Arithmetic Problems Research Articles

Critical Thinking Abilities Students Solving Social Arithmetic Numeracy Problems Based On Initial Mathematics Proficiency

This study aims to present the results of the analysis of critical thinking skills of students with low, medium, and high initial abilities in solving social arithmetic numeracy problems and to determine the critical thinking skills of students in each critical thinking indikator. Critical thinking ability is an important skill that students must have to evaluate information, make rational decisions, and solve problems effectively. Students trained in critical thinking have the ability to face problems, examine them, and find appropriate solutions. This research is qualitative research with descriptive qualitative method. The research subjects were seventh grade junior high school students in Surakarta. Data were colleccted through written tests, student interviews, and observations. The results and conclusion of this study indicate that students’mathematical critical thonking skills on social arithmetics material in terms of initial ability are still relatively low, from the results of the analysis based on the four critical thinking indicators that are the reference in this study students tend not to be able to fulfill the four critical thinking indicators.

Analysis of Junior High School Students' Misconceptions Based on Constructivism Theory in Solving Numeracy Literacy Problems

This study aims to use constructivist principles to find out how misunderstandings arise when solving arithmetic problems among students of grade 7 C of SMPN 2 Ciruas and to identify the factors responsible for them so that this problem can be presented to students and teachers as a reference for more effective learning. The subjects of this study were students of grade 7 C with high, medium and low comprehension skills. This study is qualitative and uses descriptive methods. It uses test instruments in the form of AKM sample questions and interview guides related to constructivist principles. The data analysis techniques used are data reduction, data display and inference. The results of this study explain the misunderstandings that students, especially those with low comprehension, experience when presented with numerical problems in a mathematical format. According to constructivist theory, factors that cause misunderstandings include: 1) lack of additional study time; 2) poor prior knowledge; 3) lack of understanding of the problem; 4) not taking an active role in the classroom; and 5) incorrect interpretation of the problem.

WORKING ON COLLABORATIVE PROBLEMS IN ELEMENTARY MATH LESSONS

Problem is a complex category, which does not have a single definition accepted by everyone, but representatives of different fields have interpreted the concept of problem in different ways depending on their orientations. This article describes the characteristics of arithmetical problems, the methods and means of teaching to solve problems related to working together in primary school. Specific cases of developing students' problem-solving skills by discussing and solving any arithmetical problems are highlighted.

Prediction of Individual Learning Experience in Terms of “Number Of Steps” as Solution Components of Arithmetic Tasks

The paper is devoted to the study of learning in solving arithmetic problems in the conditions of digital learning. Learning is considered as a functional system, the level of differentiation of which can be related to the number of steps in problem solving. The goal of the paper is to find out the model that could more accurately describe the relationships between the number of steps and task types on Addition data and predict the number of steps on Multiplication data. The hypothesis is that with a given similarity, there is a correlation between the number of steps in solution of addition and multiplication tasks. We have created two experimental courses, “Addition” and “Multiplication” to make participants learn optimal methods of calculation of arithmetic tasks. The courses have the same structure and belong to a common domain (arithmetic tasks). It is a condition for similarity of learning. We have found out significant positive correlation between the number of steps in solution of addition and multiplication tasks on average for the sample. We have used a regression-based classification. Few models have been built for each individual personally and trained on the Addition data, then applied on the Multiplication data. The best of these models correctly predict the number of steps in 33–40% of tasks (SD = 17–22%, max = 88%), in other tasks they give a prediction with a small error of 1–2 units, which indicates its medium predictive ability.

WEB-SITE DESIGN (BEHAVIORAL + EDUCATIONAL) TO HELP AUTISUM CHILDRENDISORDER

Autism is a condition in which children have difficulties interacting with others or exhibit differences in how they interact with people. Children with Autism Spectrum Disorder (ASD) may respond well to web-based learning because computers can offer features such as repetition, visual stimuli, and independent interactions that appeal to them. However, there have been limited studies on websites (behavioral and educational), especially outside of institutional settings. The aim of this research is to assess the effectiveness of interactive digital programs used to teach individuals with learning difficulties, tailored to their capabilities and needs. Modern technology has provided interactive and educational opportunities through picture books. This research involves designing an educational website for children with autism, including a program to teach them basic concepts necessary for daily life, such as the Arabic alphabet, to enable them to form complete words and, consequently, complete sentences. Additionally, the program teaches numbers, enabling children to count and perform arithmetic problems such as counting money and telling time. The main interface page displays eight images that change every seven seconds automatically or via navigation links on the right and left sides of the image. A six-page website was designed, covering topics such as what autism is, symptoms, diagnosis, and more. Web technologies were utilized in the website design, with HTML as the primary language. To analyze some aspects of this study's results, the use of the computer screen is intended to capture the autistic child's attention, helping them remain in one place and stay focused on the screen for as long as possible. If a mother or female teacher can keep a child engaged with the screen for 5-10 minutes, it is considered a significant achievement.

Affective and cognitive factors associated with Chinese and Italian children’s arithmetic performance

BackgroundThis study aimed to investigate the cognitive and affective factors associated with cross-cultural differences in arithmetic tasks.MethodsA total of 404 third- and fourth- graders were recruited from China and Italy to complete exact arithmetic, arithmetic estimation and cognitive tasks (i.e., short-term memory, executive functions, and fluid reasoning). Their mathematical anxiety was also measured.ResultsThe results showed that Chinese children performed better than Italian children in both arithmetic tasks and in shifting task. Italian children performed better in visuospatial updating task and reported higher levels of mathematical anxiety than their Chinese peers. Multi-group path analyses showed that the patterns of relations among cognitive factors (i.e., short-term memory, inhibition and shifting), mathematical anxiety, and arithmetic performance were similar across groups. The only exception was that visuospatial updating uniquely predicted arithmetic estimation for Chinese but not for Italian children.ConclusionsChinese children outperformed their Italian peers in the exact arithmetic task, likely due to the greater emphasis on arithmetic fluency in Chinese mathematics education, both in schools and at home. They also had a slight advantage than Italian peers in the arithmetic estimation task. The unique link between updating and arithmetic estimation found in Chinese children but not Italian children suggests that, although arithmetic estimation is not emphasized in the curricula of either country, instruction and practice in exact arithmetic may enhance Chinese children’s efficiency in solving arithmetic estimation problems.

Revealing mental representations of arithmetic word problems through false memories: New insights into semantic congruence.

What can false memories tell us about the structure of mental representations of arithmetic word problems? The semantic congruence model describes the central role of world semantics in the encoding, recoding, and solving of these problems. We propose to use memory tasks to evaluate key predictions of the semantic congruence model regarding the representations constructed when solving arithmetic word problems. We designed isomorphic word problems differing only by the world semantics imbued in their problem statement. Half the problems featured quantities (durations, heights, elevator floors) promoting an ordinal encoding, and the other half used quantities (weights, prices, collections) promoting a cardinal encoding. Across three experiments, in French and in English, we used surprise memory tasks to investigate adults' mental representations when solving the problems. After the first solving task, the participants were given an unexpected task: either to recall the problems (Experiments 1 and 2) or to identify, from memory, the experimenter-induced changes in target problem sentences (Experiment 3). Crucially, all problems included a specific mathematical relationship that was not explicit in the problem statement and that could only be inferred from an ordinal encoding. We used the presence or absence of this relationship in the participants' responses to infer the structure of their representations. Converging results from all three experiments bring new evidence of the role of semantic congruence in arithmetic reasoning, new insights into the relevance of the cardinal-ordinal distinction in numerical cognition, and a new perspective on the use of memory tasks to investigate variations in the representations of mathematical word problems. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

What pupil size can and cannot tell about math anxiety

Math Anxiety (MA) consists of excessive fear and worry about math-related situations. It represents a major barrier to numerical competence and the pursuit of STEM careers. Yet, we currently do not dispose of many tools that can capture its multifaceted nature, e.g. moving beyond the exclusive reliance on self-reports and meta-cognition. Here we sought to probe Pupil Size (PS) as a viable tool in the study of MA by administering arithmetic problems to university students in the humanities (N = 70) with various levels of MA. We found that arithmetic competence and performance are indeed negatively associated with MA, and this is accurately tracked by PS. When performance is accounted for, MA does not further modulate PS (before, during, or after calculation). However, the latency of PS peak dilation can add a significant contribution to predicting MA scores, indicating that high MA may be accompanied by more prolonged cognitive effort. Results show that MA and mathematical competence may be too crystalized in young university students to be discernible. We therefore call for early educational interventions to tackle and mitigate this dysfunctional association early on.

On the connectedness of arithmetic hyperplanes

Discrete geometry is a geometry specific to computers that studies Zd structures. It appears naturally in image analysis or 3D printing. Our goal is to find efficient algorithms to characterise these geometric structures and their properties.We are interested in a fundamental structure of discrete geometry, the arithmetic hyperplanes, and more particularly in their connectedness. Many works have studied a connectedness defined from the neighbourhood by faces and have allowed to observe a percolation phenomenon. These studies have also allowed to decide the connectedness of a plane in an efficient way. We propose an extension of these results in the case of connectivity defined from general neighbourhoods.Beyond the new concepts that this extension requires, the main contribution of the paper lies in the use of analysis to solve this arithmetic problem and in the design of an algorithm that decides the general connectedness problem. The study of the thickness of connectedness as a function reveals discontinuities at each rational point. However, a much more regular underlying structure appears in the irrational case. Thus, the consideration of irrational vectors allows a simpler approach to the connectedness of arithmetic hyperplanes.

A holistic investigation of fraction learning: examining the hierarchy of fraction skills, misconceptions, mathematics anxiety and response confidence

ABSTRACT This study aimed to holistically investigate fraction knowledge by considering pupils’ fraction performance on various tasks (i.e. mapping, equivalence, comparison, and arithmetic) and in relation to whole number arithmetic, fraction misconceptions, mathematics anxiety, and confidence in responses. Northern Irish pupils (N = 123; 77 girls; M age = 11.1 years) demonstrated a strong understanding of fraction magnitudes with few pupils showcasing misconceptions across magnitude tasks. In contrast, fraction arithmetic knowledge, which was uniquely predicted by whole number arithmetic and fraction comparison, was still developing with many pupils incorrectly applying whole number strategies to arithmetic problems. Mathematics anxiety was low, but negatively correlated with performance, and confidence reports were more closely aligned with performance on whole number arithmetic compared to fraction tasks. Overall, researchers and educators need to consider not just fraction performance, but also foundational skills, the presence of misconceptions, and pupils’ feelings and beliefs to better understand fraction learning.

Investigating Students' Difficulties in Solving Social Arithmetic Problems

Purpose: The objective of this research was to investigate the challenges faced by junior high school students in solving social arithmetic problems. Methodology: This research method is a qualitative method with descriptive research type. This research was carried out at one of the Pekanbaru junior high schools with class VII subjects at Da`wah Pekanbaru Middle School, with a total of 30 students. Results: The data collection technique used in this research is a written test technique in the form of a description consisting of 5 questions. After students complete the questions, the answers will be analyzed and when the researcher finds unique answer results, the researcher will conduct an interview. Conclusions: Based on the research results, it was found that students' difficulties in solving social arithmetic problems were 1) difficulty in understanding the information from the questions, 2) difficulty in understanding the concept correctly. 3) lack of accuracy in the solution process and 4) time constraints which cause students to not be able to complete the questions properly and correctly. Recommendations: It is hoped that the results of this research will allow teachers to guide and overcome the difficulties faced by students so that students can develop their abilities in mathematics, especially social arithmetic material.

On improving conversational interfaces in educational systems

Conversational Intelligent Tutoring Systems (CITS) have drawn increasing interest in education because of their capacity to tailor learning experiences, improve user engagement, and contribute to the effective transfer of knowledge. Conversational agents employ advanced natural language techniques to engage in a convincing human-like tutorial conversation. In solving math word problems, a significant challenge arises in enabling the system to understand user utterances and accurately map extracted entities to the essential problem quantities required for problem-solving, despite the inherent ambiguity of human natural language. In this study, we propose two possible approaches to enhance the performance of a particular CITS designed to teach learners to solve arithmetic–algebraic word problems. Firstly, we propose an ensemble approach to intent classification and entity extraction, which combines the predictions made by two distinct individual models that use constraints defined by human experts. This approach leverages the intertwined nature of the intents and entities to yield a comprehensive understanding of the user’s utterance, ultimately aiming to enhance semantic accuracy. Secondly, we introduce an adapted Term Frequency-Inverse Document Frequency technique to associate entities with problem quantity descriptions. The evaluation was conducted on the AWPS and MATH-HINTS datasets, containing conversational data and a collection of arithmetical and algebraic math problems, respectively. The results demonstrate that the proposed ensemble approach outperforms individual models, and the proposed method for entity–quantity matching surpasses the performance of typical text semantic embedding models.

Impact of working memory on arithmetic problem solving in primary school pupils with mathematical learning difficulties

Learning arithmetic operations is fundamental for social and professional emancipation, where counting and solving numerical operations is part of everyday behavior; this reflects the more or less serious difficulties that pupils with mathematics learning difficulties (MLD) may encounter. The interest of this work is to underline the importance of the cognitive deficit at the memory level in these subjects. In this sense we selected 30 pupils aged 7 to 8 years old, educated from 2nd to3rd year of the primary cycle with MLD on whom we applied tests of arithmetic problem solving and working memory (WM). Analysis of the results indicates a significant correlation between the difficulties recorded in arithmetic and WM. These results lead us to a systematic evaluation of WM in subjects with MLD, in any therapeutic diagnostic approach.

Active maintenance in working memory reinforces bindings for future retrieval from episodic long-term memory

Many theories assume that actively maintaining information in working memory (WM) predicts its retention in episodic long-term memory (LTM), as revealed by the beneficial effects of more WM time. In four experiments, we examined whether affording more time for intentional WM maintenance does indeed drive LTM. Sequences of four words were presented during trials of simple span (short time), slow span (long time), and complex span (long time with distraction; Experiments 1–2). Long time intervals entailed a pause of equivalent duration between the words that presented a blank screen (slow span) or an arithmetic problem to read aloud and solve (complex span). In Experiments 1–3, participants either serially recalled the words (intentional encoding) or completed a no-recall task (incidental encoding). In Experiment 4, all participants were instructed to intentionally encode the words, with the trials randomly ending in the serial-recall or no-recall task. To ensure similar processing of the words between encoding groups, participants silently decided whether each word was a living or nonliving thing via key press (i.e., an animacy judgment; Experiments 1 and 3–4) or read the words aloud and then pressed the space bar (Experiment 2). A surprise delayed memory test at the end of the experiment assessed LTM. Applying Bayesian cognitive models to disambiguate binding and item memory revealed consistent benefits of free time to binding memory that were specific to intentional encoding in WM. This suggests that time spent intentionally keeping information in WM is special for LTM because WM is a system that maintains bindings.

Enhancing arithmetic skills through working memory: A review of interventions and strategies

This review article investigates the relationship between elementary school children’s arithmetic skills and working memory, and it shows strategies and interventions to improve their arithmetic proficiency. This review highlights the role of working memory in information processing while solving arithmetic problems. It also proposes the specific methods used for enhancing arithmetic skills, such as instructional techniques and cognitive training programs. In the line of comprehensive examinations of empirical studies, this article presents effective approaches to educators and researchers who are exploring to foster development of school-age children in mathematics by utilizing the functionality of working memory.

Students' Specializing Thinking in Solving Arithmetic Sequence and Series Problems

Specializing thinking is a mathematical thinking process that is very important in the mathematics learning process. Specializing thinking is thinking by starting with special things. The application of specializing thinking can be an effective strategy for teachers to improve students' mathematical thinking abilities in dealing with various problems. This research aims to describe students' specializing forms of thinking in solving problems of arithmetic sequences and series. This research method is descriptive qualitative research with a case study approach. The subjects in this research were 2 class X high school students who successfully solved arithmetic sequence and series problems. The instruments used are tests and interviews. The data in this research are the results of the subject's work and the results of interview transcripts. The research results show that two forms of specializing thinking were found in solving arithmetic sequences and series problems, that is explicit schematic representation and implicit schematic representation. It is hoped that the results of this research can provide a valuable contribution to mathematics teachers in designing more meaningful learning.

Fluency and Flexibility of Students in Solving Arithmetic Sequence Problems Based on Self Efficacy

This research is a descriptive qualitative research that aims to describe students' creative thinking in solving arithmetic sequence problems in terms of self-efficacy. This research was conducted at SMK Kesehatan Dhermajaya. The subjects of this study were 3 grade XI students who were taken according to the aspects of self-efficacy, namely magnitude, strength, generality. Creative thinking indicators in this study are fluency, flexibility, and novelty. The results of this study indicate that the magnitude subject in the fluency aspect is that students can provide 2 possible jars needed. The flexibility aspect is that students can solve with 2 alternative solutions with the arithmetic sequence formula, and write an arithmetic sequence that is at odds with 2 and if added together the result is 90. The strength of the fluency aspect is that students provide 2 possible jars needed. At the same time, the aspects of flexibility and novelty have not been fulfilled. The subject of generality in the fluency aspect is that students can provide 3 possible jars. The flexibility aspect is that students can provide 2 different alternative solutions, namely using the arithmetic sequence formula and writing an arithmetic sequence that is 2 apart and then adding them up. The three subjects, still have not shown the uniqueness of the answer or used different strategies so that the novelty aspect has not been fulfilled.

Objects as knowledge: A case study of outsight

A laboratory procedure employing insight problems allows researcher to capture how new ideas are discovered or constructed. Insight problems are relatively simple riddles designed to encourage an initially incorrect interpretation of the problem that leads to an impasse: Researchers are then poised to capture the moment the impasse is overcome, that is when a new productive interpretation of the problem is developed resulting in the solution. Researchers call this process ‘restructuring’: while the term describes the phenomenon, it is not clear how it explains it nor how restructuring comes about. The case study we describe here reveals the micro-processes involved in restructuring by using an interactive problem-solving procedure involving matchstick arithmetic problems. Originally developed by Knoblich et al., these problems present a simple but false arithmetic expression using Roman numerals: Participant must discover which matchstick can be moved and where to turn it into a true expression. The participant can manipulate matchsticks, and in doing so creates a dynamic object, the behaviour of which triggers new actions and cues new hypotheses about the solution. We present the case-study data in the form of a video of a participant instructed to narrate hunches and hypotheses as she interacts with a physical model of the solution, over three separate problems. On the basis of a granular coding of the participant’s verbal protocol along with an equally granular coding of the changes to the object (using ELAN; https://archive.mpi.nl/tla/elan ), the case study is the first to clearly reveal the restructuring process that results in the phenomenon of ‘outsight’, that is when the behaviour and polymorphic changes to the object qua model of the solution guides the participant to the solution.

Dynamic modulation of the processing of unpredicted technical errors by the posterior cingulate and the default mode network

The pervasive use of information technologies (IT) has tremendously benefited our daily lives. However, unpredicted technical breakdowns and errors can lead to the experience of stress, which has been termed technostress. It remains poorly understood how people dynamically respond to unpredicted system runtime errors occurring while interacting with the IT systems on a behavioral and neuronal level. To elucidate the mechanisms underlying such processes, we conducted a functional magnetic resonance imaging (fMRI) study in which 15 young adults solved arithmetic problems of three difficulty levels (easy, medium and hard) while two types of system runtime errors (problem errors and feedback errors) occurred in an unexpected manner. The problem error condition consisted of apparently defective displays of the arithmetic problem and the feedback error condition involved erroneous feedback. We found that the problem errors positively influenced participants’ problem-solving performance at the high difficulty level (i.e., hard tasks) at the initial stage of the session, while feedback errors disturbed their performance. These dynamic behavioral changes are mainly associated with brain activation changes in the posterior cingulate and the default mode network, including the posterior cingulate cortex, the mPFC, the retrosplenial cortex and the parahippocampal gyrus. Our study illustrates the regulatory role of the posterior cingulate in coping with unpredicted errors as well as with dynamic changes in the environment.

Towards Promoting the Efficiency of Enterprise Investment Management with Artificial Intelligence

With the continuous development and optimization of artificial intelligence, enterprises have begun to pay attention to the use of artificial intelligence for the optimization of work and the improvement of efficiency, and in the management of enterprise investment, a number of companies have begun to use a large number of artificial intelligence technologies in the integration and analysis of data, information processing and analysis, risk management, efficiency improvement, and so on. Enterprises encounter problems in analyzing data and information in investment management, and problems in risk management, all of which affect the improvement of their investment returns. Enterprises face a huge amount of data in the process of investment management, it is difficult to calculate a large number of data models in a relatively short period of time, and it is impossible to analyze and extract more information. In the face of investment risk, the control of risk in the past investment process is more based on experience to judge, there is a great deal of subjective assumptions in risk avoidance. And in the investment process companies also want to increase returns, improve efficiency, avoid risk, and achieve a more automated and intelligent trading process. Enterprises need to use artificial intelligence to technically solve the problems of data aggregation, arithmetic, and analysis; use artificial intelligence to optimize the problem of processing large amounts of information; use artificial intelligence technology to enhance risk management and predictive analysis, strengthen intelligent decision-making and portfolio optimization, and provide insights into big data analysis and market trends. The wide application of artificial intelligence technology in enterprises also has a certain impact on the development of enterprises, and it has a certain impact on the planning, feasibility, whole-process control, investment evaluation, investment report, and investment efficiency of investment in the investment link, which makes it widely concerned in the society and in enterprises.