The Effect of Note-Taking Strategy on Complex Analysis Problem

Solving Skill

Th. Kriswianti Nugrahaningsih

, Iswan Riyadi

Departement of Mathematics Education, Faculty of Teacher Training, Universitas Widya Dharma, Klaten, Indonesia

Departement of Geographic Education, Faculty of Teacher Training, Universitas Widya Dharma, Klaten, Indonesia

Keywords: Note-taking, Strategy, Problem solving Skill, Complex Analysis.

Abstract: This study aims to increase student’s problem solving skills by using note-taking strategies for Complex

Analysis. Students habituation to write the necessary materials at right colom of the paper work, will allow

them to connect mathematics topics with the related mathematical topics, which will ultimately increase

problem solving skills. This research is a classroom action research conducted in Mathematics Education

Department of Widya Dharma University Klaten. The study was conducted in several cycles. At the end of

the cycle, we did evaluation and reflection to determine the deficiencies and their advantages, then repaired

for the next cycle. The Cycles would be stoped when the indicator of success target has reached. The study

was stopped in second cycle as it already has reached the indicator of success target. The result of this research

showed that by using note-taking strategy for every step of Polya’s theory, the student’s problem solving skill

has signifantly increased. It ould be seen that the average value of problem solving skills in the first cycle was

63.26, increased to 81.28 at the end of the second cycle.

1 INTRODUCTION

Mathematics is one of the subjects that has a big share

in preparing students. Mathematics is a science that

cannot be separated with other sciences, such as

Chemistry, Biology, Physics and Economics.

Without mathematics these sciences will have

difficulty in solving problems. Mathematics is needed

as a tool in solving problems. No wonder that many

people say that mathematics is a servant of science,

as queen of science and as a language of science also

(Bell, 1996).

General objectives of mathematics learning

formulated in The Regulation of National Education

Ministry regarding Content Standards are students

have the ability, 1) to understand the concept of

mathematics, explain the interconnection between

concepts and apply the concept or algorithm flexibly,

accurately, efficiently and appropriately in problem

solving, 2) to use reasoning in patterns and traits,

performing mathematical manipulations in

generalizing, compiling evidence, or explaining

mathematical ideas and statements; 3) to do problem

solving that includes the ability to understand

problems, designing mathematical models, solving

models and interpreting solutions obtained; 4) to

communicate ideas and symbols, tables, diagrams, or

other media to clarify circumstances or problems 5)

to have an appreciative attitude to the use of

mathematics in life, that is to have curiosity, attention,

and interest in learning mathematics and resilience

and confidence in problem solving (Menteri

Pendidikan Nasional Republik Indonesia, 2006).

According to the National Council of Teaching

Mathematics the goals of learning mathematics in

schools are: (1) problem solving; (2) mathematical

reasoning and proof; (3); mathematical

communication (4) mathematical connection; and (5)

mathematical representation (Midget and K.Edin,

2001). Problem solving becomes an important part of

mathematics learning. that have the potential to

provide intellectual challenges for enhancing

students' mathematical understanding and

development (Bradbury, 2010). Problem solving is

also needed in everyday life and at work. Referring to

the purpose of learning mathematics, problem solving

is the goal of learning mathematics but is also a tool

for doing so. Most mathematical concepts can be

introduced through problems based on experiences

that come from the life of students. To achieve

mathematical learning objectives well, a teacher is

required to be qualified and professional in order to

204

Nugrahaningsih, T. and Riyadi, I.

The Effect of Note-Taking Strategy on Complex Analysis Problem Solving Skill.

DOI: 10.5220/0008409902040210

In Proceedings of the 2nd International Conference on Learning Innovation (ICLI 2018), pages 204-210

ISBN: 978-989-758-391-9

improve the quality of education. So the teachers

should be able to choose and apply the right learning

strategy.

Problem in mathematics is an inquiry starting

from given conditions to investigate or demonstrate a

fact, result, or law. According to Shadiq (2004) a

question will be a problem only if the question

indicates a challenge that cannot be solved by a

known routine procedure. So to solve a problem is

treated a relatively longer time than the process of

solving regular routine problems. Meanwhile,

according to (Hudoyo, 2003), a question is a problem

only if a person does not have rules / laws that can

immediately be used to find answers to these

questions. A question is called a problem depends on

the knowledge it has. Problems are subjective to

everyone, it means that a question can be a problem

for a person, but not a problem for others (Hudoyo,

2003). Furthermore, Herman Hudoyo also stated that

for a person, the question can be answered by using a

routine procedure, but for others, it could be use a non

routine procedure. So a question can be a problem if

the question is challenging to answer which the

answer can not be done routinely. Furthermore, this

challenging question becomes a problem for someone

when the person accepts the challenge (Hudoyo,

2003).

The Department of Mathematics Education has an

obligation to prepare students to become competent

mathematics teachers who will be the spearhead of

mathematics learning. So it is necessary that the

students of The Department of Mathematics

Education be provided complete competence in

mathematics and mathematics education. Complex

Analysis is one of the subjects that taught in The

Department of Mathematics Education in 7th and 8th

semesters. To study the subject of Complex Analysis

requires previous knowledge among others set theory,

logic, trigonometry, analytical geometry, algebra,

calculus, advanced calculus, and topology. If the

student has not mastered the previous knowledge,

he/she will find difficulties in studying further

complex analysis. Instead, studying Complex

Analysis becomes a vehicle for revealing these

previous knowledge to further strengthen the mastery

of the concept. To solve the problem of Complex

Analysis requires previous knowledge such as the

skills of applying trigonometric functions,

performing operations in the form of exponents,

performing logarithmic operations, applying the

properties applicable in set theory, logic, describing

functions, operations applicable to limits, differential

or integral.

Mathematical problem solving steps were first

introduced by Polya and are still used today (Polya,

1973) are: 1). Understand the problem, What is

known and what is unknown, and what conditions are

known; 2). Devise a plan, Choose the theorems or

concepts that have been studied to be combined, so

they can be used to solve the problem; 3). Carry out

the plan, Fixed the problem as planned. Check each

step. Prove that the steps are true; 4).Look back: Re-

examine the results obtained, by matching the

answers with the problem and writing the

conclusions. In mathematical problem solving, note-

taking can help students to solve the problem by

taking the note of required previous knowledge, note

the associated formulas,

The note-taking strategy was first examined by Di

Vesta and Gray (1972), who found that making notes

contained two activities at once namely, processes

and products. Taking notes (note-taking) can help

improve students' understanding and retention of the

material being studied. (Kirkgoz, 2010) stressed that

the main purpose of making notes is to capture

important points from textbooks or lessons and save

them, with the aim of being able to be used later in

the framework of revisions, especially for the purpose

of facing exams or writing summaries or reports that

need notes (Kirkgoz, 2010). Making notes requires

high-level skills. Note-taking can be useful when

students re-learn the subject matter. (Cardetti,

Khamsemanan and M. Carolina Orgnero, 2010)

confirmed that partial notes in mathematical

assignments are related strongly to high academic

performance.

It is believed that students’ notes which are written

in class during the lesson or while reviewing a course

material or comprehending a text are essential tool for

learning. Good note-taking practices can lead to

efficient study practices, better course outcomes, and

improve retention of content beyond a course’s

conclusion. It is because learning can occur during

both the production and review of notes by allowing

learners to make connections between the idea units

and engage in deep processing of course content

(Bohay et al., 2011)

Note-taking in solving mathematics problem, is a

strategy to improve learning of both oral and written

materials. It is a beneficial technique for studying

the content, developing language skills, and learning

task in general (White, 1996). Hebert, Graham, &

Ganson (2014) prove that note-taking is useful tool

for improving students’ reading comprehension. The

beneficial effect of note-taking covers two major

functions as process and product (Boch & Piolat,

2005), First, the process of taking notes facilitates

The Effect of Note-Taking Strategy on Complex Analysis Problem Solving Skill

205

learning. It works well to increase students’ attention,

to raise awareness of text organization, and to store

the information into memory. Second, the notes, as

product serve as an external storage of information

that is useful to retrieve the content in delayed recalls

or answering some exam questions.

Although note-taking is not a substitute for

attendance, practice, instruction, or tutoring, it is one

of many ingredients that can lead student to success

in developmental math courses and is cited as an

important, common student practice impacting

student behaviour and performance (Bauer and

Koedinger, 2006, 2008). Note-taking is believed to

simulate the generative process in which students

encode connections between prior knowledge and

learning content. Note-taking strategy provides

students with a method for increasing their short-term

and long-term memory (Boyle, 2010). Although there

are many new methods of teaching and learning have

been developed, Boyle (2011) believes that note-

taking is still an important learning skill for students.

Note-taking remains an essential study skill for

students. Note taking can be done in various activities

such as lectures, reading, or when making simple

observations. In the classroom, students who used

notes can improve their learning experience. As

students move on to post secondary education, note-

taking will become even more essential as it is

reported that 98% of college-level classes are in the

form of lectures (Eades, Carol; Moore, 2007) (Boyle,

2011). In making notes, students have to write notes

that are organized, can distinguish between important

and unimportant points, connect to prior knowledge,

and make a re-statement (Boyle, 2011).

This study will develop a note-taking strategy in

solving complex analysis problems for Mathematics

Education students, through classroom action

research. To solve mathematical problems, students

need to develop strategies, such as making

appropriate diagrams, choosing the right formula,

connecting with previous knowledge, finding suitable

patterns, trying out values or special cases. These

strategies can be applied by using note-taking

strategies at each problem-solving step, This

strategies need to be taught to students so that

students can practice to monitor their thinking as they

solve problems. Thus, it is expected to improve

student problem solving skills.

In this study, making notes while solving the

Complex Analysis problem is by writing down the

essential contents of the text on the right-hand side of

work paper. Things to note include prior knowledge,

necessary formulas and other important things. By

keeping in mind the prior knowledge and taking the

notes on the right side of the worksheet, will make it

easier for students to solve problems. According to

opinions of Shrager & Mayer (1989) that note-taking

activities will also improve students' problem solving

skills and recall ability.

The purpose of this study is to increase students’

problem solving skills by using note-taking strategies

for Complex Analysis problem solving.

2 METHOD

This research is a Classroom Action Research which

is conducted in several cycles. Each cycle has four

main activities: a) planning, b) implementation, c)

observation, and d) reflection. An advanced cycle will

be implemented if success indicators have not been

achieved, by correcting the weaknesses of the

previous cycle. The cycle will be stopped if the

success indicator is reached. The indicator of success

in this study is if more than 70% of students obtain a

score of problem solving skills Complex Analysis at

least 70.

Subjects in this study are students who studied

Complex Analysis in the 7th semester on

Mathematics Education Department of Universitas

Widya Dharma Klaten, with 23 students consisting of

15 female students and 8 male students.

The learning instrument was validated by 3

validators before being used in the study. As a

validators are 3 lecturers on Mathematics Education

Department. If it is less valid, the learning instrument

should be revised according to the suggestion of the

validator.

To see the effectiveness of this strategy, the

results of post-test in the first cycle and the last cycle

are compared using the difference mean test. If the

value of problem solving skills has increased

significantly then the cycle is stopped.

3 RESULT AND DISCUSSION

3.1 Validation for Learning Instrument

An instrument is said to be valid if it is able to

measure what should be measured. To determine

valid or not an instrument is, we need validation

action. In this study, we employed expert’s judgment,

i.e. the instrument validated by validators who are

experts in mathematics, mathematics education, and

educational psychology.

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3.1.1 The Validation Result of Lesson Plan

Lesson plan is validated by three validators, the

average value given by the three validators is 3.7. All

three validators conclude that Lesson Plan can be

used as a guide in the implementation of learning.

3.1.2 The Validation Result of Student’s

Worksheet

The validation of student’s worksheet by three

validators obtained an average value of 3.6. As per

the criteria of the scoring scale, each aspect obtained

a good category. All three validators conclude that the

Student’s worksheet can be used with a few revisions.

3.1.3 The Validation Result of the Post-test

of Each Cycle

Based on the validation result of each post-test by

three validators, the average score of the post-test of

each cycles can be categorized as valid,

understandable and can be used without revision.

Thus the post test of each cycles can be used without

revision.

3.2 Result from the First Cycle

Based on observations in the first cycle we obtained

the following results.

3.2.1 Result of Lecturer Observation

From the results of learning observation, it have

found that the learning was begun by direct learning,

the lecturer explained the problem solving steps. To

explain the definition, lecturer used expository

method. In proving the theorem or solving complex

analysis problems, the lecturer has involved students

to actively participate in thinking. Lecturers solved

the problems by Polya's problem solving steps. At

each problem solving step, the lecturer wrote down

everything needed based on the students' opinions.

The lecturer conditioned students to express the initial

knowledge needed. In the next activity, students

solve the Complex Analysis problem by using

Student Worksheets that have been provided by the

lecturer, as a guide to solving problems using note-

taking strategies.

3.2.2 Result of Student Activity Observation

From the results of students’ activity observation, it

have found that the students who participate actively

in the learning process were not much. Many students

were just silent, did not dare to express his opinion.

This is because of students forgot the prior knowledge

that needed. Likewise in working on worksheets,

many students who had not been able to write the

prior knowledge or the things needed in problem

solving, so not many students got good results.

The average score on the post test of the first cycle

is 63.26. The students who reached a score more than

70 are only 52.17%. It means that the success

indicator has not reached, so it should be continued to

second cycle.

Based on that description it can be concluded that the

study should be continued in second cycle, by

eliminating the weaknesses and utilizing the

advantages. The improvements should be do in

second cycle are:

1. Lecturers must remind students how to make

notes when solving problems. In solving problem

of Complex Analysis, students are accustomed to

work on using problem solving steps according

to Polya and write down everything needed to

solve the problem. In understanding the problem,

students need to be accustomed to: 1) write down

what is known and what is being asked, 2) write

down prior knowledge, 3) write down the goals,

4) sketch or draw that can help solve the problem.

When doing device a plan, students need to be

accustomed to: 1) write down the relationship

between the data and the question, 2) write down

something useful from the data, 3) write down

the necessary prior knowledge, 4) write down a

related problem, 5) write down the tool if the

relationship cannot be found, 6) write down the

plan of the solution, 7) write down the formula

that used at each step. When carrying out the

plan, students need to be accustomed to: 1) write

down the formula that used, 2) write down the

steps of solving problem, 3) write down the

important information. When doing look back,

students need to be accustomed to: 1) check the

truth of the step, 2) convince that the evaluation

is correct, 3) evaluate goal achievement.

2. In demonstrating note-taking strategies at front

of the class, lecturer are required to be smarter in

expressing student opinions.

3. The lecturer gives task to strengthen the prior

knowledge that needed to solve The Complex

Analysis problem.

4. The lecturer requires students to write down the

necessary prior knowledge, and matters that

related to the existing problems on the right side

of the worksheet.

5. Lecturers should give intensive guidance and

motivation.

The Effect of Note-Taking Strategy on Complex Analysis Problem Solving Skill

207

3.3 Result from the Second Cycle

Based on observations in the second cycle we

obtained the following results.

3.3.1 Result of Lecturer Observation

In addition to using direct learning, the lecturer added

a cooperative method of think-pair-share type. In this

cooperative type, students discussed with their peers

to solve the problem and write down what is needed

in the space that provided on the worksheet.

3.3.2 Result of Student Activity Observation

Students who actively participate in the learning

process has increased. By discussions with their

friend, students become more dare to express their

opinions and be able to write down what is needed in

problem solving. Because students often using the

initial knowledge, they become more understand the

mathematics mater that required. Thus, students'

ability to solve problems has increased, the mastery

of other mathematical material related to Complex

Analysis has increased too.

Recapitulation of student’s ability in solving

Complex Analysis problem at each cycle can be seen

in Table 1.

From the Table 1 it can be seen that the lowest

value increased from 25 to 45, the highest score

increased from 85 to 95, the average value increased

from 63.26 to 81.28.the average score on the final test

of the second cycle is 81.28, and who reaches a score

of more than 70 to 86,97%, it means that the success

indicators have been reached, so the cycle can be

stopped.

To be more strengthening, we did the mean

differences test between the average post test score of

students’ problem solving skill in the first cycle and

the second cycle. Calculations were done by using the

Minitab program. The results shown at Table 2.

Table 1: Score of student’s ability in solving complex

analysis problem.

Score

Cycle

Information

The Highest

score

Increased

Average score

63,26

81,28

Increased

The Lowest

score

Increased

Percentage

earned a score

of ≥ 70

52,17%

86,97%

Indicator of

success has

been achieved

Table 2: Calculation of mean differences test.

Two sample T for first vs second

Mean

StDev

Mean

First cycle

63.26

8.94

0.59

Second cycle

81.36

9.97

0.96

95% CI for mu First - mu Second ( -23.57, -12.63)

T-Test mu First = mu Second (vs <): T= -6.49

P=0.0000 DF= 44

From these results, we obtain a t-test value of -

6,49 with a probability of 0,000. It mean that there is

a significant difference between the average score in

the first cycle and the second cycle. From the results

it can be concluded that there is a significant increase

between the average post test scores in the first cycle

to the second cycle. So, the cycle can be stopped.

The results of this study are that note-taking

strategies can improve the problem-solving skills of

Complex Analysis. While (Senkowski, 2016) also

conducted research about structured note-taking

techniques to improve the mathematics performance

of K 12 students. In his research he divided subjects

into two groups, one group was given a structured

note-taking strategy treatment, the other one was not

given treatment. The result showed there is no

significant difference between students' mathematics

performance in treatment and non-treatment groups.

However, this study will continue for different

schools. Although, student perceptions of note-taking

showed growth based on student survey responses.

Meanwhile, (Riyadi, Hersulastuti and Theresia

Kriswianti N., 2017) developed metacognitive

learning strategy that consisting of highlighting, note-

taking, summarizing and concept maps for reading

comprehension. It was concluded that note-taking

helps someone to carry out a range of intellectual

processes, especially in making judgment, resolving

issues, and further making decisions. This is not much

different from our research. By noting important

things when solving the problems, students become

actively thinking in constructing their own

knowledge. It will make students’ knowledge more

meaningful. Every time doing an action, they should

have a logical reason. This will keep students

accountable for what they do. By writing down the

necessary formulas, the mastery of mathematical

material related to Complex Analysis will increase

and integrated one and other. This is in accordance

with the opinion of (Bohay et al., 2011) that active

engagement with material, such as note-taking,

appears to have the greatest benefit at the deeper

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levels of understanding. (Hartley, 2002) claims that

note-taking as an effective information-processing

tool that is commonly used both in daily life and in

many professions. Note- taking helps someone to

carry out of a range of intellectual processes,

especially in making judgments, resolving issues, and

making decisions. Teachers should develop a

problem-solving culture in classroom to make

problem solving as a regular and consistent part of

one’s classroom practice. The strength of the note-

taking strategy are:

1. Students become more active, more critical and

have high motivation because students are

actively involved in the problem-solving

process.

2. By applying note-taking strategies on solving

complex analysis problems, students can be

trained to construct their own knowledge with

teacher scaffolding.

3. Mastery of mathematics materials increased and

integrated one and other

4. Student problem solving skill has increased

While the weakness of the implementation of this

strategy are:

1. For students who have not mastered the initial

knowledge yet, such as number operations,

trigonometric formulas, logic, functional graph,

limit, differential, integral, they will find

difficulty to solve the problem.

2. Many students lazy to write down the things

needed on the right side of the worksheet,

because they are still confused what to write.

4 CONCLUSIONS

This study shows that by using note-taking strategy in

learning Complex Analysis can improve problem

solving skills of mathematics education students. In

addition, by using note-taking strategy, can improve

the mastery of mathematical material. Students who

are accustomed solve problems by using note-taking

strategies on every step of Polya problem solving, can

improve metacognitive ability and metacognitive

awareness. Furthermore, students have self-

confidence, thorough, critical, systematic, and skilled

in making decisions. Students can master

mathematical material such as Set Theory, Logic,

Trigonometry, Algebra, Analytical Geometry, and

Calculus as a whole and integrated, so there are not

easy to be forgotten. As a math teacher candidate, this

mastery is needed, as a provision to become a

competent teacher.

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