in the Islamic treasures that were used in the previous Arab society, they are ratl, uqiyah, nish, nawat, and dirham, as

Figure 2 .
Figure 2. Differences in multiples of international and Arabic units of weight

Figure 1 .
Figure 1.The unit of weight of the early Arab societies

1 . 1 or 40 : 1 .
If simplified, the second form becomes40 Based on these two comparisons, it can be concluded that for every 40 dirhams, there is 1 dirham of zakat.The concept of comparison found is the concept of equal comparison, which is shown in Figure3.

Figure 3 .
Figure 3.The concept of value comparison based on hadith Darimi number 1572

Figure 4 .
Figure 4. Linear equation graph based on Hadith narrated by Darimi number 1572.