Algebraic Problem Solving Research Articles

Analysis of students' computational thinking skills in solving algebraic problems in cultural contexts

This research aims to find out about students' computational thinking abilities in solving algebraic problems in cultural contests. This research is qualitative research carried out at Yogyakarta Middle School. The participants involved were 31 students in the even semester of grade 7. The data sources in this research were the results of students' computational thinking tests, interviews with students who were selected based on their communication skills and the results of test answers. Data instrument testing uses validity and reliability tests with data validity using triangulation techniques. Data analysis in this study used the pullulation technique between student test results and student interview results, then data reduction, data categorization, power display and conclusion drawing were carried out. The results of this research are that students in the high category can complete all indicators of computational thinking and problem-solving abilities. Students in the medium category can only complete two indicators of computational thinking and problem-solving abilities. Students in the low category have not been able to complete all indicators of computational thinking and problem-solving abilities. The study reveals a significant variance in the computational thinking abilities among junior high school students in Piyungan Development class VIII when solving algebra problems within a cultural context. High-achieving students demonstrated proficiency across all indicators of computational thinking, effectively navigating through various stages from abstraction to solution verification. In contrast, students categorized as moderate showed partial success, managing only a subset of the indicators, while struggling with the more complex stages of problem decomposition and implementation. Meanwhile, students classified in the low category were unable to achieve any indicators of computational thinking and problem-solving skills. This indicates a clear need for targeted educational interventions to enhance computational thinking among students, particularly those who are struggling, to ensure all students can develop the necessary skills to solve problems effectively.

English learners learn from worked example comparison in algebra

Comparison is an important mechanism for learning in general, and comparing two worked examples has garnered support over the last 15 years as an effective tool for learning algebra in mainstream classrooms. This study was aimed at improving our understanding of how Modified for Language Support-Worked Example Pairs (MLS-WEPs) contribute to effective mathematics learning in an ESOL (English to Speakers of Other Languages) context. It investigated a novel instructional approach to help English Learners (ELs) develop better understanding in mathematical reasoning, problem solving, and literacy skills (listening, reading, writing, and speaking). Findings suggest that MLS-WEPs not only enhanced ELs’ ability to solve algebra problems, but it also improved their written explanation skills and enabled them to transfer such skills to different mathematical concepts. Moreover, when controlling for ELs’ prior knowledge, the effectiveness of the MLS-WEPs intervention for performing and explaining calculations did not vary by their English proficiency.

Student’s Reversible Thinking Processes: An Analysis Based on Adversity Quotient Type Climbers

Reversibility thinking carried out mentally in mathematical operations has an important role in the process of understanding concepts as it involves developing a thinking process from beginning to end and from end to beginning. This qualitative research aims to describe students' reversible thinking processes in solving algebra problems, specifically in climber-type adversity quotient. A total of 2 students who have the climber type were selected as participants from 36 potential subjects involved in the research. Data collection was carried out by providing Adversity Response Profile questionnaires, Test of Thinking Reversible, and semi-structured interviews. Our participants solved problems according to polya stages and through forward and reverse processes. The results of data analysis show that in the forward process, there are 2 aspects of reversible thinking, namely negation and reciprocity, while in the reverse process, they involve 2 aspects of reversible thinking, namely the capability to return to initial data after obtaining the result and negation. The results suggest that student's ability to perform mental reversals indicates a strong reversible thought process, leading to more precise cognitive thinking.

Students’ Algebraic Proficiency and Attitude towards Learning Algebra

Learning algebra is a difficult process that necessitates a positive attitude in order to maintain interest and master key concepts. Previous research found that students' attitudes influenced their algebra learning. As a result, more input is required to observe the current influence of attitudes on algebra learning. This study aims to investigate secondary school students’ levels of proficiency and attitudes towards learning algebra. A case study was employed to collect data using an algebra test, a questionnaire on attitude, and task-based interviews. The subjects of this study were Form Three and Form Four students who were in the Dual Language Programme (DLP) in a school in Malaysia. A total of 93 students volunteered to participate in this study, and three of them were interviewed for insights into solving algebra problems. This study revealed that (1) there was no significant difference in algebra achievement between the Form Three and Form Four students; (2) there was a negative correlation between the achievement and attitudes; and (3) the students displayed rather low proficiency in answering the test questions, which could be attributed to difficulties with comprehension of problems in algebra and inadequate reasoning when applying problem solving strategies. These findings have implications for developing positive attitudes towards the learning of algebra. It is recommended that educators look into these areas to equip students with the right attitudes and knowledge for advanced learning at university.

Analisis Kesalahan Siswa SMK dalam Menyelesaikan Soal Aljabar Berbasis Teori Kastolan

The concept of algebra is very important in learning mathematics, students' ability to understand advanced mathematics lessons depends on mastery of algebraic concepts. Therefore, it is necessary to analyze the errors that often arise when students solve algebra problems. The purpose of this study is to analyze the errors of vocational students in class XI in solving algebra problems. This research uses a qualitative method that is analyzed descriptively. The research subjects were 28 students of class XI with the object of research, which is the errors that arise when students solve algebra problems. The results showed that based on Kastolan's Theory, procedural errors occur most often, followed by technical errors, and concepts.

Students' Numeracy Ability in Solving Algebra Problems in View of Gender

Numeracy is a skill in using various kinds of symbols related to basic mathematics. Numerical ability is important to be applied in teaching and learning activities in schools to be able to solve math problems. The purpose of this study was to determine the numeracy skills of male and female students in solving algebra problems. The research method uses qualitative methods with a descriptive approach. The subject taking technique used purposive sampling, the subject consisted of 3 male students and 3 female students. Data collection techniques in this study used written tests, interviews, and documentation. The results of this study indicate that the numeracy skills of male and female students with a high level of ability are able to analyze information, make and carry out solving steps, and are able to draw conclusions about answers correctly. Male students with moderate ability levels are able to make and carry out completion steps, and are able to make conclusions about answers correctly. Female students with moderate ability levels are able to make and carry out solving steps. Male students with a low level of ability are only able to make steps for completion but have not been able to take steps for completion, female students with low levels of ability are only able to analyze the information in the problem. Based on this analysis it can be concluded that the numeracy skills in solving algebra problems in male and female students are different.

An investigation on the effects of attitude towards algebraic problem-solving achievement

The main focus of this work is to explore the effects of students’ attitudes towards problem solving (ATPS) in algebra with respect to gender and type of school. The contribution of the predictor variables of ATPS in algebra to the prediction of problem-solving achievement (PSA) is being investigated. For the study, 200 class IX students are randomly selected from the government (GOVT) and private (PVT) schools in the Morrigan district, India. The algebraic attitude scale (AAS) is used to determine students’ ATPS, whereas the problem-solving test (PST) is used to determine students’ PSA in algebra. The AAS instrument consists of three subscales: perseverance (PE); self-confidence (SC), and willingness (WL). The t-test and multiple regression analysis are used to analyze the collected data. The finding reveals that there are statistically significant differences in students’ ATPS based on gender and type of school. The finding also reveals that PE, SC, and WL have a significant positive relationship with the PSA in algebra. Therefore, it is suggested that teachers should make an effort to provide support in the form of explanations, modeling, coaching, and other forms of assistance, as well as a conducive environment that encourages students’ overall ATPS that can enhance their PSA in Mathematics.

Self-Regulated Strategy Development for Algebra Problem Solving

In the era of 21st century learning, many secondary students with learning disabilities continue to struggle with mathematics problem solving. Emerging evidence suggests self-regulated strategy development can be combined with existing evidence-based and promising practices during mathematics instruction. These practices include explicit instruction, metacognition, use of visual representations, ongoing formative assessment and feedback, multiple examples, and self-regulation. We describe the promising and practical potential of SRSD and STAR, a research-based, metacognitive problem-solving strategy, for instruction in algebraic problem-solving. A practical example is provided to illustrate the combination of practices.

Linking Transformation and Problem Atomization in Algebraic Problem-Solving

The transition from arithmetic to algebra requires students to change both their thinking and the way they learn. We often observe students using arithmetic formalism also when solving algebraic problems. This formalism manifests itself primarily in the acquisition of coherent computational procedures. Students must be sufficiently aware that the computation steps are sequential transformations of the problem. This creates a problem for them in solving more complex problems. Our research investigated whether problem transformation coupled with atomization is a suitable alternative for students to learn coherent algorithms. Although atomization is not based on precise rules, it was reported by students to be a comprehensible way of solving problems and providing them with sufficient confidence. If students are motivated to understand a computational method, this understanding represents fulfilling the student’s need for security.

AN ALGEBRAIC THINKING SKILL TEST IN PROBLEM-SOLVING FOR SEVENTH GRADERS

Diagnostic tests have been developed previously to measure algebraic thinking skills; however, the tests do not specifically address algebraic problem-solving. Thus, an Algebraic Thinking Test (ATT) Instrument was developed to measure algebraic thinking skills in problem-solving involving linear equations. ATT comprises nine open-ended questions with three algebraic thinking constructs: Generalized Arithmetic, Functions and Modeling. Generalized arithmetic involves students in efficient calculation and generalization; functional involves identifying number patterns, while modelling involves solving open-ended problems, identifying similarities, and performing calculations involving variables. This study is meant to determine the quality of ATT instruments through the validity and reliability analysis using the Rasch Measurement Model. The sample consisted of 120 seventh graders aged 12 to 13, selected from two secondary schools in the Tuaran district, Malaysia. The instrument was found to have a strong dimensionality and high construct validity. The reliability of Cronbach Alpha (KR-20) demonstrated a value of .90 (very high), and item and respondent reliability of .98 (excellent) and .86 (good), respectively, with an item separation index of 6.29 and 2.45 for the person separation index. ATT has good validity and high reliability in measuring algebraic thinking skills among seventh graders in secondary schools. Keywords: algebraic thinking skills, linear equations, problem-solving, Rasch analysis, validity and reliability

Thinking Trajectory of Students with Thinking and Feeling Personality Types in Solving Algebra Problems

The strategies students use in solving mathematical problems are quite diverse, so they affect students' personality types. This research focuses on analyzing the trajectory of students' thinking in solving algebraic problems in terms of thinking and feeling personality types. This research is qualitative research with a descriptive method. The population is 34 students; the sampling is done by purposive sampling—data collection techniques through personality questionnaire sheets, algebraic test questions, and interviews. Qualitative data analysis was done through data reduction, display, and conclusion/verification stages. The results showed that the students' thinking path in solving algebraic problems in terms of thinking and feeling personality types is that in the problem analysis cycle, thinking students can correctly show what is known from the problem. The problem-solving process is made sequentially up to the simplification cycle. In the completion cycle, students think until they get the final answer by completing the steps properly and correctly. Based on these results, students need help solving algebra problems properly compared to students with the thinking personality type. It is because students feel that the steps could be more sequential in solving problems with algebraic forms, and it is difficult to consider based on right or wrong (objective). Therefore, sometimes he needs to be more wishy-washy or even needs clarification in taking a stand.

ANALISIS KESULITAN SISWA DALAM MEMAHAMI KONSEP DAN MENYELESAIKAN SOAL ALJABAR

This research is aim to describe the difficulties in learning and solving Algebra problems experienced by class VII Students of SMP Negeri 7 Cimahi. This research method uses a descriptive method with a qualitative approach. The subjects used in this research were five Students of class VII H who were randomly selected, and the teacher concerned. The instrument used in this study were written tests, questionnaires and interview guides. The results of this research indicate the various difficulties experienced by Students and the factors that cause them. These difficulties include difficulties in identifying coefficients, determining like terms, and performing various arithmetic operations in Algebraic forms. The factors that cause Student difficulties are divided into two, namely internal and external factors. The internal factor is that Students don't understand the concept and don't master arithmetic operations on integers, while the external factor is the lack of Interest, talent and motivation of Students in learning Algebra.

Analysis of Mathematics Connection Ability in Solving Algebra Problems at VIII Grade Junior High School

This study aims to determine the mathematics connection ability of VIII Grade students in solving algebraic questions in one of the public junior high schools in Makassar City. This research was qualitative. The research subjects consisted of three students selected based on the results of the basic ability test. Data collection techniques used basic ability tests, mathematics connection skills tests, and interviews. Data analysis techniques were data reduction, data presentation, and conclusion. The results showed that: (1) the mathematics connection ability of subjects with high basic abilities met three indicators of mathematical connection ability, namely connecting mathematical concepts, connecting mathematical concepts with other fields of science, and connecting mathematical concepts with everyday life (2) The subject's mathematics connection ability moderate basic ability met two indicators of mathematics connection ability, namely connecting between mathematical concepts and connecting mathematics concepts with everyday life (3) mathematics connection ability of subjects with the low basic ability only meets one indicator of mathematical connection ability, namely connecting between mathematical concepts.

A Novel Interpolation Method for Cutting Trajectories in Spatial Coherent Cutting Machine

Coherent lines are generally more complex spatial curves, and the study of coherent lines is the basis for studying cutting trajectories of spatial coherent cutting machines. In this paper, the spatial geometry problem is transformed into an algebraic problem solving by establishing a mathematical model of spatial coherent line to find its parametric equations. Interpolation refers to the process of data densification. In this paper, a speed planning method that adapts to the curvature change of the Non-Uniform Rational B-Splines ( NURBS ) curve is proposed. After inputting the starting points and endpoints to the Computer Numerical Control (CNC), the computer will calculate the coordinate data of each step according to the characteristics of the line segment, carry out the speed planning and then complete the curve trajectory interpolation. The accuracy of the algorithm is verified by comparing the theoretical coherent trajectory and interpolated trajectory.

Analisis Kemampuan Berpikir Kritis Matematis Pada Materi Aljabar Siswa Kelas VII MA Al-Mutmainnah Desa Punti Kecamatan Soromandi Kabupaten Bima

Critical thinking is thinking deeply, according to facts. The purpose of the study was to describe the mathematical critical thinking skills of MTs Al-Mutmainah Punti students in solving Algebra problems. This type of research is descriptive. Qualitative research approach. The subjects of this study were 1 high-ability student, 1 medium-ability student and 1 low-ability student. The data collection technique used a written test instrument. The data analysis technique used a qualitative descriptive analysis technique. The results showed that high critical thinking students met the four indicators, namely Analyzing and focusing, students were able to describe and simplify questions as the first step of completion. Identifying assumptions students make the completion steps to determine the results of the algebraic addition correctly. Determine and answer students with high abilities to solve problems in detail and systematically until they find the right answer. Making conclusions students rewrite the final results of the questions clearly and precisely. Furthermore, moderately capable students only meet the three indicators, namely analyzing and focusing questions correctly, identifying assumptions correctly and determining and answering a problem. While the indicators conclude that moderately capable students cannot do it. Finally, low-ability students cannot fulfill these four indicators. The conclusion is that high critical thinking students can solve problems according to the four indicators, while moderate and low thinking students solve problems that do not match the four indicators

Relational Thinking And Problem Solution Strategies Beginning Algebra High School Students

Many students' difficulties in learning early algebra are associated with deficiencies in learning during the student's transition from arithmetic to algebra. relational thinking; a way of thinking that can be a gateway to algebraic thinking, is touted as one of the solutions to these difficulties. This study aims to determine the profile of relational thinking and early algebra problem solving strategies for junior high school students. Through the phenomenological design, the researcher selected six participants who fit the research criteria. The data analyzed refers to several theoretical frameworks on relational thinking from several experts. This study focuses on the indicators of interpreting the equals sign , using the relationship between numbers and applying the basic properties of number operations, as well as the methods students use in solving initial algebraic problems (algebraic forms and linear equations of one variable). As a result and its implication, students' relational thinking is seen in several items, namely the first 3 indicator items: each item is seen in S1, S4, and S6; The second 2 indicator items are visible on the S4; and the third 3 indicator items are seen in S1. The majority of subjects do computing dominantly and or apply the nature of operations based on procedural knowledge. Similarly, in solving early algebra problems, it was found that the dominant tendency of students to consider algebraic expressions from a procedural perspective rather than a structural perspective (based on mathematical concepts or structures). From these results, it is deemed necessary to develop relational thinking since students study arithmetic in elementary school, including by familiarizing students with number sentences in various forms and encouraging understanding of mathematical structures (relationships between elements and understanding of the nature of number operations).

Relational Thinking And Problem Solution Strategies Beginning Algebra High School Students

Many students' difficulties in learning early algebra are associated with deficiencies in learning during the student's transition from arithmetic to algebra. relational thinking; a way of thinking that can be a gateway to algebraic thinking, is touted as one of the solutions to these difficulties. This study aims to determine the profile of relational thinking and early algebra problem solving strategies for junior high school students. Through the phenomenological design, the researcher selected six participants who fit the research criteria. The data analyzed refers to several theoretical frameworks on relational thinking from several experts. This study focuses on the indicators of interpreting the equals sign , using the relationship between numbers and applying the basic properties of number operations, as well as the methods students use in solving initial algebraic problems (algebraic forms and linear equations of one variable). As a result and its implication, students' relational thinking is seen in several items, namely the first 3 indicator items: each item is seen in S1, S4, and S6; The second 2 indicator items are visible on the S4; and the third 3 indicator items are seen in S1. The majority of subjects do computing dominantly and or apply the nature of operations based on procedural knowledge. Similarly, in solving early algebra problems, it was found that the dominant tendency of students to consider algebraic expressions from a procedural perspective rather than a structural perspective (based on mathematical concepts or structures). From these results, it is deemed necessary to develop relational thinking since students study arithmetic in elementary school, including by familiarizing students with number sentences in various forms and encouraging understanding of mathematical structures (relationships between elements and understanding of the nature of number operations).

Brain‐Anatomy Differences in the Commission of Reversal Errors during Algebraic Word Problem Solving

AbstractAn important line of research related to the resolution of word problems is the study of the cognitive processes involved when subjects translate problems into the language of algebra. One of the most common errors in problem‐solving is the reversal error (RE), which occurs when students reverse the relationship between two variables when translating equations from comparison word problems. The aim of this neuroeducational study is to investigate the brain anatomy differences between two groups, one group that commits RE and a second group that does not. Magnetic resonance images of 37 normal and healthy participants between the ages of 18–25 years were acquired. Differences in gray matter were assessed using voxel‐based morphometry analysis. Our results show that the RE group has a larger volume in the putamen, suggesting that these subjects have to make a greater effort to solve problems.

The effect of distance education on the problem-solving success of university students taking algebra and students' opinions on the practice

This study aims to examine the effect of distance education in formal education on the success of university students taking algebra in solving algebraic problems and to determine students' opinions on practice. The research design was determined as a posttest quasi-experimental design with a control group. The data collection tools of the research consist of the Algebra Problem Solving Test (APST) consisting of open-ended questions and the Semi-Structured Interview Form (SSIF). SPSS software package version 22.0 was used in the analysis of the data. As a result of the independent samples t-test, it was observed that there was no statistically significant difference between the posttest scores of the experimental and control groups obtained from APST. The qualitative data of the research were analyzed by content analysis. When the opinions of the experimental group students about the practice were examined, it was seen that they stated that distance education had various advantages, but they mostly experienced various difficulties. Students stated the disadvantages of distance education as not being able to ask questions, not feeling like in the classroom, not being motivated to the lesson, not being disciplined due to the comfort of a home environment, internet-related difficulties, inadequate communication, and socialization.

Teachers’s practices in teaching and learning algebraic problem solving

Algebraic problem solving is one of the important areas in learning mathematics. However, the result shows that student’s performance in algebra mainly in solving problem is not satisfying. This study had two folds aim that are capturing teacher’s view on the teaching and learning algebraic problem solving and also to grasp the idea whether the teacher have implicitly implemented problem posing strategy in a classroom. Thus, the objectives of this study are 1) to gain teacher practices in teaching and learning algebraic problem solving, 2) to find out the difficulties faced by teachers while teaching Form Two students to solve algebraic problem solving, and 3) to find out whether the teachers have implicitly imposed problem posing strategy in a classroom. Participants in the study were 8 experienced teachers who were been teaching mathematics especially mathematics Form Two syllabus and have teaching experience for more than five years. Data were gathered through qualitative technique that is using semi structured interview. Results from the study showed that teachers are still using teachers’ centered approach in teaching and learning algebraic problem solving, the difficulty faced by the teachers in teaching algebraic problem solving is students lack of mathematics skills, and teachers rarely used problem posing strategy in a classroom. This study provides an overview that teacher should implement new strategy in teaching problem solving algebra in order to increase student’s performance. One of the promising strategies is known as problem posing strategy.