The "Insertion" Error in Solving Linear Equations

Journal of Problem Solving, 2014

Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed algebraic misconceptions using an in-depth error analysis on algebra students’ problem solving efforts at different points in the school year. Results indicate that different types of errors become more prominent with different content at different points in the year, and that there are certain types of errors that, when made during different levels of content, are indicative of math achievement difficulties. Recommendations for the necessity and timing of intervention on particular errors are discussed.

Kalamatika: Jurnal Pendidikan Matematika

This study aimed to analyze students’ errors in problem-solving activities for systems of linear equations. The descriptive qualitative method was adopted and applied to obtain and process the research data. Research subjects were selected using the purposive sampling technique. Three participants were chosen according to their mathematical proficiency levels. Data collection was conducted by tests to measure students’ problem-solving abilities and semi-structural interviews to gather qualitative information about students’ errors in solving systems of linear equations. The interview results were analyzed using narrative analysis to obtain accurate conclusions. The study found that (1) low-ability students tend to perform error at the comprehension stage, (2) medium-ability students are likely to perform error at the transformation stage, and (3) high-ability students tend to perform error at the process skills stage. The solutions based on the ability level are: (1) low-ability stu...

Zenodo (CERN European Organization for Nuclear Research), 2023

In solving algebraic problems, there are two possible student answers, namely right or wrong. However, the correct answer is not necessarily through a process that is in accordance with the actual concept or what is called pseudo. Errors and pseudospheres made by students when solving algebraic problems can be grouped into conceptual errors and procedural errors. Conceptual errors and procedural errors are mistake that cannot be ignored in the learning of prospective mathematics teachers. Teachers need to identify these errors in order to provide corrective or corrective instructions. The purpose of this study was to identify and characterize the types of student errors in solving algebraic problems and to describe students' conceptual and procedural errors in solving algebraic problems. The design used for this research is a mixed method. There are two stages in this research. The first stage, identifying and characterizing the types of student errors in solving algebraic problems. The second stage, describes students' conceptual errors and procedural errors in solving algebraic problems. The subjects of this study were 92 students of the Mathematics Education Study Program at a university in South Sulawesi. The results of the study show that conceptual errors in algebra are caused by misconceptions about certain concepts, making equivalence between several concepts without regard to conditions, and ambiguity in interpreting mathematical symbols. Meanwhile, procedural errors are more errors at the completion stage due to the generalization of the rules.

Universal Journal of Educational Research, 2020

Many factors influence and cause the learners feel difficult in resolving mathematical problems. One of these factors is the mistake of students when solving problems in mathematics. The research aims to analyze students' mistakes in working with mathematical diagnostic tests. The method used in this study is a quantitative descriptive where the data was taken through a diagnostic test result of 251 students. The instrument used in this research is a valid and reliable two-tier multiple-choice test instrument. The researcher later corrected student test results. Once fixed, the answer was later analyzed using Newman's theory based on four indicators, i.e. (1) Error understanding, (2) error transforming, (3) Error processing skills, and (4) Error writing answers and then described. Results in research shows the mistakes that students do in resolving mathematical problems in calculus material are largely due to errors in understanding, errors of transformation, and error in process skills. Based on the results of the study, researchers concluded that students have done mistakes in resolving mathematical problems in calculus material largely due to errors in understanding, error transformation, and error in process skills. To overcome the mistakes that students do when solving mathematical problems can be used by several scaffolding solutions, using a creative and innovative learning model and tell students what they are doing and instantly fix them.

In this paper some common mistakes are investigated, referred to linear mappings and to the solution of algebraic equations, with reference to High School students (students aged 16-19 years). We conclude that pupils sometimes improperly extend «simple» rules, and this is caused by algebraic weakness and by affective elements, too. As regards strategies against misguided generalisations, we underline that the effect of counterexamples with pupils is frequently weak, since often they are not able to interpret counterexamples in an adequate way.

Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021

Schoenfeld and Sloane argued that the main task of mathematics education is to explain students' thought processes in order to improve the quality of mathematics learning. Many students make errors in answering maths tests. It turns out that various types of errors depend on students' learning styles. The focus of this research was to analyze students' errors in solving mathematics problems based on differences in students' learning styles according to David Kolb's theory of experiential learning. The study was conducted at Vocational Middle School in Cirebon-Indonesia. The research used a qualitative research case study approach. The instrument used in this study was the Kolb Learning Style Inventory (KLSI version 3.1), and math tests. For data analysis, this study used triangulation techniques. The four categories of learning orientations were found among 24 students who participated in this study, namely converging, accommodating, assimilating, and diverging. The difference with other studies is that this study focuses on discussing student errors based on learning styles. Each type of learning style was associated with its unique errors. Errors made by divergers were procedural errors and misunderstandings; the assimilators' types of error were procedural and conceptual errors; the convergers' error type was a procedural error; the type of error made by accommodators was a theoretical error. Conceptual errors were caused by a misunderstanding of existing concepts, leading the students to make errors in the answer to math tests. Strategy errors can b e encountered by students when they were stuck in the answer to a math test. A procedural error occurred when students used a non-systematic method in completing the test.

International Journal of Learning, Teaching and Educational Research, 2019

This research aims at describing errors as well as knowing the factors causing students to make an error in solving problems in the material of the Two-Variable Linear Equation System (SPLDV). This research involved 31 students from grade eight students of Indonesian junior high school. To collect the data, tests, observation, and interview methods were used. The data validity was triangulation in which it required a comparison of data with interviews. The technique of data analysis was in three stages, starting from data reduction, data presentation, and conclusion. The analytical framework was developed based on the Newman error category. The results obtained are three types of errors, namely error understanding problems, transformation errors, and process skills errors. Factors causing these errors, in general, are students who find difficulties to acknowledge the meaning of the questions, students have a low level of understanding and creativity in identifying problems into mathematical models, and students' carelessness in process skills.

2019

In the ClassRoom section of the November 2018 issue of At Right Angles, Prof. Hridyakant Dewan wrote about the interpretation of errors in arithmetic. The paper lists errors made by students while doing arithmetic. The author asserts that algorithms (he calls them “quick fixes”) given by teachers contribute to students’ errors and diverts them from conceptual understanding. He mentions that these errors could be a result of over generalisations made by students. However, he also states that these are “transmitted to students as short-cuts to get the required answer”. In the end, he makes an appeal that teachers plan tasks which help students in gaining conceptual understanding.

Desimal: Jurnal Matematika

The forms of concept construction errors are divided into 4 forms, namely (1) Pseudo Construction, (2) Construction Holes, (3) Mis Analogical Construction, (4) Mis Logical Construction. This research aims to determine the process of concept construction errors in solving mathematical problems based on the assimilation and accommodation framework in terms of student learning styles. This research is qualitative descriptive research. The results showed that 1) students with visual learning styles experienced True Pseudo Construction, False Pseudo Construction, and Construction Pits. 2) Students with auditory learning styles experience True Pseudo Construction, False Pseudo Construction as well as Construction Pits and Mis Logical Construction. 3) Students with kinesthetic learning styles experience Construction Pits, True Pseudo Construction, False Pseudo Construction, and Mis Logical Construction. Concept construction errors in the material of a System of Linear Equations with Three ...

maccs.mq.edu.au

Mathematics and reasoning are two skills which appear to be related based on observation and research examining cognitive capacities important in children's mathematical ability. However, it is not clear if these two skills are linked. The present study investigated the relationship between different forms of mathematical problem error detection and deductive reasoning error detection with undergraduate students. Surprisingly performance on mathematical and reasoning error detection tasks were found to have little in common, despite the fact that participants viewed their abilities on the two tasks as related. Factors important for each type of task including mathematical experience and the task type were also examined. Results suggest that mathematical experience, while important for mathematical error detection has little effect on reasoning. Further implications for the manipulation of the context in the WST and reliance on reasoning were found.