IMPLEMENTATION OF DIDACTIC DESIGN OF
COUNTING DIVISION OF FRACTIONS IN LEARNING AT THE FIFTH-GRADE OF ELEMENTARY SCHOOL
Rosmayasari 1*, Didi Suryadi 2, Tatang Herman 3, Sufyani Prabawanto 4
1* School of Postgraduate Studies, Universitas Pendidikan Indonesia, INDONESIA
2, 3, 4 Departement of Matematics Education, Universitas Pendidikan Indonesia, INDONESIA
* corresponding author
A R T I C L E I N F O A BSTR ACT
Article history Received Revised Accepted
This research is motivated by the existence of learning obstacles experienced by students in learning material for counting division of fractions. The learning obstacle is due to the fact that the learning design that is designed does not facilitate compatibility between material, methods, use of media, ways of thinking and student characteristics. The purpose of this study was to obtain a comprehensive description of the implementation of the didactic design of counting operations on fraction division in learning at the fifth-grade in terms of learning obstacles, hypothetical learning trajectory and Didactic and Pedagogical Anticipation developed by teachers based on Didactic Situation Theory and student characteristics. The research method uses Didactical Design Research. The research subjects were fifth-grade students at a public elementary school in Cluster 23 Bandung City, as many as 10 students. Data collection techniques used documentation studies, learning observations, test data collection, interviews and triangulation. The research results show. Learning Obstacles (LO) that emerged after the initial didactic design was implemented in learning included ontogenic psychological obstacles such as finding students who were not ready to learn due to not liking the content of mathematics lessons and having low motivation.
Instrumental ontogenic obstacle, namely the technical incompatibility of the demands of the questions with the answers completed by the students. The ontogenic conceptual obstacle is the lack of students' understanding of the intent of the questions, especially about stories. The epistimological obstacle is the limited experience of students in solving word problems. The didactical obstacle is that students always get a solution without looking for and finding it themselves. The learning trajectory (LT) that was found included one student who had previous learning experience related to dividing fractions. Students are more interested in ways of solving in the form of pictures and number lines, with the aim of eliminating boredom in mathematics lessons. Spontaneous didactic anticipation is given, namely by providing scaffolding in understanding the intent of the problem, for example determining the characteristics of a story problem which is done by means of counting division operations, determining and changing the unit size of length, weight, and volume.
This is an open access article under the CC-BY-SA license.
Keywords:
Learning Obstacle, Learning Trajectory, Didactic Design, Division of Fractions
1.Introduction
Mastery of fraction material for elementary school students is very important because fraction material is the basis for learning Algebra [1], [2]. Learning fractions is an interesting activity to learn more about, because the concept of fractions has access to other mathematical concepts such as the concept of decimals, percents, and scales or comparisons. At a higher education level, fractional material is a prerequisite that students must master in the context of everyday problems and learn advanced mathematical concepts [3], [4], [5]. The results of research by [6] showed that by the end of fifth-grade,
Fractional materials that are considered difficult are fraction counting operations. As research has been conducted by [7], [8], [9], [2] explained that in the material for fraction counting operations, students' difficulties were when solving word problems. The causes of student difficulties are due to students' lack of understanding of the basic concepts of fractions, mistakes in applying fractions in solving fraction problems, carelessness in understanding the language of the questions, lack of understanding of the prerequisite material, and errors in computing or the calculation process.
Analysis of the problems experienced by students when studying counting operations on division of fractions in the form of word problems found three learning obstacles. This finding is also supported by [10] who suggests the types of learning obstacles or learning barriers, namely ontogenic, epistemological and didactical obstacles. In the preliminary study, ontogenic obstacles occurred due to the lack of motivation and interest of students which caused students' conceptual understanding of the material to be low. The epistimological obstacle found was that 18 out of 28 students had difficulty understanding the meaning of the questions in word problems about dividing fractions. The reason is that students are not used to being given problems in the form of word problems and how to solve these problems. Didactical obstacles occur because learning activities do not involve students in finding and finding ways to solve problems. The learning obstacles found in the preliminary study became the basis for researchers to design research questions about the types of learning obstacles and the causal factors experienced by students when learning the counting operation of dividing fractions.
Subsequent findings from the results of interviews with teachers obtained that understanding related to the material for counting division of fractions is still lacking. The teacher only mastered one way of completing the counting operation of dividing fractions, namely by multiplying without knowing the stages of obtaining the process. The findings of the problem during interviews with teachers were also supported by the results of previous research conducted by [11] who found an elementary school teacher had difficulty answering his student's questions, regarding why he had to reverse fractions in the counting operation of dividing fractions, if it was done in multiplication.
[12] examined the ability of elementary school teachers to add and subtract fractions, as well as interpret and compute multiplication and division of fractions. The results of his research are only 1 out of 17 teachers who can interpret what is meant by dividing two fractions. [13] research results found that teachers experience many conceptual difficulties in posing problems about dividing fractions than in posing problems about multiplying fractions. [14] the results of his research found that the most common type of error found in elementary school teachers was the inability to express the use of the multiplication method in carrying out the operation of dividing fractions.
[15], the results of his research found that teachers had difficulty in giving examples of appropriate problem solving in working on word problems on dividing fractions.
The role of the teacher in learning activities besides having to master the concept of material, can also act as a facilitator in learning. The teacher must create a learning process that provides opportunities for students to be directly involved in discovering concepts and procedures related to material and how to solve problems independently. Learning activities obtained by students will feel more meaningful, so that students are able to apply them in solving problems that occur in their daily lives. [10] explains that the actions of a teacher in the learning process will create a situation that can be the starting point for the learning process, which is then referred to as the
Didactical Situation Theory (Theory of Didactical Situation / TDS). [16] explains that learning activities will be optimal if the teacher masters the concepts of the material to be taught and the characteristics of student learning, and can design didactic situations that can facilitate students' learning and thinking abilities.
The results of observations and interviews with teachers found learning activities had not been directed to a problem and ended to solve problems. [17] explained that the nature of good mathematics learning is preceded by problem posing and aims to solve problems. This is what seems to have not been well developed in the student learning process in material for counting division of fractions. As previously revealed, learning interactions are still dominated by the teacher when discussing material and solving a problem. Students are less involved in the process.
Indications of a lack or perhaps not having gone through a series of mental actions in students can lead to students' ways of thinking regarding limited fraction counting operations [18].
The students' way of thinking regarding the limited fractional counting operations material also results in ways of generating understanding and ways of finding problem solving strategies for students related to fractional counting operations material not being facilitated properly. So it is necessary to design learning activities that are able to create situations where students can develop their own understanding of the problems given.
These findings became the basis for researchers to design a didactic design for counting division of fractions that facilitates Learning Obstacle (LO), Learning Trajectory (LT), and Didactic and Pedagogical Anticipation (ADP). The benefits of the results of this study are expected to be able to contribute knowledge and comprehensive insights about the didactic design of counting division of fractions in fifth-grade.
2.Method
This research uses Didactical Design Research (DDR) which was developed by [19]. There are three stages in DDR research, namely 1) prospective analysis; 2) metapedidactic analysis; and 3) retrospective analysis. Prospective analysis, namely analysis of the didactical situation prior to learning in the form of hypothetical didactic design and pedagogical didactic anticipation (ADP).
Metapedadidactic analysis is in the form of didactical and pedagogical analysis, namely the relationship between the teacher, students, and the material during the implementation of the didactic design. Retrospective analysis is in the form of the results of a hypothetical didactical situation analysis that is linked to the results of the metapedidactic analysis [16].
The research design was chosen as an alternative solution to solve the problem of counting operations for dividing fractions that the researchers found based on the results of previous research literacy studies and the results of preliminary studies on learning activities in fifth-grade of elementary school. The findings of the preliminary study on the Learning Implementation Plan (RPP) created and developed facilitate improvements in the design, implementation and analysis of class interactions in learning fraction division counting operations. The didactic design developed was in the form of a series of didactic situations based on the results of an analysis of student learning obstacles (LO), student learning trajectory (LT), and gaps in the relationship between students, teachers, and material (learning gaps) as well as findings during the process learning takes place.
Sources of data collection in qualitative research according to [20] include: observations, interviews, documents, and audio-visual material. While the data collection techniques in this study used triangulation techniques (combined). [21] states that triangulation is defined as a data collection technique and existing data sources. If the researcher collects data by triangulation, the researcher actually collects data while testing the credibility of the data, namely checking the credibility of the data using various data collection techniques and various data sources [22].
3.Results and Discussion
The implementation of the didactic design of the fraction division counting operation was carried out in fifth-grade. The following describes the findings from the didactic design implementation activities, learning obstacle analysis, learning trajectory and ADP that emerged after the initial didactic design was carried out in learning and the final evaluation questions. The didactic design of the counting operation for dividing fractions that has been developed, in general,
consists of three activities, namely: 1) dividing natural numbers with ordinary fractions; 2) division of ordinary fractions by natural numbers; and 3) division of common fractions with common fractions. Each didactic situation is given to students in the form of Student Worksheets (LKS).
Completion of LKS is done in groups and individually. The three activities in the didactical design form a learning flow. so that in its implementation in class a variety of didactic situations, learning obstacles, learning trajectories, and various didactic contracts are illustrated. In addition, for some didactic situations, several visual aids are used to facilitate students' concrete thinking skills.
Activities carried out before the implementation of learning using the initial didactic design, first divided into groups taking into account the heterogeneous levels of student abilities (high, medium and low) based on an analysis of previous learning outcomes (Prabawanto & Mulyana, 2017). Students are divided into three groups of three or four people. In addition, the atmosphere in the class is also designed to be comfortable and conducive using a U-shaped classroom setting, with students sitting in groups (three or four people) so that teacher mobility becomes easier so that students can be accessed more evenly and make it easier for students to interact well. within groups or between groups.
The implementation of didactical situation 1 begins with presenting the problem of dividing natural numbers into common fractions which aims to provide a challenge for students to think, while to facilitate concrete thinking students use real object media in the form of ribbons, granulated sugar, and packaged liquid milk. Each group is assigned to solve problems in the form of word problems in the LKS with the help of different real object media. Learning begins with a group representative (one student) choosing envelopes numbered 1, 2, and 3 which contain problems or questions. Then the group representative returned to the bench to open and read it with group members so they could determine the appropriate real object media. Furthermore, the group representatives took the selected media and had it prepared at the front desk of the class. In practice, beyond predictions students experienced difficulties in understanding the purpose of word problems, such as confusion in determining the appropriate counting operations to use whether addition, subtraction, multiplication, or division. Of the three groups, there were two groups who were still confused and asked again about the purpose of the question including the division operation or not. So that students are reminded again that the material for the meeting that day is the division of fractions. In addition, students are also given didactic anticipation in the form of ways to understand the meaning of story problems. When the findings were confirmed in the form of questions and answers, students gave reasons that story problems were rarely given, therefore they were not used to it so they did not understand how to solve them.
Based on these findings, students are indicated to experience epistemological obstacles. In addition, students also had difficulty determining the correct size for natural numbers 2 and fractions 1
4 (in meters (m), kilograms (kg), and liters), for example, group one was still confused about determining the length of 2 m and the length of 1
4 m when converted to centimeters (cm) using a ruler. So that scaffolding is given by being reminded again how to change the unit of length. For example: 1 m equals 100 cm, so 1
4 m equals 25 cm, because 100 is divided by 4. Group two also has difficulty determining the weight of 2 kg and 1
4 kg when converted to grams (gr) using a digital cake scale. So that scaffolding is given by being reminded again how to change the unit weight. For example: 2 kg equals 2000 gr because 1 kg equals 100 gr and 1
4 kg equals 250 gr because 1000 gr is divided by 4. Likewise, group three are still confused about determining 2 liters and 1
4 liters if converted into milliliters (ml) using a measuring cup. For example: 2 liters equals 2000 ml and a 1
4 liter equals 250 ml, because 1
liter equals 1000 ml divided by 4. So scaffolding is given by reminding again how to change volume units.
Based on the difficulties stated above, students experience conceptual ontogenic obstacles, namely the incompatibility of students' thinking demands with problem orientation. These findings were beyond predictions because the authors assumed that students had learned word problems in the previous fraction counting operations, namely addition, subtraction, and multiplication of fractions. Likewise in changing units of length, weight, and volume, students have studied in previous classes. Thus the anticipation of this response is spontaneous.
The next activity is the didactic situation, which starts from an action situation with students in groups assigned to solve problems. To create mental action students are tasked with finding and finding their own way of solving it using the help of real object media. While the author made observations on the activities of individual and group students in working on worksheets by going around so that they could help students who were experiencing difficulties and needed assistance.
As shown in Figure 1. below:
Fig. 1. The author is observing group discussion activities Group one uses the help of the tape to solve the following problem:
"You have 2 meters of ribbon and will make flowers. Each flower requires a 1
4 meter tape. How many flowers can sister make?”
Based on the results of observations, it was found that the formulation situation of group one was that one student measured a 200 cm or 2 m long tape using a tape measure, then cut it using scissors. Then measure the tape again 25 cm or 1
4 meters long using a ruler repeatedly until the end of the tape and mark it, then cut each part of the tape. Next the student asked the other student to count the pieces of tape, obtained 8 pieces of tape with a length of 25 cm or 1
4 meters from 200 cm or 2 m and wrote them down on the LKS. While one other student was silent and did not try to ask or do. The author clarifies by visiting and asking students why students are not enthusiastic and participate in group activities.
P : “Ananda, I noticed from the start that you were just silent and didn't participate in your group discussion, why is that?"
BM :”Can't ma'am, I'm confused how to answer it.
P : “AnandaYou can discuss with friends if you can't or ask the teacher if you don't understand."
BM :(thought for a moment) "Actually I don't like math lessons because there are calculations, the material is also difficult, especially when I have to write down how to do it, I'm tired of writing it, so I'm lazy ma'am."
P : "If the problem is like that, you can learn it, as long as you practice diligently."
BM :”Still, ma'am, when you practice you also tend to forget, where there's a lot of material, you have to remember the previous material too. Like today's material, fractional surgery makes you dizzy, ma'am."
The interview excerpts above identify that there are symptoms of psychological ontogenic problems with the finding of students who are not ready to learn due to low motivation or interest in mathematics, especially the material for dividing fractions. Meanwhile, group two used sugar to solve the following questions:
"Mother has 2 kg of sugar to make cake batter. Each cake dough requires 1
4 kg of sugar.
How many cookie dough can mother make?”
The results of observing the formulation situation in group two, it was found that one student led the discussion and gave directions for the distribution of tasks, for example, two students were assigned to measure with a plastic container and weigh 250 grams of granulated sugar, another person transferred the weighed sugar to in a plastic container containing 250 grams, and another person is in charge of counting the number of plastic containers containing 250 grams of sugar and recording the results on the LKS. The findings obtained by the author in group two, the four students were very enthusiastic and unified in solving the problems given in the LKS. When confirmed, students feel happy because they can find their own solution by manipulating real objects directly, not just imagining them. This has an impact on increasing student motivation in learning fraction division material. Meanwhile, group three used packaged liquid milk to solve the following questions:
“Father bought 2 liters of pure milk. The pure milk will be put into a glass. Each glass contains a 1
4 liter. How many glasses do you need daddy?”
The results of observations in group three found that a student led the discussion and gave directions for the division of tasks, such as one person pouring pure milk into a measuring cup up to 250 ml, one student transferring pure milk from a measuring cup into a plastic cup, and one another person counts the number of cups and records them on the LKS. Just like group two, group three was very enthusiastic in participating in learning activities. After the three groups finished working on the LKS, the validation situation was continued by each group taking turns presenting the results of their group discussion in front of the class while the other groups responded.
The presentation activity starts from group one by using the help of tape to solve problems, from three students, who are in charge of writing on the blackboard and explaining that one person and two other people manipulate the tape by measuring using a ruler and tape measure, dividing the ribbon and cutting using scissors, and calculate the result. As shown in Figure 2. below:
Fig. 2. The author observes the presentation of group 1 work results (tape media)
Before continuing with the next group presentation, a question and answer session was first held.
Because no one asked questions, then the group presentation was continued by using sugar to solve the problem, of the four students who were in charge of writing on the blackboard and explaining
one person, three students measured the sugar, weighed it, and divided the sugar into containers. in the form of a plastic cup. As shown in Figure 3. below:
Fig. 3. Students presenting the results of group 2 work (sugar media)
The next activity after the second group finished the presentation, was also held a question and answer session. Just like the pause in group one's presentation, group two didn't ask any questions. So the presentation was continued by a group of three using packaged liquid milk to solve the problem, of the three students who were in charge of writing on the blackboard and explaining one student, two students measured liquid milk with a measuring cup and transferred it into a container in the form of a plastic cup. As shown in Figure 4. below:
Fig. 4. Students presenting the results of group 3 work (packaged liquid milk media)
The findings from the activity in this activity were that no one asked questions in the three groups, so the teacher assigned students in groups to give reasons for using this method, look for other ways that could be used in answering questions, and choose the easiest and most practical way from all the ways they found. As predicted, students had difficulty finding other ways to do the problem. Pedagogical anticipation is given in the form of assistance using colored folding paper that can be folded, cut and pasted. These findings indicate that students experience didactical obstacles because of their dependence on real objects. As shown in Figure 5. below:
Fig. 5. Students are manipulating folded paper
Furthermore, in validation situations students are assigned to write questions in the form of mathematical sentences or what they call numbers. As follows, 2: 1
4 = … students are reminded how to solve the division of numbers, namely by repeated subtraction as in the division of natural numbers, using the number line method as in the concept of expressing fractions in the form of a number line, using pictures or the area of plane shapes, and the multiplication method. To confirm students' understanding of the solution above.
The activity continued with an institutional situation, namely students were assigned to make a problem in the form of a mathematical sentence dividing natural numbers with ordinary fractions, then exchanged with their friends and then filled in using the four methods, then returned and corrected by the question maker in group discussions. After that students are assigned to choose the easiest and most practical way of the four ways that have been discussed. As predicted, students choose the multiplication method. However, there were still students who had difficulty with the excuse that they forgot to multiply natural numbers by the inverse of the divisor. In this case students experience didactical obstacles. This is because students' concept of counting division operations is still weak. So according to predictions of student responses. In the next activity, all students were assigned to pay close attention to the similarities in the steps to solving the three problems, so that a pattern of relationships was found. Then students are assigned to conclude the relationship pattern and replace numbers with letters so that they can be used in other problems with different numbers. In reality, this anticipation only applies to students whose thinking skills are relatively fast, while for other students this anticipation needs to be done repeatedly. As an enrichment, students are also introduced to using the relationship pattern of dividing natural numbers with common fractions in dividing natural numbers with mixed fractions. However, there are still students who experience difficulties and confusion in changing the form of mixed fractions into common fractions. even though they had studied the material before. This indicates that students experience an ontogenic obstacle in terms of technical unpreparedness which is key in how to change the form of mixed fractions to ordinary fractions.
Based on the description and description of the implementation of the didactic situation 1 above, the authors conclude that there are learning obstacles experienced by students in the form of ontogenic obstacles (psychological, conceptual, and instrumental), epistemological obstacles, and didactical obstacles. From the question and answer activities after group presentations, especially when students were assigned to find other solutions, new learning trajectories were found that were not in the HLT designed by the author. In addition, at the beginning of the learning, spontaneous didactic anticipation also occurred related to story problems and changing units of length, weight, and volume.
The implementation of didactical situation 2 begins with presenting a problem about common fractions divided by natural numbers in the form of mathematical sentences. Students are assigned to solve problems by multiplication. The form of the question is as follows:
Solve the following problems by multiplication!
a. 3
4 : 2 = …
b. 2
3 : 5 = …
The next activity is the didactic situation, starting with an action situation, in which students are individually assigned to solve the problem. Before starting to work on students are given the opportunity to ask in advance regarding the way of completion. There are two students who ask, can you apply the multiplication steps to dividing natural numbers with common fractions, for dividing common fractions with natural numbers. Then there was one student who responded and tried to explain that the multiplication steps for dividing natural numbers and ordinary fractions can be used for dividing ordinary fractions with natural numbers. When confirmed, the student who answered his friend's question turned out to have participated in studying with his older brother at home when the material for distributing fractions was done
online. That way the student has gained previous experience. Apart from that, to help other students understand, they are reminded again of the steps for solving by multiplying natural numbers divided by common fractions.
The next activity after all the students had finished working on the questions, namely the formulation situation in the form of student representatives consisting of two students were assigned to the front of the class to rewrite the questions and the steps for working on them on the blackboard, while other students listened carefully. Then another student whose work was the same as the student in front was assigned to give reasons regarding the steps for working on the problem.
Students are also assigned to pay close attention to the similarities in the steps to solving the two questions, so that a pattern of relationships is found. Then students are assigned to conclude the relationship pattern and replace numbers with letters so that they can be used in other problems with different numbers. As an enrichment, students are assigned to apply the pattern of relationships formed in the division of mixed fractions with natural numbers. In the next activity, students in groups are assigned to find ways of solving other than what has been discussed, on the following questions:
“My sister has a 3
5 chocolate bar that will be given to her two friends. Each friend should get the same amount of chocolate. How many pieces of chocolate did each friend receive?”
The findings in this implementation were as predicted, the three groups experienced confusion and had difficulty finding a solution other than what had been discussed. This indicates that students experience epistemological obstacles. After being confirmed, it turned out that all this time students were not used to looking for and finding various ways of solving problems. So that a validation situation is given in the form of anticipation by way of students being reminded again about the form of word problems and how to understand the meaning of the problem. Then students are assigned to write down what is known in the problem, namely the younger sibling has a 3
5 chocolate bar and will be given to his two friends. Furthermore, students were assigned to write down what was asked with the characteristics of the sentence starting with a question word and ending with a question mark.
In the next activity, students were assigned to write questions in the form of mathematical sentences. Students are reassigned to complete mathematical sentences by means of multiplication.
After that, students are assigned to check the correctness of their answers by multiplying the resulting fraction by the divisor and the fraction divided by the inverse of the resulting fraction.
Finally, students are assigned to conclude the results of their answers, usually marked with the word "so". Even though they have been guided in solving problems by solving word problems, students still have difficulty determining what is known, asked, and concluded. This causes students to experience a didactical obstacle because students have minimal experience and are not used to solving problems by solving story problems so that they feel foreign to them. To confirm students' understanding regarding the distribution of fractions by solving word problems, students are conditioned into an institutional situation by being given practice questions to work on individually in class.
Based on the description and description of the implementation of the didactic situation 2 above, the authors conclude that there are learning obstacles experienced by students in the form of epistemological obstacles and didactical obstacles. The next finding is in the form of a new learning trajectory related to students' experiences learning fraction division material. As for the didactic and pedagogical anticipation carried out by the teacher according to the design.
The implementation of didactical situation 3 begins with a presentation of a problem about dividing ordinary fractions by ordinary fractions in the form of questions in the form of mathematical sentences. Students are assigned to solve problems by multiplication. The form of the question is as follows:
Solve the following problems by multiplication!
c. 5 6:1
3=…
d. 7
8:1 4=…
The next activity is the didactic situation which consists of action situations, formulation and validation. Students are individually assigned to solve the problem. Before students work, they are given the opportunity to ask questions first. However, none of the students asked. After all students have finished working, student representatives consisting of two students are assigned to the front of the class to copy the questions and the results of their work on the blackboard. Then assigned two more students whose answers were the same as the students who came to the front of the class to explain the steps in the process. To strengthen students' understanding regarding the division of ordinary fractions with ordinary fractions, students are assigned to pay close attention to the similarities in the steps for solving the two problems, so that a pattern of relationships is found.
Student activity was still not critical and not thorough in reading the questions. This finding was based on the fact that no students asked or found a way to solve the division of ordinary fractions with ordinary fractions that could be done directly in the form of division. This indicates that students experience didactical obstacles because students are used to being given direct problem-solving methods and are rarely involved in finding and determining how to solve problems. That way, in the end, students also experience conceptual ontogenic obstacles due to the low thinking or conceptual demands of students so they do not explore the potential that exists in students. Enrichment activities in institutional situations students are assigned to apply the pattern of relationships formed in the division of mixed fractions with mixed fractions.
Based on the description and description of the implementation of didactic situation 3 above, the authors conclude that there are learning obstacles experienced by students in the form of didactical obstacles and conceptual ontogenic obstacles. As for the didactic and pedagogical anticipation carried out by the teacher according to the design. The next activity, students are assigned to work on the final evaluation of learning in the form of questions. The purpose of this final evaluation is to find out and evaluate students' understanding of the division of fractions material that has been implemented in learning. In addition, also to know and measure the achievement of learning objectives.
4.Conclusion
Learning Obstacles (LO) theappears after the initial didactical design is implemented in learningincludes psychological ontogenic obstacles such as finding students who are not ready to learn as a result of not liking the content of mathematics lessons and having low motivation.
Instrumental ontogenic obstacle, namely the technical incompatibility of the demands of the questions with the answers completed by the students. The ontogenic conceptual obstacle is the lack of students' understanding of the intent of the questions, especially about stories. Students experience difficulties in changing the units of length, weight and volume. Lack of understanding of the concept of repeated subtraction, on division of fractions. Difficulty in representing fractions in the form of a number line, and pictures or plane areas. The epistimological obstacle is the limited experience of students in solving word problems by solving Heuristic Polya problems. Students have never been given a step to check the correctness of the answers to the story questions. The didactical obstacle is that students always get a solution without looking for and finding it themselves. The learning trajectory (LT) that was found included one student who had previous learning experience related to dividing fractions. Students are more interested in ways of solving in the form of pictures and number lines, with the aim of eliminating boredom in mathematics lessons. Didactic anticipation is given spontaneously, namely by providing scaffolding in understanding the intent of the problem, for example determining the characteristics of story problems which are done by means of counting division operations, determining and changing the unit size of length, weight, and volume.
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