Teaching Probability using Snakes and Ladders Games in Middle

School

Ririn Suparti Kurnianingsih

, Ratu Ilma Indra Putri

and Yusuf Hartono

Mathematics Education Department, Universitas Sriwijaya, Palembang, Indonesia

Keywords: Probability, Snakes and Ladders Games, PMRI, Design Research.

Abstract: This study aimed to support students’ understanding in probability using snake and ladders’ game as context.

We used design research as approach then designed three learning activities using Pendidikan Matematika

Realistics Indonesia (PMRI), a Hyphotetical Learning Trajectory (HLT) was develop and a set of activities

using snake and ladders game as context. There are 33 students of SMPN 55 Palembang were participated in

teaching experiment. The theoretical development is driven by an iterative process of designing instructional

activities, performing teaching experiments and conducting retrospective analysis in order to contribute to

Local Instruction Theory (LIT) to support students’ problems solving on probability. Retrospective analysis

of teaching experiment showed that using snakes and ladders game context can support students

understanding on the Probability materials.

1 INTRODUCTION

Probability is a sub-topic of the discussion of the

mathematical sciences of probability and statistics

(Sina, 2011). Probabilities represent real-life

mathematics and students need to explore the process

of probability, probabilities also relate to many

subjects in mathematics, especially counting and

geometry (Taylor, 2010). De Walle (2008) also states

that the concepts of realistic probabilities require a lot

of development before children are ready to build

formal ideas about the probability of future events. It

is expected to occur when children consider and

discuss with their peers.

The use of general context also influences

students' difficulties in developing correct intuition

about basic ideas about probabilities (Huerta, 2011;

Garfield and Ahlgren, 2006; Sharma, 2006; Azhar,

2011). Context is also closely related to students'

personalities such as traditional children's games

(Putri, 2010). The importance of using context in

learning materials should begin with situations

known to students (Putri, 2012). In this study, snake

and ladder games were chosen as context to help

students in learning probabilities. The snake and

ladder game provides an activity in which

probabilities and possibilities can become

experiences, in situations where the probability of an

event is not immediately known (Melrose, 2007).

According to Lalos, Lazarinis and Kanellopoulos

(2008) snake and ladder games are an educational

based game. In games, education is given through

practice or practical learning (learning by doing),

indirectly by educating humans through what they do

in the game (Purnanindya, 2012).

Pendidikan Matematika Realistik Indonesia

(PMRI) is a mathematical learning approach that can

be used in this learning. PMRI is an adaptation of

RME (Realistic Mathematics Education) which is a

learning approach that will lead students to

understand mathematical concepts by constructing

themselves through prior knowledge by discovering

the concepts themselves, so that student learning is

expected to be meaningful. In other words,

mathematics must be close to students and related to

everyday life, and also mathematics as human

activities so students must be given the opportunity to

do learning activities in every topic in mathematics

(Zulkardi & Putri, 2010; Putri, 2011). Students as

center in learning is expected to create a pleasant

atmosphere and the creation of activities and

creativity of students (Putri, 2009).

Based on the illustration, the researchers designed

the learning probability using snake and ladder games

using PMRI approach for the seventh grade students.

Then, it was designed by using Hypothetical Learning

Trajectory (HLT) which contains a series of activities

194

Suparti Kurnianingsih, R., Ilma Indra Putri, R. and Hartono, Y.

Teaching Probability using Snakes and Ladders Games in Middle School.

DOI: 10.5220/0009995000002499

In Proceedings of the 3rd Sriwijaya University International Conference on Learning and Education (SULE-IC 2018), pages 194-198

ISBN: 978-989-758-575-3

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

to help students understand probabilities. The purpose

of this research was to obtain the learning trajectory

in probability learning using snakes and ladders

games using PMRI approach and to determine the

role of snakes and ladders games in learning

probabilities.

2 LITERATURE REVIEW

2.1 Pendidikan Matematika Realistik

Indonesia (PMRI)

PMRI is an adaptation of Realistic Mathematics

Education (RME), a learning theory developed in the

Netherlands since the 1970s by Hans Freudhental.

Two important views from Freudenthal are: (1)

mathematics must be connected with reality and (2)

mathematics as human activity (Zulkardi & Putri,

2010). Gravemeijer (1994) states that the role of a

teacher must change from a validator (stating whether

the student's work and answers are right or wrong),

being a person who acts as a mentor who appreciates

each student's contribution (work). The main

principles of PMRI are as follows (Gravemeijer,

1994; Zulkardi, 2002; Zulkardi & Putri, 2010):

a. Guided reinvention and progressive

mathematizing

Guided discovery and progressive mathematics

can mean that students are given the opportunity

to experience the same process when mathematics

is found. The teacher guides students to move

from one level to another level of mathematical

thinking.

b. Didactical phenomenology

Situations that contain the phenomena that are

used as material and application areas in teaching

mathematics must depart from the real conditions

of students before reaching the formal

mathematics level.

c. Self-developed models

The principle of model development has a very

important role for students. The role of the

principle of the development of the model itself is

to bridge students from real or concrete situations

to abstract situations, or from the informal stage

to the formal stage of mathematics. This means

that students make their own models in solving

problems from situations that are close to the

nature of students, for example the use of the

context of snakes and ladders games that are

involved in learning mathematics to find concepts

in the material probabilities for an event.

The principles of PMRI above can be explained

more broadly through their characteristics. The five

characteristics of PMRI (Zulkardi, 2002; Zulkardi,

2005; Zulkardi & Putri, 2010): (1) Use of contexts for

phenomenologist exploration. (2) Use of models for

mathematical concept construction'. (3) Use of

students' creations and contributions. (4)

Interactivity. (5) Intertwining mathematics concepts,

aspects, and units.

2.2 Probability

There are 4 competencies in the subject matter of

probability, namely: understanding randomness,

sample space, comparing and measuring

probabilities, and understanding correlations or

relationships between events (Bryant & Nunes,

2012). According to Coladarci (2011: 175),

probability theory is the possibility of certain events

occurring. The possibility of the emergence of the

front side of throwing a coin as much as once is 0.5.

Because there are only two possible outcomes when

throwing a coin. Thus an probability is a comparison

that is between 0-1 denoted by p. The chance of an

event A is the result of the number of sample points

for event A with the number of members of the event

sample room A, formulated as Equation (1).

𝑃𝐴  𝑛𝐴/𝑛𝑆 (1)

2.3 Snakes and Ladders Games

The snakes and ladders games is a board game for

kids that is played by two or more people. The board

of snakes and ladders is divided into small boxes and

some boxes are drawn by a number of "ladders" or

"snakes" that connect them to other boxes (Yumarlin,

2013). The snakes and ladders games is played on a

board with a 10x10 grid, a sequence number in a

zigzag pattern from 1 (beginning, in the lower left

corner) to 100 (end, in the top left corner). At various

locations on the board are snakes and ladders placed,

each or connecting a pair of boxes. All players start

outside the board and take turns rolling the dice and

moving according to the dice that appears. If the

settlement moves at the foot of the ladder, then go

straight up. Also, if you move above the snake's head,

you are forced to slide to the snake's tail to the

previous square. there is no consequence of landing

on a ladder or snake tail. Snakes and stairs are one

way of mathematical parts, this is called a directed

graph. The first players to reach the 100 box win

(Berry, 2012; Connors & Glass, 2014). This game

was created in 1870. There is no standard board game

in snakes and ladders, so everyone can create the

Teaching Probability using Snakes and Ladders Games in Middle School

195

board size of a snakes and ladders games, with the

number of boxes, snakes and stairs as desired

(Yumarlin, 2013).

The game of snakes and ladders provides an

activity in which opportunities and possibilities can

be experiences, in situations where the probability of

events is not immediately clear (Melrose, 2007). In

the snakes and ladders games, students can use game

boards and dice to determine opportunities. On board

games there are snakes and ladders, and dice that can

provide experience of opportunities and possibilities

in opportunities. This game is an interesting

application of pure mathematical works (Melrose,

2007).

3 METHODOLOGY

In this study, researchers used design research

methods. Design research aims to develop Local

Instructional Theory (LIT) in collaboration with

researchers and teachers to improve the quality of

learning (Gravemeijer and van Eerde, 2009).

According to Gravemeijer and Cobb (2006: 19-43),

the design and development process in design

research includes three stages, namely: preparing for

the experiment, design experiment, and retrospective

analysis.

The cyclic process in the design research is carried

out to get the learning trajectory. The learning

trajectory is the result of the revision of the learning

design that was tested on the material under study.

This research was carried out in class VII of SMP N

55 Palembang, the first cycle was carried out with 6

students, and in the second cycle with 33 students.

Data collection was done through several things such

as based on the results of the pre-test and post-test,

observation, video recording, student work and

interviews were analyzed to improve HLT. Then the

designed HLT is compared with the actual learning

path of students to do retrospective analysis. Analysis

is carried out by researchers and mentors to improve

their reliability and validity.

4 RESULT AND DISCUSSION

This learning was designed to produce learning

trajectory using snakes and ladders games by PMRI

approach to help students understand probabilities

and to determine the role of snakes and ladders games

in probabilities learning. We will discuss the results

of experimental learning in the second cycle

involving 33 students.

Activity 1: Using Tables, Tree Diagrams,

Registering, and Cartesian Diagrams (Determining

how to present all the events that occur and the chance

of an event).

The learning process begins the same as with

previous meetings, greetings, checking student

attendance and apperception. Apperception is done

by interacting between the model teacher and students

through several questions posed by the model teacher

regarding previous learning. Followed by the teacher

conveying the learning objectives and providing

motivation in learning the material today. Students sit

based on groups that have been formed before. Before

starting a group discussion, students are asked to pay

attention to the learning video first, after which the

teacher informs them that the time given for

discussion is 40 minutes. Furthermore students are

welcome to start with their respective groups.

Activity 1, learning was starts with students

reading the problem and writing down the

information needed from the problem. Students are

given several ways to present the sample space. So

students can choose how to present a sample space

which they think is easy for them to understand.

There are 4 ways to present the sample space, namely:

how to register, using tables, tree diagrams and

cartesian diagrams. Then the students play a snake

ladder game that is found in activity 1, in this activity

students are asked to determine the sample space

between the snake and ladder game boards.

Figure 1: Board game for snakes and ladders in activity 1.

After the game is finished, students read the

problem first and continue by writing down some

information about the problem. This activity aims to

direct students to determine Probabilities for an event.

First the students write down the number of

possibilities of the dice and the snakes and ladder

game board. Then students can determine the overall

value by multiplying the number of steps in the

snakes and ladder game board (36) with the number

of dice (6). Next the students compare the number of

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stairs in the snakes and ladder game board with the

many steps in the game board. Then students make

conclusions about the probability of an event.

Figure 2: Conclusion of student activity 1.

Based on the students' answers to the conclusions

(Figure 2), it can be seen that students begin to get

used to drawing conclusions, even though only by

using words they understand. Students already

understand how to determine the probability of an

event and its application. This can be seen through

additional

questions given at the end of activity 1

(Figure 3).

Figure 3: Student answers about additional activities 1.

Observer: Where did you get 3/10?

Students: 3 are chocolate-book, continue to compare

with all of them 5 candies, 3 chocolates

and 2 wafers added to 10. So it can be 3/10

or 0.3.

From Figure 3, students mistakenly determine the

sample space. So that the amount of candy, chocolate

and wafers should be added, but in their answers

multiplying to get the sample space. Although the

answer is wrong, it can be seen in the picture that

students understand in determining the probability of

an event. The following are the students' answers to

the last problem in activity 1. Each group can finish

correctly.

5 CONCLUSSION

Based on the results of research and discussion, it can

be concluded that the learning trajectory which was

obtained in this study is students can use the

multiplication method in determining the number of

samples. Then students determine the probability of

an event through snake and ladder games. In addition,

the results showed that the use of snakes and ladders

games in learning probability materials have a role to

help students in comprehening the probabilities.

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