CJR KELOMPOK 3

CRITICAL JOURNAL REVIEW
TRIGONOMETRY
Arranged by
Group 3
Bertha Oktavika Sembiring
(4183111113)
Latifah Anggraini Siregar
(4181111001)
Mula Tua Elia Simbolon
(4183111064)
Supported Lecture
Andrea Arifsyah Nasution, S.Pd., M.Sc.
Study Program
Bilingual Mathematics Education 2018
Faculty of Mathematics and Natural Science
State University of Medan
2019
PREFACE
Praise and gratitude for the presence of the Almighty God, because of his mercy and
grace, we are from group 3 can complete this critical journal review (CJR) on time. The
theme of CJR is Analysis Student’s Errors in learn Trigonometry
This CJR is structured to fulfill one of the Trigonometry course assignments. On this
occasion, we would like to thank Mr. Andrea Arifsyah Nasution S.Pd, M.Sc as a lecturer in
Trigonometry courses who have supported us in the completion of this CJR.
This CJR preparation is far from perfect, and this is a good step from the real study.
Therefore we are very hopeful of constructive criticism and suggestions from the readers.
Hopefully, this CJR can be useful for compilers in particular and for general readers.
Medan, March 2019
Author
i
CONTENTS
PREFACE .................................................................................................................................. i
CONTENTS..............................................................................................................................ii
CHAPTER I ............................................................................................................................. 1
INTRODUCTION.................................................................................................................... 1
1.1.
Background of the paper ............................................................................................ 1
1.2.
Problem Formulation................................................................................................... 1
1.3.
Purpose of The Paper .................................................................................................. 1
CHAPTER II ............................................................................................................................ 2
JOURNAL’S IDENTITY ........................................................................................................ 2
2.1
First Journal ................................................................................................................. 2
2.2
Second Journal ............................................................................................................ 2
CHAPTER III .......................................................................................................................... 3
JOURNAL’S REVIEW ........................................................................................................... 3
CHAPTER IV......................................................................................................................... 13
CONCLUSION ...................................................................................................................... 13
4.1 Conclusion...................................................................................................................... 13
4.2 Suggestion ...................................................................................................................... 13
BIBLIOGRAPHY .................................................................................................................. 14
ii
CHAPTER I
INTRODUCTION
1.1.
Background of the paper
In learning mathematics especially in Trigonometry, everyone must face the
problem in learn it. Trigonometry is not an easy topic in mathematics but must have
good reasoning. In addition, there are so many students made many errors. In
trigonometry also student make repetitive errors in solved the question or in to
understand about that. Actually in learning mathematics especially in trigonometry, at
this time teachers just teach student how to remember about the equation but didn’t
make student understand full of the concept. And finally many students made errors.
So, because of that, we will discuss two journals which express about
Student’s Errors in Trigonometry.
1.2.
Problem Formulation
1. Based on the journal, what is the students errors in learning trigonometry?
2. What is contents both of two journals?
3. How the two journal express about Student’s errors in Trigonometry?
1.3.
Purpose of The Paper
1. To know about Students errors in learn Trigonometry based on the journals.
2. To revew or retell the contents both of two journals
3. To know how the difference both of description of two Journals.
1
CHAPTER II
JOURNAL’S IDENTITY
2.1 First Journal
Title
: Ghanaian Senior High School Students’ Error in learning Mathematics
Author
: Farouq Sessah Mensah
Name Journal
: International Journal of Environmental and Science Education
Year
: 2017
City
: Ghana
Volume
: 12
No.
:8
Page
: 1709-1717
2.2 Second Journal
Title
: Analysis of Students’ Errors in Learning of Trigonometry Among
Senior
Secondary School Students in Zaria Metropolis, Nigeria
Author
: Mu’awiya Haruna Usman and Muhammad Mukhtari Hussaini
Name Journal
: IOSR Journal of Mathematics
Year
: 2017
City
: Zaria
Volume
: 13
Page
: 1-4
E-ISSN
: 2278-5728
2
CHAPTER III
JOURNAL’S REVIEW
NO
1
REVIEWED
FIRST JOURNAL
ASPECT
Title
SECOND JOURNAL
Analysis of Student’ Error in Ghanaian
Learning
Senior
High
Trigonometry School Students’ Error in
of
Among
Senior
Secondary Learning of Trigonometry
School
Students
in
Zaria
Metropolis, Nigeria.
2
Abstract
 Research
1. To determine the Student’ 1. To
purposes
error
in
learning
of
error
trigonometry.
2. Find
out
students’
in
learning
trigonometry
the
categorization
analyze
possible
of
which
focused
these
on
the
manipulation
errors in the learning of
of
trigonometry ratios.
trigonometry.
 Research subject
80
senior
secondary
2 100 students
who
were
mathematics student randomly final year students preparing
selected
from
two
private to write the 2017 West
school in Zaria with a mean age African
of 17.
Senior
Certificate
School
Examination
(WASSCE) in the Central
region of Ghana.
 Research
Instrument
1. The
mathematics 1.
achievement tests (MAT)
Trigonometric
Diagnostic Test (TDT)
2. Trigonometrical diagnostic 2.
test (TDT)
The
mathematics
achievement
3. Diagnostic interview
tests
(MAT)
3.
Research interview
3
 Data
analysis Using
technique
 Keywords
descriptive
statistics: The interpretative qualitative
percentage and frequency
Trigonometry,
error,
research paradigm
comprehension Trigonometry, process skill
transformation
error, error, transformation error,
process skill error
3
Comprehension error
Introduction
 Research
Background
Trigonometry is an
Trigonometry is a lesson
that has been introduced to area of study in mathematics
students
from
high that student believe to be
school. But even though it is a particularly difficult and
lesson that is very often abstract compared with the
mentioned,
remains
junior
trigonometry
one
of
the
mathematical parts that students
believe is very difficult and
abstract. Few students like and
succeed in learning it, but most
students hate this lesson and
other
content
areas
in
mathematics. Many studies
concerned with mathematics
education
explain
students
that
have
misconceptions and make
errors, and these situations
even avoid it.
grow
out
of
learning
complexities. Found that the
students did not develop the
concepts of trigonometry
certainly and that they made
some mistakes.
 Theoretical
Many studies related to In the process of problem
framework
mathematics education explain solving there are two kinds
that
students
have of
obstacle
that
hinder
misunderstandings and make students from arriving at
mistakes
that
directly
or
often
occur correct answers:
unintentionally
a.
ranging from writing to oral and linguistics
even
calculation
(Zakaria, conceptual
Problems
in
fluency
and
understanding
4
2010). The study conducted by that correspond with level of
Brown (2006) shows that many simple
reading
and
students have incomplete or understanding meaning of
fragmented understanding of problems, and
the three main ways to see
b.
Problems
in
sinuses and cosines. Mastery of mathematical processing that
basic mathematical concepts is consists of transformation,
an important step in developing process skills, and encoding
concepts. When basic concepts answers.
are not learned at an early stage, This classification implies
the learning process in the later that the students have to
stages becomes more difficult. interpret the meaning of the
This
happens
because
the question before they proceed
learning process in mathematics to mathematical processing
which is categorized as
a to obtain appropriate answer.
hierarchical learning process is The outcome of the written
widely interrelated (Liew & students’ work in their test
wan Muh'd, 1991). The model will be evaluated according
of error investigation proposed to the type of error in
by Newman (1977) has proven Newman Error Hierarchical
to be a reliable model for Model based on the first
mathematics
teachers.
This breakdown point.
framework has six types of
errors:
reading
errors,
understanding, transformation,
process skills, coding errors and
carelessness. This model has a
hierarchy that classifies types of
errors based on the level of
problem solving performed by
students.
5
 Research
questions
1. To
what
extent
will
1.
What are students’
individual students‟ error
errors
influence the learning of
trigonometry
trigonometry?
using formulae?
2. What
is
the
categorization
possible
of
2.
these
in
solving
ratio
What are students’
errors
in
solving
errors in the learning of
trigonometry
trigonometry?
using right – angled
3. What
are
the
student’s
ratio
triangle?
answers that help us explore
the students’ thinking and
reflection about learning of
trigonometry?
4
Research Method
Finding the type of mistakes
This
study
exploratory
that students often make is approach, which emphasises
based on the Newman Error the use of open – ended
Hierarchy
Model
which questions and probes, giving
includes the types of reading participants an opportunity to
errors,
comprehension, respond to their own words.
transformation, process skills, And using the Trigonometric
and coding errors, using the Diagnostic Test (TDT), The
mathematical achievement test mathematics
method
(MAT)
achievement
and tests (MAT) and the research
trigonometric diagnostic tests review.
(TDT)
5
Experiment
The study used a set of
The study used a set
trigonometrical diagnostic test of Trigonometric Diagnostic
(TDT) questions designed by Test.
The
reliability
the investigator to identify type coefficient as computed from
of error committed by students.
Pearson’s Product Moment
Prior to the commencement correlation for Trigonometric
of the study, the questions were Diagnostic test. The value
6
subjected to face and Pearson’s suggest that the test question
product
moment
content were reliable and as such
validated test respectively, with would test what it was
the reliability coefficient as designed for. In addition,
computed for (TDT) was r= content and face validity of
0.85.
the instrument was carried
In addition, content and out by the research who is a
face validity of the instrument specialist in mathematics and
was carried by the investigator other specialists in cognate
who
is
a
specialist
mathematics
specialists
in
compared
to
in field compared to the overall
and
other objective of the curriculum.
cognate
field Prior to the investigation, the
the
overall respondents were subject to
objective of the curriculum.
general
Mathematics
Prior to the investigation, Achievement Test (MAT).
the respondents were subject to
The
primary
general math achievement test. objective of the MAT items
The primary objective of the was
to
categorize
the
MAT items was to categorize students into high achievers
the students into high achievers (A) for those that scored
(A) for those that scored 65% 70.0% and above medium
and above and achievers (B) for achievers (B) for those that
those that scored 50-64%.
The
investigator
interviewed
based
on
the
the
scored 50.0 − 69% and low
also achievers (C) for those who
respondent scored 49.0% or less (based
modified on the data). The researcher
procedure of Newman Error also
interviewed
the
Hierarchical Model from the respondent based on the
outcome of the written test. The modified
procedure
of
questions for the respondent Newman Error Hierarchical
included:
Model from the outcome of
a) Can you read the problem? the
(Reading level)
written
test
(
see
Appendix B).
7
b) What does the question ask
you to do? (Comprehension
level)
c) What do you use to solve
the
question?
(Transformation level)
d) Can you show me the
working steps that you have
used in order to find the
answer? (Process Skills)
e) Tell
me
what
is
your
answer? (Encoding)
6
Research result and
discussion
 Research result
Results
from
Distribution
Student The research result about this
According
to study
that
respondent’s
Various Achievement Levels profile according to gender
showed that as many as 22 of and their achievement is
the 42 male students were high represented on the data. The
achievers (A) and the rest were students were grouped in
achievers (B), while 20 of 38 three different category of
high achieving female students achievement: low, medium
(A) and the rest were achievers and high. Based on the data
(B).
that 16 male and 21 female
Then there are 7 questions students belonged to the high
about trigonometric ratios in achievers category, 20 male
two ways, namely by using a and 18 female belonged to
formula, and by using the right- the
medium
angled triangle. Based on the category
and
achievers
the
low
results of student answers using category of achievers had 10
formulas there are 0 frequencies males and 15 females.
of errors in reading, 58 in
comprehension,
183
in
8
transformation, 238 in process
skills, and 6 frequency of errors
in carelessness.
While based on the answers
of students using the rightangled triangle there were 0
frequency errors in reading, 38
in
comprehension,
172
in
transformation, 303 in process
skills, 33 in encoding and 10 in
carelessness.
 Discussion
From the results of the
The error in process
research obtained it can be seen skill seems more pronounced
that the mistakes most often in the use of right angled
made by students in solving triangle than using formulae.
problems
in
include
misunderstanding, fact that students failed to
transformation
trigonometry This error may be due to the
errors
and understand
process skill errors.
and
describe
what is required by the
Students
often questions. Most students did
misunderstand the demands of not manage to perform the
the question. This may be due operation especially when
to the lack of emphasis by the numerical
teacher
in
values
are
teaching involved. This results in
simplification of concepts when failure to solve the problems.
they arise. Maybe also because
The error type in
memorizing is part of the transformation
student.
The
during computation process
type
of
error
in especially
transformation occurs during multiplication.
the
occurred
calculation
during
This
takes
process place due to computation
especially during multiplication. problem especially among
This
happens
because
of low
achievers.
Most
9
calculation problems, especially students make error at the
among those who excel. Most process skill level especially
students make mistakes at the in the manipulation of trig
level
of
process
skills, ratios using right angled –
especially in trigonometric ratio triangle.
Students
often
manipulation using formulas, misunderstand the demands
because most students who get of trigonometric question.
items using the right triangle This may be due to the lack
method cannot replicate the of emphasis by teachers in
same answer using the formula teaching the simplification of
as a result.
concepts as they appear. It
Errors in process skills seem may also be due to rote
to be clearer in the use of learning on the part of the
formulas than right triangle learner.
methods. This error may be due
Gur noted that errors
to the fact that students fail to committed by students in
understand and explain what is learning trigonometry may
needed by the question. Most be useful for the teacher in
students do not succeed in evaluating his teaching so as
surgery,
especially
when to be able to correct the
numerical values are involved.
students
as
and
appropriate.
when
Therefore,
teachers must ensure that the
teaching
of
mathematical
concepts must be balanced
with the arithmetic skills.
The
findings
from
the
present study is consistent
with previous studies. Who
observed that emphasis on
algorithmic
skills
without
explanation on the concept or
principle are the factors that
10
cause
difficulties
mathematics
in
and
by
extension poor achievement
in trigonometry.
7
Conclusion
The results of this study The conclusion of this study
revealed
that
committed
by
transformation
most
error is that most errors committed
students
are by students irrespective of
errors
and the
method
used
were
process skills errors. In general, process skills errors and
students irrespective of different transformation
cognitive ability are susceptible Students
errors.
irrespective
of
to error in solving problems in different cognitive ability are
trigonometry.
susceptible
to
solving
error
in
problems
in
trigonometry. As a result, the
outcome of the research can
be
shared
with
their
colleagues in order to solve
the students’ problem. This
study
will
also
help
mathematics educators get
information on the students’
problem
in
mathematics
learning.
8
Recommendations
1. The teacher must encourage
1.
To counter students’
students to concentrate on
problem,
one
should
point
and
proceed
teachers
be
well
gradually in a logical way to
prepared and be able
reduce the difficulty of the
to conduct analysis
officers
on students learning
faced
in
trigonometry.
2. The teacher must
2.
make
The teacher must be
analysis
the
each
11
interesting
lessons
in
eliminate
student’s
trigonometric
groups
the
to
will
difficulties
problem
enable
the
teachers to plan their
faced in problems involving
teaching
trigonometry.
and meaningful
3. Students
must
be given
3.
effectively
Teachers will identify
enough opportunities to do
the
the exercises regularly.
problems in students’
4. This
research
must
be
roots
learning
of
and
the
then
repeated with other similar
teach to the student
mathematical
based
the solution without
concepts so that they can
relieve the students
compare findings.
analysis
12
CHAPTER IV
CONCLUSION
4.1 Conclusion
By the data of this journal based on the problem in trigonometry that most errors
committed by students irrespective of the method used were process skills errors and
transformation errors. Generally, students irrespective of different cognitive ability are
susceptible to error in solving problems in trigonometry, and the solution to solved this
problem so teachers to plan their teaching effectively and meaningful. Based on analysis, the
teacher be facilitator on learning process, teacher should make interesting trigonometric
lessons or teachers should be well prepared and be able to conduct analysis on students
learning, teacher must be analysis the each student’s problem. So Students need to see and
understand why their learning of trigonometry matters. Students did develop the concepts of
trigonometry certainly and minimalize even loss made some mistakes in trigonometry If the
student understand the concept of trigonometry.
4.2 Suggestion
Based the journals, there are some recommendation to the teachers to increase the
reasoning skill of trigonometry of the students. Based on the journals, teacher should make
the exciting learning on mathematics. And then on learning mathematics especially
trigonometry, the study should be repeated with other similar mathematically based concepts.
And teacher as a facilitator should encourage the students to concentrate at the point at time
and proceed stepwise in logically manner to reduce attendant difficulty face in trigonometry.
13
BIBLIOGRAPHY
Mensah, Farouq Sessah. (2017). Ghanaian Senior High School Students’ Error in learning
Mathematics. International Journal of Environmental and Science Education. Vol 12
(8): 1709-1717
Usman, Haruna Mu’awiya et al. (2017). Analysis of Students’ Errors in Learning of
Trigonometry Among Senior Secondary School Students in Zaria Metropolis,
Nigeria. IOSR Journal of Mathematics. Vol 13 (2): 1-4
14