Number Sense Ability of Elementary Students Through ―Mathematical Games‖

INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 12, DECEMBER 2019 ISSN 2277-8616 Number Sense Ability Of Elementary Students Through ―Mathematical Games‖

Sulistiawati, Surya Wijaya

Abstract: This research was motivated by most of junior high school students‘ first grade face difficulties in calculating 15 × 6 with mental calculation. Based on a diagnostic test can be seen that many students lack of number sense understanding when they were in 4th or 5th grade. It happened in some of Papuan Students in Surya Intensive Program (SIP) Tangerang - Indonesia, Indonesia who learned arithmetic operation like addition, multiplication, subtraction, and division. This research aimed to find out how students use mathematical games, how students‘ number sense ability was, and what students‘ response toward the learning. This research was conducted using qualitative research method. Participants of this study were 13 students 4th graders in year 2013. The result of this study showed that learning with mathematical games like game 24 and game 15 could be one of learning strategies to stimulate students‘ number sense in arithmetic operation. Students‘ number sense ability increased with percentage was 18.91%. Students also have positive response after the learning used game 24 and game 15. This percentage was 69.75%.

Index Terms: Number sense, Mathematical games, Arithmetic operation, Game 24, Game 15 ————————————————————

1 INTRODUCTION 1.1 Number Sense AN observation result that was conducted in Bandung, According to [2], number sense is related to numbers Indonesia showed that teachers apply formal and rigid comprehension as well as their operations. Furthermore, it approaches in teaching [1]. Teachers were in front of the class also refers to one‘s capability in using this comprehension in to explain and students sat upright to listen and record what such a way to be flexible and innovative in dealing with teachers wrote on the whiteboard. After explaining and giving numbers and their operations mathematically. As in [3] examples of questions, teachers provide exercises for number sense has defined as an intuitive feel for numbers and students with more mechanistic competence instead of a common sense approach to use them. Number sense is a reasoning competence, for example exercises related to topic of great interest in school [2]. It is also nebulous and number sense. As in [1] found that most of junior high school difficult to describe, although it is recognizable in action. students‘ first grade in Bandung had difficulties in calculating Continuous productive discussion of number sense (by 15 × 6 with mental calculation. They inclined to finish it with researchers, teachers and curriculum developers) must at writing algorithmic. Research in US found that 45% Senior some stage be based on a definition, characterization, or High School students (age 17 year) could not calculate 90 × model which portrays number sense in a clear yet 70 with mental computation [1]. Number Sense is not only a comprehensive manner. The Curriculum and Evaluation competence to recognize and able in calculating but also to Standard for School Mathematic has mentioned that that must be controlled so that children could have a good characteristics of student who have a good number sense are: number sense, those are have a good intuition to recognize 1) understand the meaning of numbers, 2) recognize relative numbers, good understanding of numbers properties, and number size, 3) recognize the number‘s properties very well, knowing the relation of numbers very well. Either The 4) understand number operation and its properties, 5) apply Curriculum and Evaluation Standards for School Mathematics the understanding of numbers in daily life [4]. (NCTM) or The National Statement on Mathematics for New Jersey Curriculum Number Sense framework [3] has Australian School (AEC) described that number sense is a stated that indicators and activities of students which are major essential part as outcome of school mathematics [2]. related to topics addition, subtraction, multiplication, and Based on the diagnostic test of students from Surya Intensive division are: 1) understand and use of the meaning and size of Program (SIP) in Tangerang, Indonesia we got students‘ numbers, 2) understand and use of equivalent forms and number sense was very less. It was shown by the right representations of numbers, 3) understand the meaning and answers percentage of number sense questions answered by effect of operations, 4) understand and use of equivalents the students, which is 23.33% for fourth grade and 32.83% for expressions, 5) Compute and count strategy, and 6) fifth grade. For this reason, we studied the use of Measurement benchmark. This research use indicators which mathematical games to develop students‘ number sense. The had developed by [2], that are 1) Understanding of the research was aimed to investigate: a) how was learning trough meaning and size of numbers (Numbers Concept), 2) mathematical games (game 15 and game 24), b) how was Understanding of the meaning and size of numbers (Numbers students‘ number sense ability that used mathematical games Concept), 3) Understanding the meaning and effect of (game of 15 and gam 24) in arithmetic operation learning? And operations (Effect of Operation), 4) Understanding and use of c) what was students‘ response after the learning? equivalent expressions, 5) Computing and Counting Strategy.

1.2 Mathematical Games ———————————————— Mathematics can be seen as knowledge about pattern and  Sulistiawati is a lecturer at Sekolah Tinggi Keguruan dan Ilmu connection in mathematical idea and connection of each other. Pendidikan Surya (Surya College of Education), Indonesia, Email: Students must be able to see whether mathematical idea has [email protected]  Surya Wijaya is a lecturer at Sekolah Tinggi Keguruan dan Ilmu similarities or difference from the previous idea. For instance, Pendidikan Surya (Surya College of Education), Indonesia, Email: students who understand about a basic concept of addition 3 + [email protected] 4 = 7 have a connection with a basic concept of subtraction 7 – 3 = 4. Another example is a basic fact of multiplication 2 × 3 3315 IJSTR©2019 www.ijstr.org INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 12, DECEMBER 2019 ISSN 2277-8616

= 6 has connection with basic concept of 6 ÷ 2 = 3. As a manipulate four integers so that the end result is 24. The teacher, we need to understand all facts, so that teacher must players can use addition, subtraction, multiplication, or use variety of activities in mathematics learning to make division, but sometimes, they can use other operations to students enjoy mathematics, be active in learning, and make four digits from one to nine equal to 24. For example, understand the meaning of mathematics learning or concept. card with the numbers 4, 7, 8, 8, have solution: (7 – (8/8)) × 4 One way to realize those conditions is to use mathematical = 24. In this research we just use four operations like addition, games in learning. As in [5], game has been defined as a set subtraction, multiplication, and division. Below is an example of criteria of which includes task or activity. These are: (1) a of the 24 game cards: game involves a challenge against either a task or an opponent, (2) a game is governed by a definite set of rules, (3) a game is freely engaged in, (4) psychologically, a game is an arbitrary situation clearly separate from real-life activity, (5) socially, the events of a game situation are considered, in and of themselves, to be of minimal importance, (6) a game has a Fig. 1 The cards to play game of 24 definite number of possible solutions; that is, only a finite (Source: Triplett, 2011) number of things can happen during play, (7) a game must always be ended, although the end may come simply because For example, a card consist of numbers 9, 4, 8, and 5 has time has run out. In [6], [7], it can be found that children enjoy possible solutions of ((9-5) × 4) + 8 and (9+5-8) × 4. Another playing games. Based on experience, games give positive card consist of numbers 1, 7, 3, and 4 has possible solutions contribution in learning activities, included in mathematics such as ((1+3) × 7) – 4, (4-1) + (7×3) and ((4-1)) × 7 + 3. Many learning. Teacher need to consider the use of games when combinations of numbers can be manipulated to have result teaching mathematics, teacher should distinguish between an 24 but some of them are impossible. List of four digits ‗activity‘ and a ‗game‘. Moreover, Gough stated that ―A ‗game‘ combination from 1 to 9 for which it is impossible to form 24 is needs to have two or more players, who take turns, each showed a box at figure 2 which there are 91 combinations. competing to achieve a ‗winning‘ situation of some kind, each able to exercise some choice about how to move at any time through the playing‖. The key idea in this statement is that of ‗choice‘ [6]. Oldfield stated that mathematical games are ‗activities‘ which: 1) involve a challenge, usually against one or more opponents; 2) Are governed by a set of rules and have a clear underlying structure; 3) Normally have a distinct finishing point; 4) Have specific mathematical cognitive objective [8]. Davies stated the advantages of using game are: (1) Students Fig. 2 The impossible combination to form 24 have meaningful situations to implicate mathematics skill, (2) (Source: Triplett, 2011) Students have motivation which children freely choose to participate and enjoy playing, (3) Increased learning because 1.3.2 The Game 15 games can increase the interaction between students and give The game 15 is a two players game in which each player opportunity to test intuitive ideas and problem solving takes turn to choose a single digit number (except zero), so strategies, (4) Game can provide ‗hands on‘ activities, (5) that three of their numbers add up to 15. The player who first Children can work independently of the teacher, (6) Students has three of their numbers added up to 15 is the winner [11]. have positive attitude which games build self-concept and This game is equivalent to ―game of 9 cards‘. The starting of develop positive attitudes towards mathematics, through this game, laydown all of 9 cards, face up, so the numbers reducing the fear of failure and error [9]. seen. Players take in taking one card at a time until someone wins, or all cards are taken. As a note, we may end up with 1.3 Mathematical Games Varieties more than three cards in our hand, but we may only use three There are many kinds of mathematical games to enhance of those cards to make a combination that sums to 15. The students‘ activities in mathematics learning, such as domino, game 9 cards is two persons game, played with nine cards. Sudoku, close to zero, close to 20, close to 100, close to 1000, Each card has different numbers on it. The players alternate the game 24, the game 15, geometry bingo, etc. In this study picking up the cards. The winner is the first who has exactly the researchers used game 24 and game 15 to investigate three cards whose sum is 15. Although player 1 had four cards students‘ number sense ability. at the end of the game, that player won because the sum of a set of there of those cards was exactly 15. There are many 1.3.1 The Game 24 possibilities to make 15 uses these nine cards. Illustration of Triplett stated that the 24 game is commercially available the possibility can be seen in table 1 and table 2 below. game made by Nasco [10]. You are given a card with four digits taken from 1–9. The objective is to add, subtract, multiply and/or divide and get a result of 24. The result state that you must use all four digits on a card and you must use each digit only once. The game sounds easy, but most people find it very challenging. Basic level of mathematics competence is involved in this game and it enhances mathematician paid their interest on it. The 24 Game is an arithmetical card game in which the object is to find a way to 3316 IJSTR©2019 www.ijstr.org INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 12, DECEMBER 2019 ISSN 2277-8616

TABLE 1 TABLE 3 POSSIBLE PLAYING OF GAME 15 (POSSIBILITY 1) INDICATORS AND QUESTIONS REPRESENT NUMBERS SENSE

No Number Sense Indicators Number Sense Aspects Question 1 Understanding of the Students understand simple 6 meaning and size of inequality numbers (Numbers Students can estimate the number of 8 Concept) boxes needed without doing actual division 2 Understanding and use of Students can get the answer without 4 equivalent forms and doing any calculation, but by representations of numbers understanding the meaning of (Multiple Representations) arithmetics operations 3 Understanding the meaning Students able to estimate the result 5 and effect of operations without doing actual multiplication TABLE 2 (Effect of Operation) and division POSSIBLE PLAYING OF GAME 15 (POSSIBILITY 2) 4 Understanding and use of Students can find the answer 3 equivalent expressions efficiently

5 (Equivalent Expressions) Students are expected to use informal 1, 2 Computing and Counting strategies Strategy Students can estimate the money 7 needed without adding actual numbers

2 METHODS

2.1 Research Design Research method of this study was qualitative method. Data is collected directly from the source. In this method, the researchers are the key instrument because the tools used to collect data could be changing anytime according to the researchers‘ need. Qualitative method emphasizes more on processes rather than products or [12]. TABLE 4 NUMBER SENSE SCORING RUBRIC 2.2 Research Instrument The researchers were the key instrument developed test form, questionnaire form, interview guideline, and observation form. Test instrument was used to explore students‘ number sense ability. The test questions were same as diagnostic test at preliminary study. Questionnaire was used to explore students‘ response about the use of mathematical games in mathematics learning, which is game 24 and game 15. Interview guideline was used to guide researchers to interview students related to the learning. Observation was used to observe the students‘ activities along the learning. Test Questionnaire test was developed by the researchers using instrument was developed refers to number sense indicators. indicators of students‘ response. There are two aspects whose To give score to students‘ works, researcher used rubric score will be explored that is students‘ responses after mathematical with minimum score is 0 and maximum score is 3 for each games learning and students‘ response about the questions. number. Indicators and questions represented either numbers The questionnaire consist of 8 questions with score 1 to 5 for sense or score. Rubric is presented in table 3 and table 4 each question. The scores were given for the answer which 5 below. for Strongly Agree (SA), 4 for Agree (A), 3 for Neutral (N), 2 for Disagree (D), and 1 for Strongly Disagree (SD) in a positive type of questions and vice versa in a negative one. The indicators of the questionnaire could be seen in table 5 below.

TABLE 5 writing. Specifically, they lack of understanding on meaning of INDICATORS OF STUDENTS RESPONSE equal signs. This finding is supported by research conducted by Helmy, etc. that students focus to solve the problems in calculations or operations and did not understand the meaning [13]. Furthermore, students also lack of understanding on order of arithmetic operation and using of brackets. It shows that students ignore the set of brackets, as in [14], [15]. Some of students were reluctant to write their answer; instead they come to us and try to explain their answer orally. See table 6 below. TABLE 6 EXAMPLES OF STUDENTS’ ANSWERS

An interview was used to support questionnaire to explore students‘ response after the learning. This interview was guided interview because we used an interviewing guidance that consists of 5 questions. We also wanted to find what students‘ problems or what students taught of game 24 and game 15 so we can scaffold them to solve the game. Otherwise, this interview to help students to solve the given questions after the mathematical games learning. Interview could be done as long as we observed of the learning.

2.3 Research Subject The subject of this study was 13 fourth grade students from SIP. While participants in diagnostic test are 20 grade fifth grade and 13 fourth grade students in year 2013..

2.4 Data Analysis For problem number 1, there are five students who answered Data analysis of this research was descriptive analysis. like first solution and five students who answered like second Descriptive means data collected is in the form of words or solution. The following is some interesting cases which show figures rather than numbers. Descriptive analysis is used by that students have problems in communicating their examining the data collected throughout the research; they are mathematical ideas in writing. Problem number 2, there are six test, questionnaire, interview, and observation. students who answered like the first solution, one student who answered like the second solution, and three students who 3 RESULT AND DISCUSSION answered like the third solution. Some interesting cases of students answer show that students still have problem in 3.1 Learning trough Mathematical Games Analysis communicating and writing their idea. Figure 4 shows some Learning trough mathematical game 24 and game 15 is given examples of students‘ work. to 13 students grade IV. These games use card like bridge card. Below is analysis of learning process use game 24 and game 15.

3.1.1 Learning Use Game of 24 Game 24 is game use card consist of number from 1 to 9 and the players are asked to use sign arithmetical operation like +, ×, •, and ÷ to get the result 24. Mathematics learning use game 24 was held in two meetings. Fig. 3 Students’ Works of Game 24 3.1.1.1 First Meeting of Game of 24 First meeting was started with explanation about the game rule Fig. 3 shows that students have problems in communicating and some examples about how to play. Furthermore, make mathematical ideas in writing. It can be said that students can group students consist of 4 persons (in this case one group not share and clarify their ideas to others [16]. Meanwhile, consist of 5 persons) so that there were 3 groups. Students National Council of Teachers of Mathematics has mentined play bridge card consist of Ace, number 2 to 9 and find the that communication is an essetial part in mathematics result is 24 use arithmetic operations. After finishing the game education, that is mathematics learning [16]. students were asked to do the questions including: a) 6, 6, 5, 10; b) 5, 5, 4, 5; c) 3, 5, 4, 1; d) 4, 7, 2, 3; e) 5, 4, 7, 8; f)7, 7, 4, 3.1.1.2 Second Meeting of Game of 24 1; g) 3, 5, 6, 7; h) 7, 7, 3, 10; i) 9, 3, 4, 9 and j) 4, 10, 1, 4. The meeting starts with making three members group, 2 Students were asked to arrange those number use +, ×, •, and persons as players and 1 person as a judge. The game use ÷ signs to get the result 24. Most of students got the right sets of ―handmade‖ of cards, each card consist of four answer with mental computation when playing game but had numbers. Player who first get 24 with arithmetic operations problems when communicating their mathematical ideas in keep the card. Player who has more cards wins the game. The difficulties level of cards is different. The 24 game students‘ 3318 IJSTR©2019 www.ijstr.org INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 12, DECEMBER 2019 ISSN 2277-8616 activities can be seen in figure 4 below. 3.1.2.1 First Meeting of Game of 15 Learning was started with technical explanation about game 15 rules by researchers. Furthermore, students were divided in two groups and compared them in a competition with the role as player 1 and player 2. Before competition was started students tried in the group to exercise game 15. In this process researchers act as controllers of the class let students play by themselves. When students finished, researchers ask the winner of the game about their strategy. The game 15 activities can be seen in figure 5 below.

Fig. 5 Students’ Activities in Playing the Game 15 Fig. 4 Students’ Activities in Playing the Game 24 After each group finished exercises, two groups were asked to At the first of game many students have difficulties to come in front of the class to play the game and researchers recognize what operation should be used. For example, some act as instructors to finish the game. Instructor writes numbers students in different group need more time to understand or to 1-9 in the whiteboard and the groups must be finished the get a sense until they choose a strategy to use +, ×, •, and ÷ game. Each group get opportunity to be first player to make signs. Then, they solved the problem. If any group is too long fair competition. Based on this first game, strategy that is used to solve the problem, the researcher comes on them to give still not appear yet because some of groups were seen just scaffolding. The score of groups can be seen in table 7 below. mention the numbers and focus on their own expectation result. In this game the number sense of students has not TABLE 7 been seen. SCORE OF PLAYING THE GAME 24 AT THE SECOND MEETING 2 3.1.2.2 Second Meeting of Game of 15 The meeting is started by make a student group with member two persons with the name of the groups are A, B, C, D, and E. Two groups were compete each other, which shown by figure 6 below.

From the winning groups, each group compete each other. After finishing the second game, students are given questions, as in the first meeting but with different set of numbers, including a) 1, 2, 6, 6; b) 2, 4, 8, 8; c) 1, 5, 5, 9; d) 5, 6, 8, 9; e) 2, 2, 4, 7; f) 1, 3, 4, 7; g) 2, 5, 6, 8; h) 2, 2, 3, 5; i) 3, 3, 6, 8; j) Fig. 6 Students Compete Game 15 in Front of The Class 2, 3, 5, 7. The result of this test is some problems persist and they can write slightly better than their first try. Students were In the second meeting the game was held in two rounds. First fluent in fast calculation competition to get the result in this round is competing groups each other and each group gets game, but some of students difficult to write the answer in twice opportunities to make fair game. The result of the first writing. Moreover, there was student who were very fast in round can be seen in table 8. mental computation did not want to write the answer. Most students have to understand how to put the operation signs. TABLE 8 As an example, a student does not understand that the result SCORE OF STUDENTS OF THE FINAL PLAYING OF THE GAME 15 of 1 × 2 × (6 + 6) and 1 × 2 × 6 + 6 was different. This was a constraint of student to write the answer in mathematical writing.

3.1.2 Learning Use Game of 15 In this game 15, students understand about numbers sense in arithmetic operation if the game was draw. Game 15 activities were held in two meetings with explanations following.

It can be seen from table 8 that most of students only focus on 3.2 Number Sense Ability Analysis After the Learning used how to get 15 but often fail to prevent their opponent to get 15. Mathematical Games After finishing the game 15, students are given 3 tasks as Diagnostic test is given to assess students‘ prior knowledge of follows: numbers sense. Diagnostic test consist of 8 questions that 1. List all the three different numbers, choose among 1, 2, contain 5 indicators. Subject of this diagnostic test are Surya 3, 4, 5, 6, 7, 8, 9 so that their sum equal to 15. Intensive Program (SIP) students grade V and grade IV. 2. List all the three different numbers, choose among 10, Students do diagnostic test for arithmetic operation like 20, 30, 40, 50, 60, 70, 80, 90 so that their sum equal to addition, subtraction, multiplication, and division related to 150. number sense. Diagnostic test questions was also used to 3. List all the three different numbers, choose among number sense test for participants to see a changes students‘ 11,12, 13, 14, 15, 16 , 17, 18, 19 so that their sum equal number sense ability after mathematics learning use to 45 mathematical game 24 and game 15. A number sense question that is tested has been validated by mathematics There are relations among the questions number 1, number 2, lecturer in Surya College of Education, Tangerang, Indonesia. and number 3. Based on students‘ works, it can be seen that Based on diagnostic test we saw that students lack of students were not difficult to finish those questions but there numbers sense understanding, students grade IV have correct were things that were not understood by students. As an answer as many as 23.38% and students grade V have example, if questions number 1 has been finished then correct answer as many as 32.83%. Moreover, average score question number 2 does not need to be calculated. Students of students based on grade are very low. The average score of just have to see the relation that question number 1 has a grade IV is 1.06 and average score of grade V is 1.45. As relation with question number 2 that is the kind of tens and comparison the highest score is 3 correspond to numbers question number 1 is ones, similarly to question number 3. sense rubric score. Diagnostic test score of students grade IV What was happened to the works are most of students that is used as a pretest score of participants. Moreover, this struggle to solve the second and third tasks. Almost all score was compared with posttest score after mathematics students got the ideas after we gave them some clues, such learning use game 24 and game 15. It can be seen in table 9. as this dialog. Researcher : ―Look at the equations that you have written TABLE 9 before!‖ SCORE OF STUDENTS OF THE FINAL PLAYING OF THE GAME 15 Students : Common reactions ―ah, add a zero!‖ Researcher : ―What the meaning of adding zero?‖ Students : Common Answer ―Just add zero, multiply by zero‖ When we further asked the meaning of ‗adding zero‘, the students got confused. Few students realize that to change 4 to 40, just have to multiply by 10. The same thing happened, when we ask how to change 8 to 18. Researcher : ―Look at this, how to change 8 to 18‖, Students : Common reaction ―add 1, or multiply by 1!‖. Students have common answer ‗add 1‘ and ‗multiply by 1‘, students learned by rote learning. Then, we continue the questions.

Researcher : ―How about 4 × 300?‖ Students : ―1200‖ It can be seen from table 8 that many students easily solved Researcher : ―How it can be?‖ the problems related to computing and counting strategy, Students : ―4 × 3 = 12, then add 2 zeros‖ especially on using informal strategy, as many as 2.23 out of When we asked what 4 × 300 is, most students immediately 3. The lowest ability was when students were asked to found the answer. But, when we asked the process, most of estimate the number of boxes needed without doing actual students said 4 × 3 = 12 and simply add 2 zeros. They have division, as many as 0.48 out of 3. The average of number no idea what the mathematical meaning of adding those two sense posttest score was 1.27 out of 3. There was increasing zeros is. The examples of students‘ works can be seen in of the number sense score. The difference of the score was figure 7. 0.57 and the percentage as many as 18.91%. It can be concluded that students have better number sense ability after the learning used game 24 and game 15.

3.3 Students’ Response Based on the response of the questionnaire about learning used mathematical game 24 and game 15, it seems that students have positive response as many as 69.75 %. These findings were supported by the improvement of students‘

Fig. 7 Students’ Works of Game 15 Questions number sense competence based on their post test score. Observation during the learning showed that students were active and enthusiastic in using the game. Moreover, number sense has been appeared in students were seen from different 3320 IJSTR©2019 www.ijstr.org INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 12, DECEMBER 2019 ISSN 2277-8616 strategies used in solving the problems. [4] National Council of Teachers of Mathematics Commission on Standards for School Mathematics. Curriculum and evaluation 4 CONCLUSION standards for school mathematics. Reston VA: The Council, Learning used mathematical games like game 24 and game 1989. Available at http://www.standards.nctm.org/index.htm, 15 can be one of learning strategies to stimulate students‘ May 2013. number sense in arithmetic operation. It was implemented by [5] G. W. Bright, J. G. Harvey, & Mqr, ―Learning and mathematics separating students in groups to make students compete and games. Journal for Research in Mathematics Education. cooperate with others. This learning can also improve Monograph, 1, i-189, 1985. students‘ number sense ability. The difference of pretest and [6] J. Gough, ―Playing mathematical games: When is a game not posttest is 0.57 out of 3 or as many as 18.91%. Students are a game?,‖ Australian Primary Mathematics Classroom, vol. 4 so actively participate with this learning. It shows from the no. 2 pp. 12-15, 1999. positive response of students about the learning which gain [7] J. Way. Learning Mathematics Through Games Series: 1. 69.75%. Otherwise, we found that participants Papuan Why Games?, 2011. Available at https://nrich.maths.org/2489, Students were usually get bored easily, physically active and Jun 2013. aggressive but also they need some time to adjust with a new [8] B. Oldfield, Games in the Learning of Mathematics. Part 1: A teacher. The outcome of this research shows that learning Classification. Mathematics in School, vol. 20 no. 1, pp. 41-43, mathematics used game 24 and game 15 in arithmetic 1991. operation improved students‘ number sense ability, therefore [9] Davies, B. ―The role of games in mathematics. Square One . this learning strategy recommended to use in other Vol.5. No. 2, 1995. mathematical topics such as algebra, geometry, probability, [10] A. M. Triplett, A Closer at the 24 Game. International Journal etc. On the other hand students‘ mathematical games learning of Applied Science and Technology, vol. 1 no.5, pp. 161-164, also recommended to find other students‘ abilities, are more 2011. specific in mathematics. Students had good response related [11] J. Mahoney, What the Name of this Game. Mathematics to mathematical games learning, game 24 and game 15 Teaching in the Middle School, vo. 11 no. 33, pp. 150-154, specifically. As a result, future learning could use other 2005. mathematical games as an innovative strategy. Because this [12] Sugiyono, Research Methods in Education ―Metode Penelitian research was qualitative method which is carried out to 13 Pendidikan‖, Bandung: Alfabeta, 2013. students of 4th grader in private school, the major limitation of [13] N.F. Helmy, R. Johar, and Z. Abidin, ―Student‘s Understanding the research was the generalization of its conclusion. of Numbers Through the Number Sense,‖ Proc. The 6th South However, this research could be a reference for researchers in East Asia Design Research International Conference (6th research, course, or other studies. Furthermore, the future SEA-DR IC), 2018. research can be conducted to address such this issue in [14] J.A. Blando, A.E. Kelly, B.R. Schneider, & D.Sleeman, quantitative research or in bigger population. ―Analyzing and modeling arithmetic errors,‖ Journal for Research in Mathematics Education, Vol. 20 No. 3, pp. 301- ACKNOWLEDGMENT 308, 1989 We would like to express our gratitude to Miss Ani Fransisca [15] I. Papadopoulus and R. Gunnarson, ―The Use of ‗Mental‘ as a class advisor of grade IV in SIP who help us to control Brackets When Calculating Arithmetic Expressions,‖ and monitor students in this study. We would also like to thank Proceedings of the 42nd Conference of the International to lecturers in Mathematics Education Department of Surya Group for the Psychology of Mathematics Education, Vol. 3, College of Education, the students and all stake holders who pp. 451-458, 2018. support our research. This research was fully funded by Surya [16] L. Sammons, Teaching Students to Communicate College of Education. Mathematically, 2019, available at http://www.ascd.org/publications/books/118005/chapters/The-

Essentials-of-Mathematical-Communication.aspx, Aug. 2019. REFERENCES [1] T. Herman, Mental Strategies that Used by Elementary School Students in Numeracy ―Strategi Mental yang Digunakan Siswa Sekolah Dasar dalam Berhitung,‖ presented in National Seminar of Mathematics Education in Universitas Negeri Yogyakarta (UNY), Yogyakarta-Indonesia, 2001, available at http://file.upi.edu/Direktori/FPMIPA/JUR._PEND._MATEMATIK A/196210111991011-TATANG_HERMAN/Artikel/Artikel16.pdf, Jun. 2013. [2] A. McIntosh, B. J. Reys, and R. E. Reys, ―A Proposed Framework for Examining Basic Number Sense," For the Learning Mathematics, vol. 12 no. 3, pp. 2–8, 1992. [3] J. G. Rosenstein, J. H. Caldwell, and W. D. Crown, ―New Jersey Mathematics Curriculum Framework: A Collaborative Effort of the New Jersey Mathematics Coalition and the New Jersey Department of Education,‖ New Jersey: Rutgers University, 1996.