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2015
Calculus in high schools is a discipline of advanced mathematics. Its intrinsic complexity is very high. Many researchers around the world have pointed out difficulties and obstacles that students have encountered when studying it. To understand a concept and a theorem of calculus is not easy; therefore, when solving calculus problems students cannot avoid errors. Find out the errors of students in mathematics learning have been a problem that several of mathematics educators around the world interested in. In this paper, we report the answers to the following two research questions: (1) In solving calculus problems, what errors have 12 th grade-students committed? (2) What are the teachers' opinions about how often the errors of the students have occurred? The data collection was performed in high schools in Tan Chau town, An Giang province, Vietnam
Jurnal Pendidikan Matematika Universitas Lampung
This study aimed to identify mathematical errors committed by senior school students in calculus. Specifically, this study analyzes the various types of errors committed when solving problems involving calculus. The study is a descriptive study that employed a mathematics performance test on calculus (MPT-C) as the research instrument. The study considered two independent variables which are: error type and gender. The research sample for the study comprised all senior secondary school three (SS III) students. A random sampling technique was used to select the participating schools. A total of 300 senior secondary school students were involved in the selected schools. All research questions were answered using mean gain difference while all research hypotheses were tested using chi-square. All the research hypotheses were tested at a 0.05-significance level. The results of the analysis indicated that: there were no significant differences in the frequencies of structural, suppositio...
2012
This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due to knowledge gaps in basic algebra. We also noted that errors and misconceptions in calculus were related to learners' lack of advanced mathematical thinking since concepts in calculus are intertwined. Also in this study we highlight some common errors/ mistakes which can be done by lecturers during the teaching process.Students studying calculus often make the same mistakes and similarly lecturers teaching calculus have patterns of mistakes. This paper is derived from practical situations hence it is open to updating and can be adapted by other calculus teachers in different setups.
Jurnal Cendekia : Jurnal Pendidikan Matematika, 2021
Learning mathematics is a crucial part of education. Mathematics is one of the subjects feared by students. One of the problems in the object of mathematics study is the material for X class of Senior High School. Students of grade X are undergoing adaptation from the junior high school level to the high school level so that the findings of conceptual errors, calculations, and thinking patterns in problem-solving algorithms are often found. This also happened to the students of the Muhammadiyah Senior High School Special Program of Kottabarat Surakarta. In connection with the above problems, the author analyzes student errors in solving math problems at the Muhammadiyah senior high school special program of Kottabarat Surakarta.This study aims to find out errors, causes of error, and alternative problem solving related to students' errors in solving math problems. This research is qualitative descriptive research. The research subjects were taken by sampling purposes. they are ...
ACTA DIDACTICA NAPOCENSIA, 2012
This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due to knowledge gaps in basic algebra. We also noted that errors and misconceptions in calculus were related to learners' lack of advanced mathematical thinking since concepts in calculus are intertwined. Also in this study we highlight some common errors/ mistakes which can be done by lecturers during the teaching process.Students studying calculus often make the same mistakes and similarly lecturers teaching calculus have patterns of mistakes. This paper is derived from practical situations hence it is open to updating and can be adapted by other calculus teachers in different setups.
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.
Cambodian Journal of Humanities and Social Sciences, 2023
Errors and misconception in students' mathematics learning have become hot topics for teachers, educators and researchers for decades. Consistent errors may lead to misconception which ultimately affect the students' learning performance. This study centered on errors made by the students when they attempted to solve mathematics word problems. The objective of this study was to identify the errors the students made in solving quadratic function word problems. Qualitative method with students' test paper analysis and the in-depth interview using Newman's Error Analysis (NEA) framework were used to identify the students' errors and mistakes. Forty grade 12 students studying in a Cambodian public high school participated in the study. It was found that the students made the most errors in comprehension level (36.2%), reading errors accounted for 2.15% while transformation errors made up of 12.27%. Process skills errors made up of 19.94% while encoding errors (29.44%) ranked second among errors the students made. Failure to know or understand individual mathematical concept, for example vertex, symmetry line, interception point, range and domain of function etc. had hindered the students' comprehension of the problem and led to difficulties in solving math problems. This study suggested careful attention should be taken into account when introducing specific mathematics concept to students, especially at the early stage. Emphasizing the
Proceedings of the Proceedings of the 1st International Conference of Science and Technology in Elementary Education, ICSTEE 2019, 14 September, Makassar, South Sulawesi, Indonesia, 2019
The problem in this study is about students' mistakes in solving mathematical story problems. The formulation of the problem studied is 1) What mistakes do students make at each step in solving a story problem ?, 2) What is the level of student mistake in solving a story problem ?, 3) What causes students to make mistakes in solving a story problem ?, and 4) Is the level of student mistake significant in solving story problems? The purpose of this study is to: 1) Know what mistakes students make at each step in solving story problems, 2) Obtain an overview of students' mistake rates in solving story problems, 3) Know the causes of students making mistakes in solving story problems, and 4) Knowing whether the level of student mistake is significant in solving story problems. The approach in research is a quantitative approach and the type of research is ex post facto. The variable that was investigated was a single variable, namely students' mistakes in solving story problems. The population in this study were all fifth grade students of SD Tanete Riattang Barat District, totaling 626 people from 3 clusters consisting of 13 schools and research samples were fifth grade students from schools selected by purposive cluster random sampling technique, namely SDN 22 Jeppe'e, SD Inpres 12/79 Bulu Tempe, and SD Inpres 10/73 Watang Palakka as many as 137 students consisting of 72 men and 65 women. Data collection techniques used were tests and interviews. The data analysis technique used 1) descriptive statistics, which were calculating the average score and percentage of students' mistakes, and 2) inferential statistics using one sample t-test. The results showed 1) The types of mistakes made by students were not complete writing down answers, wrong in writing answers, and not writing answers, 2) The level of students' mistakes in completing story problems at each step of solving math story problems was in the high category, 3) The cause of students making mistakes is students do not understand the purpose of the problem, not careful in writing answers, accustomed to abbreviating answers, lack of understanding and wrong way of working on problems (incorrectly using formulas, incorrect concepts, and wrong operations), and 4) The level of student mistakes is significant in solving math story problems.
South African Journal of Childhood Education, 2014
Error analysis is the study of errors in learners' work with a view to looking for possible explanations for these errors. It is a multifaceted activity involving analysis of correct, partially correct and incorrect processes and thinking about possible remediating strategies. This paper reports on such an analysis of learner tests. The tests were administered as part of the evaluation of an intervention project that aimed to teach mathematical problem solving skills to grade 1-4 learners. Quantitative error analysis was carried out using a coding sheet for each grade. A reliability coefficient was found for each test, as were item means and discrimination indexes for each item. The analysis provided some insight into the more common procedural and conceptual errors evidenced in the learners' scripts. Findings showed similar difficulties across intervention and control schools and highlighted particular areas of difficulty. The authors argue that this analysis is an example of large-scale error analysis, but that the analysis method could be adopted by teachers of grades 1-4.
Proceedings: First International Conference on Teaching & Learning, 2015
Students' errors and misconceptions are intelligent generalizations of their experiences and incomplete knowledge acquired. In order to help students unlearn the misconceptions and relearn the correct conceptions, it is important that teachers are aware of these errors and misconceptions, and their formation. The purpose of this paper is to bring awareness of some of the errors students make and the misconceptions they have with regard to mathematical concepts, and suggest how the formation of these errors and misconceptions can be prevented and remedied. This paper reports the findings based on analysis of 2,411 examination papers of students enrolled in pre-University mathematics courses between January 2012 and April 2015. The literature discussed in this paper makes a case for K-12 school teachers to have an in-depth and more flexible understanding of the mathematics they teach, so they can recognize how the structure of mathematical concepts should be presented while teaching mathematics.
JIPM (Jurnal Ilmiah Pendidikan Matematika)
This qualitative descriptive study aimed to analyze student errors to solve mathematical problems in gender. The subject in this research were Mathematics Education students in the Linear Program subject. The sample selection used purposive sampling by looking at the results of student tests on linear program material categorized by gender. The analysis data using observation methods, test methods and interview methods, meanwhile to validity test of the data using triangulation of data source and triangulation method. Based on the results of the study obtained results: 1) Errors experienced by male and female students are almost similar, but the mistakes experienced by female students are fewer than male students, 2) Female and male students with high ability categories possess different types of errors, namely female students only experience process errors and results of errors, while male experience transformation errors, process errors, results in errors, 3) Female and male stude...
2017
Solving mathematical word problems is a difficult, complex and intellectual activity. The formation of problem solving skills is much more difficult than calculation skills because the problems are related to many concepts and a lot of mathematical relationships. Therefore, students are inevitable to commit errors to deal with them. This study shows the errors of 160 3rd grade students regarding some kinds of word problems in Mathematics 3 in Vietnam. The results indicate that children commit many errors due to many different reasons such as: subjectivity, carelessness, wrong application of the calculation rules, incorrect identification of problem kinds and wrong calculation. Article visualizations:
Procedia - Social and Behavioral Sciences, 2011
One of the important components that shape both the pedagogical and mathematical content knowledge is the component of being aware of students' mistakes. This study tries to investigate in what degree mathematics teachers correctly built their mathematical content knowledge by using the component that shapes both their mathematical and pedagogical content knowledge. According to this aim, teachers were subjected to a test that includes three questions. The content of the test include incorrect solutions of questions related to sequences, derivative and integration and teachers were asked to explain the reasons of such mistakes based on mathematical knowledge. It was assumed that there is a direct relation between their determination of the reasons of the incorrect solutions and their mathematical content knowledge on such subject. The situation was presented descriptively. The data gathered in the study revealed that mathematics teachers experienced difficulty in determining and in explaining the reasons of the incorrect solutions in general, even, some of them have different mistakes on subject.
Asian Social Science, 2015
This study aims to identify the level of difficulty, discrimination and errors based on symbols, graphs and problem-solving in mathematics achievement. The participants consisted of 315 grade 10 students randomly selected from eight secondary day schools situated in the state of Kedah, Malaysia. The mathematics written test consisted of 15 open-ended items with five items each for symbols, graphs and problem-solving and all the items were analyzed using the difficulty and discrimination index. Semi-structured clinical interviews were also carried out among 20 selected students to identify the errors they had made in mathematics. In the content analysis, the descriptor code key was used to identify conceptual, careless, problem-solving and value errors. The findings showed that item 4 (Standard Form) of the symbols, item 6 (Linear Equation) of the graphs, and item 15 (Line & Plane in 3 Dimension) of the problem-solving was the most difficult item in mathematics. All of these items had a good discrimination as well as difficulty index. Content analysis showed that 52 (57%) students made conceptual errors, 22 (24%) made careless errors, 12 (13%) made problem-solving errors and 5 (6%) made value errors. The major reasons given for errors made were a lack of understanding, procedures being forgotten, negligence in transcribing information from the question, carelessness and guesswork. This study has implications for the student learning process and understanding graphs because graphs are widely used in daily life to manage, communicate and analyze information.
British Journal of Teacher Education and Pedagogy, 2024
This study identified the strategies employed and common errors committed by freshman BEED students in Solving Basic Mathematics problems. It emphasized the enhancement of the identified strategies through the implementation of a tutorial program. Identifying the common errors made by the respondents in the study will make students aware of their presence and prepare them for their exposure to such problem-solving situations. In effect, these identified errors will be minimized if not totally put to end. Three (3) strategies and common errors were revealed in the study. The three (3) strategies were identifying the target goal, identifying the key information, and drawing diagrams/tables. The three (3) common errors were being unable to derive and identify the correct working equation, being unable to label the final answer, and being unable to use the least common denominator in adding and subtracting fractions. To determine the relationship between the respondents' achievement in basic mathematics and their achievement in high school mathematics, attitude towards mathematics, and attitude towards the teacher, the Pearson r and the t-tests were computed. The results indicate a noteworthy correlation between students' performance in High School Mathematics and their achievement in Basic Mathematics. However, no significant relationships were observed among the remaining paired variables. In conclusion, a strong foundation in mathematics helps students strategize their solutions to worded problems well, thereby getting rid of errors along the way.
2021
This study aims to determine students' mistakes in solving math problems on the topic 'Algebraic Forms' and their relation to the ability of teachers and prospective mathematics teachers. This type of research is descriptive quantitative. This research sample was 116 students of class 8 SMP in Pamulang district, South Tangerang city, while the teachers and prospective mathematics teachers were 37 people. The results of the study showed that the mistakes made by the students were in the form of 1) 23% misconception; 2) 14% errors of algebraic operations; 3) 9% errors due to carelessness; 4) the students' ability towards the topic of algebraic forms in the medium category; 5) the ability of teachers and prospective mathematics teachers to be in a good category, and 6) The contribution of the ability of teachers and prospective mathematics teachers to students' mathematics abilities is in the medium category.
loss and rate of interest committed by the primary school students on mathematics. The sample of the present study has been selected simple randomly from the primary school students of Gautam Budh Nagar of UP. The finding of the present study revealed that more than twenty five percentage of primary school students committed mathematical errors in addition, subtraction, multiple, division, decimal, fraction, profit and loss and rate of interest.
Mathematics Education Forum Chitwan
Research shows that college students make numerous algebra and other prerequisite content-related errors in Calculus courses. Most of these errors are common, persistent, and often observed in simple mathematical tasks. This qualitative study is an attempt to identify the potential sources of such errors. Based on our observations of student errors, we wrote a Precalculus and a Calculus test and administered them in twelve sections of four different undergraduate mathematics courses for which either Precalculus, Calculus I or both were a prerequisite. The tests were announced on the first day of the class and administered the following week. All the questions on the test were True or False questions. Based on our experience as college mathematics instructors, we assumed that many students would perceive the True answers as False and the False as True. Therefore, if students’ selected a given answer, mathematical statement, process or solution as True, they were asked to justify why ...
Networks: An Online Journal for Teacher Research, 2013
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.
2012
The research problematised the learning of mathematics in South African high schools in a Pedagogical Content Knowledge context. The researcher established that while at best, teachers may command mathematics content knowledge, or pedagogic knowledge, that command proves insufficient in leveraging the learning of mathematics and differentiation. Teachers' awareness of their learners' errors and misconceptions on a mathematics topic is critical in developing appropriate pedagogical content knowledge. The researcher argues that the study of learner errors in mathematics affords educators critical knowledge of the learners' Zones of Proximal Development. The space where learners experience misconceptions as they attempt to assign meaning to new mathematical ideas to which they may or may not have obtained semiotic mediation. In their Zones of Proximal Development learners may harbour concept images that are incompetition with established mathematical knowledge.Educators nee...
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