10 Models of Learning Mathematics in Elementary Schools _ Mathematics is a subject that is considered difficult for some people, this cannot be separated from the dominant field of study of mathematics regarding formulas and numbers so that for some people learning mathematics seems complicated and requires special techniques to learn it. Learning mathematics is indeed abstract, so it needs an intermediary or special media in teaching mathematics.
Models of Mathematics Learning in Elementary Schools
Mathematics is a basic science that supports other knowledge in its application, therefore understanding mathematics correctly will have implications for the ability to study several sciences related to mathematics. Since when should mathematics be studied? is a question asked by some people. Learning mathematics should start from the family environment. but what is most appropriate is that mastery and understanding of learning mathematics should be instilled since the child is still in elementary school.
Learning mathematics in elementary schools (elementary schools) is the initial provision for children to develop their abilities in mathematics lessons, besides that elementary school age is a moment for children to learn mathematics because at elementary school age children’s abilities in several aspects are very prominent.
But how do you teach math subjects in elementary school? to teach mathematics in elementary schools should not be arbitrary because the abstract nature of mathematics sometimes makes it difficult for children to understand it. learning models are needed that are in accordance with mathematics subjects so that the goals of learning mathematics can be achieved. What are the 10 models of learning mathematics in SD (elementary school)? The following is a brief review of the Mathematics Learning Model in Elementary Schools.
10 Models of Mathematics Learning in Elementary Schools
- Realistic Mathematical Learning Model
Realistic Mathematics Learning (PMR) is an operationalization of a mathematics education approach that has been developed in the Netherlands under the name Realistic Mathematics Education (RME), which means realistic mathematics education.
Realistic mathematics learning is basically the use of reality and the environment that students understand to expedite the process of learning mathematics, so as to achieve the goals of mathematics education better than in the past. What is meant by reality is real or concrete things that students can observe or understand through imagining, while what is meant by the environment is the environment where students are located both in the school, family and community environment that students can understand. The environment in this case is also called everyday life.
The steps in the process of learning mathematics with the PMR approach are as follows.
1. The first step: understanding contextual problems, namely the teacher gives contextual problems in everyday life and asks students to understand these problems.
2. The second step: explaining the contextual problem, that is, if students experience difficulties in understanding the problem, the teacher explains the situation and conditions of the problem by giving instructions or in the form of suggestions as necessary, limited to certain parts of the problem that have not been understood.
3. The third step: solve contextual problems, namely students individually solve contextual problems in their own way. Ways of solving and answering different problems are preferred. By using worksheets, students work on questions. The teacher motivates students to solve problems in their own way.
4. The fourth step: compare and discuss answers, namely the teacher provides time and opportunity for students to compare and discuss answers to problems in groups. Students are trained to issue the ideas they have in relation to student interaction in the learning process to optimize learning.
5. The fifth step: concluding, namely the teacher gives students the opportunity to draw conclusions about a concept or procedure.
- Open-Ended Learning Model Theopen-ended learning model
isthe same as problem-based learning, namely a learning model in which the process begins by giving a problem to students. This is in accordance with the opinion of Shimada (1997: 1) the open-ended learning model is a learning approach that presents a problem that has more than one correct method or solution. Open-ended learning models can provide opportunities for students to gain knowledge/experience in finding, recognizing, and solving problems with several techniques
Open-Ended Problems are not easily developed by students with various abilities. Through research in Japan, several things were found that became a reference in creating these problems including: 1) Present the problem through a real physical situation 2) Proof questions can be changed in such a way that students can find the relationships and properties of the variables in the problem. 3) Present geometric shapes or figures. 4) Present a sequence of numbers or tables so students can find math rules. 5) Give some concrete examples in several categories 6) Give some similar exercises so students can generalize from their work
Developing a Lesson Plan After the teacher constructs well, three things must be considered in learning before the problem is presented in class, namely: · Is the problem rich in mathematical concepts and valuable? Problems should encourage students to think from different perspectives.
Is the math level of the problem suitable for the student? When students solve Open-ended problems, they must use the knowledge and skills they already have · Does the problem invite further development of mathematical concepts? Problems must have a relationship or be linked to higher mathematical concepts so that they can spur students to think at a higher level. After we have formulated the problem according to the criteria stated, the next step is to develop a good lesson plan. The stages are as follows: Write down the expected student responses Students are expected to respond to open-ended problems in various ways. Therefore the teacher must write a list of anticipated student responses to the problem. The purpose of the problem must be clear
The learning steps in the OpenEnded Problems learning model are as follows:
- Preparation
Before starting the teaching and learning process, the teacher must make a Learning Implementation Plan Lesson Unit Program (RPP), create Open Ended Problems questions.
2 . Implementation , consists of:
- Introduction, namely students listen to the teacher who provides motivation that what will be learned is related or useful for everyday life so that students are enthusiastic about learning. Then students respond to the teacher’s apperception so that the teacher can find out students’ initial knowledge about the concepts to be studied.
- The core activity, namely the implementation of learning with the following steps:
- students form groups of five people per group;
- students get Openended Problems questions regarding statistical calculations and mathematical calculations;
- students discuss with their respective groups regarding the completion of the Open Ended Problems questions that have been given by the teacher;
- Each group of students, through their representative, expresses opinions or solutions offered by the group in turn;
- Students or groups then analyze the answers that have been put forward, which are correct and which are more effective.
- Final Activity, namely students conclude what they have learned, and then these conclusions are refined by the teacher;
- Evaluation
After the end of the teaching and learning process, students receive individual assignments or daily tests containing Open Ended Problems questions which are evaluations given by the teacher. In the international journal J.Nikos, mortos, et al
- Example non-example learning model
The Example non Example model is a learning strategy that uses media images in the delivery of learning material that aims to encourage students to learn to think critically by solving the problems contained in the examples of the images presented.
Example non example
- Material: Plane Shape (identify the nature of flat shapes)
- Reason: In flat shape material, the material presented is mainly pictures
from a flat wake, so that it is suitable for using the Steps Examples Non Examples models
step in it presents the image.
- The steps are as follows:
-Teachers prepare pictures according to learning objectives
-Teacher pastes the picture on the board.
-The teacher gives instructions and gives students the opportunity to pay attention/analyze the picture
-Through group discussions of 2-3 students, the discussion results from the image analysis are recorded on paper
-Each group is given the opportunity to read the results of their discussion
-Starting from the comments/results of student discussion, the teacher begins to explain the material according to the goals to be achieved
-Conclusion
- Picture n picture learning model
The picture and picture learning model is a learning model that uses pictures and is paired/sorted into a logical sequence. This learning model relies on images as a medium in the learning process. These pictures become the main factor in the learning process. So that before the learning process the teacher has prepared an image that will be displayed either in the form of a card or in the form of a large size chart
The steps of the Picture and Picture Learning Model According to Jamal Ma’mur Asmani, there are seven steps
to the implementation of Picture and Picture, namely:
1. The teacher conveys the competencies to be achieved.
In this step the teacher is expected to convey what is the Basic Competence of the subject concerned. Thus, students can measure to what extent they must master. Besides that, the teacher must also convey KD achievement indicators, so that students can reach the KKM that has been set.
2. Presenting material as an introduction
Presentation of material as an introduction to something very important, from here the teacher provides the momentum for the beginning of learning. Success in the learning process can start from here. Because the teacher can provide motivation that attracts the attention of students who have not been ready so far. With good motivation and techniques in providing material, it will attract students’ interest to learn more about the material being studied.
3. The teacher shows / shows pictures related to the material.
In the process of presenting the material, the teacher invites students to be actively involved in the learning process by observing each picture shown by the teacher or by their friends. With pictures we will save our energy and students will more easily understand the material being taught. In further developments as a teacher can modify pictures or replace pictures with videos or demonstrations of certain activities.
4. The teacher appoints/calls students in turn to place/sort the pictures into a logical sequence.
In this step the teacher must be able to innovate, because direct appointments are sometimes ineffective and students feel punished. One way is by drawing lots, so that students feel they have to carry out the tasks that must be given. The existing pictures were requested by students to be sorted, created, or modified.
5 NHT Learning Model (Numbered heads together)
Number Head Together is a learning model that puts more emphasis on student activities in finding, processing, and reporting information from various sources which is finally presented in front of the class (Rahayu, 2006). NHT was first introduced by Spencer Kagan et al (1993). The NHT model is part of the structural cooperative learning model, which emphasizes specific structures designed to influence student interaction patterns. The Kagan structure requires students to work interdependently in small groups cooperatively. This structure was developed as an alternative material to the traditional class structure such as raising your hand first and then being appointed by the teacher to answer the questions that have been asked. This kind of atmosphere creates an uproar in the class.
These steps were then developed by Ibrahim (2000: 29) into six steps as follows:
Step 1. Preparation
In this stage the teacher prepares lesson plans by making Learning Scenarios (SP), Student Worksheets (LKS) that are in accordance with the NHT type cooperative learning model.
Step 2. Group formation
In forming groups adapted to the NHT type cooperative learning model. The teacher divides the students into several groups consisting of 3-5 students. The teacher gives each student a number in a different group and the name of the group. Numbering is the main thing in NHT, at this stage the teacher divides students into groups or teams of three to five people and gives students a number so that each student in the team has a different number, according to the number of students in the group. The groups formed are mixed in terms of social background, race, ethnicity, gender and learning ability. In addition, in group formation, pre-test scores were used as the basis for determining each group.
Step 3. Each group must have a textbook or manual
In forming groups, each group must have a textbook or guidebook to make it easier for students to solve LKS or problems given by the teacher.
Step 4. Discussion of the problem
In group work, the teacher distributes LKS to each student as material to be studied. In group work each student thinks together to describe and ensure that everyone knows the answers to the questions that are already in the LKS or the questions that have been given by the teacher. Questions can vary, from specific to general in nature.
Step 5. Calling the member’s number or giving an answer
In this stage, the teacher calls out a number and students from each group with the same number raise their hands and prepare answers to the students in class.
Step 6. Give a conclusion
The teacher and students conclude the final answers to all questions related to the material presented.
Numbered head together
- Material: Circumference and Area of Flat Shapes
- Reason : Basically this model can indeed be used.
- Steps:
Students are divided into groups, each student in each group gets a number
The teacher gives assignments and each group does it
The group discusses the correct answer and ensures that each group member can do it/knows the answer
The teacher calls one of the student numbers with the number called to report the results of their collaboration
Responses from other friends, then the teacher pointed to another number
Conclusion
- Jigsaw Learning Model
The jigsaw cooperative learning model is a cooperative learning model that focuses on student group work in the form of small groups, as Lie (1993: 73) said, that this jigsaw cooperative learning model is a cooperative learning model in which students learn in small groups that consists of four to six people heterogeneously and students work together with positive interdependence and are responsible independently.
according to Stephen, Sikes and Snapp (1978) quoted by Rusman (2008), suggests the steps of the Jigsaw Cooperative Learning Model as follows:
>Students are grouped as many as 1 to 5 students.
>Each person in the team is given a different part of the material
>Each person in the team is given an assigned piece of material
>Members of different teams who have studied the same sub-sections meet in new groups (expert groups) to discuss their sub-chapters.
>After finishing the discussion as an expert team, each member returns to the original group and takes turns teaching their mates about the sub-chapter they have mastered and each other member listens carefully.
>Each team of experts presented the results of the discussion.
> The teacher gives an evaluation.
>Cover
Jigsaw
- Material: Converting Fractions to Percents and Decimals and Vice versa
- Reason : This model increases collaboration between students, involves all students, and can be used for calculation problems in mathematics.
- Steps:
-Students are grouped into = 4 team members
-Each person on the team is given a different part of the material, there are percent, fractions, and decimals.
-Each person on the team is given an assigned piece of material
-Members from different teams who have studied the same section/sub-chapter meet in a new group (expert group) to discuss their sub-chapter
-After finishing the discussion as a team of experts, each member returns to the original group and takes turns teaching their teammates about the sub-chapter they are good at and each other member listens intently
-Each team of experts presented the results of the discussion
-The teacher gives an evaluation
-Closing
- Role playing learning models
Role playing or role playing is a kind of movement game in which there are goals, rules and at the same time involves an element of pleasure (Jill Hadfield, 1986). In role playing students are conditioned in certain situations outside the classroom, even though at that time learning occurs in the classroom. In addition, role playing is often intended as a form of activity where students imagine themselves as if they were outside the classroom and playing the roles of other people (Basri Syamsu, 2000).
Role Playing Learning Model is a way of mastering learning materials through the development of imagination and appreciation of students. The development of imagination and appreciation is carried out by students by playing them as living figures or inanimate objects. This game is generally done by more than one person, it depends on what is being played.
The learning steps are as follows:
-Teacher arranges/prepares scenarios to be displayed.
– Appoint several students to study scenarios within a few days prior to the implementation of the Teaching and Learning Activities.
-The teacher forms a group of students whose members are 5 people.
-Provide an explanation of the competencies to be achieved.
-Calling students who have been appointed to act out the scenarios that have been prepared.
-Each student is in his group while observing the scenario being demonstrated.
-When finished showing, each student is given a worksheet to discuss/give an assessment of the performance of each group.
-Each group presents its conclusions.
-The teacher gives general conclusions.
-Evaluation.
-Closing.
Role Playing
- Material: Currency / Buying and selling
- Reason: The practice of buying and selling can be demonstrated by students to make it easier to understand.
- Steps:
– The teacher arranges/prepares the scenarios that will be displayed
– Appoint some students to study the scenario two days before the kbm
-The teacher forms a group of students whose members are 5 people
– Provide an explanation of the competencies to be achieved
– Calling the students who have been appointed to act out the scenarios that have been prepared
– Each student sits in his group, while paying attention to the scenario being demonstrated
– After the performance is finished, each student is given paper as a worksheet to discuss
-Each group presents its conclusions
-The teacher gives general conclusions
-Evaluation
-Closing
- Learning models based on problems
According to Suherman (2003: 7) the learning model is intended as a pattern of interaction between students and teachers in the classroom concerning strategies, approaches, methods and learning techniques applied in the implementation of teaching and learning activities in the classroom. The concept put forward by Suherman explains that the learning model is a form of how the interactions created between teachers and students relate to the strategies, approaches, methods, and learning techniques used in the learning process. Gijselaers (1996) Problem-based learning is derived from the theory that learning is a process in which the learner actively constructs knowledge.
Here are the steps of PBM.
There are 5 phases (stages) that need to be carried out to implement PBL.
Phase Teacher activity
Phase 1: Orient students to the problem. Explaining the learning objectives, the necessary logistics, motivating students to be actively involved in the selected problem solving activity
Phase 2: Organizing students to learn. Helping students limit and organize learning tasks related to the problems faced
Phase 3: Guiding individual and group investigations. Encourage students to gather appropriate information, carry out experiments, and seek explanations and solutions
Phase 4: Develop and present the work. Help students plan and prepare appropriate work such as reports, videos, and models, and help them to share assignments with friends.
Phase 5: Analyze and evaluate the problem solving process. Helping students reflect on investigations and the processes used during problem solving.
Problem Based Learning
- Material: Get to know the unit of time
- Reason: Calculating time is easy. In story problems, this can be a problem that must be solved. So you can use this model.
- Steps:
-The teacher explains the purpose of learning. Describe the logistics required. Motivate students to engage in selected problem-solving activities.
-The teacher helps students define and organize learning tasks related to the problem (setting topics, assignments, schedules, etc.)
-Teachers encourage students to collect appropriate information, experiments to get explanations and problem solving, data collection, hypotheses, problem solving.
– The teacher assists students in planning to prepare appropriate works such as reports and helps them share assignments with their friends
-Teachers help students to reflect or evaluate their investigations and the processes they use.
- Examples of questions that can be given:
Bagas and Soni plan to eat at Pak Bimo’s stall and go to softball practice together. Softball practice starts at 10.00. It took Bagas ¾ hour to pick up Soni and go to Pak Bimo’s stall near the softball practice site. It takes 1 ¼ hours to eat and walk to the training location. They want to arrive at the practice site 15 minutes before it starts. What time should Bagas leave his house?
- Course review horay learning model
Cooperative learning model of Course Review Horay typenamely a learning model that can create a lively and fun class atmosphere because each group that can answer correctly, the student is required to shout “HOREY” or other yells that are liked. Course Review Horay is a learning model that encourages students to actively participate in learning. With the Course Review Horay learning model it is hoped that it can train cooperation in solving problems by forming groups, the learning is interesting and encourages students to plunge into it, not monotonous because it is interspersed with a little entertainment so that the atmosphere is not tense and students are more enthusiastic about learning because the learning atmosphere is fun so that it can help students to achieve high scores.
According to Widodo (2009: 1) the steps for applying the Course Review Horay method in learning are as follows:
-The teacher conveys the competencies to be achieved, these competencies are conveyed so that learning is more goal-directed.
-The teacher demonstrates or presents material according to the topic being taught.
-To test understanding, students are asked to make a place for answers. The answers here are in the form of a table (box) containing nine, sixteen or twenty-five boxes. The number of boxes for the answers is adjusted to the needs and each answer box is filled with a number according to the tastes of each student.
-The teacher reads the questions randomly according to the numbers that have been prepared beforehand. Students write answers in the box whose number is mentioned by the teacher. Questions that have been read are immediately discussed, if correct, fill in a correct mark (v) and incorrect, enter a cross (x). Here honesty is needed from students who have answered wrong or right.
-Students who have received a mark (v) vertically or horizontally, or diagonally must immediately shout hooray or other yells.
-Student grades are calculated from the correct answers and the number of horays earned.
-Closing the discussion. The closing of this discussion can be in the form of conclusions from the teacher or concluded by the students themselves,
Course review horay
- Material: Operation arithmetic addition
- Reason : This model can be used for calculation problems in mathematics.
- Steps:
Þ The teacher conveys the competencies to be achieved
Þ The teacher demonstrates/presents the material
Þ Give students the opportunity to ask questions
Þ To test understanding, students are told to make boxes 9/16/25 according to their needs and each box is filled with numbers according to each student’s tastes
Þ The teacher reads the questions randomly and students write answers in the box whose number is mentioned by the teacher and immediately discussed.
Þ Students who have received an Ö mark vertically, horizontally, or diagonally must shout hooray… or other yells
Þ The value of students is calculated from the number of correct answers obtained horay
Þ Penutup
- Example: The teacher gives multiplication questions to 9 closed boxes, randomly from the easy level to the difficult level, then students who choose a certain number of questions will get a question, if they are correct they are given a tick, if they are wrong they are given a cross, if they form a line then everyone cheers !!
- The learning model Take you Give
Take and give linguistically means taking and giving, the meaning of take and give in this learning model is where students take and give lessons to other students. “Some experts believe that a subject is really mastered a lot if students are able to teach it to other students.
Peer teaching provides an opportunity for students to learn something good at the same time as being a resource for others. This strategy also provides teachers with extras when teaching is carried out by students” (Melvin Silberman, active learning 101 active learning strategies).
The learning model of receiving and giving (Take and Give) is a learning model that has syntax, requiring students to be able to understand the subject matter given by the teacher and their peers (other students). The steps of the take and give learning model
In
carrying out this take and give method there are several the steps that must be taken by educators are:
-Prepare the class as it should.
-Explain the material according to the topic of the minute.
-To strengthen participant mastery, each student is given one card each to study (memorize) for approximately 5 minutes.
-All students are asked to stand up and find a partner to inform each other about the material according to their respective cards. Each student must record the name of his partner on the control card.
-And so on until each participant can give and receive each other’s material.
-To evaluate success, give students questions that match their cards (other people’s cards).
-This strategy can be modified according to circumstances.
-Conclusion.
Take n give
- Material: Operation arithmetic multiplication
- Reason : This model can be used for calculation problems in mathematics.
- Steps:
-Prepare class accordingly
-Explain the material according to TPK
-To strengthen participant mastery, each student is given one card each to learn (memorize) in approximately 5 minutes
-All students are asked to stand up and find a partner to inform each other. Each student must record the name of his partner on the sample card
-And so on until each participant can give and receive each other’s material (take and give)
-To evaluate success, give students questions that do not match their cards (other people’s cards)
-This strategy can be modified according to circumstances
-Conclusion Thus 1 0 Mathematics Learning Models in Elementary Schools As for the application, all that remains is to adjust which model is most appropriate to the theme or mathematics subject matter to be taught . admin time will review it.When it comes to mathematics education in elementary schools, teachers use various models of instruction to ensure effective learning outcomes for their students. These models serve as frameworks that guide educators in teaching mathematical concepts and skills in a way that caters to the diverse needs and learning styles of young learners.