How Are High IQ Students Thinking in Making Mathematical

Connections in Solving Mathematics Problem?: A Case of Gender

Difference

Karim

, I Ketut Budayasa

, Tatag Yuli Eko Siswono

Universitas Lambung Mangkurat, Banjarmasin, Indonesia

Universitas Negeri Surabaya, Surabaya, Indonesia

Keywords: thinking, mathematical connections, gender.

Abstract: The study aims to describe male and female high IQ students thinking of making mathematical connections.

The qualitative-explorative research was conducted with two students of 12th grade who have high IQ.

There were male and female students. The data was collected through interviews and analyzed by data

reduction, data display, and conclusion drawing/verification. The results of this research are that a male high

IQ student did processing of thinking consist of some steps. First, he accepted information by reading

mathematical problems, doing attention and rehearsal, then recall and recognition some information on

mathematical concepts. He manipulated the information by making the connection between mathematical

concepts and principles in solving the mathematical problem. He created six different ways to find the

solution. The six ways were Pythagoras Theorem (first way), tangent rules, sinus rules, Pythagoras Theorem

(second way), wide triangle, and scale. A female high IQ student actually made connections relatively

similar to the male student. She could use similar steps but she created five different ways to find the

solutions. The five ways were sinus rules, Pythagoras Theorem, tangent rules, triangular area, and scale. The

male and female students are also different in recalling information at the time-solving problems using

Pythagoras Theorem and triangular area.

1 INTRODUCTION

The mathematical connections can be interpreted as

the connections between mathematical concepts,

principals, topics; the relation between mathematics

and other disciplines, and the link between

mathematics and real-life context problems (NCTM,

1989; Goos, Gloria, Colleen, 2007; NCTM, 2000).

The mathematical connections is the implication of

mathematics as a single unity. Thus, in order for the

students to be successful to learn mathematics, they

have to be given opportunities to see the connection,

either between mathematical concepts principles,

concepts, and branches. The mathematical

connections is one of the skilled processes in

mathematical learning. Kemendikbud (2014)

explains the importance of mathematical

connections in mathematical learning which is

included in the 2013 Curriculum.

In order to create a mathematical connection, it

needs a process of thinking. Thinking is a process

which produces mental representation through the

transformation of information to help in formulating

and solving a problem as well as taking a decision

(Ruggiero, 1984; Solso, 2001). One of the widely

used thinking theories is Information Processing

Model. According to this theory, the processing of

information in memory is including the process of

encoding, storage, and retrieval. Encoding is the

process of inserting information to the memory,

storage is the retention of information from time to

time, and retrieval is recalling information for the

memory (Santrock, 2010; Slavin, 2011). The

differences of student’s individual which is

commonly becoming the research focus on the

education discipline are intelligence and gender.

Intelligence is the skill to act with aims, solve the

problems, think rationally, adapt to the environment,

and learn from daily life (Santrock, 2010; Stemberg,

2008; Winkel, 2009). Intelligence Quotient (IQ) is a

score received from an intelligence test tool which

describes the level of someone’s intelligence. A

student is said to have high IQ if he/she is on the

superior or very superior level. Meanwhile, gender is

Karim, ., Budayasa, I. and Siswono, T.

How Are High IQ Students Thinking in Making Mathematical Connections in Solving Mathematics Problem?: A Case of Gender Difference.

DOI: 10.5220/0009016200002297

In Proceedings of the Borneo International Conference on Education and Social Sciences (BICESS 2018), pages 48-51

ISBN: 978-989-758-470-1

a trait attached to the male or female which is

influenced by the conditions of social and cultural.

The male individual has masculine traits while the

female individual has feminine traits (WHO, 2015;

Showelter, 1989) The gender difference has a high

influence on the differences in the students’ thinking

process of creating mathematical connections.

The research result (Deary, Strand, Smith, and

Femandes, 2007) stated that there is a significant

positive correlation between IQ and students’

learning achievements. (Zhu 2007)reported that

there are differences of abilities between male and

female in solving mathematical problems which are

located on the abilities of spatial, verbal, and

quantitative. Sugiman and Ruspiani (Sugiman, 2010;

Ruspiani, 2000) respectively reported their research

about the low ability of mathematical connection

among junior and senior high school students which

will imply on the low students’ ability to solve

mathematical problems and their result. The research

(Sugiman, 2010; Ruspiani, 2000) had not describe

the students’ thinking process in making the

mathematical connection. Thus, it needs further

research to get the description about students’

thinking process of creating mathematical

connections. In order for classical learning to be

successful, the individual differences also need

attention. So, this research will relate to

mathematical connections, IQ, and gender. The goal

of this research is to describe the thinking process of

high IQ male and female students in making the

mathematical connections. The type of this research

is explorative with a qualitative approach. The

subject is focused on high IQ students because they

have the potential to make a good mathematical

connection..

2 METHOD

This research uses an explorative type of research

with the qualitative approach. The subjects of this

research are two students of 12th grade in state

senior high school 1 Banjarmasin which consists of

1 high IQ female and 1 male student. Both subjects

have relatively the same IQ level and mathematical

ability. The students’ IQ is measured by a

psychologist. Meanwhile, their mathematical ability

is measured using tests and based on their report

score. In this research, both subjects IQ are the

same, which is 123 (superior).

The instruments which are used in this research

consists of the researcher as the main instrument,

student worksheet, and interview guidance. The

analytical procedure (Miles & Huberman, 1994)

model that includes data reduction, data display, and

conclusion drawing/verification. The result data of

this research will be explained according to the

Information Processing Theory. This is the

following student worksheet.

Joshua is a member of the Basketball Team of

senior high school 1 Banjarmasin. One day after

training, he stands on a school park corner while

seeing to the flag attached to the flagpole on the

school field. It was known that the distance between

his toe and eyes is 170 cm. On his standing position,

he saw the peak of the flagpole and formed on the

elevation angle of 15o. Later, he walked straight to

the flagpole for 29,5 m and saw the peak of the

flagpole with the elevation angle of 45o. Determine

the height of the flagpole!.

3 RESULT AND DISCUSSION

3.1 Thinking Process of High IQ Female

Student

The following thinking process of high IQ

female student in making the mathematical

connections.

a. Female student (FS) received the information by

reading the mathematical problem repeatedly

(rehearsal), doing attention, trying to recognize

the mathematical concepts and principles on the

problem, and continued by processing

information through representing her idea in

form of a sketch to make it easier in

understanding the problem.

b. After she understood the problems, FS make a

plan and does it through recognizing and using

the relation between mathematical concepts and

principles, as well as using a certain calculating

operation. FS sets five solving plans and then

implements it. The five sets respectively are

sinus rules, Pythagoras Theorem, tangent rules,

triangular area, and scale.

c. FS rechecked her works by matching

information on the mathematical problems with

her answers. FS processes information through

recognizing equivalent representation from the

same concept so she concluded that the

mathematical problems can be solved through

three approaches: geometry, trigonometry, and

algebra.

d. FS recalled information through recall and

recognition. The recall is happened when

How Are High IQ Students Thinking in Making Mathematical Connections in Solving Mathematics Problem?: A Case of Gender Difference

remembering, ever experienced the similar

problem but more simple and can be solved

only in one way. Meanwhile, recognition

happens when remembering mathematical

concepts and principals related to the problem-

solving. FS was able to recall mathematical

materials from elementary school, junior high

school, and high school which was she learned.

The concepts of triangular area and Pythagoras

Theorem were recognized by FS since learning

mathematics in elementary school.

3.2 Thinking Process of High IQ Male

Student

The following thinking process of high IQ male

student in making a mathematical connections.

a. Male student (MS) received the information by

reading the mathematical problem repeatedly

(rehearsal), doing attention, trying to recognize

the mathematical concepts and principles on the

problem, and continued by processing

information through representing her idea in

form of a sketch to make it easier in

understanding the problem.

b. After he understood the problems, MS made a

plan and does it through recognizing and using

the relation between mathematical concepts and

principles, as well as using a certain calculating

operation. FS sets 6 solving plans and then

implements it. The six sets respectively are

Pythagoras Theorem (first and second way),

tangent rules, sinus rules, triangular area, and

scale. For the solving using Pythagoras Theorem,

MS did it using two distinct ways. The solving

using Pythagoras Theorem (first way), tangent

rules, sinus rules, triangular area, and scale, is the

same idea which is used by FS. However, the

second way of Pythagoras Theorem is a different

idea.

c. MS recheck his work by matching the

information on the mathematical problems using

the answer he got. MS processed the information

by recognizing the equivalent representation

from the same concept so it can be concluded

that mathematical problem can be solved using

three approached: algebra, geometry, and

trigonometry.

d. FS recalled information through recall and

recognition. The recall is happened when

remembering, ever experienced the similar

problem but more simple and can be solved only

in two ways. Meanwhile, recognition happens

when remembering mathematical concepts and

principals related to the problem-solving. FS was

able to recall mathematical materials from junior

high school and high school which he learned.

MS was able to recall the junior high school and

senior high school materials.

MS and FS had solved mathematical problems

using various ways. It shows that they were able to

create mathematical connections using many

mathematical concepts and principles. This is

supported by Hodgson (1995) who stated that

mathematical connections as a tool to solve

mathematical problems. It means that when a

student can make more mathematical problems, it

will be easier for him/her to solve the problems and

the ways he/she solves the problems will be more

varies. This is also supported by Winkel (Suhaman,

2005) who stated that high IQ students have chances

that materials management will be deeper so it can

improve memory achievement which is very needed

when a student solves mathematical problems.

The thinking process of MS and FS as a whole is

relatively the same, either when receiving,

processing, and recalling information. This can

happen because both students have high IQ. It is in

line with Suharnan [20] who stated that there are 4

abilities which are had by high IQ students, those are

a short memory, general knowledge, reasoning and

problem solving, and adaptiveness.

Despite the relatively the same thinking process,

but there are a few differences in terms of the

numbers of solving ways and the recalled

mathematical materials when solving a problem. The

solving problems by MS are the same idea as 5

solving ways created by FS. However, when MS

used Pythagoras Theorem, MS can develop it with

first and second way. Another difference is when FS

can recall materials she learned in elementary, junior

high, and senior high school. Meanwhile, MS can

only recall the materials he learned in junior high

and senior high school. This difference can happen

because according to Jensen (2008) the factors that

can influence a certain ability between male and

female student are the development of psychologic,

physical, and brain. This is also explained by Slavin

[8] that by processing information is highly

influenced by the mind, past experiences, previous

knowledge, and motivation.

4 CONCLUSIONS

Base on result and discussion above it can be

concluded that the thinking process of high IQ male

BICESS 2018 - Borneo International Conference On Education And Social

and female student as a whole is relatively the same,

either when receiving, processing, and recalling

information. However, high IQ male student can

solve mathematical problems using six different

ways, while high IQ female student can solve it

using five ways only. This can happen because high

IQ male student can develop mathematical

connections on the implementation of the

Pythagoras Theorem. The male and female students

are also different in recalling information at the

time-solving problems using Pythagoras Theorem

and triangular area. The implication of this research

is on the students’ classical learning need to be

taught to recognize and use the connection between

mathematical concepts and principals with paying

attention to their thinking process. Thus, the

problems faced by the students in learning

mathematics can be known to be given help to the

individual.

REFERENCES

Moore, R., Lopes, J., 1999. Paper templates. In

TEMPLATE’06, 1st International Conference on

Template Production. SCITEPRESS.

Smith, J., 1998. The book, The publishing company.

London, 2

edition.

APPENDIX

Deary, I.J., Strand, S., Smith, P., & Fernandes, C. 2007.

Intelligence and Educational Achievement.

ScienceDirect, Intelligence 35.13-21, (www.

sciencedirect.com).

Goos, M., Gloria, S., & Colleen, V. 2007. Teaching

Secondary School Mathematics, Research and Practice

for the 21st Century. Australia: Allen & Unwin.

Hodgson, T. R. 1995. “Connections as Problem-Solving

Tools”, in year-book P.A. House (1995), Connecting

Mathematics across the Curriculum. Virginia: The

National Council of Teachers of Mathematics, Inc.

Jensen, E. 2008. Brain-Based Learning: Pembelajaran

Berbasis Kemampuan Otak, Cara Baru dalam

Pengajaran dan Pelatihan. Yogyakarta: Pustaka

Pelajar.

Kemendikbud. 2014. Peraturan Menteri Pendidikan dan

Kebudyaan No. 59 Tahun 2014. Tentang Kurikulum

2013 Sekolah Menengah Atas/Madrasah Aliyah.

Jakarta: Kemendikbud.

Miles, M. B., & Huberman, A. M.1994. Qualitative Data

Analysis. Second Edition. SAGE Publications.

International Educational and Professional Publisher.

NCTM. 1989. Curriculum and Evaluation Standards for

School Mathematics. Reston, VA: Arthur.

NCTM. 2000. Principles and Standards for School

Mathematics. Reston, VA: Arthur.

Ruggiero, V. R. 1984. The Art of Thinking. A Guide to

Critical and Creative Thought. New York: Longman,

An Imprint of Addison Wesley Longman, Inc.

Ruspiani. 2000. Kemampuan Siswa dalam Melakukan

Koneksi Matematika. Unpublished Thesis. Bandung:

Pendidikan Indonesia University.

Santrock, J.W. 2010. Psikologi Pendidikan. Edisi Kedua.

Penerjemah Tri Wibowo, B.S. Jakarta: Kencana.

Showalter, E. 1989. Speaking of Gender. New York &

London: Routledge.

Slavin, R.E. 2011. Psikologi Pendidikan, Teori dan

Praktik. Edisi Kesembilan. Penerjemah Marianto

Samosir. Jakarta: PT. Indeks.

Solso, R.L. 2001. Cognitive Psychology. Sixth Edition.

Boston: Allyn and Bacon, Inc.

Sternberg, R. J. 2008. Psikologi Kognitif. Edisi Keempat.

Terjemahan dalam Bahasa Indonesia (Penerjemah:

Yudi Santoso). Yogyakarta: Pustaka Pelajar.

Sugiman. 2010. Koneksi Matematika dalam Pembelajaran

Matematika di Sekolah Menengah Pertama. Artikel.

Jurusan Pendidikan Matematika, Universitas Negeri

Yogyakarta. Diperoleh dari http: //www.

staff.uny.ac.id/sites/default/ files/ 131930135/

2008_Koneksi_Mat.pdf.

Suharnan. 2005. Psikologi Kognitif. Surabaya: Srikandi.

WHO. 2015. What is gender. Diperoleh dari http:

//www.who.int/gender/whatis-gender/en/. Diakses

pada tanggal 5 November 2015.

Winkel, W. S. 2009. Psikologi Pengajaran.Yoyakarta:

Media Abadi.

Zhu, Z. 2007. Gender differences in mathematical problem

solving patterns: A review of literature. International

education Journal. 8(2), 187-203. ISSN 1443-1475,

(http: //iej.com.au).

How Are High IQ Students Thinking in Making Mathematical Connections in Solving Mathematics Problem?: A Case of Gender Difference