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Journal of Physics: Conference Series

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Mathematical Reasoning: The characteristics of students' mathematical

abilities in problem solving

To cite this article: Sri Indriati Hasanah et al 2019 J. Phys.: Conf. Ser. 1188 012057

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The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

Mathematical Reasoning: The characteristics of students'

mathematical abilities in problem solving

Sri Indriati Hasanah, Chairul Fajar Tafrilyanto, and Yuniatul Aini

Universitas Madura, Jl. Raya Panglegur km, 3.5 Pamekasan, Jawa Timur, Indonesia

E-mail: indriati_math@unira.ac.id

Abstract. Mathematics and mathematical reasoning are two things that cannot be separated.

Understanding mathematics is obtained through reasoning, while reasoning is understood and

trained through learning mathematics. Therefore reasoning skills are needed by students when

learning mathematics. Students who have the ability to reason during the process of

understanding, reasoning during planning problems, reasoning in resolving and reasoning in

drawing conclusions will make it easier for them to understand Mathematics. So that

mathematical reasoning ability is needed to build a student's mathematical abilities. It can be

said that the character of students 'mathematical abilities influences students' mathematical

reasoning. This study aims to describe students' mathematical abilities in solving mathematical

problems by using mathematical reasoning. This study uses a qualitative approach. The

subjects of this study were two eighth grade students of junior high school. The results showed

that students with high mathematical abilities could be described as having good mathematical

reasoning because it had fulfilled four indicators of mathematical reasoning. Whereas for

students with low mathematical abilities are still very lacking in the process of reasoning

because they cannot fulfill the four indicators of mathematical reasoning. Subjects are only

able to understand the problem

1. Introduction

Mathematics is an important lesson in improving the quality of education because its role is quite

relevant to the development of science and technology. Through mathematics lessons, students can

practice their abilities continuously so that they are increasingly developing. Purwosusilo [1] said that

fundamentally mathematics is a science that is needed in various fields, both in mathematics itself and

in other fields. Mathematics not only meets the needs of the present but also meets the needs of the

future.

There are five Process Standards that students need to possess and master in mathematics learning:

(1) problem solving; (2) reasoning and proofing; (3) communication; (4) connections; and (5)

representation. Thus, reasoning ability is one of the important things that need to be mastered by

students to support their success in learning mathematics [2]. However, the essence of solving

mathematical problems that are needed is reasoning ability. Through reasoning, students are expected

to see that mathematics is a logical study. Thus, students feel confident that mathematics can be

understood, thought out, proven and can be evaluated, as well as to do things related to mathematics

required reasoning.

The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

The reasoning is a process in thinking that combines two or more thoughts to draw a conclusion to

get new knowledge. Meanwhile, reasoning is "the process of thinking that attempts to connect facts or

evidence that are known to lead to a conclusion". So, reasoning can be interpreted as a thought process

to obtain logical conclusions based on relevant facts that truth has been proven or assumed beforehand

[3,4].

Mathematical reasoning is a process that is carried out to get a conclusion based on logical-

mathematical premises based on relevant facts and sources that have been assumed to be true. This

was also conveyed by Wahyudi [5] who said that mathematical reasoning is a process for obtaining

conclusions based on mathematical premises that have been known or assumed. Based on the

explanation above it can be concluded that mathematics and mathematical reasoning are related. This

was also mentioned by [6,4] that "mathematical material and mathematical reasoning are two things

that are inseparable, mathematical material understood through reasoning and reasoning is understood

and trained through learning mathematical material". So that reasoning skills are needed by students

when learning mathematics. Baroody [7] stated that reason is an important tool in mathematics an in

daily life since many problems in mathematics and daily life requisite reasoning to solve then.

Students are able to do reasoning if they are able to use reasoning skills in patterns and traits,

manipulate mathematics in generalizing or explain mathematical ideas and statements. The higher the

level of students' reasoning, the faster the learning process will be in achieving learning indicators.

The reasoning ability is the basic ability of mathematics itself. This is in accordance with the results of

Sppaile [8] that mathematical reasoning ability has a positive influence on mathematics learning

achievement.

Mathematics learning achievement is the result achieved by students after the learning process.

Mathematical skills can be divided into 3 levels: high mathematics skills, moderate mathematics skills,

and low mathematical abilities. The reasoning ability becomes one of the goals in the learning of

mathematics to train the way of thinking and reasoning of conclusions and develop the ability to solve

mathematical problems. The goal in learning mathematics in schools is to practice thinking and

reasoning in drawing conclusions, developing problem-solving skills, and developing the ability to

convey information or communicate ideas through oral, written, graphic, map, diagram, and so on [9].

However, in this study reasoning ability is an ability that must be possessed by students in drawing

conclusions, and the ability to solve problems.

In studying mathematics, students must solve mathematical problems. This is supported by Branca

[10] states that "Problem-solving is the heart of mathematics" which means the main core of

mathematics is problem-solving. Problems usually contain a situation that encourages someone to

solve it but can not directly determine what the solution are.

In solving mathematical problems, students should have the ability to reasoning during the process

of understanding, reasoning during planning problems, reasoning in resolving and reasoning in

drawing conclusions, so that mathematical reasoning skills are needed to build mathematical abilities

in a student. Problem-solving in mathematics engaged the student to coordinate [11]. It can be said

that the character of students 'mathematical abilities influences students' mathematical reasoning.

Some research about mathematical reasoning have been done by some researches, such as the result of

research from Risqi [12] said that mathematical reasoning abilities are still low, its proof by result the

students answer that analyzed use the indicator. While Menderes [13] said that there is a significant

difference in gender about mathematical reasoning. The differences of this study are in this study

analysis the characteristic of student mathematical abilities especially about mathematical reasoning,

that the subjects consist of students with high ability and students with low ability in math. While in

Risqi look a mathematical reasoning student by classical students and Menderes look a mathematical

reasoning student by gender. The purpose of this study was to find out how the characters, and the

differences between junior high school students in the process of reasoning between students who

have high ability in mathematics and students with low math abilities.

The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

2. Method

This research is qualitative research. Qualitative research is research that intends to understand the

phenomenon of what is experienced by research subjects such as behavior, perception, motivation,

action, etc. Holistically, and in a descriptive way in the form of words and language, in a specific

context that is natural and utilizing various natural methods [14]. The type of research used in this

study is a case study. Case Study is a type of research carried out intensively, in detail, and in-depth on

a particular organism, institution, or object.

This research was conducted at SMPN 1 Larangan Pamekasan Madura. The subjects of this study

were 2 students of eight grade, consisting of one student who had high mathematics skills and one

student who had low mathematics skills. There are three instruments used in this study. First, the

Mathematics Ability Test (TKM), which is used in the subject selection process which is adapted from

the junior high school National Examination (UN) questions. Second, Problem Solving Test (TPM)

consisting of TPM 1 and TPM 2, Tests are conducted to determine the level of students' ability to

solve mathematical problems based on their mathematical abilities. Problem-solving test (TPM) is

done by giving a question to the research subject and asking students to solve it. In this study,

researchers made questions in the form of a description problem. The question is made by the

researcher and, validated by an expert validator. After validation, a legibility test is conducted to find

out whether this problem is suitable for use or not. If it is not valid, a new TPM draft will be prepared.

Readability test is done by giving TPM to 1 class VIII student who is not the subject of research.

Readability testing is done to find out whether the TPM draft can be understood or not. If the draft

TPM can be understood properly, the TPM is ready to be used as a research instrument, otherwise, it

will be corrected until the TPM can be read and understood well. The last interview, in this study,

using open interviews in which this interview is used to find out the opinions of students while

working on problem-solving tests (TPM) and to explore and explore students' understanding of

integers. This interview guide is just an outline of the question. Other more in-depth questions can be

submitted and developed in the interview activity, depending on the process conditions in solving

mathematical problems. The interview guide refers to what is seen in reasoning.

In this study, researchers used written tests and interviews to collect data. The validity of the data is

done by using time triangulation, by checking the degree of trust of several data sources obtained at

different times. This data collection is done at least twice with different problem-solving tests but the

contents of the test remain the same. This research was conducted by comparing the results of task-

based interviews from TPM 1 with the results of task-based interviews from TPM 2 (equivalent to the

first problem) at different times. If the same tendency is obtained, data collection on the subject has

been completed and conclusions can be drawn. But if the data from the interview from TPM 1 and

TPM 2 shows a different tendency then an interview from TPM 3 (equivalent to the first and second

questions) is conducted. If it tends to be the same as the data from the interview from TPM 1, then the

data about mathematical reasoning in solving math problems of junior high school students is obtained

from the TPM 1 and TPM 3 interview data. Data about mathematical reasoning in solving

mathematical problems of junior high school students is obtained from the TPM 2 and TPM 3

interview data. If from the data comparison all the data tend to be different then it is carried out

repeatedly until valid data is obtained. Data is said to be valid if there is consistency, opinion or

thought on the results of task-based interviews that have been conducted by the researcher. Thus, it is

expected that all data reinforce each other and provide in-depth details about solving mathematical

problems of junior high school students.

In this study time triangulation was used as an analysis of test and interview data, checking the data

carried out by giving almost the same questions at different times. The analysis refers to the reasoning

indicator at each stage of the Polya problem-solving. Data analysis in this study is based on the

following stages:

2.1 Data reduction

Data reduction is the process of selecting, focusing, simplifying, abstracting, and transforming field

notes or transcripts. Data reduction is a form of analysis that simplifies, directs, and organizes data so

The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

that conclusions can be drawn. Data reduction continues until the final report is complete. If there is

invalid data, then the data will be analyzed. This study uses triangulation of data collection time. The

data reduction process that will be carried out includes (1) Gather problem-solving test results, check

and review problem-solving test results. Then make a data transcript consisting of students'

explanation of the problem solving given in written form; (2) Review the results of the interview.

Then make transcripts of the interview results about students' mathematical reasoning in solving

problems; (3) Play the results of interview recordings repeatedly so that researchers can write

appropriately about the students' mathematical reasoning process in solving problems such as those

that have been the subject of the interview; (4) Re-examine the results of the transcript by listening to

the results of the interview with the related subject.

2.2 Data display

Data display is a collection of information that is organized and categorized so that it is possible to

draw a conclusion. The data displayed in this study is to classify data about students' mathematical

reasoning in terms of high mathematical abilities in solving mathematical problems.

2.3 Drawing conclusion

Drawing conclusions in this study are the stage of understanding the patterns, information, and

possible arrangements, as well as the causes that arise during the research process. The conclusion of

this study is used to reveal the characteristics of the mathematical abilities of junior high school

students in solving mathematical problems with mathematical reasoning.

3. Results and discussion

Subject selection is selected based on the results of the mathematic ability test. Subject candidates

consist of 20 students of eighth grade SMPN 1 Larangan. Furthermore, these students were given a

mathematics ability test instrument (TKM) to identify their mathematical abilities. Based on the test

results obtained 7 students with low ability, 8 students with moderate ability, and 5 students with high

abilities. Furthermore, the results of these abilities are re-analyzed so that 2 students will be used as

research subjects consisting of 1 student with low mathematical abilities and 1 student with high

mathematical abilities. The selection of 2 subjects of this study, besides using their mathematical

abilities, also used the consideration of the teacher who taught mathematics in the eighth grade.

Selected research subjects are presented in Table 1.

Table 1. The List of Research Subjects

Based on Table 1, it as can be revealed that two subjects own different skills in tern of mathematic

competence, i.e. The first subject with poor co ability in mathematics having score 37, while the

second subject with the better ability having score 90. Figure 1. is a problem-solving test that is used

to reveal reasoning based on the characteristics of students' abilities. This test is an essay about algebra

that requires a solution and cannot be immediately solved by routine procedures.

Figure 1. Problem-solving test 1

PROBLEM SOLVING TEST (1)

Suppose that a, b, c, and d are positive integers which, when divided by 13,

will have 12.9.11, and 7, respectively, then specify the remainder of 3a +

4b-3c + 2d if divided by 13?

The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

Figure 2. is a is a problem-solving test that is used to reveal reasoning based on the characteristics

of students' abilities. The test has difficulty level which is almost the same as figure 1.

Figure 2. Problem-solving test 2

Research Results Shows that the differences in mathematics abilities of junior high school students

in solving mathematical problems with mathematical reasoning between students who have high

mathematical abilities and students who have low mathematical abilities are very different, the

differences are as follows: (1) Students with high mathematical abilities at the stage of understanding

the problem, they are able to understand the details of information to help answer the problems; (2)

Students with low mathematical abilities at the stage of understanding the problem cannot mention the

information that is known, they only able to mention information about the question; (3) Students with

high mathematical abilities able to plan a problem solving to answer the mathematic question; (4)

Students with low mathematical abilities do not able to plan a problem solving to answer the

mathematic question; (5) Students with high mathematical abilities have been able to solve problems

based on plans that have been made in the previous stage; (6) Students with low mathematical abilities

cannot carry out the problem-solving stage, because they are not able to make planning in the previous

stage; (7) Students with high mathematical abilities are able to re-examine with what has been done in

the previous stages, and students are also able to analyze conclusions related to the results obtained;

(8) Students with low mathematical abilities do not able to re-examine because they cannot complete

the existing problems correctly so that students cannot draw conclusions from existing problems. The

results of the research on mathematics ability of junior high school students with mathematical

reasoning above can be described in detail as follows:

3.1 Subjects with High Mathematical Ability

In understanding the problem both for the first test and the second test, it is described that the subject

gives reasons or proof of the truth of the solution by reading the problem carefully and can identify so

that students understand what is known and asked about the problem, this is in line with the research

conducted by Putra and Novita [15] who stated that high mathematics ability student was able to

identify the problem by making the information know In the next stage the subject can examine the

validity of an argument by suggesting that the information obtained is correct and in accordance with

the problem. So the subject draws conclusions by summarizing the information obtained from the

problem (both known of data and questioned data) by using a standard sentence and based on what has

been understood about the question.

In the problem-solving planning stage to test both number one and number two questions, it is

described that the subject can manipulate mathematics by designing a settlement model or

mathematical strategy that will be used to solve the problem using the first three methods, both

substitutions, and the third distributive property in integers. Furthermore, the subject gives reasons or

proof of the truth of the solution by explaining that the design of the mathematical model is used to

find the values of a, b, c, and d. Which is then the value is subsidized and then used using distributive

properties in integers. Then the subject checks the validity of an argument by suggesting that the

mathematical model that has been made is correct. And the next step the subject draws conclusions by

concluding the solution plan that is done to solve the problem by using his own language.

In the staging problem solving for the first and second tests, it was described that the subject in

carrying out the problem-solving plan in accordance with the problem-solving plan subject did

mathematical manipulation by making a mathematical model, and solving the problem based on a plan

PROBLEM SOLVING TEST (2)

Suppose that a, b, c, and d are positive integers which when divided by 9

remain at 15.11.7, and 5, then specify the remainder of 2a + 3b + 4c + 2d if

divided by 9?

The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

that had been done previously. Then the subject gives reasons or proof of the correctness of the

solution by saying that after assuming the values of a, b, c, and d just subscribe to it then use the third

step which uses distributive properties in integers. Next, the subject checks the validity of an argument

by suggesting that the results obtained are correct. And the last step of the subject draws conclusions

by concluding the solution to the problem that has been done. These findings are in line with research

of Irawati and Hasanah [16] subjects with high ability to provide logical reasons for each step taken in

solving problems.

In the re-examine stage described that the Subject checks the validity of an argument by rereading

the answers already obtained, and checking the correctness of the steps correctly. The subject draws

conclusions by concluding the resolution of the problems that have been carried out which have been

verified.

3.2 Subjects with Low Mathematical Ability

In t he stage of understanding the problem both for the first and second tests, it is described that the

subject is less able t o provide reasons or proof of the truth of the solution and this is seen when the

subject reads the problem in a less accurate way and cannot identify so that the student is unable to

mention complete information, this is same with research of Minarni etc [17] that student ability is low

in understanding problem . but was able t o mention the information asked about the problem . In the

next stage, the subject is able t o exami ne the validity of an argument by suggesting that the

information obtained is correct. Then the subject is less able to draw conclusions (both known of data

and questioned data) given in the problem.

In the stage of problem-solving planning for the first and second tests, it is described that the

subject is unable to manipulate mathematics and cannot design a settlement model or strategy that will

be used to solve the problem. Furthermore, the subject is unable to provide reasons or proof of the

truth of the solution. The subject is also unable to check the validity of an argument. And the next step

the subject is unable to draw conclusions. This can be seen when the subject is unable to answer the

test given either verbally or by writing.

In the staging problem solving for the first and second tests, it was described that the subject was

unable to carry out the problem-solving plan because the subject could not carry out a problem-solving

plan both orally and in writing. So that the subject is not able to provide reasons or proof of the truth

of the solution, this is due to a lack of capacity for their kick off ability related to evidence material

[18] The subject is also unable to check the validity of an argument. And the subject was also unable

to draw conclusions.

In the re-examine stage described that the subject is unable to check the validity of an argument

because he cannot answer the questions given in the form of verbal or verbal. So that the subject is

unable to draw conclusions from the problem.

Based on the description above it is clear that students with high math abilities are better than

students who have low mathematical abilities both in accuracy and in reasoning in problem-solving.

The similarity of mathematical reasoning between junior high school students with high mathematical

abilities and students with low math abilities lies in the stage of understanding the problem when

mentioning the information asked. Whereas the difference lies very significantly because students who

have high math skills have fulfilled these four indicators and can solve the problems given correctly

and correctly, while for students with low mathematical abilities they cannot fulfill all four indicators

so that they become obstacles for the students to be able to solve the problem given.

The results of research for students with low ability have the same results as the research conducted

by Risqi [12] , that they have a low level of mathematical reasoning in solving a problem. Most of

them are still low in giving examples in solving problems, compiling evidence, checking the validity

of answers and drawing conclusions, States that in general most students in mathematical reasoning

are in the middle and low stages [19].

The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

Based on the observations of researchers, students' inability in mathematical reasoning is because

they have just entered the "formal operational" stage. This is in accordance with the opinion of Piaget,

students are in the 11-15 years are in formal operation development [20]. In these ages, the thing

needed to consider is teenagers development aspect. Where the student can experience a transition step

from the usage on a concrete operation into operation.

4. Conclusion

The results showed that the character of students with high mathematical abilities at the stage of

understanding the question was described by collecting information obtained from the problem (data

that was known and asked) by using a standard sentence and based on what was understood about the

problem. Meanwhile, at the stage of problem-solving planning the subject manipulates mathematics by

designing a settlement model or strategy that will be used to solve the problem. This is done because it

is considered that the mathematical model can be used to facilitate the problem-solving process. At the

stage of the problem solving the subject manipulates mathematics by creating a mathematical model,

by saying that after assuming the values of a, b, c, and d just subscribe to it then use the third step

which uses distributive properties in integers. Subjects have also carried out problem-solving in

accordance with the steps that have been planned. Meanwhile, in re-examining stage the subject

checks the truth/truth of an argument by re-reading the answers that have been obtained and checking

the truth of the steps correctly. Then the subject draws conclusions by concluding the resolution of the

problem that has been carried out which has been checked for truth. As for the character of students

with low mathematical abilities, it is described that the subject is only able to understand the problem.

While at the stage of making a problem-solving plan, the stage of carrying out the problem-solving

plan, and the reexamination stage of the subject cannot show the reasoning process

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The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018

IOP Conf. Series: Journal of Physics: Conf. Series 1188 (2019) 012057

IOP Publishing

doi:10.1088/1742-6596/1188/1/012057

[13] Menderes and Abdullah 2017 Analysing Mathematical Reasoning Strategy Of Secondary

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... Reasoning also enables students to determine various ideas from facts or use various existing information to solve mathematical problems. According to the National Council of Mathematics Teachers (NCTM, 2000), mathematical activities are inseparable from reasoning because it plays a vital role in solving problems (Rohana, 2015;Napitupulu et al., 2016;Hasanah et al., 2019). Mueller & Maher (2009) stated that reasoning forms the basis of mathematical understanding. ...

... This happens because of the (2000) that mathematical reasoning occurs when the learner: 1) observe a pattern, 2) formulate generalization and conjecture related to observed regularity, 3) assess/test the conjecture; 4) construct and assess mathematical arguments, and 5) describe (validate) logical conclusions about some ideas and its relatedness. This is also in line with the opinion of experts that reasoning works when someone tries to understand problems, make relationships and representations between concepts, as well as assumptions and generalizations, to prove these allegations (Napitupulu et al., 2016;Hasanah et al., 2019). Students' reasoning abilities are built when they are involved in the problem-solving process. ...

... Napitupulu et al. (2016) stated that students have difficulties constructing proof due to a lack of understanding of the materials that need to be applied. Most students with low reasoning abilities have weaknesses in providing examples in solving problems, compiling evidence, checking the validity of answers, and drawing conclusions (Hasanah et al., 2019). ...

... The researchers considered that there are still many high school students who have difficulty in solving mathematical problems, particularly problems related to the concept of comparison. This is because the character of mathematical problems invokes challenges and situations that encourage students to solve but cannot immediately obtain the solution [26]. It is important for the researchers to examine students' mathematical problem-solving abilities on the concept of comparison. ...

... Subjects were derived from the highest score of each category. 26 understand the problem given, but he cannot write well based on his understanding. He missed one information, age ratio. ...

... In Figure 4, the students were still confused in finding the volume of the pyramid so that they had difficulty in answering question number 3. This finding also reinforced by another research that shows students still have an error in drawing conclusions [3], particularly students with the low mathematical ability [9] In general, almost all students had difficulties answering this question. Consequently, Students still have the inadequate ability in drawing conclusions from a given statement. ...

... Many come up with arguments that mathematics education in elementary schools do not adequately emphasize reasoning development or students' logical and thinking process. Mathematical reasoning is a process that purports to obtain a conclusion based on the logical-mathematical premise, and according to facts and relevant sources considered valid [5]. In general, mathematics education is dominated by introductions of formulas and concepts verbally but without sufficient focus on students' reasoning. ...

... Student character can affect mathematical reasoning skills. Mathematical reasoning in students is influenced by students' mathematical abilities so that students' low mathematical skills are still challenging to improve mathematical reasoning, so several indicators are needed to develop mathematical reasoning [10]. Mathematical materials will be readily understood through reasoning ability, and reasoning ability can be trained through math learning [11]. ...

... Seen the students have not good mathematical abilities, especially the ability to reason. The ability of reasoning in patterns and properties, mathematical manipulation, generalization as well as explaining ideas and statements can be done by students to train and apply reasoning in learning [10]. ...

... Penalaran matematis adalah prosedur yang digunakan dalam memperoleh sebuah hasil berdasarkan premis matematis logis yang didasari dengan fakta serta sumber yang telah dianggap benar dan relevan (Hasanah, Tafrilyanto, & Aini, 2019). Lebih lanjut, Brodie et al., (2010) menjelaskan bahwa penalaran matematis adalah kunci pokok utama dan menjadi keterampilan dasar yang harus ada dalam pembelajaran matematika di sekolah. ...

Bq. Malikah Hr
Indah Arry Pratama
Pyo Apriliana Munawarah

The purpose of this research was to describe the effect of fully online learning to the mathematical reasoning abilities of students. The research was a mixed-method using quantitative and qualitative methods with one group pretest-posttest design. There were 32 students of class XI MIA MA NW Wanasaba, Wanasaba Sub-District, East Lombok Regency as the sample. Instrument of this research was the mathematical reasoning abilities essay test consists of 10 questions on learning materials of limit function. The quantitative data analysis using descriptive statistics with paired sampel t-test. According to the results of data analysis, it was discovered that (). This indicated that there was a significant difference between pretest and posttest. Based on the percentage of the mathematical reasoning abilities test of students, the percentage of pretest was 63% of the students have the mathematical reasoning abilities with good category and posttest was 34% of the students have the mathematical reasoning abilities with good category. In addition, there were 84% of the students prefer the blended learning than the fully online learning, because it was effective to the mathematical reasoning abilities of students. Based on the results of the research it can be concluded that the fully online learning was no more effective than blended learning.

... Mathematics and reasoning are two terms that relate to one another. Mathematical content requires reasoning to understand it, whereas reasoning requires learning mathematics to be trained (Hasanah, Tafrilyanto, & Aini, 2019). ...

Mohamad Salam
Salim Salim

This study examines students' mathematical reasoning based on Discovery learning models in terms of gender. This research was conducted at the SMPN 3 Kendari with quasi-experimental methods involving two classes with different treatments. The simple random technique is used to determine the class of research. Class VII. 6 (experimental class) consisted of 15 women and 11 men, while class VII.9 (control class) consisted of 15 men and 7 women. The instrument used was a student's mathematical reasoning ability test consisting of four items in the form of essays tested. Data processing using 2-way ANOVA with further tests using Scheffe. The conclusion obtained is that students are given a learning discovery model, the reasoning ability of male students excels in the ability to give mathematical problems verbally and in writing provided in the form of logical diagrams that contain existing data, perform mathematical manipulation related to the problem, and ensure validity as an argument, whereas women excel in the ability to draw conclusions based on relationships between mathematical concepts. The discovery learning model can increase students' mathematical penalties and overcome gender discussions.

Tina Sri Sumartini

ABSTRAKPenelitian ini dilatarbelakangi oleh hasil-hasil penelitian terdahulu yang menunjukkan bahwa kemampuan pemecahan masalah matematis siswa belum sesuai dengan yang diharapkan. Salah satu pembelajaran untuk meningkatkan kemampuan pemecahan masalah matematis adalah pembelajaran berbasis masalah. Tujuan penelitian ini adalah untuk mengetahui peningkatan kemampuan pemecahan masalah matematis siswa sebagai akibat dari pembelajaran berbasis masalah. Penelitian ini adalah kuasi eksperimen yang menerapkan dua pembelajaran yaitu pembelajaran berbasis masalah dan pembelajaran konvensional. Populasi dalam penelitian ini adalah siswa di salah satu SMK di Kabupaten Garut. Pengambilan sampel dilakukan secara purposive sampling, dan diperoleh dua kelas sebagai sampel penelitian. Instrumen penelitian yang digunakan adalah tes kemampuan pemecahan masalah matematis. Berdasarkan hasil analisis tersebut diperoleh kesimpulan bahwa: (1) peningkatan kemampuan pemecahan masalah matematis siswa yang mendapat pembelajaran berbasis masalah lebih baik daripada siswa yang mendapat pembelajaran konvensional, (2) Kesalahan-kesalahan yang dilakukan oleh siswa ketika mengerjakan soal-soal yang berkaitan dengan kemampuan pemecahan masalah matematis adalah kesalahan karena kecerobohan atau kurang cermat, kesalahan mentransformasikan informasi, kesalahan keterampilan proses, dan kesalahan memahami soal.ABSTRACTThis research is motivated by the results of previous studies that showed that students' mathematical problem solving ability is not as expected. One lesson to improve mathematical problem solving is based learning problems . The purpose of this study was to determine the increase in students' mathematical problem solving ability as a result of problem-based learning. This study is a quasi-experimental study that applies two problem-based learning and conventional learning. The population in this study were students in one of the vocational schools in Garut. Sampling was done by purposive sampling, and obtained two classes as the study sample. The research instrument used was a test of mathematical problem solving abilities. Based on these results we concluded that: (1) the increase in students' mathematical problem solving ability that gets problem-based learning better than students who received conventional learning, (2) mistakes made by student when working on the problems related to mathematical problem solving ability was a mistake due to carelessness or less closely, tansform fault information, error process skills, and misunderstanding question.Keywords: problem based learning, mathematical problem solving ability

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show that in solving the problem PISA on shape and space, high mathematics ability students were able to identify the problem by making the information known from PISA issues related to the shape and space content.

This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the participants and the criterion was determined as taking the course of geometry in the graduate program. Data was collected in two steps: a diagnostic test form about the definition and features of diagonal was applied to participants firstly and according to the answers of the participants to the diagnostic test form, semi-structured interviews were carried out. Data collected form the diagnostic test form and the semi-structured interviews were analyzed with descriptive analysis. According to the results of the study, it is understood that the prospective teachers had difficulties with the diagonals of parallelogram, rhombus and deltoid. Moreover, it is also seen that the prospective teachers were inadequate to support their ideas with further explanations although they could answer correctly. İt is thought that the inadequacy of the prospective teachers stems from the inadequacy related to proof.

Abstract This paper is the result of the first phase of the research about the development of students' mathematical understanding and representation ability through Joyful Problem-based Learning (JPBL) at Public Junior High School in North Sumatera, Indonesia. The population is all of the students of public junior high school (PJHS) in North Sumatera. Samples choose based on stratified random sampling. The samples are the students of PJHS 27 Medan, PJHS 1 Percut Sei Tuan, PJHS 1 Tebing Tinggi, and PJHS 2 Pematangsiantar. The techniques used for collecting data is observation, interview, and essay test. The research findings: (1) Based on interview and observation found that conventional approach still uses in all of the class of PJHS, the students engagement in learning activity is very low, and most of the students do not attain minimal mastery achievement. (2) Based on essay test found that performance of the students in mathematical understanding and representation test is categories small. Keywords: mathematical understanding, mathematical representation, joyful problem-based learning

Arthur J. Baroody

"Problem solving, Reasoning, and Communicating, K-8: Helping Children Mathematically" describes the rationale for a reflective, problem-based view of teaching elementary-level mathematics, including the pros and cons of such an approach. The book's focus is why teachers should promote problem solving, reasoning, and communicating among young children; how these aspects of mathematical thinking develop in early childhood, and practical guidelines and activities for promoting these important mathematical processes. An electronic or paperback version of book is not available, and , the book is out of print. The following website promises to find a copy in a local library: <https://www.worldcat.org/title/problem-solving-reasoning-and-communicating-k-8-helping-children-think-mathematically/oclc/26308297> The book is available through online dealers such as AbeBooks <https://www.worldcat.org/title/problem-solving-reasoning-and-communicating-k-8-helping-children-think-mathematically/oclc/26308297> (for less than $10), eBay <https://www.ebay.com/sch/i.html?_from=R40&_trksid=m570.l1313&_nkw=problem%2Bsolving%2C%2Breasoning%2C%2Band%2Bcommunicating%2C%2BK-8&_sacat=0> for less than $15, or Amazong.com <https://www.amazon.com/s?k=Problem+solving%2C+reasoning%2C+and+communicating&ref=nb_sb_noss> for less than $10.

An analysis of seventh-grade students' mathematical reasoning Cukurova Universitesi Egitim Fakultesi Dergisi

E Erdem
R Gurbuz

Erdem E and Gurbuz R 2015 An analysis of seventh-grade students' mathematical reasoning Cukurova Universitesi Egitim Fakultesi Dergisi 45 142

dan Komunikasi dalam Pembelajaran Matematika (Yogyakarta: Departemen Pendidikan Nasional Direktorat Jenderal Pendidikan Dasar dan Menengah Pusat Pengembangan Penataran Guru (PPPG) Matematika)

Pemecahan Penalaran
Masalah

Penalaran Matematis Siswa Berkemampuan Tinggi dan Rendah dalam Menyelesaikan Persamaan kuadrat Jurnal Pendidikan Teori

Wahyudi

Wahyudi, et al 2016 Penalaran Matematis Siswa Berkemampuan Tinggi dan Rendah dalam Menyelesaikan Persamaan kuadrat Jurnal Pendidikan Teori, Penelitian, dan Pengembangan 1 1296