An Analysis of Values in Mathematical Problem Solving in Secondary

School

Nyimas Aisyah, Vira Nurkomaria, Scristia

Department of Mathematic Education, Universitas Sriwijaya, Indonesia

Keywords: Problem solving, character value, mathematical value, value of mathematics education

Abstract : This is a descriptive qualitative study that aims to find out what values appear in problem solving learning in

secondary school. The research subjects of this study are secondary school students in Palembang city. Data

was collected through observation of problem solving student worksheet and was analyzed descriptively. The

results show that the most dominant values that emerged at the stages of problem solving are the value of

discipline, the value of relational understanding, the value of rationalism, the value of control and the value

of reasoning. Otherwise, the value that are not appear at the stage of problem solving is the value of relevant

knowledge and the value of objectivism. Therefore, it is advisable for teachers to optimize the material of

prerequisites relate variables further.

1 INTRODUCTION

Getting good quality education will continue to be

improved by the teacher through learning strategies

that will be apply in the learning process (Parlaungan,

2008). These strategies are choose and then manage

by the teacher with integration, leading students to

think logically, analytically, systematically, critically,

and creatively, which can help students in developing

their abilities in problem solving. In order to achieve

it, the teacher as an intermediary for students in

achieving these abilities cannot be separate from their

role in integrating values in the problem solving

learning process(Aisyah, 2016). Student’s

mathematic values represents affective qualities

develope by teachers through the mathematics

materials in school (Bishop, 2008). Integrating the

values in problem-solving learning helps the teacher

and the students to understand the problems in order

to get success in problem solving (Dollah, 2005). The

values that can be developed by the teacher in the

study of mathematics through problem solving are the

character value, mathematical value and the value of

mathematics education (Seah et al., 2001). Character

values, mathematical values and the value of

mathematics education related to the affective

domain helping students to understand mathematical

problems and support students to develop their

thinking ability to carry out problem solving plans. 

The importance of integrating these three values

in problem-solving approach has not been concerned

in previous learning. The teachers only used this

method only to look at how students' cognition is

developed in solving mathematical problems.

Therefore, a deeper study on how to integrate values

in problem

solving learning is needed. The purpose

of this study was to find out what values appear at the

problem solving learning step is based on the problem

solving step developed in students' worksheet. The

analyzed problem-solving steps values are the step of

understanding the problem devise a plan, carry out the

plan, and look back (Polya, 2004).



2 METHOD

The type of research used by researchers was

qualitative descriptive research. The subjects were

tenth grade students in Senior High School

Palembang, with 5 students where one student has

high ability, two students who have middle ability and

two students who have low ability.The object of the

research was validated students problem solving

worksheet developed by the researcher. It was

developed by integrating the values of character such

as discipline and hard work; the value of mathematics

education such as relevant knowledge and reasoning;

mathematical values such as objectivism, rationalism

Aisyah, N., Nurkomaria, V. and Scristia, .

An Analysis of Values in Mathematical Problem Solving in Secondary School.

DOI: 10.5220/0009996100002499

In Proceedings of the 3rd Sriwijaya University International Conference on Learning and Education (SULE-IC 2018), pages 215-220

ISBN: 978-989-758-575-3

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

215

and control (Seah & Bishop, 2000). The data

collection included the documentation with the

problem solving worksheet and the observation of

completing problem solving worksheet process. The

researchers act as the main instrument for data

collection assisted by additional instruments in form

of the field notes and check lists.

Table 1: Analysis of value in mathematical problem

solving.

Step of Problem

Solving

Explanation Values

Understanding

the Problems

Students could identify

problems sequentially by

writing down the known

information to help solve

problems

Students could interpret

stated problems to be

resolved

Students could collect

unknown information

appeared in the problem

students tried to summarize

the information read

Discipline

Planning the

Problem

Solving

Strategy

Students could make

mathematical symbols

correctly

Students understood the

chosen mathematical symbols

Objectism

Executing the

Strategy

Students could use the

systems of equation with

three variables concepts and

principles in executing the

planned strategy

Students could use

mathematical procedures to

solve the problems

Students could produce

mathematical procedures

Students could use obtained

schemes or structures from

the results of connecting

various mathematical

concepts related to problem-

solving

Relevant

Knowledge

Control

Relational

understand-

ing

Evaluating the

Result

Students could generalize the

mathematical procedures

applied

Students could give reasons

for the generalization they

make

Reasoning

Rationa-lism

The implementation of value in mathematical

problem-solving was analyzed based on the

appearance of the values that existed at each step of

problem solving that the researchers have mapped as

in Table. 1.

As the data had been analyzed with the problem

solving worksheet and coded based on the rubric on

Table 1, the appearance of values at each step of

problem solving done by students was analyzed and

presented in narrative form next.

3 RESULT AND DISCUSSION

The learning process was done based on the lesson

plans developed by the researchers based on values in

problem solving learning. The distributed worksheet

contained daily life issues related to systems of

equation with three variables material. During the

work process, the worksheet used four stages of

problem solving that must be completed by students.

During the learning process, students were given

problem solving problems in form of traditional fish

cake orders that must be completed in accordance

with

the time given by the buyer.

To solve these problems, step of problem solving

were used. At the step of understanding the problem,

students were trained to understand the problems in

daily by writing down what was stated and asked,

representing the value of discipline. At the step of

planning the problem solving strategy, students were

first asked to change the problem into the model of

mathematics using a variable, representing the value

of objectivity and control. Furthermore, students were

trained to make mathematical models from the

problems, then solve the problems using mathematical

models obtained, indicated the existence of relevant

values and relational values. Last, students did a look

back and made conclusions from the mathematical

model made whether it is included in the definition of

systems of equation with three variables, indicated the

appearance of rationalism and reasoning value.

Furthermore, analysis of values in problem solving

was seen by paying attention to student activities

while answering value-based worksheet by analyzing

the values that emerge at the step of problem solving.

The following is the conclusion of the researchers on

the value-based worksheet analysis, presented in

Table 2

. Table 2 shows the values appearing while

students do the work on problem solving worksheet

based on the systems of equation with three variables

material.

Table 2: Values that appear at the step of problem solving.

Ste

Values a

Values not a

I - disci

line

II - Objektis

III

Control and relational

understanding

Relevant

knowledge

Rationalism and

reasoning value

Information:

I : Understanding problem

II : Planning the problem solving strategy

III : Executing the strategy

IV : Evaluating the result

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1. Value of Discipline at the step of Understanding

Problems

The value of discipline did not appear at the step of

understanding the problem, at this stage students

identified the problem sequentially by writing down

the information that is known and writing down what

was asked on the answer sheet, but misinterpreting

the problem asked, as showed in Figure 1.

Figure 1: the answer in the step of understanding the

problem for discipline value.

2. Value of Objectivity at the step of Planning the

Problem Solving Strategy

Value of objectivity did not appear at the stage of

planning a settlement strategy, Figure 2 below shows

that students could make mathematical symbols, but

did not understand the meaning of the chosen

mathematical symbol. The value of objectivism

almost appeared in the planning strategy for the

completion, but the symbols/variables are used

inappropriately according to the given problem.

Figure 2: The answer at the stage of planning a settlement

strategy for the value of objectiveness.

3. Value of Relevant Knowledge in the Step of

Executing Planned Strategy

Figure 3: The answer at the stage of executing the

settlement strategy for relevant knowledge values.

4. The Relevant Value at the Step of Executing the

Strategy

Relevant knowledge did not appear. Based on Figure

3, it can be seen that the error was on interpreting 1

box of orders with 1 day of workmanship. Students

did not use the systems of equation with three

variables concept in solving the problem. It is

assumed that it is because the students is not

understand the meaning of the variables they make at

the planning step

5. Control Value at the Step of Executing the

Strategy

Figure 4: The answer in the run the settlement strategy stage

for control values.

The value of the control appears, in Figure 4 it can be

see that students carry out mathematical procedures

using the concept of division to carry out the

settlement strategy.

6. Relational Understanding Value at the Step of

Executing the Strategy

The value of relational understanding arise when

students carry out a settlement strategy, using

structures obtained from the results of procedures that

is carry out previously. Figure 5 below shows the

emergence of relational values.

An Analysis of Values in Mathematical Problem Solving in Secondary School

217

Figure 5: The answer at the stage of completing the

completion strategy for the value of relational

understanding.

7. Reasoning Value for the Step of Evaluating the

Result

Reasoning values appear, students could generalize

from the mathematical procedures obtained to lead to

a conclusion. Figure 6 shows the reasoning values

that is appear.



Figure 6: The answers at the checking stage for reasoning

value.

Figure 7: The answers in the Re-checking stage for

rationalism values

8. Rationalism Value for the Step of Evaluating the

Result

Rationalism values arise, students could give reasons

(conclusions) that have been done. Figure 7 shows the

value of rationalism appear.

Based on the analysis on problem solving

worksheet above, the value that are not appear at the

problem solving step for the category of character

education is the value of discipline which is the value

that students use in understanding mathematical

problems, students are categorized into understanding

mathematical problems if they understand from what

they read and understand what they are going to solve

from the problem stated. From the students’ results in

completing worksheet, they actually could write the

information stated and write down the question asked

in sequence, but are wrong in interpreting the

problems stated. If the students only write "asked:", it

is not enough for them to be categorized into

understanding mathematical problems without

understanding the presented information in the

problem given. Later, it can support them to choose

what strategy for solving the problem. The problems

occurred due to the lack of 'ability to digest problems

in this term, the story problem, also due to their faults

in changing problems into mathematical situations.

The results of this study are also support by research

that is carry out (Sun et al., 2005) which results was

that students' verbal abilities in digesting sentences in

story problems are still low. Moreover, from the

finding by (Seah & Bishop, 2000) and (Seah et al.,

2001), it is state that students fail to solve problems

because they are not have good reasoning in changing

the real situation into mathematical situations. 

The mathematical values appearing are the value

of control and the value of rationalism, while the

value that are not appear is the value of objectivism.

Control value is the value that appear at the stage of

carrying out the settlement strategy. The emergence

of control values is discover able when students use a

division procedure they are learn before in order to

carry out a settlement strategy. Students who could

associate prior knowledge, then students are able to

solve problems (Meltzer, 2002) Students could use

the knowledge they have to solve problems in

worksheet that make control values appear. The value

of rationalism appear at the re-checking stage,

because at that stage students could give reasons for

what has been written and mention the definition of

the systems of equation with three variables meaning

that students had already understand the definition of

the systems of equation with three variables.

The value of objectivity are not appear in the

planning strategy for completion, this is assume

because students do not have understanding of

variable concept relate to the knowledge of

prerequisites in learning the systems of equation with

three variables material, namely knowledge of

variables, whereas knowledge of variables is need in

order to solve the systems of equation with three

variables problems. In the analysis of worksheet

results, students could translate problems into

variable forms. The variables use are not appropriate

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base on the problem give, the variables x, y, and z are

use for replacing the number of days use in

accordance to the provisions of the problem give.

Understanding the variables correctly in the systems

of equation with three variables material strongly

determines the outcome of the correct resolution. The

results of this study are in line with the results of

research conducted by (Osta & Labban, 2010) which

show that students don’t have good planning in a

completion strategy until the stage of applying the

strategy.

The values that arise in the step of problem

solving in the value of mathematics education are

reasoning and relational understanding, while the

value of relevant knowledge are not appear. The value

of relational understanding arise at the step of

applying the strategy. Students are able to connect the

facts state in order to solve problems. Otherwise,

students are not understand the meaning of the

variables used before, making their answers are not

precisely good. This is in accordance with opinion

(Leung et al., 2006) that to solve a problem, other

skills such as organizing data, classifying or

determining certain relationships or patterns are need

so that it is possible that there are unusual ways use

to solve problems.

Reasoning is that students can connect one fact

with other to lead into a conclusion (Bishop, 2008) in

doing this value-based worksheet. In this study, the

reasoning value appear at the evaluation step.

Students were able to deduce ideas from the results

obtain after connecting the ideas obtain in solving

problems. There are three similarities in the problem

call the systems of equation with three variables.

The students are firstly expected to be able to

solve problems in a real context by using value-base

worksheet, but the fact showed that the value of

relevant knowledge is not appear at the step of

applying strategy. They are able to apply the

knowledge obtain at the planning step but they make

wrong in using the concepts and principles of the

systems of equation with three variables when

applying the solving strategy because students is not

understand the meaning of the variables. According

to (Ellison, 2009)the problem is give so that students

can practice and think deductively, then students can

see the relationship and the use of mathematics in

daily, also able to master

mathematical skills and

strengthen the mastery of mathematical

concepts.



4 CONCLUSION

Based on the observation analysis of value in

mathematical problem solving in secondary school, it

is know that some important values occurrence when

students do the value-based worksheet. For the

character value category, discipline values is not

appear at the step of understanding problem because

students cannot understand the problem correctly. For

the mathematics education value category, that is not

appear at the step of executing the strategy

is the

relevant knowledge because the students is not

understand how to interpret the variables they make,

and the value that appears are the value of relational

understanding and the value of reasoning. For the

mathematical value category that is not appear at step

of planning the problem solving strategy

is the value

of objectivism because students do not have good

understanding of variable concept related to the

knowledge of prerequisites in learning of systemsof

equation with three variable material which is

knowledge of variables, and the value that appears are

value of control and rationalism.

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