Arithmetic Problems Research Articles

Spatial configuration of hundreds charts influences children's knowledge of base‐ten concepts

AbstractThe hundreds chart is a valuable tool for teachers in elementary mathematics classrooms. The present study investigated the effects of spatial configurations of virtual hundreds charts on children's knowledge of base‐ten concepts. Kindergarten and first‐grade students were assigned to three instructional conditions in which they worked with a researcher to solve arithmetic word problems. The charts used in the conditions differed by the spatial configuration of the numbers: (a) top down, with numbers increasing from top to bottom; (b) bottom up, with increases from bottom to top; and (c) explicit bottom‐up, with a bottom‐up chart and an explicit visual cue that prompted a comparison between the “up‐is‐more” structure to a cylinder filling with water. Participants were more likely to count by tens than by ones to solve problems when the numbers in the chart increased from top to bottom than when they increased from bottom to top. No effects of spatial configuration on place‐value knowledge was observed. One account of the findings is that participants were more accustomed to the movements in the top‐down chart because they matched the direction in which children learn to read. The role of spatial affordances of instructional materials in children's mathematics learning is discussed.

The effects of operator position and superfluous brackets on student performance in simple arithmetic

For students to advance beyond arithmetic, they must learn how to attend to the structure of math notation. This process can be challenging due to students' left-to-right computing tendencies. Brackets are used in mathematics to indicate precedence but can also be used as superfluous cues and perceptual grouping mechanisms in instructional materials to direct students’ attention and facilitate accurate and efficient problem solving. This online study examines the impact of operator position and superfluous brackets on students’ performance solving arithmetic problems. A total of 528 students completed a baseline assessment of math knowledge, then were randomly assigned to one of six conditions that varied in the placement of higher-order operator and the presence or absence of superfluous brackets: [a] brackets-left (e.g., (5 * 4) + 2 + 3), [b] no brackets-left (e.g., 5 * 4 + 2 + 3), [c] brackets-center (e.g., 2 + (5 * 4) + 3), [d] no brackets-center (e.g., 2 + 5 * 4 + 3), [e] brackets-right (e.g., 2 + 3 + (5 * 4)), and [f] no brackets-right (e.g., 2 + 3 + 5 * 4). Participants simplified expressions in an online learning platform with the goal to “master” the content by answering three questions correctly in a row. Results showed that, on average, students were more accurate in problem solving when the higher-order operator was on the left side and less accurate when it was on the right compared to in the center. There was also a main effect of the presence of brackets on mastery speed. However, interaction effects showed that these main effects were driven by the center position: superfluous brackets only improved accuracy when students solved expressions with brackets with the operator in the center. This study advances research on perceptual learning in math by revealing how operator position and presence of superfluous brackets impact students’ performance. Additionally, this research provides implications for instructors who can use perceptual cues to support students during problem solving.

Related consistent lures increase the judgment of multiplication facts: Evidence using event-related potential technique.

Simple multiplication errors are primarily shown in whether the lures are related to the operands (relatedness, such as 3 × 4 = 15 vs. 17) or whether the same decades are shared with the correct answers (consistency, such as 3 × 4 = 16 vs. 21). This study used a delayed verification paradigm and event-related potential technique to investigate the effects of relatedness and consistency in simple multiplication mental arithmetic for 30 college students in an experiment of presenting probes in auditory channels. We found that, compared to the related inconsistent lures, the related consistent lures showed significantly faster reaction time and induced significantly large amplitudes of N400 and late positive component. The findings suggest that related consistent lures are less affected by the activation diffusion of the arithmetic problem, and the credibility of being perceived as the correct answer is less; the lures related to operands and sharing the same decades with the accurate results can promote the judgment of multiplication mental arithmetic, and the results support the Interacting Neighbors Model.

Gender peculiarities of the influence of training loads of different orientation on the indicators of mental performance of young sportsmen of adolescent age

There are close associative relationships between physical and mental development of a person, and it has been established that systematic exercise has a positive effect on physical and mental performance. The purpose of the study is to identify the possibility of a specific effect of training loads of different orientation on the indicators of mental performance of young female athletes aged 13-15 years.
 The features of specific influence of training loads of different orientation on indicators of mental performance of young sportsmen of specialized boarding sports institutions are considered. The sportswomen of Brovary sports professional college (experimental group) (n=75) took part in the research, who according to the classification of sports by Dembo (1980) were divided into two groups: group A - speed and power sports (n=28); group B - endurance sports (n=47). The control group consisted of female students aged 13-15 years (n=30) who did not play sports. The mental performance of the subjects was assessed by the results of solving arithmetic problems. A comparative analysis of changes in the indicators of mental performance of the subjects is given. It is revealed that the specificity of the training process leaves an imprint on the nature of changes in the indicators of the mentioned performance in young female athletes aged 13-15 years. The orientation of the training process specializes the peculiarities of the development of mental performance of young sportsmen of adolescent age. Under the influence of training loads mainly aimed at developing the quality of endurance, there is an improvement in mental performance (there is a significant decrease in the indicator of time of solving problems and a decrease in the number of errors made during testing), while under the influence of loads of speed and power character there are insignificant changes in the average values of time of solving problems and a significant increase in the number of errors made.

Modeling “Stag and Hare Hunting” Behaviors Using Interaction Data from an mCSCL Application for Grade 5 Mathematics

This study attempted to model the stag and hare hunting behaviors of students using their interaction data in a mobile computer-supported collaborative learning application for Grade 5 mathematics. Twenty-five male and 12 female Grade 5 students with an average age of 10.5 years participated in this study. Stag hunters are more likely to display personality dimensions characterized by Openness while students belonging to hare hunters display personality dimensions characterized by Extraversion and Neuroticism. Students who display personality dimensions characterized by Agreeableness and Conscientiousness may tend to be either hare or stag hunters, depending on the difficulty, types of arithmetic problems solved, and the amount of time spent solving arithmetic problems. Students engaged in a stag hunting behavior performed poorly in mathematics. Decision tree modeling and lag sequential analysis revealed that stag and hare hunting behaviors could be identified based on personality dimensions, types of arithmetic problems solved, difficulty level of problems solved, time spent solving problems, and problem-solving patterns. Future research and practical implications were also discussed.

EVALUATING THE INTEGRATION OF WORD PROBLEMS, WORLD EXPERIENCE, AND MATHEMATICAL KNOWLEDGE IN YOUNG CHILDREN

This study arose from research conducted in a school where students aged seven to nine struggled to solve mathematical problems. The study's goal was to find out how children make sense of their problems. Students were given a few simple arithmetic problems and then individually interviewed to determine and comprehend the difficulties that the students were experiencing. The problems' stories involved a quantity being increased by or combined with another quantity to form a total. The quantities were small natural numbers that did not exceed 20. The findings revealed a number of problems with mathematics learning. The results were derived from how students understood the word problems, the relationship between the word problems and real-life experience, the relationship between real-life experience and mathematical knowledge, and the integration of word problems, world experience, and mathematical knowledge. How students work and verify their answers in order to better understand their thinking was observed. The usefulness of word problems in school can be realized only if students' understanding of a particular situation can be elicited, enriched, or embellished with their experience before that experience can be re-examined in light of the theory that is applied to the real-life situation.

Arithmetic Word Problem-Solving and Math Anxiety: The Role of Perceived Difficulty and Gender

ABSTRACT A crucial component of mathematics curriculum in primary education is represented by the ability to solve arithmetic word problems. Previous studies investigated predominantly the cognitive factors underlying this skill, neglecting the role of emotional (e.g. math anxiety – MA) and metacognitive aspects (e.g. perceived difficulty). Some findings suggested that emotional factors could influence perceived task difficulty which would, in turn, impair students’ performance. However, the relation between MA, perceived difficulty, and math problem-solving has not been explored yet. Moreover, although many studies reported gender differences in MA levels, findings involving primary school children are contrasting. Thus, this study aimed to evaluate the role of MA and perceived task difficulty on arithmetic word problem-solving proficiency in a sample of Italian primary school students, and to investigate gender differences in those variables. Results showed that MA had a direct and indirect effect through perceived difficulty on problem-solving performance. Furthermore, findings confirmed that girls exhibited higher MA levels, however no gender difference was observed in problem-solving accuracy nor in perceived difficulty. The study underlines the need to consider emotional factors when investigating children’s difficulties in math problem-solving and highlight the importance of MA interventions, especially for girls, already in primary education.

EXPRESS: Resisting the Urge to Calculate: The Relation Between Inhibitory Control and Perceptual Cues in Arithmetic Performance.

Subtle visual manipulations to the presentation of mathematical notation influence the way that students perceive and solve problems. While there is a consistent impact of perceptual cues on students' problem solving, other cognitive skills such as inhibitory control may interact with perceptual cues to impact students' arithmetic problem-solving performance. We present an online experiment in which college students completed a version of the Stroop task followed by arithmetic problems in which the spacing between numbers and operators was either congruent (e.g., 2 + 3×4) or incongruent (e.g., 2+3 × 4) to the order of precedence. We found that students were comparably accurate between problem types but might have spent longer responding to problems with congruent than incongruent spacing. There was no main effect of inhibitory control on students' performance on these problems. However, an exploratory analysis on a combined performance measure of accuracy and response time revealed an interaction between problem type and inhibitory control. Students with higher inhibitory control performed better on congruent vs. incongruent problems whereas students with lower inhibitory control performed worse on congruent vs. incongruent problems. Together, these results suggest that the relation between inhibitory control and arithmetic performance may not be straightforward. Further, this work advances perceptual learning theory and contributes new findings on the contexts in which perceptual cues, such as spacing, influence arithmetic performance.

Teaching the methods of solving mathematical problems

Following questions was affected in this article - types of mathematical problems, role and meaning of solving problems in men’s life (pupil, student), difficulties in solving  mathematical problems, classification of mathematical problems due to the way of solving key. Tasks of arithmetics are various according to the contents and on difficulty of the decision. At the solution of some tasks doesn't meet difficulties in a choice of this or that action. The choice of arithmetic actions and at the solution of many tasks is carried out on the basis of the communications existing between these sizes. Solution of each task purely arithmetic actions and logical conclusions, but not to the same extent: in one tasks arithmetic actions prevail, and reasonings and logical conclusions play so prevailing role others, after the logical conclusions the solution of a task is consolidated to thought tension. If the necessary data on arithmetics are acquired and problems of detailed type are already sorted, other problems of this sort are solved without effort. The article presents the results of a survey of teachers on the methodology of teaching mathematics and solving problems by schoolchildren. Keywords: quantily , problem, teaching the methods of problem solving , types of arithmetical problems , ways of problem solving.

How negative emotions influence arithmetic performance: a comparison of young and older adults

We investigated the influence of negative emotions on arithmetic problem-solving performance and age-related differences therein. Participants were asked to verify complex multiplication problems that were either true (e.g., 4 × 26 = 104) or false (e.g., 5 × 41 = 201). Half the problems were five problems (e.g., 5 × 28 = 140) and half were non-five problems (e.g., 6 × 36 = 216). False five problems violated the five-rule, the parity-rule, both rules, or no rule. Problems were preceded by emotionally neutral or negative pictures. For true problems, emotions impaired performance while verifying non-five problems in young adults only and while verifying five problems in older adults only. For false five problems, negative emotions influenced young adults’ performance while verifying both-rule and no-rule violation problems but not when verifying parity-rule violation or five-rule violation problems. Negative emotions did not influence older adults’ performance whichever false five problems they solved. These findings suggest that negative emotions may change the mechanisms that participants use to solve arithmetic problems and that emotions influence young and older adults via different mechanisms.

Analisis Kesalahan Peserta Didik Dalam Menyelesaikan Soal Cerita Matematika Tentang Operasi Hitung Pecahan Kelas V Sekolah Dasar

Abstract. This study aimed to (1) described the type of student error in solving fractional arithmetic operation story problem, (2) described the factor that cause student to made mistake in solving fractional counting operation story problem and, (3) described solution to correct student error in solving fractional calculation operation story problem. This research was a descriptive qualitative researched. The subject in this study was class V student and class V teacher at SD Negeri Setono. Data collection techniques used test question result, interview result, and observation. The data validity test technique used source triangulation technique. The data analysis technique used Miles and Huberman which includes 4 stages, namely: (1) data collection, (2) data reduction, (3) data presentation, (4) drawing conclusion. The results showed that the analysis of students' errors in solving story problem about calculating operations on error indicators interpreted mathematical symbols 8.90%, error in formulating a problem solving model 44.07%, transformation errors 9.26%, mathematical skill errors 14.81%, and final answer writing skills 22.96%. Based on the results of the study, it can be concluded that the analysis of student errors in solving story questions about fractional calculation operations on error indicators formulating a problem solving model was the most common indicator.

Analysis of Class VII Students' Mathematical Communication Ability in Algebra Calculating Operations

The problem is that teachers dominate class communication by explaining concepts, showing examples, and directing questions and answers. This study aims to analyze the communication skills of junior high school students in solving algebraic arithmetic operations. The research was conducted on class VIII students of SMP Negeri 1 Rawamerta for the 2022/2023 academic year. The method used in this research is qualitative, with a descriptive approach. Data collection in this study was carried out by providing mathematical communication ability test instruments used by previous researchers. Based on the data analysis that has been done, the percentage of students communicative abilities in the average score for solving algebraic arithmetic problems is 14.58%. Understanding communication in completing algebraic arithmetic operations for class VIII students of SMP Negeri 1 Rawamerta needs to be more profound.

Learning to solve arithmetic problems with a virtual abacus

Acquiring mathematical skills is considered a key challenge for modern Artificial Intelligence systems. Inspired by the way humans discover numerical knowledge, here we introduce a deep reinforcement learning framework that allows to simulate how cognitive agents could gradually learn to solve arithmetic problems by interacting with a virtual abacus. The proposed model successfully learn to perform multi-digit additions and subtractions, achieving an error rate below 1% even when operands are much longer than those observed during training. We also compare the performance of learning agents receiving a different amount of explicit supervision, and we analyze the most common error patterns to better understand the limitations and biases resulting from our design choices.

Computer-based multimedia testing: Effects of static and animated representational pictures and text modality

Static representational pictures (RPs) have been focused in research on the multimedia effect in testing and might be especially important in arithmetical word problems, which require a multi-stage mental processing to segment the task. To further highlight the task segments visually, dynamic visualizations could help. However, conventional animations might not apply to this context and the role of dynamic visualizations with temporal segmentations (i.e., animated RPs) is unexplored. This classroom experiment with 456 students investigated multimedia and modality effects in 24 mathematical word problems. Our 3 × 2 mixed design included three multimedia conditions (static RPs, animated RPs, and text-only) and two modality conditions (written text vs spoken text). We investigated effects on response correctness, metacognitive ratings, item-solving satisfaction and time on task. Both static and animated RPs increased response correctness, item-solving satisfaction, and metacognitive ratings compared to text-only. Time on task was affected in distinctive ways in both RP conditions and also varied depending on text modality. Spoken text barely increased response correctness in animated RP items but not at all in static RP items. Moderator analyses revealed that the effects of static and animated RPs on response correctness were dependent on the text modality but varied across school types and the level of mathematical prior knowledge. For students at non-academic-track schools or with low prior knowledge, static and animated RPs improved response correctness compared to text-only across both modalities. For students at academic-track schools or with high prior knowledge, mainly combinations of static or animated RPs with spoken text were effective.

The influence of home environmental factors on kindergarten children's addition strategy use.

Young children vary widely in their levels of math knowledge, their abilities to solve math problems, and the strategies they use to solve math problems. As much of later math builds on children's early understanding of basic math facts and problem-solving strategies, understanding influences on children's early problem solving is important. Few studies, however, have examined the home environment in relation to children's strategy use during arithmetic problems. We examined how both structural characteristics of children's home environments, such as socioeconomic status (SES), as well as the learning environment, such as engagement in math and literacy activities at home, related to their use of problem-solving strategies for numerical addition problems. Kindergarten children from diverse backgrounds completed a measure of addition problem solving and strategy use, including simple and complex numerical problems. Strategies were coded based on a combination of accuracy and strategy sophistication, with higher scores indicating problems solved correctly with more sophisticated strategies. Parents completed a home activities questionnaire, reporting the frequency with which they and their child had engaged in math and literacy activities at home over the past month. An exploratory factor analysis identified three components of the home activities - a basic activities factor, an advanced math activities factor, and a literacy activities factor. Findings indicated that SES related to children's strategy sophistication, and frequency of engaging in advanced math and literacy activities at home predicted strategy sophistication, however, engaging in activities at home did not moderate the relations between SES and strategy sophistication. This suggests that family engagement in activities at home may promote early arithmetic skills, and that the role of home environmental characteristics should be considered in children's arithmetic strategy use and performance over development.

Effects of a Complex Physical Activity Program on Children's Arithmetic Problem Solving and Arithmetic Reasoning Abilities.

Research has shown that higher levels of physical activity are associated with better cognitive performance in children. However, the benefits of physical activity on academic achievement and specifically on mathematics performance need to be further explored. Therefore, this study aimed to investigate the effects of a complex physical activity (CPA) intervention program, including cognitive involvement, on children’s mathematics performance. The participants were 128 children (aged 12−13 years) attending third grade in three middle schools. They were randomly allocated into a CPA intervention (n = 64) or a waitlist control group (n = 64), the latter of which was given a regular and easy-to-perform activity program. At baseline and after the intervention, students’ physical fitness was measured using a battery of standardized motor tests (20 m shuttle run test, curl-up test, push-up test, and sit and reach test). In addition, the AC-MT 11-14 test was administered to allow a standardized and comprehensive assessment of arithmetic problem-solving and arithmetic reasoning abilities. In comparison to the control, the intervention group showed significant improvements (p < 0.001) in comprehension and production (d = 1.88), arithmetic reasoning (d = 2.50), and problem solving (d = 1.32), as well as in 20 m shuttle run test (d = 1.81), push-up test (d = 1.88), curl-up (d = 3.52), and sit and reach (d = 2.52). No significant changes were found in the control group. In conclusion, findings showed that a 12-week CPA intervention program can improve mathematical performance in children in the third grade of middle school. CPA intervention may be an effective method to improve academic performance and avoid student failure.

Hex-Derived Molecular Descriptors via Generalized Valency-Based Entropies

Entropy is a thermodynamic function in chemistry that, based on the number of possible configurations for a given system or process, measures the randomness and disorder of molecules in that system or process. Many problems in arithmetic, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. A topological descriptor also connects certain physical aspects of the underlying chemical substances, in contrast to a topological index, which in chemical graph theory is a numerical representation of a chemical network. When building models for any chemical network, the graph is crucial. Simonraj et al. produced a brand-new category of graphs known as the third kind of hex-derived networks. In our work, we discuss the third class of hex-derived networks, which includes hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {HDN}_{3}$ </tex-math></inline-formula> ), triangular hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {THDN}_{3}$ </tex-math></inline-formula> ), rectangular hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {RHDN}_{3}$ </tex-math></inline-formula> ), and chain hex-derived networks ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {CHDN}_{3}$ </tex-math></inline-formula> ). We compute exact results for newly defined entropies by utilizing their topological indices based on end vertex degrees.

Reasoning arithmetic word problems entailing implicit relations based on the chain-of-thought model

&lt;abstract&gt;&lt;p&gt;Solving arithmetic word problems ($ AWPs $) that involve deep implicit relations can be quite challenging. However, the paper proposed two approaches to tackle this issue. The first approach used the modifier-to-matrix ($ MTM $) model to extract noun modification components from the problem text. Specifically, a missing entity recovery ($ MER $) model translated explicit expressions into a node dependency graph ($ NDG $). The nodes on the graph then recursively acquired connections from the knowledge base through the $ MER $ model until the goal was achieved with a known quantity. The solving engine then selected the appropriate knowledge as the prompt. The second approach proposed in the paper was a comprehensive one that combined explicit and implicit knowledge to enhance reasoning abilities. The experimental results of the dataset demonstrate that the proposed algorithm is superior to the baseline algorithms in solving $ AWPs $ that require deep implicit relations.&lt;/p&gt;&lt;/abstract&gt;

The role of verbal and visual domain storage in solving arithmetic word problems with figures Focusing on analysis of integration time in problem-solving

The role of verbal and visual domain storage in solving arithmetic word problems with figures Focusing on analysis of integration time in problem-solving

Matemáticas en la prensa diaria española del siglo XVIII. Los primeros años del Diario de Barcelona

Abstract During the 18th century, many newspapers were published in Spain. Many of them covered scientific topics, even if it was not their main goal. In fact, it was possible to find scientific contents in daily newspapers whose main goal was essentially informative. Mathematics was not an exception. In this paper, we focus on the early years of Diario de Barcelona . We have identified the relevant presence of Mathematics in 51 out of the 3013 initial issues of the daily paper. Then, we provide an overview of the mathematical contents presented in this newspaper, that can be classified into two main categories (isolated collaborations and interactions) and, furthermore, we have a closer look at some of these contents. In particular, we describe interactions between readers around arithmetic and algebraic problems proposed by some of them, as well as some isolated collaborations about different topics. In both cases it is possible to detect interesting questions and debates about several aspects of Mathematics.