Mathematical Problem-solving Test Research Articles

INVESTIGATION OF STUDENTS' BEHAVIOR IN MATHEMATICAL PROBLEM SOLVING

This study is a qualitative research by using the descriptive method that aims to examine the behaviour of eighteen students in Bandung, Indonesia. Six issues related to geometry were given to eighteen of second-grade junior high school students with heterogeneous abilities. The problems given to the students contained all of the problem-solving strategies such as guessing and checking, make a picture, make a list, make a table, working backwards, looking patterns, and using a logical reason, solving simple problems and making questions. Data collection was conducted through mathematical problem-solving tests, recording students’ presentations, and interviewing among researchers and students after doing the problems. The result of recording was a video during the presentation process, and the interview would explore their understanding of the given problems to see the behaviour used by subjects of the research. The data in this research showed that many students’ behaviour identified; in the relevant literature, there are terms of the behaviour of problem-solving naive, routine, and sophisticated. However, the category "naïve," "routine," and "sophisticated" did not fully draw various behaviours observed, it was obtained additional category termed behavioural problem solver "naïve," "routine," "semi-sophisticated" and "sophisticated". It was due to the category of regular students can be divided into two, some students can be directed, and some of them cannot be directed to sophisticated behaviour. Thus, the routine category can be classified into two categories: routine and semi-sophisticated.

Choleris Students' Critical Thinking Process In Mathematics Problem Solving

The purpose of this study was to describe the critical thinking process of junior high school students with choleric personalities in solving mathematical problems. This research is a descriptive study with a qualitative approach. The subjects in this study were two students of MTs Hasanuddin Sidoarjo class VIII who had choleric personalities obtained from the results of personality tests. The research stages used by the researchers consisted of three stages, namely the preparation stage, the implementation stage, and the analysis stage. The data collection technique in this research is the technique of giving the Mathematical Problem Solving Test (TPMM) and interviews later to obtain valid and credible data, researchers use source triangulation. Based on the results of data analysis, it can be concluded that the choleric subject in solving mathematical problems shows the criteria for critical thinking: focus, reason, inference, situation, clarity, overview at the stage of understanding the problem. At the stage of making a plan for the completion of the choleric subject, it fulfills the criteria for critical thinking, focus, reason, inference, situation, clarity, overview. Likewise, at the stage of implementing the completion plan, the choleric subject meets the criteria for critical thinking, focus, reason, inference, situation, clarity, overview. Meanwhile, at the stage of re-examining the completion plan, the choleric subject only met the criteria for critical thinking, focus, reason, inference, situation, clarity, did not meet the criteria for critical thinking overview.
 Keywords: Critical Thinking, Mathematical Problem Solving, Choleric Personality

The Effectiveness of a Program Based on Problem-Solving in Mathematical Problem Solving among Grade Ten Students

This study examined the impact of a program based on problem-solving in mathematical problem-solving among 10th grade students. The sample of this study consisted of (89) male and female students; Wadi Bani Kharous Basic Education School and Om Hakeem Basic Education School located in AlBatina South Governorate (Oman). The study followed the quasi-experimental research design with experimental group consisted of (48) students, and control group consisted of (41) students. The instructional materials of Polynomial and Algebraic Functions Unit and Trigonometric Functions Unit for Grade 10th were designed according to a program based on problem-solving. The problemsolving test was valid and reliable. The findings indicated that there were significant statistical differences in mathematical problem-solving test between the experimental and control group due to teaching method in favor of experimental group. The findings indicated that there were no significant statistical differences in mathematical problemsolving test between male and female students. The findings also indicated that there were statistical significance differences in mathematical problem-solving test due to the interaction between and teaching method and gender. The study recommended organizing training workshops for mathematics teachers to introduce programs based on problem solving, training them to build educational programs based on problem solving, and urging them to adopt it due to the positive impact it has shown in teaching mathematics.

The Role of Emotional Intelligence as a Mediating Variable in Predicting Intrinsic Motivation in Solving Mathematical Problems among Fourth-Grade Students in the Sultanate of Oman

This study aimed to investigate the role of emotional intelligence as a mediating variable in intrinsic motivation prediction of the ability to solve mathematical problems among fourth-grade students in the Sultanate of Oman. The study sample consisted of 183 male and female students from six schools of the first cycle of basic education. The study tools are: Goleman's Emotional Intelligence Scale, the Intrinsic Motivation Scale of Lepper, and a mathematical problem-solving test prepared by the researchers. The content validity, and internal consistency reliability of the three tools were measured. The results found a weak and negative correlation between the ability to solve mathematical problems and each of: emotional intelligence, intrinsic motivation, and weak and positive correlation between emotional intelligence and intrinsic motivation. The results of this study also indicated that there is no mediating role for emotional intelligence in predicting intrinsic motivation in the ability to solve mathematical problems.
 
 Received: 24 February 2021 / Accepted: 18 March 2021 / Published: 10 May 2021

THE EFFECTIVENESS OF A PROBLEM-SOLVING PROGRAM IN SOLVING THE MATHEMATICAL PROBLEM AMONG 10TH GRADERS IN LIGHT OF THEIR VARIANCE OF THE MATHEMATICAL SELF-CONCEPT

This study aimed at investigating the impact of a problem-solving based program on mathematical problem-solving among 10th-grade students due to the variance of their mathematical self-concept. The purposive sample of this study consisted of (89) male and female students from Wadi Bani Kharous Basic Education School and Om Hakeem Basic Education School at Sultanate of Oman. The sample was divided into an experimental group, which consisted of (48) students, and the control group consisted of (41) students. The instructional materials of Polynomial and Algebraic Functions Unit and Trigonometric Functions Unit for Grade 10th were designed based on the problem-solving program. The problem-solving test and mathematical self-concept scale were developed, and both were valid and reliable. The findings showed that: there were significant statistical differences in the mathematical problem-solving test in favor of the experimental group. The findings indicated that the significant statistical differences in the mathematical problem-solving test are due to the mathematical self-concept and the absence of statistically significant differences in the mathematical problem-solving test is due to the interaction between teaching methods and mathematical self-concept in light of the findings, the study suggested some crucial recommendations including the importance of enriching mathematics curricula with mathematical problem-solving strategies and having professional development workshops to train teachers on how to use mathematical problem-solving strategies and urge them to use these strategies in teaching Mathematics

PROFILE OF HIGH SCHOOL STUDENTS REFLECTIVE THINKING IN SOLVING ALGEBRA PROBLEMS VIEWED FROM MATHEMATICAL ABILITY

This study aims to describe students' reflective thinking in solving algebraic problems with different mathematical abilities. This study used reflective thinking components by Surbeck, Han, and Moyer, including reacting, elaborating, and contemplating. This study was descriptive qualitative research that used a qualitative approach. The instruments in this study were mathematical ability tests, mathematical problem-solving tests, and interview guidelines. This study was conducted by selecting three subjects from 31 students of SMAN 1 Pacet with female gender who have high, medium, and low mathematical abilities. This study's results were at the reacting stage; the three students analyzed what was known and asked according to the information provided, analyzed the relationship between what was known and asked, and reasons. At the elaborating stage, the three students were able to analyze the theory used. High and low-ability students have encountered similar questions. Medium ability students admitted that they had never met similar questions but examined the differences. High and medium-ability students explain the results obtained in detail at the contemplating stage, check their results, and make conclusions. Low ability students only explain part of the solution because they cannot find the solution. They try to correct their mistakes but give up, so they do not make conclusions. For low-ability students, the teacher can provide practice questions that trigger reflective thinking to solve math problems correctly and improve their weaknesses.
 Keywords: reflective thinking, mathematics problems, high school algebra, mathematical ability.

Development of Mathematical Problem Solving Tests on Geometry for Junior High School Students

One of the cognitive skills that students must have is problem-solving ability. Therefore, a standardized test is needed to measure this ability. However, until now, the tests used to measure mathematical problem-solving ability were not standardized. This research aims to develop a valid and practical mathematical problem-solving test in the discussion of triangles and rectangles. This research is part of the R&D 4D type with steps: Defined (analysis to develop a test), Design (designing a problem-solving test form), and Develop (expert judgment and small group trials). The instrument in this research was the validation sheet used by the validator to assess each test item. The data analysis technique used the Aiken method for expert judgment and qualitative descriptive for development testing. The result is a valid and practical mathematical problem-solving test because the V-Aiken value is more than 0.532. Based on this, the instrument can be used to measure the mathematical problem-solving ability of junior high school students in the discussion of triangles and rectangles.

فاعلیة استراتیجیات التفکیر المتشعب فی مهارات حل المشکلات الریاضیة لدى طالبات المرحلة المتوسطة The Effectiveness of Cross Thinking Strategies in Mathematical Problem-Solving Skills among the Middle School Female Students

هدف البحث إلى معالجة التدني في مهارات حل المشکلات الرياضية لدى طالبات المرحلة المتوسطة بمدينة الرياض بالمملکة العربية السعودية من خلال استراتيجيات التفکير المتشعب. ولتحقيق الهدف من البحث تم اتباع المنهج شبه التجريبي، حيث تکونت عينة البحث من (50) طالبة بالصف الأول المتوسط بمدرسة عمارة بنت حمزة بمدينة الرياض بالمملکة العربية السعودية، تم تقسيمهن إلى مجموعتين متساويتين قوام کل منهما (25) طالبة، الأولى تجريبية درست باستخدام استراتيجيات التفکير المتشعب، والأخرى ضابطة درست بالطريقة المعتادة. وتمثلت أداة البحث في اختبار حل المشکلات الرياضية وفقا لاستراتيجيات التفکير المتشعب، ومن خلال تطبيق مهارة تحديد المشکلة، والتخطيط لحل المشکلة، وتنفيذ الحل، والتأکد من صحة حل المشکلة. وأهم ما أسفرت عنه الدراسة من نتائج وجود فروق ذات دلالة إحصائية بين متوسط درجات طالبات المجموعتين التجريبية والضابطة في جميع مهارات حل المشکلات في التطبيق البعدي للاختبار لصالح المجموعة التجريبية، ما يدل على فاعلية استراتيجيات التفکير المتشعب في تنمية مهارات التفکير وحل المشکلات لدى طالبات المرحلة المتوسطة. The current research aimed to reveal the effectiveness of cross-thinking strategies in developing mathematical problem-solving skills among the middle school female students in Riyadh. To achieve the objective of the research, the quasi-experimental method was adopted. The sample of the research consisted of (50) female students in the first grade at AmaraBintHamzaSchool in Riyadh as the participants were distributed into two equal groups consisting of (25) students. The first experimental group studied using cross-thinking strategies, and the control group studied via the usual way. The researcher used the mathematical problem-solving test according to cross-thinking strategies as a research instrument by applying the skill of defining the problem, planning to solve the problem, implementing the solution, and making sure the problem is solved correctly. The most important results of the research were that there was a statistically significant difference between the mean scores of students of both groups in all the problem solving skills in the posttest in favor of the experimental group indicating the effectiveness of the cross thinking strategies in developing thinking skills and problem solving among the middle school students.

THE EFFECT OF MULTIMEDIA ON ENHANCING MATHEMATICAL PROBLEM-SOLVING SKILLS AMONG SEVENTH GRADE STUDENTS IN NORTH EASTERN PROVINCE, SULTANATE OF OMAN

This quantitative, analytical study discusses the impact of multimedia on enhancing mathematical problem-solving skills among seventh graders in the Northeast District. Where the problem arose in that research and studies indicated the low level of performance of seventh-graders in solving mathematical problems, and that the teaching method used is dominated by speech and instruction on the part of the teacher, and memorization and memorization on the part of the student, without interest in improving the level of his higher thinking capabilities, including the ability to Mathematical problem solving. Therefore, the study aims to discuss the impact of multimedia on enhancing mathematical problem-solving skills among seventh graders, and to know the suggestions of teachers and specialists in developing the multimedia program. The researcher used the descriptive approach and the semi-experimental approach to a sample of students of (153) students for mathematics. The study tools included; the achievement test in the skills of solving the pre and post mathematical problems of the control and experimental group, as well as a motivational measure in mathematics. The sample was divided into a control group (77) students, and an experimental group (76) students. The results showed that there was a statistically significant difference at the significance level (0.05) between the mean scores of the pre and post measurements of the experimental group students, which were studied according to the multimedia program on the mathematical problem-solving test for mathematics course. And the presence of a statistically significant difference at the significance level (0.05) between the mean scores of the experimental group students and the students of the control group on the problem-solving test.

ADAPTIVE REASONING OF SOCIAL SECONDARY STUDENTS

Adaptive reasoning is a component of basic mathematical skills that needs to be developed for students so that they can use mathematical procedures effectively. This research is a qualitative research that aims to describe the adaptive reasoning profile of secondary students in the Social Sciences department in solving mathematical problems. Research subjects were three students that solving mathematical problems correctly, solving mathematical problems less correctly, and solving mathematical problems incorrectly. The method used to collect data was to provide mathematical problem-solving tests and interviews. Data were analyzed based on students' adaptive reasoning activities in their activities to solve mathematical problems seen from three main aspects of adaptive reasoning, namely reflecting, explaining, and justifying. The results show that student who solved mathematical problems correctly indicated adaptive reasoning abilities in every aspect; student who solved mathematical problems less incorrectly demonstrated adaptive reasoning abilities that almost met all indicator aspects, and student who solved mathematical problems incorrectly did not demonstrate adaptive reasoning abilities in every aspect. Keywords: adaptive reasoning, problem solving, social secondary students.

Pengembangan Perangkat Pembelajaran Himpunan dengan Model Problem Based Learning Berorientasi Pendidikan Karakter untuk Meningkatkan Kemampuan Pemecahan Masalah

This study aimed to know the characteristics of the device and the results development of set learning device with Problem Based Learning models oriented character education that was quality is valid, practical and effective. In this study developed learning tools in the form of Teacher Book and Student Books. The type of research used is design research. The subjects of this study were students of Denpasar State Middle School Saraswati 1. The Development of the learning tool follows the Plomp development procedure which includes the preliminary phases, prototype phase, and assessment phase. The learning device validity data was based on expert opinion. The practicality data of instructional devices is based on instruction learning device data, student response questionnaire and teacher response questionnaire. Data on the effectiveness of instructional tools were collected using mathematical problem-solving tests. The validation results indicated that the teacher book and the student books manuals developed obtained valid categories. The results of observation of the implementation of learning, repons students and teacher responses indicate that the implementation of learning was categorized as practical. Based on the results of the test the learning device was included in the effective criteria.
 

Students’ specializing in mathematics problem solving

The ability to think mathematically in solving problems is an important goal of schooling. It is an ultimate goal of teaching that students will be able to condut a mathematical investigation by themselves and that they will be able to identify where the mathematics they have learned is applicable in real-world situations. The first strategy of mathematical thinking is specializing. Specializing means turning to some examples to learn more about the main goal of a concept or problem and these examples are specific and particular instances of more a general situation in a concept or problem. This study based on students’ difficulties to think mathematically in mathematics problem solving. There are still many students who feel confused when solving problem. The purpose of this study is to investigate the specializing of two sixth grade students in solving mathematics problems. They were selected from ten students taking mathematical skills and problem solving tests. They were classified in high and low mathematics abilities. Then they were interviewed based on their work of the given task. When solving the problem, the subject with high mathematics ability was able to describe the known, the way to determine the solution and try to look at the other examples. While the subject with low mathematics ability knows about a concept that can be used to help the problems but she didn’t know the way to determine the solution. Even though taking more time, by applying both a structured-scaffolding and using specializing systematically that fit the problem they succeeded in solving tem. These results may contribute mathematics teachers in a way how to help students use specializing in solving problem.

Pembelajaran Berbasis Masalah dalam Meningkatkan Kemampuan Pemecahan Masalah Matematika

This study aims to improve the learning process and the student’s mathematical problem solving skill by applying Problem Based Learning (PBL) model. This type of research is classroom action research with two cycles. This research was conducted in collaboration between researcher and teacher of mathematics. Subjects were students of class SMPN 9 Pekanbaru. Study was conducted in the odd semester of academic year 2019/2020. The research instrument consists of mathematical learning instruments and instruments to collect data. Mathematical learning instruments used in this study are syllabus, lesson plans, and activity sheets. Data collection instruments used in this study is observation sheets and mathematical problem solving tests. Data analysis technique in this study is analysis descriptive narrative of qualitative data and descriptive statistical analysis of quantitative data. The result of this study showed that the implementation of PBL improved the learning process and the student’s mathematical problem solving skill. The student’s average value in cycle I which is 70,27 had improved to 84,07 in cycle II. The improvement also found in the indicator average value in understanding the problem (94,99), planning a solution (69,71), implementing the pland (82,77), and checking again (54,85). This study concludes that the implementation of PBL improved the student’s mathematical problem solving skill at class SMPN 9 Pekanbaru.

PENERAPAN PBL UNTUK MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH MATEMATIS SISWA KELAS X TKR 1 SMK MUHAMMADIYAH 1 PEKANBARU

This study aimed to improve the learning process and the student’s mathematical problem solving skill by applying Problem Based Learning (PBL)l. This type of study is classroom action research with two cycles. This study was conducted in collaboration between researcher and teacher of mathematics. Subjects were students of class X TKR 1 SMK Muhammadiyah 1 Pekanbaru. The study was conducted in the second semester of academic year 2018/2019. The research instrument consists of mathematical learning instruments and instruments to collect data. Mathematical learning instruments are syllabus, lesson plans, and students’ worksheets. Data collection instruments are observation sheets and mathematical problem solving tests. Data analysis techniques are analysis descriptive narrative of qualitative data and descriptive statistical analysis of quantitative data. The result of this study showed that the implementation of PBL improved the learning process and the student’s mathematical problem solving skill. The average of student’s mathematical problem solving skill in firts cycle which is 72,09 had improved to 85,67 in second cycle. The improvement also found in the indicator average value in identifying the problem, devising a plan to solve the problem, carrying out the plan to solve the problem, and interpreting the solution. This study concludes that the implementation of PBL improved the student’s mathematical problem solving skill at class X TKR 1 SMK Muhammadiyah 1 Pekanbaru. PBL can be used as an alternative to learning, because through this learning can improve mathematical problem solving skill of the students.

Students’ critical ability of mathematics based on cognitive styles

The strategies used in solving problems can be influenced by cognitive style. This research is a qualitative descriptive study. The purpose of this study was to describe the mathematical critical thinking skills of junior high school students based on the cognitive style of Dependent Field and cognitive style Field Independent in solving SPLDV problems. The subject of this study consisted of 1 student who had the field-dependent cognitive style and 1 student who had the field-independent cognitive style chosen by purposive sampling. Data collection techniques were carried out by administering the cognitive style test of the Embedded Figure Test Group, mathematical problem-solving tests, interview guidelines, and documentation. Data were analyzed based on FRISCO critical thinking category indicators (Focus, Reason, Inference, Situation, Clarity, and Overview) in each step of problem-solving, namely understanding problems, arranging plans, implementing plans, and checking again. Data analysis is done by reducing data, presenting data, and drawing conclusions. The results showed that students who had the cognitive style of field-dependent and students who had the cognitive style FI had good critical thinking skills in each step of problem-solving according to Polya.

استخدام استراتیجیة التعلم التولیدی فی تدریس الریاضیات لتنمیة التخیل الریاضی وبعض المهارات الحیاتیة لدى تلامیذ المرحلة الإعدادیة

هدف البحث الحالي إلى دراسة فاعلية استخدام استراتيجية التعلم التوليدي في تدريس الرياضيات لتنمية التخيل الرياضي وبعض المهارات الحياتية لدى مجموعة مکونة من (82) تلميذا من تلاميذ الصف الثاني الإعدادي بإحدى مدارس مدينة أسيوط، قسمت إلى مجموعتين: إحداهما تجريبية درست وحدة المساحات وفق استراتيجية التعلم التوليدي، والأخرى ضابطة درست بالطريقة الاعتيادية. وقد تم إعداد دليل المعلم وکراسة أنشطة في وحدة المساحات، کما تم بناء اختبار التخيل الرياضي تضمن المهارات الفرعية الثلاثة: (استرجاع الصور العقلية- التحويلات العقلية - إعادة الترکيب)، واختبار حل المشکلات الرياضية الحياتية بمهارته الفرعية (فهم وتحليل المشکلة- تکوين خطة الحل- تنفيذ خطة الحل- مراجعة وتقويم الحل)، ومقياس اتخاذ القرار. وبعد تنفيذ تجربة البحث تم تطبيق اختبار التخيل الرياضي، واختبار حل المشکلات الرياضية الحياتية، ومقياس اتخاذ القرار. کشفت نتائج البحث عن فاعلية استخدام استراتيجية التعلم التوليدي في تنمية التخيل الرياضي ومهارة حل المشکلات الرياضية الحياتية ومهارة اتخاذ القرار. وأوصى البحث بضرورة استخدام استراتيجية التعلم التوليدي في تدريس موضوعات الرياضيات، وتضمين کتب الرياضيات مجموعة متنوعة من الأنشطة والمشکلات الرياضية الحياتية التي تسهم في تنمية التخيل الرياضي واتخاذ القرار. The research aimed at investigating the effective of Generative Learning Strategy in teaching Math for developing Mathematical Imagination and Life Skills among 2th year preparatory students in Assiut. The research sample comprised (82) students, divided into two groups: the control group and the experimental one. After carrying out the research experiment, the following study instruments were administered: Mathematical Imagination test (recall mental image –mental transformation – recombination), Mathematical problem solving (life Skills) Test and Decision Making Scale. The results revealed the effective of Generative Learning Strategy in developing Mathematical Imagination, Mathematical problem solving skills and Decision Making. The research recommended the following: Using the Generative Learning Strategy in teaching Math. Including Math Textbooks with tasks and real life problem which aims to develop Mathematical Imagination and Decision Making.

Architecture Game-Based Mathematical Learning by Making

In this design-based research project, we investigated how and to what extent participating in architectural building and problem solving via a simulation game–based learning platform (called E-Rebuild) would facilitate mathematical practices of middle-school students in the informal learning setting. This study encompasses 2 iterative design experiments in which 20 middle graders completed E-Rebuild-based learning tasks as part of an afterschool program and a summer math camp. Data were collected via screen- and webcam-recorded participation actions and reactions, mathematical problem-solving test, and interviewing. Enriching prior research on math and science learning through making, this study informs how and under what contexts mathematical practices and disposition emerge during the making-centered learning processes.

Formal student thinking in mathematical problem-solving

The purpose of this research is to find out the students’ thinking process in formal cognitive development in solving mathematical problems. The problem solving used in this study uses patterns from the pattern that have been adapting to the habits of students in Indonesia, namely the first stage is known, the second stage is asking, and the third stage is answering. This study was included in a qualitative descriptive study using six junior high school students with formal that were used as research subjects. The research instrument used in this study is Test of Logical Operations and mathematical problem-solving tests. Data analysis techniques are used using Milles, Huberman, and Sandana. From the results and discussion of the research carried out, it can be concluded that students with formal cognitive in the first and second stages tend to think about assimilation and abstraction. While in the third stage, students in formal tend to think about assimilation processes even though there are subjects who do the accommodation thinking process.

A test construction based on mathematical problem solving ability for quadrilateral

The ability to solve mathematical problems becomes an important skill the students should possess. Thus, it becomes an important duty for the teachers to help the students solve any encountered problem in their daily life. In the classroom learning, they need to teach the students how to solve the problem. It is not enough by assigning the routinized problems. This research aimed to construct a mathematical problem-solving test to assess students mathematical problem-solving ability. The research method included several steps, namely: analysis, developing test, evaluating test, trial, revising the test and collecting data on test validity and reliability. The research data were collected by using a written test, which was administered to 31 seventh-grade students at one of state Junior High Schools. The test consists of four essay questions with four indicators. The results showed that: (1) the mathematical problem-solving test was considered valid and applicable; (2) the test showed a good distinguishing power; and (3) the difficulty levels of the instrument were moderate and difficult. In conclusion, the constructed mathematical problem-solving instrument is applicable to assess the students mathematical problem-solving ability.

Analysis of Eight Grade Students Failure in Solving Mathematical Problems

This research aimed to investigate the ability of eighth-grade students and types of error they made in solving mathematical problems. To obtain data, as many as 102 PJHS students are included in mathematical problem solving (MPS) test. The aspects of MPS ability used in this research consisted understanding the problem, proposed and used the strategy to solve the problem and conclude the solution in accordance to the initial problem. Results of the research: First, students MPS ability belong to the low category. The second one, types of error the students made in solving MPS consisted lack of algebra knowledge including algebra manipulation, lack of mathematical concept, and lack of informal and formal strategy including creating a picture. The third one, results of the interview reveal that the students view algebra as complicated material and does not have a definite pattern to conquer. Meanwhile, the students could not make a picture because they confuse in understanding words problems. Keywords: mathematical problem solving