Utilization of Literature Based Math in Developing Didactic Designs for Students' Mathematical Understanding in the Decimal Concept

This research is motivated by learning barriers and low understanding of the mathematical students of Madrasah Ibtidaiyah on the concept of decimal fraction. The purpose of this research is to determine the effective learning technique for decimal fraction by using storybook. This type of research uses didactical design research which includes the stages of prospective analysis, metapedia didactic analysis, and re-prospective analysis. The draft of the design applied to twenty-eight students' sixth grade of Madrasah Ibtidaiyah Nurul Hidayah Kadupandak Serang City. Observation sheets, interviews, and test comprehension were used as a data collection instrument for implementation execution. Didactic design using literature based math was made through one revision and it consist of eight steps. The results showed that the implementation of didactical design using literature based math can help students build their mathematical understanding of the decimal concept. It can be seen from the reduced percentage of students' errors in solving comprehension test questions from 71.6% to 11.6%. Therefore, for elementary teacher who has storybooks related to mathematical concepts are advised to try the eight learning steps developed in this study. school. From the psychological aspect, learning by utilizing the storybook can help bridge the abstract mathematical concept with the students’s level of thinking are still in the thinking phase of concrete operations. This is in line with the research of Hamidah et al (2018) that the use of story contexts can help students understand. An interesting story with illustrations and related to the context of real awareness makes students easier to understand and interpret the mathematical concepts learned. Piaget in Anwar, et al (2018) revealed children in the age range of 7-12 years thinking its logic is based on the physical manipulation of objects or events directly experienced by the child. concept and straighten the wrong concept; and (9) give exercises of varying problems to sharpen understanding. The results of this study are in line with the results of Yun-fang's research (2012) which stated that didactic design needs to be reviewed and reviewed with student learning and characteristic teaching principles. In line with that, Lo & Hew (2017) provide advice on course planning, out-of-class learning, and classroom learning.


INTRODUCTION
The understanding of mathematical concepts is fundamental proficiency (Purpura et al., 2011;Cragg & Gilmore, 2014;Wulandari, 2015;Yanti et al., 2019) which must be accomplished in the process of learning mathematics (Reys et al., 2014;Purwanti et al., 2016;Sari, 2017;Edriati et al., 2017). Understanding the concept of mathematics affects students' mathematical Learning outcomes (Stylianou, 2011;Planinic et al., 2012;Novitasari & Leonard, 2017). Considering that mathematics is a lesson that requires centralizing thought to remember and re-identify the material learned (Hadi & Kasum, 2015), it takes appropriate learning methods. According to Herman (2004), There are several consequences of mental processes that occur when learning is focused on understanding and purposing. The consequences are support memory, reduce the amount to remember, increase the transfer, and influence students's belief in mathematics.
Furthermore, Hendriana et al. (2017) stated that mathematical understanding is an important foundation for thinking and resolving mathematical and real-life issues. Besides, the ability of mathematical understanding is very important in the development of other mathematical capabilities, namely communication, problem-solving, reasoning, connection, representation, critical thinking, and creative thinking. Thus, the achievement of conceptual understanding can make students more enjoy in learning math. Because if the student reaches Wida Rachmiati, Helnanelis, Juhji, Utilization of Literature Based Math in Developing Didactic Designs… Al Ibtida: Jurnal Pendidikan Guru MI,Vol. 7 No. 2, October 2020 150 a strong understanding of the concept, then the student will reach the high level in conquering the math, so students will be inclined to enjoy the lessons.
Based on the observation and results of Class 6 interviews in three Madrasah Ibtidaiyah Serang City of Banten Province, it was found that another cause that resulted in the low understanding of students' mathematics on the concept of fractional is because students are faced with more complex symbols and lack of the concept of fractional use in daily life. Fazio and Segler's (2011) in his research cited by Palpialy & Nurlaelah (2015) suggests that in many countries, the average of student has never gained a good conceptual knowledge of fractions. For example on the national exam in the Americas, only 50% of Grade 8 students are able to sort three shards correctly, from the smallest to largest value. While in countries such as China and Japan, the fraction is considered a difficult topic (Palpialy & Nurlaelah, 2015). Thus, the fractional concept of mathematical learning is difficult for students to teach.
A preliminary study of Grade 6 students in three Madrasah Ibtidaiyah Serang City of Banten Province reported that students have not been able to solve problems in understanding the concept of a decimal fraction when they have learned the concepts. It has tested the previous class. Besides, some findings were obtained that: 1) students do not know the numbers on decimal fraction, it showed by some errors in performing arithmetic calculate operations and comparing decimal fractions; and 2) Students can operate fewer decimal fractions of 1 into the form of images, but they are experiencing difficulties for decimal fractions of more than 1 (mixed decimal fraction). Hurst and Cordes's study (2018), reported that children had greater learning experience with fraction notation when they processed fractional notation. As for Desmet et al., (2010) reported that zero right after the decimal point is understood better and earlier than zero at the end of the fractional part of the number. Meanwhile, Lee et al., (2016) Warries (1990), Dick et al. (2001), and Chang (2006). Yun-fang's research (2012) reported in the paper that synchronizing pedagogical theory on didactic design is one of the important content. He also discussed "teaching design for learning" combined with learning characteristics in the engineering profession, basic principles in teaching, and presentation of the framework of both courses. Thus, it is considered important to develop didactic design because this book is a story related to the concept of mathematics for elementary school students quite a lot in the market. Haury (2001) mentioned that the learning source of mathematics is presented as literature-based mathematics. In the early 1980, NCTM has already reviewed the benefits of using the storybook in Mathematics Learning (Lidinillah et al., 2015), the results of the study explaining that the storybook can: (1) present a rich context to understand mathematical ideas; (2) Show students how to view the world from a mathematical perspective; (3) Illustrate how mathematics has been used throughout history by humans to live their lives; (4) Illustrate interdisciplinary relationship to mathematics; and (5) awaken the imagination of the child and his curiosity.
According to Bafile (2001), combining mathematics and storytelling is a way for teachers to invite children into the world of mathematics, reading books that put together mathematical ideas into compelling stories that help dispel the myth that mathematics is dry, unimaginative, and inaccessible. Children's books can not only generate interest in mathematics but also provide the context that helps them to understand the meaning of an abstract concept. While Haury (2001)  (7) as well as to refer to mathematical concepts and skills. Based on these issues, the study aims to determine effective mathematical learning methods and techniques on the concept of decimal fractions by using storybooks as learning resources. (2013)

RESULTS AND DISCUSSION
The results of the study through interviews with grade 6 teachers in three Madrasah Worksheets (SW) used are not teaching materials as guides for learning activities but rather a form of practice questions; and (6) teaching materials on the package book does not present understanding of students mathematical concepts but is more likely to direct them to the steps (procedural) computing.
Furthermore, a test for students to explore the extent to which the learning obstacle faced them on the material changed the fractional shape to the decimal form and vice versa, as well as comparing the fraction and implementation of decimal fraction concept. Diagnostic test results show that students have a learning obstacle in the ability to conceptualize the material basic concept of decimal fraction shown in table 1. forms of mathematical representation. In measuring this ability, students are asked to describe a shape indicating a specific decimal fraction. In addition, most students are also did mistakes in applying the concepts of the decimal fraction logically. To measure this ability students are asked to solve a story related to a decimal fraction.
Based on the results of the diagnostic test, it is determined that the design of didactic to be designed is the didactic by utilizing a storybook related to fractional material. The storybook used consists of two storybooks titled "Menyelamatkan Diri dari Pulau Tengkorak" and "Potong Semakin Kecil dan Semakin Kecil Lagi".

Didactical Design Plan
The preparation of the design was done through three phases: prospective analysis, metapedadidactic analysis, and re-prospective. These three stages will be outlined as follows.

Prospective analysis
At this stage, precise design of teaching materials and learning scenarios is determined by utilizing the storybook. In making the effective learning process, students are equipped with Student Activity Sheet (SAS) which contains several questions and instructions that are expected to help students better understand the book and direct students to the achievement of indicators. The chosen learning model is a cooperative learning model with several methods, including observation methods, questions and answers, discussions, and assignments.
In general, in group learning activities, students are asked to understand and discuss the contents of the storybook as a material to fill the SAS. For students to be more active in the discussion process, during the discussion process the teacher conducts the assessment.
Decimal fractional material studied in grade 6 of the K-13 curriculum is associated with the Gramedia Pustaka Utama Jakarta.  The design of the first and second meetings has three phases of core activities: exploration, elaboration, and confirmation. The three stages of each meeting will be outlined below.

Exploration
At this stage, teacher provides several questions to explore the students ' initial ability to share, for example the first question: "There is a mother buying 10 oranges if a family member is 5 people." What should a mother do? How many oranges does each family member have? How is the mathematical sentence of the problem? Second question: "How if there is 1 citrus distributed to 2 people?" How does the mathematical sentence form? Can I find the split difference on the first and second questions?
At this stage, students answer: "Share the orange, each of which gets 2 pieces, 10:5 = 2. As for answering the second question, students answered: "Each got 1/2 the result of the first division of the horns intact and the two horns were not intact." From students' answers, it appears that the split results are two possibilities, i.e. original number or fraction.

Elaboration
At this stage, teachers do the activities: (1) Ask, who likes to read the story book?
Then, inform students that they will learn the divisions that are not intact through the story book; (2) Ask students to read and understand the books shared with each group; (3) Ask students to discuss filling the SAS in groups (Teachers monitor, assess and provide guidance if necessary); and (4) Ask students to present the results of the discussion (teachers guiding the presentation).
While students do the activity answered the teacher question. "I am, I am...," Students then read and understand a storybook with a group of friends (3 people), followed by a discussion to answer the SAS, and concluded with the activity of presenting the results of the discussion by their respective groups.

Confirmation
At this stage, teachers comment on student discussion results (reinforcing correct answers and straightening out erroneous answers) and directing students to make conclusions.
Students pay attention to the teacher and make conclusions.

Exploration
At this stage, teacher gives a question of digging up the students' initial skills regarding the value of place number, for example: "Mother has 2 bands bound by one hundred and one hundred, 4 bands tied by ten and 3 rods which are not bound. What is the right number to symbolize the number of mothers?" While students are: "Lidi, Lidi..."; 243 (two hundred and forty-three); 2 Hundred, 4 ten and 3 units; Students (perhaps) think and answer because 2 shows many of bonds a hundred, 4 the number of ten-ten and 3-no-group bonds; Unit place value; Students think (maybe students do not answer); Students replied: The "decimal number" (probably) student is confused by the name of the place of the number behind the comma. From this activity, it is hoped that students want to know about the value where the numbers are behind a comma on decimal numbers and are expected to emerge a spirit of reading the storybook. Therefore, Guru continues, "well... To get this answer let, we together read the storybook! "

Elaboration
At this stage, teachers: ask students to read and understand the books shared with each group (teachers judge); Retelling the core of the storybook and explaining the instruction in the Student Activity Sheet (SAS); Have students discuss completing the SAS in groups (Teachers monitor, assess and member guidance if necessary); and have students present the results of the discussion (teacher guides and assesses the presentation). At this stage, students read and understand the storybook with a group of friend, they follow along, and discuss to fill in the SAS, and then they present the results of the discussion through teacher's guidance.

Confirmation
At this stage, teacher comments on the results of the student's discussion (reinforcing the correct answer and straightening out the wrong answer), informing him that the value of the number place behind a comma is tenth (one digit behind a comma), a hundredth (two digits behind a comma) and so on and directing students to make conclusions. While the students follow along, then conclude that the fraction 0.1 = 1/10 (one part of 10 parts) and 0.01 = 1/100 (1 part of the 100 section).

Metapedadidactic Analysis
First Learning The first didactical design for the indicator: [5.2.1] redefines the meaning of fractions, and [5.2.2] explains the meaning of decimal fractions, as a whole has not been done as planned. Some activities that appear outside of planning include: (1) Although students are very enthusiastic at the time the teacher shares the storybook, however, it turns out that students need a very long time to fill in the activity sheet. This is because students only focus on the story, but not focus on the mathematical concept that appears on the story; (2)  and (4) The teacher first explains the intent of the questions or instructions on the SAS before the student initiates the discussion activity.

Second learning
Revisions made to the didactic design for a second meeting based on the events that arose at the first meeting gave enough meaningful changes to the learning process. Student responses by the predictions are actionable by the teacher by giving anticipated pre-planned anticipation. While students' responses that appear outside of the prediction can be followed up by the teacher by giving the didactic response according to the existing conditions.

Retrospective Analysis
Based on the observation results, the first didactic design implementation shows that there are still discrepancies between the concept and its implementations. However, the learning process demonstrates different learning nuances with previous learning. Because Wida Rachmiati, Helnanelis, Juhji, Utilization of  students are actively learning through the provided resources (storybooks) and there are also multi-directional interactions (students, student-teaching materials, and students-teachers).
The implementation of the second didactical design shows progress compared to the first meeting. A more conducive and meaningful learning process depicts students more relaxed and enjoying the mathematical learning process. Timing to share Student Activity Sheets (SAS) after students understand the content of the storybook greatly impacts the student's concentration on reading and understanding the mathematical stories and concepts in it.
The use of the decimal fraction concept in Storybook has been implemented in the learning process. It has been following to the theory of mathematical learning in elementary school. From the psychological aspect, learning by utilizing the storybook can help bridge the abstract mathematical concept with the students's level of thinking are still in the thinking phase of concrete operations. This is in line with the research of Hamidah et al (2018) that the use of story contexts can help students understand. An interesting story with illustrations and related to the context of real awareness makes students easier to understand and interpret the mathematical concepts learned. Piaget in Anwar, et al (2018) revealed children in the age range of 7-12 years thinking its logic is based on the physical manipulation of objects or events directly experienced by the child.
From the theories of learning, learning is following to the paradigm of constructivism, because the learning process is done by students by self-construction with the help of teaching materials provided. The development theory of Piaget represents constructivism as it sees cognitive development as a process in which the child actively builds the system of meaning and understanding of real threads through their experiences and interactions.

The final form of didactic design by utilizing storybook
Based on the results of the first and second didactical design development, it can be concluded that the storybook is very likely to be used as a teaching material for learning mathematics at the elementary school level. The steps that teachers need to note are as follows: (1) analyzing the suitability of mathematical concepts covered in storybooks with competency standards, basic competencies and learning indicators; (2) Ensure students have mastered prerequisite material such as reading smoothly; (3) Prepare Student Activity Sheets (SAS) to assist students in achieving understanding of the mathematical concepts listed on the story; (4) Group students into small groups (2-4 people); (5) Ask students to read the story and record the conclusion while reading results; (6) Asking students to discuss activities on the student activity sheet (the tinting is not shared in conjunction with the storybook, but after Stage 5 is performed); (7) Ask students to present the reading results and the Student Activity Sheet (SAS) that have been discussed; (8) Confirm the correct concept and straighten the wrong concept; and (9) give exercises of varying problems to sharpen understanding. The results of this study are in line with the results of Yun-fang's research (2012) which stated that didactic design needs to be reviewed and reviewed with student learning and characteristic teaching principles. In line with that, Lo & Hew (2017) provide advice on course planning, out-of-class learning, and classroom learning.