Students’ Metacognitive Errors based on Newman’s Error Types within Deep Learning Approach

The intention of this study was to clarify students’ difficulties in solving context-based mathematics tasks as used in the Programme for International Student Assessment (PISA). The study was carried out with 362 Indonesian ninth- and tenth-grade students. In the study we used 34 released PISA mathematics tasks including three task types: reproduction, connection, and reflection. Students’ difficulties were identified by using Newman’s error categories, which were connected to the modeling process described by Blum and Leiss and to the PISA stages of mathematization, including (1) comprehending a task, (2) transforming the task into a mathematical problem, (3) processing mathematical procedures, and (4) interpreting or encoding the solution in terms of the real situation. Our data analysis revealed that students made most mistakes in the first two stages of the solution process. Out of the total amount of errors 38% of them has to do with understanding the meaning of the context-based tasks. These comprehension errors particularly include the selection of relevant information. In transforming a context-based task into a mathematical problem 42% of the errors were made. Less errors were made in mathematical processing and encoding the answers. These types of errors formed respectively 17% and 3% of the total amount of errors. Our study also revealed a significant relation between the error types and the task types. In reproduction tasks, mostly comprehension errors (37%) and transformation errors (34%) were made. Also in connection tasks students made mostly comprehension errors (41%) and transformation errors (43%). However, in reflection tasks mostly transformation errors (66%) were made. Furthermore, we also found a relation between error types and student performance levels. Low performing students made a higher number of comprehension and transformation errors than high performing students. This finding indicates that low performing students might already get stuck in the early stages of the modeling process and are unable to arrive in the stage of carrying out mathematical procedures when solving a context-based task.

Students lack metacognitive ability despite its vital role in mathematical problem-solving. The problem-based Learning (PBL) model is one of the learning models to improve metacognitive ability in problem-solving. This study aimed to analyze the students'metacognitive ability in mathematical problem solving through PBL and examine its improvement. This present study applied the explanatory sequential mixed-method design. The population was the Year 11 students from one of the senior high schools in South Aceh Regency, Indonesia. Data collection was conducted using three instruments: pre-test, post-test, and interview guidelines. The pre-test and post-test data were analyzed using the t-test, while students' metacognitive ability was analyzed qualitatively. The results showed that students' metacognitive ability in mathematical problem solving through the PBL model was increased. Furthermore, students' metacognitive abilitywas at the semi-reflective use, the strategic use, the aware use levels for high-ability, medium-ability, and low-ability groups.

Penelitian ini bertujuan untuk menganalisis kesalahan mahasiswa dalam menyelesaikan masalah geometri analitik berdasarkan Newman’s Error Analysis. Kesalahan-kesalahan yang dilakukan oleh mahasiswa dalam mneyelesaikan soal geometri analitik perlu dianalisis untuk mengetahui beragam kesalahan yang dilakukan. Kesalahan tersebut perlu diidentifikasi untuk melihat letak kesalahan serta penyebab kesalahan tersebut. Dengan demikian informasi tersebut dapat menjadi umpan balik untuk peningkatan mutu pendidikan yang lebih baik. Penelitian ini merupakan penelitian deskriptif dengan menggunakan pendekatan kualitatif. Penelitian ini dilakukan di Program Studi Pendidikan Matematika FMIPA Universitas Negeri Jakarta. Partisipan penelitian adalah 81 mahasiswa yang mengambil mata kuliah Geometri Analitik pada. Data yang dikumpulkan merupakan data kuantitatif dan data kualitatif yang diperoleh dengan menggunakan teknik tes dan wawancara. Berdasarkan hasil analisis, mahasiswa masih melakukan kesalahan dalam menyelesaikan masalah geometri analitik di antaranya merupakan kategori kesalahan reading (decoding), comprehension, transformation, process skill, dan encoding. This study aims to analyze students' errors in solving analytic geometry problems based on Newman’s Error Analysis. The mistakes made by students in solving analytic geometry problems need to be analyzed to identify the various types of errors. These errors need to be identified to determine their locations and causes. Thus, this information can serve as feedback for improving the quality of education. This research is descriptive, using a qualitative approach. The study was conducted in the Mathematics Education Study Program at FMIPA, Jakarta State University. The participants were 81 students enrolled in the Analytic Geometry course. The data collected includes both quantitative and qualitative data obtained through testing and interviews. Based on the analysis, students still make errors in solving analytic geometry problems, including errors in reading (decoding), comprehension, transformation, process skills, and encoding. Keywords: Error analysis, analytic geometry, Newman’s Error Analysis.

Metacognitive ability refers to a student's awareness and understanding of their own cognitive processes, which can be enhanced by adopting an appropriate learning style. This study aimed to examine the metacognitive ability levels of students with different learning styles in a basic physics experiment course, specifically focusing on the topic of a simple pendulum. A quantitative descriptive research method was employed. Data were collected from 15 students (5 from each learning style group) using a validated and reliable questionnaire. The results indicated that auditory learners predominantly exhibited Tacit Use and Tacid Use levels, with one student at the Reflective Use level; visual learners demonstrated a range from Tacit Use to Strategic Use; and kinesthetic learners showed levels from Tacit Use to Reflective Use. In terms of metacognitive indicators, students across all learning styles exhibited moderate to high abilities in declarative, procedural, and conditional knowledge. Overall, following the simple pendulum experiment, students demonstrated moderate to high levels of metacognitive ability, reflecting a solid understanding of the experimental process and data collection related to gravitational acceleration. Notably, students with auditory, visual, and kinesthetic learning styles exhibited varying levels of metacognitive ability, which were not confined to a specific level. Additionally, students with lower basic physics scores generally demonstrated lower metacognitive ability (Tacit Use). Despite their diverse learning styles, students with low physics scores and low metacognitive abilities require a gradual, reflective, and structured approach to enhance their awareness and critical thinking skills.

This research is a qualitative research that aims to find out student errors. The research subjects consisted of 3 students. The technique of taking the subject in this study amounted to three students with high, medium and low mathematical ability categories. The instrument in this study used tests and interviews. Data collection techniques in this study are giving tests and interviews. The data analysis technique uses the Miles and Huberman model, namely data reduction, data presentation, and conclusions. Based on the results of the study, it showed that students with low abilities made four types of errors, namely, comprehension errors, transformation errors, process skill errors. Students with moderate math skills make three types of errors, namely, transformation errors, process skill errors, and encoding errors, and students with high math skills make 2 types of errors, namely transformation errors and encoding errors.

This study aims to identify the types of errors made by students in solving problems related to the concept of intervals in the Real Analysis course, based on Newman’s Error Analysis theory. The research employed a qualitative approach with 10 participants from the 2022 cohort of Mathematics Education students at Universitas Negeri Medan, selected through purposive sampling. The object of the study was the students’ errors in solving interval-related problems. Data were collected through a test consisting of four open-ended questions administered via Google Form. The data were analyzed using Newman’s five categories of error: reading, comprehension, transformation, process skills, and encoding. The results showed that students made various types of errors, with different dominant errors across each question. Comprehension and transformation errors were most frequent in question 2, reading errors dominated question 3, and process and encoding errors were most prevalent in question 4. These findings indicate that students still face challenges in understanding fundamental concepts and mathematical notation in Real Analysis. This is in line with Newman’s framework, which suggests that errors can occur at various stages of the mathematical problem-solving process.

The rapid development of science and technology demands a transformation in mathematics education to develop higher-order thinking skills. This study investigates the effectiveness of deep learning approaches in improving mathematical flexibility (MF) and mathematics self-regulated learning (MSRL) among grade 8 junior high school students in Indonesia. Employing a sequential explanatory mixed-methods design, this quasi-experimental study involved 99 students (68 experimental, 31 control) who completed pre-tests and post-tests measuring MF and MSRL. Quantitative data were analyzed using ANCOVA, t-tests, and regression analysis, followed by qualitative interviews and classroom observation to explain the findings. Results revealed that the deep learning approach significantly improved students' mathematical flexibility (t = 14.92, p 0.05), with an average gain of 4.27 points, but did not significantly improve MSRL (p = 0.165). Regression analysis demonstrated a significant positive relationship between MSRL and MF (r = 0.524, p 0.001), with MSRL accounting for 27.2% of the variance in mathematical flexibility. This study contributes to mathematics education research by providing empirical evidence that deep learning approaches effectively develop mathematical flexibility while highlighting the need for multifactorial interventions targeting affective and metacognitive dimensions to improve self-regulated learning.

The research aims to analyze students' mistakes in solving straight-line equations and then find the learning barriers experienced during distance learning conducted in the 8th grade of a superior private junior high school in Surakarta City. The research uses qualitative descriptive design with assistive instruments in the form of three straight-line equations material test questions and interview guidelines. Triangulation used is a triangulation method and analysis data is done with the stages of data collection, data reduction, data categorization, presentation and withdrawal of conclusions. Referring to the Newman Error Analysis theory, it is identified that all five types of errors are made by students in solving straight-line equations. The five types of errors are reading errors, comprehension errors, transformation errors, process skill errors, and encoding errors. Student errors that appear to indicate obstacles in learning. The rights that arise are the ownership of mobile phones and unstable internet networks, minimal learning supervision, and the availability of fewer learning resources. The results of this study can be used as a basis for developing a learning medium that can be used and supporting online teaching.

Mathematics is a logical means of thinking. Reasoning is one part of thinking that we must understanding about mathematics learning. But in fact, there still were students made errors. The aim of study is to describe the causes of students making errors in working on the matter of System of Linear Equation in Two Variables. The research was a qualitative descriptive study. Subjects in this study were four eighth grade students. Data collection was done by tests, interviews and documentation. The types of errors used in this study were the types of errors according to Newman, namely: (1) reading errors, (2) comprehension errors, (3) transformation errors, (4) process skills errors, and (5) errors in writing answers (encoding errors). The results of data analysis showed that students made errors in solving the problem form of System of Linear Equation in Two Variables. Moreover, the errors made by the students lied in the concept, interpretation of language, procedures, and calculations. While the cause factor the students were less thorough, did not understand the meaning of the problem, less know the concept of the formula, and students who did not check again the answers that have been made. In addition, we found that students were still having difficulties when understanding the meaning of the problem and wrong in process to answer the problem.

Normality testing is an essential part of statistical analysis to determine whether observed data are normally distributed or not. This study aims to document and analyze various types of errors frequently made by non-mathematics students when conducting normality tests. Furthermore, this descriptive qualitative research involved 32 second-year non-mathematics students as participants, who were given tasks requiring them to perform normality tests on datasets. The research findings indicate that the most common type of error made by non-mathematics students in conducting normality tests is encoding error, accounting for 40.7% of errors. This occurs when students mistakenly compare decimal values between Lcalc and Ltable. Consequently, the conclusions drawn from these normality tests may be inaccurate. Additionally, other types of errors identified include reading error, comprehension error, transformation error, and process skills error.

This study aims to determine whether Discovery Learning can influence students’ metacognitive abilities. This research was conducted at SMA Negeri 1 Bilah Hilir. Nonequivalent Control Group Design. Samples were taken using random sampling technique. The sample for this research was class X MIA. The research instrument is in the from of multiple choice questions with 5 questions consisting of metacognitive knowledge components and 3 essay type questions consisting of metacognitive regulations. The results of hypothesis testing using the t-test show that the value of tcount 11.44 > ttable 2.03693, so Ho is accepted. So it can be concluded that the Discovery Learning learning model has a significant effect on students’ metacognitive abilities on the concept of the plant world.

Numeracy is the ability that a person has in using his mathematical knowledge in explaining events, solving problems, or making decisions in everyday life. This study aims to analyze and describe students' mistakes in solving numeracy problems in terms of self-efficacy. The method used is descriptive qualitative. Purposive sampling technique was used in selecting 6 subjects as subjects. Data is collected through tests and questionnaires. Data analysis used is data collection, data reduction, data presentation and conclusion. The triangulation technique used is the source triangulation technique. Based on the results of the study, seen from the aspect of self-efficacy, subjects with high self-efficacy made two types of mistakes, namely errors in understanding the problem and errors in processing skills. The subject of self-efficacy is making three types of errors, namely errors in understanding the problem, transformation errors and process skills errors. Subjects with low self-efficacy made four types of errors, namely errors in reading the problem, errors in understanding the problem, errors in process skills and errors in writing the final answer. Student self-efficacy and numeracy skills have a highly correlated and positive relationship which explains that the higher the student's self-efficacy, the higher the student's numeracy skills.

This research is motivated by the existence of the 2013 curriculum, students are required to have the ability to solve problems independently. In supporting this, the strategy in the 2013 curriculum is learning to apply HOTS type questions. This is also applied in the Muhammadiyah Boarding School Pleret. However, when students worked on HOTS questions, it was seen that students still made many mistakes in working on HOTS questions. This study aims to: (1) Know the types of errors made by students of class XI MBS Pleret in solving Higher Order Thinking Skills (HOTS) Mathematics questions based on Newman's error analysis (2) Know the factors that cause errors in class XI MBS Pleret students in solving problems Higher Order Thinking Skills (HOTS) Mathematics. This type of research is descriptive qualitative. The subjects of this study were students of class XI MBS Pleret, while the object of this research was HOTS (High Order Thinking Skill) type questions. Data collection methods are conducting tests and interviews with students. The instruments used in this study were test questions, interviews and documentation. The analytical method used in this study is data reduction, data presentation, and drawing conclusions. The results of this study were (1) Types of errors made by students of class XI MBS Pleret in solving HOTS questions on trigonometry equation material based on Newman's error analysis consisting of reading errors, understanding errors, transformation errors, skills errors, and errors in writing the final answer. Based on the student error percentage table, the most students made mistakes in the process skills of 98.8% and the errors in writing the final answer was 98.8%. Then for the transformation error of 90.4%, the error in understanding is 67.3% and the smallest error is a reading error which is 66.67%. (2) The causal factors are that students do not know the α symbol (reading errors), students are not used to writing and are known and asked questions other than story questions (comprehension errors), students forget the formula to work on HOTS questions (transformation errors), the result of previous mistakes students made process skill errors and mistakes in writing the final answer.

This study aims to determine and analyze service waiting times, identify the root causes of long queues, and develop a strategy to improve service performance at the 5361137-gas station (SPBU) at the Surabaya-Gresik Toll Rest Area. The research method used is a mixed-methods approach with an exploratory sequential design. This study combines quantitative analysis using Queuing Theory to measure system performance (arrival rates and service times) and descriptive qualitative analysis using a Fishbone Diagram. Data were collected through direct observation, interviews, and g-form techniques. The results indicate that the current queuing system performance is in a critical or severe condition, indicated by a server utilization rate of 0.94 to 1.02 during peak hours. The average time spent by vehicles in the system is 14.3 minutes, of which 9.6 minutes (67%) is spent waiting in the queue. Fishbone diagram analysis revealed that the root cause of the main problem lies in the complex interaction of factors: Machine factors (EDC signal failure and pump repair downtime), Human and Method factors (implementation of static shifts and reactive maintenance), and Environmental factors (narrow layouts that hinder large vehicle maneuvers). As a solution, this study formulated a hybrid improvement strategy that includes short-term business process engineering (the use of Floating Staff and lane segregation) and long-term investment in additional pumps to change the queuing model from Single Channel to Dual Channel. This strategy is expected to reduce the utility level to a safe zone below 0.80 with a target waiting time of 3–5 minutes.

This study aimed to describe the students’ fault in finishing the problem-solving questions. This research uses the descriptive qualitative method. The research subjects are as much as 40 learners. The results are 1) most of the male students’ fault are in encoding aspect 199 or 41.29%, 2) most of the female students’ fault are in the process skill and encoding aspect 189 or 28.64%, 3) most of the fault of the grade learners are found in the process skill and encoding aspect 175 or 36.31%, 4) the fault of the under grade students are found in encoding aspects 213 or 32.27%, 5). The causes factor errors 1) The students cannot identify information of questions, 2) The students do some false in writing the formula and cannot determine the elements up flat, 5) The students do not know how to count the concept and to finish it, 6) The students write the answer incorrectly. The recommendation to solve the cause of the error are reading errors, comprehension errors, transformation error, error process skills, and encoding error solution.