Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors (original) (raw)
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Analysis of Errors in Student Solutions of Context-Based Mathematical Tasks
Acta Mathematica Nitriensia, 2015
The submitted contribution is concerned with analysis of errors made by students when solving context-based mathematical tasks. The contribution comprises evaluation of four tasks which were designed by the authors of the contribution within project KEGA 015 UKF -4/2012 in Slovakia. Altogether 56 first and second year students of primary teacher training university master programme were asked to solve the tasks. The errors in the student solutions were identified and classified primarily following Newman´s error categories and additional categories suggested by the authors of the contribution, who furthermore propose 13 error subtypes. In total 127 inappropriate solutions of the four tasks were included in the evaluation. The authors present a sign scheme and a correspondence map of student errors based on statistical analysis. As evidenced by the analysis, students make similar errors when solving tasks of the same type. The objective of the authors is to identify accurately and classify the error types occurring in student solutions.
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2014
This paper reports an investigation of the difficulties experienced by (Indonesian) students when solving context-based mathematics tasks. A total of 362 students from 11 schools located in rural and urban areas in the Province of Yogyakarta participated in a paper-and-pencil test. The test items comprised 34 tasks which were selected from the released items of the Programme for International Student Assessment (PISA) tasks. Students’ difficulties were examined through an error analysis for which an analysis framework was used. The framework consisted of four error types: comprehension, transformation, mathematical processing, and encoding. The data analysis revealed that the most dominant errors made by the students were comprehension errors (38%) and transformation errors (42%). Of all errors made by students 17% were mathematical processing errors and only 3% were encoding errors. These findings indicate that (Indonesian) students mostly had difficulties in comprehending a contex...
Student Error Analysis in Solving Mathematical Problems
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.
An Analysis of Students Error In Solving PISA 2012 And Its Scaffolding
JRAMathEdu (Journal of Research and Advances in Mathematics Education)
Based on PISA survey in 2012, Indonesia was only placed on 64 out of 65 participating countries. The survey suggest that the students’ ability of reasoning, spatial orientation, and problem solving are lower compare with other participants countries, especially in Shouth East Asia. Nevertheless, the result of PISA does not elicit clearly on the students’ inability in solving PISA problem such as the location and the types of student’s errors. Therefore, analyzing students’ error in solving PISA problem would be essential countermeasure to help the students in solving mathematics problems and to develop scaffolding. Based on the data analysis, it is found that there are 5 types of error which is made by the subject. They consist of reading error, comprehension error, transformation error, process skill error, and encoding error. The most common mistake that subject do is encoding error with a percentage of 26%. While reading is the fewest errors made by the subjects that is only 12%....
Error Analysis, Metacognition and Mathematical Problem Solving of College Students (THESIS)
ProQuest LLC, 2017
In line with the recommendations of Lannin, et al (2007) to both mathematics teachers and students to “not seek simply to correct their errors, but … to rationalize them and to understand them thoroughly” (p. 58), this study introduced error analysis (describing and categorizing errors) or coding to thirty-three (33) first-year college students taking a Pre-Calculus course and investigated how their coding proficiencies are related to their metacognitive abilities and problem solving performance. This study is a quantitative, descriptive, correlational method research and utilized a One-Group Pretest-Post-test Design, with the aim of (1) identifying and describing the prevalent error types among the respondents, (2) examining whether the coding proficiencies between ability groups differ significantly, (3) determining the extent of how coding proficiency is related to metacognition ability, and (4) determining the extent of how coding proficiency is related to problem solving performance in mathematics. The data were subject to these statistical treatments: paired t-test and Pearson Product Moment Correlation. The students’ metacognitive abilities were measured using an adapted version of the Metacognitive Awareness Inventory or MAI created by Dennison & Schraw (2004). The MAI was administered twice- before and then after the coding sessions. The open-ended items in the long tests of the Pre-Calculus course quantified the problem solving performance of the respondents. The coding proficiencies of the students in each coding session were rated by the researcher using an analytic rubric. The most notable findings suggest that: (1) Among the error types proposed by the researcher, procedural errors dominate the errors committed by the respondents, followed by transformation errors. (2) The upper group and lower group respondents differ significantly when it comes to coding proficiency. (3) Coding proficiency is moderately and positively correlated with metacognitive ability for upper group respondents. (4) A strong positive linear relationship exists between coding proficiency and problem solving performance in mathematics.
Errors Middle School Students Make When Performing Mathematical Modelling Tasks
Acta Scientiae, 2021
Background: In Costa Rica, since 2012, schoolchildren have been trained in modelling as a fundamental part of the educational curriculum. Objectives: To identify and characterise errors incurred by a group of secondary school students in Costa Rica when applying the mathematical modelling process phases when solving direct proportionality tasks. Design: Through a qualitative approach, specifically a case study, it aims to study the participants' social interpretations. Setting and Participants: The modelling tasks were applied to 24 students attending the 7th level of middle school education in the province of San José in Costa Rica, when the topic of direct proportionality is deepened and the participants have been instructed in modelling tasks since the first years of elementary school. Data collection and analysis: Information was collected through participants' written productions, researchers' observation, and interviews. Content analysis was carried out through the categorisation proposed by Abrate et al. (2006) to analyse mathematical errors. Results: The participants did not apply all phases of the mathematical modelling process, making more errors due to incorrect or unintended calculations and incorrect associations when solving the mathematical model. Conclusions: We concluded that the errors detected in this work are elements of reflection, progress, and feedback that should encourage the teachers' search for strategies that help solve the deficiencies that emerge when students solve modelling activities.
Desimal: Jurnal Matematika, 2020
This research was aimed to analyze student's errors on triangular and quadrilateral material in terms of problem-solving ability. This research was motivated by the low problem-solving ability and errors often made by students during the mathematics learning. The research approach was descriptive-qualitative that was done by analyzing the students' difficulty in solving description problems. The techniques of data collection were observation, learning outcomes tests, and interviews. The data were analyzed qualitatively based on Newman Error Analysis. Based on the results of the research, it was found that students' reading errors were in the high, medium, and low categories. Students' comprehension errors were in the medium and low categories, students' transformation errors were in the high, medium, and low categories, students' process skills errors were in the high, low, and medium categories and students writing errors (encoding error) were in the high, m...
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Error pattern analysis of the Mathematics problem solving of grade 10 learners
Journal of Social, Humanity, and Education (JSHE), 2024
Abstract Purpose: This study investigates respondents' error patterns in mathematics problem-solving, their impact on problem solving, and their attitudes towards mathematics, examining the relationship between these factors. Research methodology: This study used a convergent mix method design to analyze data from 80 Grade 10 students at Matucay National High School, focusing on error patterns in problem solving and the relationship between learners' performance and their attitudes towards mathematics. Results: The study revealed that students excel in problem solving in mathematics, but their errors are mainly in formulation. They need to improve their reading comprehension, conceptual knowledge, and reasoning skills. The study also found that students' attitudes towards mathematics were influenced by their sex but not their problem-solving performance. Limitations: The study involved grade 10 students, and the findings may be different if participants were at a different grade level (e.g., grade 8, grade 9, etc.). In addition, other disciplines of mathematics problem-solving can also be explored for the comparison of results. Contribution: Enhances the understanding of the relationship between students’ attitudes towards mathematics and error patterns committed in calculating mathematics problem-solving. Emphasizing integrating the relative day-to-day experience of students and engaging in activities to boost motivation and learning outcomes is useful in shaping effective strategies for students, teachers, administrators, and officials. Novelty: This study emphasizes the significance of real-world experiences in mathematics problem-solving to improve learning outcomes and attitudes, offering valuable insights for educators, administrators, policymakers, and students in developing effective learning strategies and highlighting the connection between positive attitudes and mathematical problem-solving experiences.