Error Analysis of Trigonometric Problem Solving by Vocational High

School Students Based on Differences in Ability and Cognitive Style

Liknin Nugraheni

, Nur Fathonah

, Sri Rahayu

and Esti Widhiarni

Universitas PGRI Adi Buana Surabaya, Jl. Ngagel Dadi III-B No. 37, Surabaya 60245, Indonesia

Institut Teknologi Adhi Tama Surabaya, Jl. Arif Rahman Hakim No. 100, Surabaya 60117, Indonesia

{liknin, nurfathonah, srirahayu}@unipasby.ac.id, esti_widhi@yahoo.com

Keywords: Cognitive styles, error analysis, vocational high schools.

Abstract: The purpose of this study was to describe the locations, types and contributing factors of the students of

mechanical Vocational High Schools in solving trigonometry problems. This was descriptive research. The

research was conducted in three vocational high schools. The main instrument in this research was the

researcher himself. Other instruments used in the research were test of mathematical ability (TOMA), The

Group Embedded Figures Test (GEFT), trigonometry problem solving tasks and interview guides. The

research data were analyzed in four stages, namely: data categorization, data reduction, data presentation,

conclusion drawing. The results obtained by discovering the locations, types, and contributing factors of the

students’ errors could reveal whether or not the learning that had been implemented in accordance with the

goals to be achieved. By doing the analysis of the students’ errors, the appropriate learning model to improve

their understanding of trigonometric problem solving in particular and improve the mathematic learning

outcomes in general is therefore recommended.

1 INTRODUCTION

Mathematical problem solving has become the center

of attention in 2013 curriculum recentnly

(Kemendikdub, 2014; Depdikbud, 2016). Many

Indonesian children have difficulty in solving

mathematical problems (Tatag, Y.E.S., et al., 2015).

Based on the result of preliminary study conducted by

researchers at 3 mechanical vacational high school in

East Java Indonesia, was that only 15% of students

able to solve mathematical problems especially

trigonometry well. To overcome these problems and

to find out the reasons that cause low understanding

of trigonometric problem solving , It is necessary to

analyze the mistakes made by mechanical vacational

high school student.

Some studies have shown that cognitive style is a

very important thing in learning (Acharya, 2002;

Tenant, 1988; Kagan, 1966; Egelan, 1974; Witkin, et

al., 1977; Witkin, et al., 1971; Tantiana, A. G., Iriana,

A. L., 2014). By knowing the cognitive style of

learners, teacher can use appropriate method in

teaching mathematical concepts, especially

trigonometry for those who have a particular

cognitive style. The cognitive style used in this study

is the cognitive style of Field dependent and Field

independent.

Students with a field dependent cognitive style are

difficult to separate items of an object from their

original form (Witkin, et al., 1971; Slameto, 2003).

Students with independent field cognitive style are

students who are able to abstract elements from their

context, they tend to be more analytic and tend to use

problem-solving approaches in a more analytic way

(Witkin, et al., 1977; Slameto, 2003).

Witkin, et al. (1971) states that, cognitive style is

a characteristic reflected from each individual and

these characteristics can be influenced by two factors,

namely: factors related to the influence of external

stimuli and individual personal influences. The

external stimulus factors is the dominant enough to

affect psychiatric problems, such as educational

environment, family environment, and community

environment.

Besides the cognitive styles, the different aspects

of students' abilities influences the mathematical

problem-solving abilities (Astunnisyah, Budiono,

Isnandar, S., 2017; Sukriadi, A., Juniati, D., Tatag,

Y.E.S., 2017; Utomo, E.S., Juniati, D., Tatag, Y.E.S.,

2017). Problem solving is defined as an attempt to

find out solution of difficult probme to achieve goals

428

Nugraheni, L., Fathonah, N., Rahayu, S. and Widhiarni, E.

Error Analysis of Trigonometric Problem Solving by Vocational High School Students Based on Differences in Ability and Cognitive Style.

In Proceedings of the 1st International Conference on Educational Sciences (ICES 2017) - Volume 1, pages 428-432

ISBN: 978-989-758-314-8

(Polya, 1973). While Cooney et al. (1975) suggested

that problem solving as a process of accepting

problems and trying to solve the problem. Problem

solving is form of a mental activity consisting of

various cognitive skills and actions intended to obtain

the correct solution (Kirkley, 2003). Thus, the

solution of the problem among individual is different.

The stages of problem solving in this study refers

to Polya's opinion (1973). Polya’s problem-solving

steps are from (1) understanding the problem, (2)

making problem-solving plan, (3) implementing

problem solving plan, (4) reviewing problem solving

result. While the aspect of ability selected from

students who have high, medium, and low ability.

The reasons why students feel difficult to solve

trigonometry problem can be reviewed from students’

method in solving trigometry problems. Therefore, it

is important to make an error analysis of students in

solving the trigonometry problem. The errors of

Students that are analyzed include (Polya, 1973) the

location, the type (Soedjadi, 2000), and the error

influencing factor. After knowing the location, type,

and error influencing factors made students in solving

trigonometry problem, the alternative solution can be

determined. Thus, it is expected that by analyzing

students’ error we can improve their understanding of

trigonometric problem solving in particular and

improve their mathematics learning outcomes in

general.

2 RESEARCH METHOD

The design of this study used descriptive research to

describe the location, type and error influencing

factors of student in solving the trigometry problems.

While the approach used in this study is a qualitative

approach because the data collected and presented in

the form of words that are arranged in a sentence,

rather than a number or value.

The subjects of this study were students with high

ability and field dependent and field independent

cognitive style, and students with moderate ability of

field dependent and field independent cognitive style,

and students with low ability of field dependent and

field independent cognitive style.

In addition to the researcher as the main

instrument, other instruments are needed as well such

as test of mathematical ability (TOMA) instruments,

problem-solving tasks, The Group Embedded

Figures Test (GEFT), and interview guidelines. The

data were collected using tests and interviews to

determine the location, type, and error influencing

factors made by the subject of research. The location

of the error viewed from the mistake made by the

subject while solving problem in using Polya’s steps.

The type of error refers to instruments made by

Sudjadi (2000), for instance ; factual errors, concepts,

operations, and principles. Error influencing Factor

relates to internal factors. Data analysis started from

the preparation of the research to the completed data

collection process. In this research, data analysis

technique is done through 4 stages, namely: data

categorization, data reduction, data presentation,

conclusion drawing

3 RESULTS AND DISCUSSION

3.1 Results

The Subjects of this research are Students of

mechanical vocational high school in East Java

Indonesia, selected using test of mathematical ability

(TOMA). The result of test is the form of score and

then is categorize as high ability (if their score is >

87), categorized as moderate ability (if their score is

more than 67 and less than 87), and categorized as

low ability (if their score is below 67).

The next step is giving the selected students a test

of mathematical ability (TOMA). The results of

GEFT results are assessed based on the guidelines

developed by Witkin, ie students who get score

between 0-9 in sections 2 and 3 are classified into the

field dependent (FD) cognitive style while students

who get score between 10-18 is classified in the field

independent (FI) cognitive style.

To determine the subject of study needs to be

tested using GEFT for 3 times, so that the selected

subject is really in accordance with the cognitive

style. Based on the distribution of mathematics

ability, cognitive style, teacher’s consideration, and

score of their learning report, so that the 6 subjects are

categorized as high, moderate, and low ability and

field dependent (FD) and field independent (FI)

cognitive style.

To determine the location, type, and error influencing

factors in solving the trigonometry problem

conducted subjects is based on differences in ability

and cognitive style in general is found in all stages

beginning at understanding the problem, planning the

problem-solving, solving the problem, reviewing the

result of problem solving.

3.2 Discussions

Based on the analysis and the results of the research,

the location of the errors of students with low ability

Error Analysis of Trigonometric Problem Solving by Vocational High School Students Based on Differences in Ability and Cognitive Style

429

and field dependent cognitive style in solving

mathematical trigonometry problem is found in all

stages beginning at understanding the problem,

planning the problem-solving, solving the problem,

reviewing the result of problem solving. While the

type of error that students with low ability and Field

Dependent cognitive style is all kinds of errors

ranging from fact, concept, opration, and principle

errors that spread at all stages of problem solving.

While error influencing factor in general are internal

factors caused by the intellectual ability, and the

cognitive conditions of the subject.

The error location of students with low ability and

field independent cognitive style in solving

mathematical trigonometry problem is found in all

steps: beginning at understanding the problem,

planning the problem-solving, solving the problem,

reviewing the result of problem solving. The type of

error that subjects with low ability and Field

Independent cognitive style is type of factual error

and principles at all stages of problem solving. While

error influencing factors in general are internal factors

caused by the intellectual ability, and the cognitive

conditions of the subject.

If compared between subjects with low ability and

field dependent cognitive style and subjects with the

low ability and Field independent cognitive, both of

them have similarity and differences. The similarity

is that both of them make mistakes at all stages of

problem solving. While the difference is subjects with

low ability and Field Independent cognitive style only

do 2 types of errors, but subjects with low ability and

Field dependent cognitive style make 4 types of

errors at once.

Error location of subjects with moderate ability

and Field Dependent cognitive style in solving

mathematical trigonometry problem is found in all

stages beginning at understanding the problem,

planning the problem-solving, solving the problem,

reviewing the result of problem solving. While the

types of mistakes made by subjects with moderate

ability and Field Dependent cognitive style are all

types of errors ranging from factual errors, concepts,

operations, and principles that spread at all stages of

problem solving. While the error influencing factors

in general are internal factor caused by the intellectual

ability, and the cognitive conditions of the subject.

The error location of subjects with moderate

ability and Field Independent cognitive style in

solving mathematical trigonometry problem is found

in three stages beginning at, planning the problem-

solving, solving the problem, reviewing the result of

problem solving. Subjects with moderate Field

Independent cognitive style do not make mistakes

(error) at understanding problem stage. The types of

mistakes made by subjects with moderate Field

Independent cognitive style are all types of errors

ranging from error concepts, and principles that

spread at all stages of problem solving. While the

error influencing factors in general are internal factors

caused by the intellectual ability, and the cognitive

conditions of the subject.

If compared between subject with moderate

ability and Field Dependent cognitive style and

subject with moderate ability and Field independent

cognitive have difference in location and types of

error made by them. The error of location that is

conducted by subject with moderate ability and Field

Independent cognitive style is located in three steps

of planning the problem solving, implementing the

problem solving and reviewing the problem solving

result. While The error of location that is conducted

by subject with moderate ability and Field Dependent

cognitive style is located in all steps, beginning from

understanding the problem, planning the problem

solving, implementing the problem solving and

reviewing the problem solving result.

While the type of error made by subject with

moderate ability and Field Dependent cognitive style

are all types of errors such as factual error, concepts,

operation, and principles. These types of errors spread

at all stages in problem solving. And 2 types of errors

made by subject with moderate ability and Field

Independent cognitive style that are concept and

principle errors that spread only at each stage of

problem solving except the stage of understanding the

problem.

The error location of subject with high ability and

field dependent cognitive style in solving

mathematical trigonometry problem is found 3 steps:

beginning at planning the problem-solving, solving

the problem, reviewing the result of problem solving.

The type of error that subjects with high ability and

Field Independent cognitive style is error principles

spread in stages of problem solving such as planning

the problem solving, implementing the problem

solving and reviewing the result of problem

solving.While error influencing factors in general are

internal factors caused by the intellectual ability, and

the cognitive conditions of the subject.

The subject with High ability and Field

Independent cognitive style do not make mistakes in

all steps of problem solving. The error influencing

factor in general are internal factors caused by high

intellectual ability, and cognitive conditions of the

Subject.

If compared between subject with high ability and

Field Dependent cognitive style and subjects with

ICES 2017 - 1st International Conference on Educational Sciences

430

high ability and Field independent cognitive style has

differences in the location and type of errors that are

made by them. The error location of subject with high

ability and Field Dependent cognitive style is found

in 3 steps: that are at planning the problem solving,

implementing a problem-solving, and reviewing the

results of problem-solving. While subjects with high

ability and Field independent cognitive style do not

make errors in solving the trigonometry problems.

Based on the results, analysis, and discussion of

research, it can be found that the cognitive style

influences the process and the results of trigonometry

problem solving of subjects with low, medium, and

high ability. The subject with Dependent cognitive

style make more mistakes (both error location and

types of error), than subject with Independent

cognitive style. This is in line with the results of

research conducted by Andi sukriani, edy, and

astunisyah that the cognitive styles (FI and FD)

possessed by high school students influence the

results of mathematical problem solving

(Astunnisyah, Budiono, Isnandar, S., 2017; Sukriadi,

A., Juniati, D., Tatag, Y.E.S., 2017; Utomo, E.S.,

Juniati, D., Tatag, Y.E.S., 2017). But in the study they

did not see the location, type, and factors that

influence the mistakes made by students in solving

mathematical problems.

4 CONCLUSIONS

The error location of the errors in solving

mathematical trigonometry problem by students with

low ability and field dependent-field independent

cognitive style is found in all stages beginning from

understanding the problem, planning the problem-

solving, solving the problem, and reviewing the result

of problem solving. While the error type of students

with low ability and Field Dependent cognitive style

is all kinds of errors ranging from fact, concept,

opration, and principle errors that spread at all stages

of problem solving. The error type of subjects with

low ability and Field Independentcognitive style is

type of factual error and principle at all stages of

problem solving.

Error location in solving mathematical

trigonometry problem of subjects with moderate

ability and Field Dependent cognitive style is found

in all stages. While the types of mistakes made by

subjects with moderate ability and Field Dependent

cognitive style are all types of errors ranging. The

location of the errorsof subjects with moderate ability

and Field Independent cognitive style in solving

mathematical trigonometry problem is found in three

stages, such as planning the problem-solving, solving

the problem, reviewing the result of problem solving.

Subjects with moderate Field Independent cognitive

style do not make mistakes (error) in understanding

problem stage. The types of mistakes made by

subjects with moderate Field Independent cognitive

style are all types of errors ranging.

The error location of subject with high ability and

field dependent cognitive style in solving

mathematical trigonometry problem is found 3 steps:

beginning at planning the problem-solving, solving

the problem, reviewing the result of problem solving.

The error type of subjects with high ability and Field

Independent cognitive style is error principles spread

in stages of problem solving such as planning the

problem solving, implementing the problem solving

and reviewing the result of problem solving. The

subject with high ability and Field Independent

cognitive style do not make mistakes in all steps of

problem solving.

While error influencing factors made by students with

high, moderate, and low ability and Field Dependent

or Field Independent cognitivestyle in general is an

internal factor caused by intellectual ability, and the

cognitive conditions of the Subject.

ACKNOWLEDGEMENTS

The author would like to thank the Ministry of

Research and Technology for providing the grants to

the author.

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