Careless Errors Research Articles

An Analysis of Students’ Error in Solving Abstract Algebra Tasks

This research aimed at determining student errors in completing abstract algebra tasks. This study can be catagorized as descriptive research involving 31 college students of mathematics education program as research participant, Riau Kepulauan University, Batam. The research instrument used 4 essays of abstract algebra tests. The students’ errors were identified and categorized into 3 types of errors namely, careless errors, computational errors, and conceptual errors. The result of this study showed that most of the students’ errors was on conceptual error with the percentage of 57.94% and followed by the careless error with 33.33%, and the computational error was 8.73%. The analysis results based on the student ability level, it was found that the high competence students mostly conducting careless error and followed by conceptual error, and computational error. Meanwhile the moderate and low competence students, mostly doing conceptual error that followed by careless error, and computational error. Also, based on the proportion of errors, the high performance students made careless error and computational error more than the students with moderate and low performance. Moreover, in case of conceptual error, the pattern was the opposite where students with moderate and lower performance conducted conceptual errors more than high performance students.

Analisis Kesalahan dalam Memecahkan Masalah Kombinatorika Ditinjau dari Gaya Kognitif

Error analysis is integral part of mathematics learning. This qualitative research aims to describe the types and causes of student errors in solving combinatorics problem based on cognitive style. Subjects are high school students with field independent (FI) and field dependent (FD) cognitive style. Error analysis refers to Newman's error analysis. FI and FD students have same errors that are comprehension error at stage of understanding problem; processing skills error and encoding error at the stage of carrying out the plan. The causes of the errors are viewed from the cognitive factors, namely understanding students' concepts in solving problems. FI students have a deeper understanding and make careless error while the FD students have a lack of understanding of the concept which cause more error. The cause of errors in both students is also due to the accumulation of errors at stage of understanding problem.

Analisis Kesalahan Siswa SMP Berdasarkan Newman dalam Menyelesaikan Soal Kemampuan Berpikir Kritis Matematis pada Materi Bangun Ruang Sisi Datar

This study used a qualitative approach and the type of research conducted is descriptive. Taking the subjects of this study were 33 students of class IX SMP Negeri 16 Bandung academic year 2017/2018. Based on the results of data analysis shows that no students can answer correctly all the questions that have been given. Based on data analysis, it can be concluded that reading error 13.0%, comprehension 3.7%, transformation 12.2%, skill 9.7%, writing final answer 16.3% and carelessness 7.7%, errors done by students include: Newman's procedure is reading errors, comprehension errors, transformation errors, process skills errors, and errors in encoding errors and careless errors. The cause factor is not able to compose the meaning of the word thought into the form of a sentence matamatika, not understand the questions asked, less thorough, less able to capture information problems contained in the problem, forgot, lack of practice working on various story form problems.

District nurses now less likely to face prosecution for gross negligence manslaughter.

In this article the author discusses the Court of Appeal decision in R v Rose [2017] that redefines the threshold for prosecution for gross negligence manslaughter. The impact on district nurses will be that they are unlikely to face prosecution where a careless error contributed to a patient's death unless there was a serious and obvious risk of death at the time the error was made.

Design of Ultra-Low Temperature Online Monitoring System Based on Data Fusion Technology

Large amounts of data in the ultra-low temperature online monitoring system is needed to monitor and transmit in real time, at the same time. The data collected is usually erroneous because of the characteristics of sensors itself. In order to solve this problem, the data fusion technology is applied to the ultra-low temperature online monitoring system, and erroneous data will be removed through correlation function careless error elimination method based on the fuzzy theory. The reliability and effectiveness of the whole monitoring system is improved. According to the theory above, an ultra-low temperature online monitoring system is designed in this paper. In this paper, the overall structure of the ultra low temperature on-line monitoring system is introduced in detail, the hardware and software design of the system was analyzed, and the whole system was tested. The test results show that the system is stable and reliable with very important market application value.

A note on: Quasi-linear quotients and shellability of pure simplicial complexes

ABSTRACTThe purpose of this note is to point out a careless error in the algebraic criterion of shellability of a pure simplicial complex Δ given in [1].

Archaeological Thinking: How to Make Sense of the Past

Archaeological Thinking: How to Make Sense of the Past

In this issue – May 2017

In this issue – May 2017

Disclosure Causes of Students Error in Resolving Discrete Mathematics Problems Based on NEA as A Means of Enhancing Creativity

<p>This article is based on research cooperation of Foreign Affairs in the first year, which was<br />carried out between the team of lecturers from the Department of Mathematics Education<br />Unnes (Indonesia) with Dr. Chin Kin Eng, a lecture of Mathematics Education from Universiti<br />Malaysia Sabah. The main objective of this research in the first year is to uncover the cause of<br />the students error in resolving Discrete Mathematics by Newman Errors Analysis (NEA). The<br />Results of this research will be used as the basis for the subsequent research that reveal the<br />mathematical creativity of the students. Outcomes of this research is the publication of research<br />results in the International Journal and seminar at the international level. As a qualitative<br />research, data collection through an analysis of the results of tests, questionnaires, observations,<br />and interviews. Data analysis are data reduction, exposure of data, synthesising the data,<br />triangulation, and the inference/verification. According to research, known that students errors<br />in resolving discrete mathematics caused by: (1) the student did not know the meaning of a<br />symbol or an existing term in the problem (Reading Errors), (2) the student did not understand<br />the meaning of the problem, namely the student fails to write what is known and what is being<br />asked (Comprehension Errors), (3) students forgot a formula that will be used or<br />strategy/procedure what to do (Transformation Errors), (4) students could not make the<br />problem-solving algorithms in sequence and correctly (Process Skills Errors), (5) the student<br />could not answer according to the question (Encoding Errors), and (6) the student could not<br />translate well, especially about which was written in English (Language Errors). Errors caused<br />by carelessness students (Careless Errors) was not found. After giving Learning Therapy for<br />the provision to resolve a problem through the algorithm and the correct sequence, the causes<br />of the error of some students could be minimized, so that the number of students who were<br />experiencing errors could also be reduced. Results of this research became the basis for<br />continued research in the second year, which will be revealed and developed the mathematical<br />creativity of students with prepare advanced research instruments.</p>

What Exam Papers Make us Think

Although errors are accepted inevitable in the foreign language learning, they give information about teaching- learning process of the students. The fact that even ELT students’ exam papers contain lots of serious errors has led to this research to find the reasons for them. With this aim, the exam papers of ELT students were examined in terms of their overall quality and the errors the students have made and they were listed according to their types. This study is a qualitative study which reflects the errors of students in their exam papers. To get the data, document analysis was conducted. The documents are the exam papers of sophomore and junior students of ELT department of Akdeniz University. It was found out that ELT students have problems in expressing their own ideas on any topic by analysing the situation. Besides, most of them are not careful with their writing, in terms of grammar, syntax and spelling. Some errors can be regarded as careless errors when the exam situation is considered. However, some of them result from overgeneralization of rules. Some errors occur because of the effect of the native language or students’ inefficiency to use correct structures in writing although they know everything by heart. It is important for ELT students to use the language accurately as they are English teacher candidates. To overcome the problem, foreign language teaching and testing processes should be taken into consideration.

Types of Student Errors in Mathematical Symbols, Graphs and Problem-Solving

This study aims to identify the level of difficulty, discrimination and errors based on symbols, graphs andproblem-solving in mathematics achievement. The participants consisted of 315 grade 10 students randomlyselected from eight secondary day schools situated in the state of Kedah, Malaysia. The mathematics written testconsisted of 15 open-ended items with five items each for symbols, graphs and problem-solving and all the itemswere analyzed using the difficulty and discrimination index. Semi-structured clinical interviews were alsocarried out among 20 selected students to identify the errors they had made in mathematics. In the contentanalysis, 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, anditem 15 (Line & Plane in 3 Dimension) of the problem-solving was the most difficult item in mathematics. All ofthese 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 beingforgotten, negligence in transcribing information from the question, carelessness and guesswork. This study hasimplications for the student learning process and understanding graphs because graphs are widely used in dailylife to manage, communicate and analyze information.

Naïve Tests of Basic Local Independence Model's Invariance.

The basic local independence model (BLIM) is a probabilistic model for knowledge structures, characterized by the property that lucky guess and careless error parameters of the items are independent of the knowledge states of the subjects. When fitting the BLIM to empirical data, a good fit can be obtained even when the invariance assumption is violated. Therefore, statistical tests are needed for detecting violations of this specific assumption. This work provides an extension to theoretical results obtained by de Chiusole, Stefanutti, Anselmi, and Robusto (2013), showing that statistical tests based on the partitioning of the empirical data set into two (or more) groups are not adequate for testing the BLIM's invariance assumption. A simulation study confirms the theoretical results.

Carelessness and Affect in an Intelligent Tutoring System for Mathematics

We investigate the relationship between students’ affect and their frequency of careless errors while using an Intelligent Tutoring System for middle school mathematics. A student is said to have committed a careless error when the student’s answer is wrong despite knowing the skill required to provide the correct answer. We operationalize the probability that an error is careless through the use of an automated detector, developed using educational data mining, which infers the probability that an error involves carelessness rather than not knowing the relevant skill. This detector is then applied to log data produced by high-school students in the Philippines using a Cognitive Tutor for scatterplots. We study the relationship between carelessness and affect, triangulating between the detector of carelessness and field observations of affect. Surprisingly, we find that carelessness is common among students who frequently experience engaged concentration. This finding implies that a highly engaged student may paradoxically become overconfident or impulsive, leading to more careless errors. In contrast, students displaying confusion or boredom make fewer careless errors. Further analysis over time suggests that confused and bored students have lower learning overall. Thus, their mistakes appear to stem from a genuine lack of knowledge rather than carelessness.

Effects ofMATAS HopscotchTechnique in the Teaching of Fractions and Error Patterns Made by Year 5 Pupils

MATAS Hopscotchtechnique was created to solve the subtraction of three types of fractions. The study involved 56 pupils from two Year 5 classes. A quasi-experimental, nonrandomized control group, pretest-posttest delayed post-test was conducted on two intact groups, randomly assigned into control and experimental groups. A pretest was administered at the early stage of this study. The study described types of error made by the pupils in solving the subtraction of fractions. Rubrics, Hodes and Notling (1998), were used to describe types of error made by the pupils in the pretest and posttest. The findings in the pretest showed both groups made concept, directions, and careless errors. However, in the posttest, the experimental group made careless errors while the control group made concept, directions, and careless errors. The number of errors made by the control group was higher than that made by the experimental group.

The Gain-Loss Model: Bias of the Parameter Estimates

Abstract The gain-loss model is a formal model developed within Knowledge Space Theory. It consists of five parameters (initial probabilities of the skills, effects of learning objects on gaining and losing skills, careless error and lucky guess probabilities of the items) that are estimated by maximum likelihood. Three simulation studies show that high values of both initial and final probabilities of an item lead to a systematic overestimation of the lucky guess parameter of that item. A re-parameterization of the model is proposed, in which a joint probability of lucky guess is introduced.

What to Trust: Reconciling Mathematical Work Done by Hand with Conflicting Graphing Calculator Solutions

This paper reports on a mixed‐methods study of 111 Advanced Placement calculus students' self‐reports of their graphing calculator use, comfort, and rationale for trusting a solution produced with or without a graphing calculator when checking written work. It was found that there was no association between gender, teacher‐reported mathematical ability, or comfort with the graphing calculator and students' trust in either a graphing calculator‐produced solution or a solution produced without a graphing calculator. Furthermore, regardless of solution choice, the same four categories were evident in students' rationale for their solution choice: (a) an awareness of the possibility of careless errors, (b) the importance of checking over work, (c) a recognition of the limitations or affordances of the graphing calculator, and (d) a confidence (or lack thereof) in their own mathematical abilities. These results have implications for mathematics teaching as graphing calculators are used extensively in middle and high school mathematics classrooms and standardized tests in the United States.

Discovery With Models

In recent years, an increasing number of analyses in learning analytics and educational data mining (EDM) have adopted a “discovery with models” approach, where an existing model is used as a key component in a new EDM or analytics analysis. This article presents a theoretical discussion on the emergence of discovery with models, its potential to enhance research on learning and learners, and key lessons learned in how discovery with models can be conducted validly and effectively. We illustrate these issues through discussion of a case study where discovery with models was used to investigate a form of disengaged behavior (i.e., carelessness) in the context of middle school computer-based science inquiry. This behavior was acknowledged as a problem in education as early as the 1920s. With the increasing use of high-stakes testing, the cost of student carelessness can be higher. For instance, within computer-based learning environments, careless errors can result in reduced educational effectiveness, with students continuing to receive material they have already mastered. Despite the importance of this problem, it has received minimal research attention, in part because of difficulties in operationalizing carelessness as a construct. Building from theory on carelessness and a Bayesian framework for knowledge modeling, we use machine-learned detectors to predict carelessness within authentic use of a computer-based learning environment. We then use a discovery with models approach to link these validated carelessness measures to survey data to study the correlations between the prevalence of carelessness and student goal orientation.

Assessing Parameter Invariance in the BLIM: Bipartition Models

In knowledge space theory, the knowledge state of a student is the set of all problems he is capable of solving in a specific knowledge domain and a knowledge structure is the collection of knowledge states. The basic local independence model (BLIM) is a probabilistic model for knowledge structures. The BLIM assumes a probability distribution on the knowledge states and a lucky guess and a careless error probability for each problem. A key assumption of the BLIM is that the lucky guess and careless error probabilities do not depend on knowledge states (invariance assumption). This article proposes a method for testing the violations of this specific assumption. The proposed method was assessed in a simulation study and in an empirical application. The results show that (1) the invariance assumption might be violated by the empirical data even when the model's fit is very good, and (2) the proposed method may prove to be a promising tool to detect invariance violations of the BLIM.

The Four-Parameter Logistic Item Response Theory Model As a Robust Method of Estimating Ability Despite Aberrant Responses

In computerized adaptive testing (CAT), aberrant responses such as careless errors and lucky guesses may cause significant ability estimation biases in the dynamic administration of test items. We investigated the robustness of the 4-parameter logistic item response theory (4PL IRT; Barton & Lord, 1981) model in comparison with the 3-parameter logistic (3PL) IRT model (Birnbaum, 1968). We applied additional precision and efficiency measures to evaluate the 4PL IRT model. We measured the precision of CAT with respect to the estimation bias and mean absolute differences (MAD) between estimated and actual abilities. An improvement in administrative efficiency is reflected in fewer items being required for satisfying the stopping rule. Our results indicate that the 4PL IRT model provides a more efficient and robust ability estimation than the 3PL model.

On the unidentifiability of a certain class of skill multi map based probabilistic knowledge structures

In the process of fitting a probabilistic knowledge structure to data, standard goodness-of-fit statistics only partially describe the correctness of the fitted model. Irrespectively of how good the fit is, a too-high value of the error rates (careless error and lucky guess probabilities) might be a symptom of a misspecification of the model. In this situation, it could be critical to interpret those values as error rates. A more reasonable solution would be to hypothesize that some modifications have to be introduced in the model. In this paper, we show that in specific cases, these modifications yield basic local independence model parameterizations that are not identifiable. The applicative consequences of the theoretical results are displayed by means of an example carried out on a set of clinical data collected through the Maudsley Obsessional-Compulsive Questionnaire.