Arithmetic Word Problems Research Articles

Indonesian Question Answering System for Solving Arithmetic Word Problems on Intelligent Humanoid Robot

This paper presents our research on Indonesian question answering system for solving arithmetic word problems using pattern matching approach on intelligent humanoid robot. The objective of this paper is to elaborate how natural language processing (NLP) and pattern matching approach works in question answering system for solving arithmetic word problems. Upon receiving a Indonesian arithmetic word problem, the robot will translate Indonesian speech to English text, resolve conjunction problem, co-references problem, question preprocessing, question analysis, represent the knowledge, and lastly the robot will answer the solution. We employed NLP for English by using Natural Language Toolkit (NLTK) in our research. Based on the experiment results, it can be concluded that: (i) the accuracy of the question answering system for each scheme ranges from 80% to 100% depend on the difficulty to comprehend the word problem, (ii) the response time is rather slow with average processing time is about 1.12 minutes.

Arithmetic learning with the use of graphic organiser

For this study, Zollman’s four corners-and-a-diamond mathematics graphic organiser embedded with Polya’s Problem Solving Model was used to investigate secondary school students’ performance in arithmetic word problems. This instructional learning tool was used to help students break down the given information into smaller units for better strategic planning. The participants were Year 7 students, comprised of 21 male and 20 female students, aged between 11-13 years old, from a co-ed secondary school in Brunei Darussalam. This study mainly adopted a quantitative approach to investigate the types of differences found in the arithmetic word problem pre- and post-tests results from the use of the learning tool. Although the findings revealed slight improvements in the overall comparisons of the students’ test results, the in-depth analysis of the students’ responses in their activity worksheets shows a different outcome. Some students were able to make good attempts in breaking down the key points into smaller information in order to solve the word problems.

Cognitive mechanisms underlying third graders’ arithmetic skills: Expanding the pathways to mathematics model

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills.

Knowing, applying, and reasoning about arithmetic: Roles of domain-general and numerical skills in multiple domains of arithmetic learning.

The longitudinal relations of domain-general and numerical skills at ages 6-7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that domain-general skills, including spatial visualization, language, rapid automatized naming, and working memory, contributed independently to arithmetic learning. These relations were mostly mediated via basic number competence (i.e., counting sequence and number system knowledge), although spatial visualization remained predictive of arithmetic outcomes. The findings underscore a similar developmental course of arithmetic learning across different cognitive domains where domain-general skills build a launchpad for advanced arithmetic via enhancing basic number competence. (PsycINFO Database Record

The Role of Executive Function in Arithmetic Problem-Solving Processes: A Study of Third Graders

ABSTRACTThis study investigated the roles of different executive function (EF) components (inhibition, shifting, and working memory) in 2-step arithmetic word problem solving. A sample of 139 children aged 8 years old and regularly attending the 3rd grade of primary school were tested on 6 EF tasks measuring different EF components, a reading task and a reading comprehension task, an arithmetic facts task evaluating basic knowledge of calculation, and three 2-step arithmetic word problems. Multiple hierarchical regression analyses were conducted to investigate the roles of the different EF components in the various phases of the problem-solving process. The results showed that EF affects the various phases of problem solving differently over and above calculation knowledge and reading abilities. The implications of these findings are discussed in relation to further understanding the role of cognitive skills in mathematical problem solving and in relation to instructional approaches that may increase children’s performance on 2-step arithmetic word problems.

Semantic alignment across whole-number arithmetic and rational numbers: evidence from a Russian perspective

ABSTRACTSolutions to word problems are moderated by the semantic alignment of real-world relations with mathematical operations. Categorical relations between entities (tulips, roses) are aligned with addition, whereas certain functional relations between entities (tulips, vases) are aligned with division. Similarly, discreteness vs. continuity of quantities (marbles, water) is aligned with different formats for rational numbers (fractions and decimals, respectively). These alignments have been found both in textbooks and in the performance of college students in the USA and in South Korea. The current study examined evidence for alignments in Russia. Textbook analyses revealed semantic alignments for arithmetic word problems, but not for rational numbers. Nonetheless, Russian college students showed semantic alignments both for arithmetic operations and for rational numbers. Since Russian students exhibit semantic alignments for rational numbers in the absence of exposure to examples in school, such alignments likely reflect intuitive understanding of mathematical representations of real-world situations.

The conceptual overlap between arithmetic and algebraic referential mapping

To investigate whether arithmetic and algebra referential mapping entail similar or different representational processes, 135 13-year-olds participated in a three-phase study. In Phase 1 (the pre-algebra phase) students solved arithmetic and algebraic equations and mapped arithmetic equations (e.g., 5 + = 9) onto simple arithmetic word problems. Nine months later (Phase 2), with the assistance of problem-solving hints provided by an interviewer, students mapped symbolic equations onto algebraic word problems. After a further nine months (Phase 3), the students solved equations and completed an algebraic word problem solving test. The results showed that algebraic equation problem-solving and the hints required for mapping symbolic equations onto word problems (Phase 2) both predicted subsequent unassisted algebraic word problem equation mapping (Phase 3) and retrospectively predicted arithmetic word problem mapping abilities (Phase 1). The findings highlight the ways in which representational ability contributes to algebraic reasoning and suggest that arithmetic representational processes may scaffold algebraic referential mapping. The pedagogical implications of the association between representational abilities in the two domains are discussed in terms of approaching arithmetic word problem-solving from a more representational perspective.

Cognitive precursors of word reading versus arithmetic competencies in young Chinese children

Word reading and arithmetic calculation are foundational to higher level reading (e.g., text comprehension) and mathematics (e.g., fraction), respectively. The present study aims to examine the similarities and differences in the cognitive precursors of word reading and arithmetic competencies in young Chinese children. A total of 75 Hong Kong Chinese children were tested first in the fall (T1) and then in the spring (T2) of their third kindergarten years. Competencies in Chinese word reading, including both single- and double-character word reading, and arithmetic calculation, including nonsymbolic arithmetic, arithmetic word problems, and written arithmetic, were assessed at both T1 and T2. Phonological awareness, orthographic awareness, rapid automatized naming (RAN), spatial perception, and spatial visualization were assessed at T1. The results showed that phonological awareness predicted later competencies in word reading and symbolic arithmetic, specifically arithmetic word problems and written arithmetic. RAN was predictive of later competencies in word reading and nonsymbolic arithmetic. Orthographic awareness was associated with later competencies in word reading but not arithmetic. Visual-spatial skills predicted later competencies in arithmetic word problems but not word reading. The findings suggest that similarities and differences both exist in the cognitive underpinnings of Chinese word reading and arithmetic competencies at a young age.

Model-based analysis of thinking in problem posing as sentence integration focused on violation of the constraints

The advancement of computer and communication technologies has enabled researchers to conduct and analyze the learning process of posing problems. This study investigates what learners think while posing problems as sentence integration in terms of intermediate products as well as the posed problems as the resultant product. Problem posing as sentence integration defines the arithmetic word problem structure, and posing a problem is a task to satisfy all the constraints and requirements to build a valid structure. A previous study shows that, in problem posing as sentence integration for arithmetic word problems, learners try to satisfy a relatively large number of constraints in the posed problems. In contrast, this study focuses on the violation of constraints in the intermediate products while posing problems. The result shows that learners were inclined to avoid as many violated constraints as possible throughout the problem-posing process. Although learners tend to avoid the violated constraints, naturally, they cannot avoid some mistakes. Further analysis shows that learners actually have difficulty in fulfilling particular constraints while posing the problems. Based on this analysis, it is possible to detect the difficulty of learners’ actions from the model perspective. Hence, it is possible to give accurate feedback and appropriately support the learners.

Component processes in arithmetic word-problem solving and their correlates.

Arithmetic word-problem solving is an important component of elementary mathematics curricula that links school mathematics to real-life problem solving. The present 3-year longitudinal study examined children’s arithmetic word-problem solving through understanding its 2 component processes: number-sentence construction and computation. Chinese first graders (n = 153) were tested on their arithmetic word-problem solving, in which they wrote down the number sentences before they solved the problems. They were also given a parallel test of arithmetic computation. Various cognitive predictors and mathematical outcomes were assessed. It was found that the children’s difficulty in solving arithmetic word problems lay more with writing number sentences rather than in computation. The results from path analysis showed that word reading and various numerical-magnitude processing and domain-general skills significantly predicted arithmetic computation whereas only domain-general skills significantly predicted number-sentence construction. Both number-sentence construction and computation significantly predicted future arithmetic computation and mathematics achievement even after controlling for previous arithmetic computation. Theoretical and practical implications are discussed.

Modeling of Mathematical knowledge in Children's Arithmetic Word Problem Solving: A Developmental Perspective (子どもの数理解と教授介入 (その3 ))

modeling of Mathematical knowledge in Children's Arithmetic Word Problem Solving: A Developmental Perspective (子どもの数理解と教授介入 (その3 ))

Unit Dependency Graph and Its Application to Arithmetic Word Problem Solving

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .

An analysis of learner outputs in problem posing as sentence-integration in arithmetic word problems

Achieving practical implementation of learning by problem posing faces the issue of inefficiency due to the time needed for assessment and giving feedback to students’ posed problems. As a solution of this problem, we have developed a tablet PC-based software for learning by posing arithmetic word problems named Monsakun. The software is based on Triplet Structure Model of arithmetic word problem. In this research, we investigated problems posed by elementary school students in Monsakun to understand whether Monsakun encourages them to think about the structure of arithmetic word problems. The result shows that students did not pose problems randomly but considered things first. We also found that the frequent errors are actually meaningful errors, and students tried to pose problems satisfying as many constraints as possible, which means they actually think about the structure to pose required problems in the assignments. The process of understanding assignment requirements and relating them to suitable sentence cards is an important point especially for young learners to reach deep understanding of the structure of arithmetic word problems.

Process-based Assignment-Setting Change for Support of Overcoming Bottlenecks in Learning by Problem-Posing in Arithmetic Word Problems

Problem-posing is well known as an effective activity to learn problem-solving methods. Monsakun is an interactive problem-posing learning environment to facilitate arithmetic word problems learning for one operation of addition and subtraction. The characteristic of Monsakun is problem-posing as sentence-integration that lets learners make a problem of three sentences. Monsakun provides learners with five or six sentences including dummies, which are designed through careful considerations by an expert teacher as a meaningful distraction to the learners in order to learn the structure of arithmetic word problems. The results of the practical use of Monsakun in elementary schools show that many learners have difficulties in arranging the proper answer at the high level of assignments. The analysis of the problem-posing process of such learners found that their misconception of arithmetic word problems causes impasses in their thinking and mislead them to use dummies. This study proposes a method of changing assignments as a support for overcoming bottlenecks of thinking. In Monsakun, the bottlenecks are often detected as a frequently repeated use of a specific dummy. If such dummy can be detected, it is the key factor to support learners to overcome their difficulty. This paper discusses how to detect the bottlenecks and to realize such support in learning by problem-posing.

Investigation of learning environment for arithmetic word problems by problem posing as sentence integration in Indonesian language

Arithmetic word problems remain one of the most difficult area of teaching mathematics. Learning by problem posing has been suggested as an effective way to improve students’ understanding. However, the practice in usual classroom is difficult due to extra time needed for assessment and giving feedback to students’ posed problems. To address this issue, we have developed a tablet PC software named Monsakun for learning by posing arithmetic word problems based on Triplet Structure Model. It uses the mechanism of sentence-integration, an efficient implementation of problem-posing that enables agent-assessment of posed problems. The learning environment has been used in actual Japanese elementary school classrooms and the effectiveness has been confirmed in previous researches. In this study, ten Indonesian elementary school students living in Japan participated in a learning session of problem posing using Monsakun in Indonesian language. We analyzed their learning activities and show that students were able to interact with the structure of simple word problem using this learning environment. The results of data analysis and questionnaire suggested that the use of Monsakun provides a way of creating an interactive and fun environment for learning by problem posing for Indonesian elementary school students.

Arabic Arithmetic Word Problems Solver

The recent evolution in Natural Language Processing (NLP) and machine learning have played a crucial role in the development of solving word problems written in human language. This paper, to the best of our knowledge, presents the first attempt of automatically solving Arabic arithmetic word problems. In addition, as part of this work, we prepared an Arabic annotated dataset by translating a standard arithmetic word problems English dataset (AddSub Dataset). The AddSub dataset has been used by several researchers to evaluate their models for English arithmetic word problems. The proposed algorithm relies on our automatic verbs learning approach based on the training dataset. Moreover, the algorithm utilizes various NLP tools to assign objects to problem states until reaching to the goal state such as Stanford Parser, Named Entity Recognition (NER), and Cosine Metric Distance. Our approach overcomes various issues such as tracking both entities and their related results during the transfer process as well as dealing with different forms of the same verb. The performance evaluation process showed promising results resolving 80.78% of the problems. On the other hand, there are still several areas that can be extended and improved. For instance, the lack of common knowledge, presence of irrelevant information, and quantity conversions.

An Investigation of Learner's Actions in Posing Arithmetic Word Problem on an Interactive Learning Environment

An Investigation of Learner's Actions in Posing Arithmetic Word Problem on an Interactive Learning Environment

The role of the updating function in solving arithmetic word problems.

We investigated how the updating function supports the integration process in solving arithmetic word problems. In Experiment 1, we measured reading time, that is, translation and integration times, when undergraduate and graduate students (n = 78) were asked to solve 2 types of problems: those containing only necessary information and those containing extraneous information. The results indicated that participants required more integration time to solve extraneous-information problems than necessary-information problems. However, the higher the updating, the smaller the increment of integration time. In Experiment 2, we investigated whether different problem models were provided by undergraduate and graduate students (n = 73) with different updating functions. Participants executed a lexical-decision task immediately following an integration process. The lexical-decision task comprised 3 conditions: necessary-information word, extraneous-information word, and novel word conditions. The RTs for both necessary- and extraneous-information word conditions were faster than that for the novel word condition. The facilitation amount in an extraneous-information word became weaker as the problem solver’s updating function increased. These results suggest that individuals with a high updating function provide a problem model that maintains only task-relevant information, while those with less-effective updating use an approach that also considers extraneous information. These 2 experiments indicate that updating is an important contributor to the integration process and different updating abilities result in different problem models. (PsycINFO Database Record (c) 2017 APA, all rights reserved)

The effects of task activities and gaming scales on eye reading and visual search performance

The effects of video gaming have been explored extensively in many learning-related fields. However, limited research has investigated whether the frequencies of exposing to gaming environments influence students' Chinese reading comprehension, arithmetic word problem test, spatial recognition, and graphical patterns recognition. To address this issue, this study adopted eye-tracking technology to explore learners' reading and visual search responses on various reading materials. Task effects and correlation analyses were conducted on a sample of 19 sophomores with varying gaming frequencies, eye reading fixations, and regressions. The results revealed that practice makes users have fewer fixation frequencies on a similar task. Meanwhile, the results demonstrated a positive gaming frequency correlation on eye fixations and regressions for Chinese reading comprehension and arithmetic word problem test, and a negative gaming frequency correlation for spatial and graphical patterns recognition tasks.

Visualizations of problem-posing activity sequences toward modeling the thinking process.

Problem-posing is well known as an effective activity to learn problem-solving methods. Although the activity is considered in contributing to the understanding of the problem’s structure, it is not clear how learners could understand it through the activity. This study proposes a method to offer a visual representation for analyzing the problem-posing activity sequence in MONSAKUN, a digital learning environment for problem-posing of arithmetic word problems via sentence integration. This system requires users to pose a problem through combinations of given simple sentences based on the requirement. The system writes every single action into logs as sequences of problem-posing activity. The sequences are considered to represent the thinking processes of learners. The thinking process reflects their understanding and misunderstanding about the structure of the problems. This study created visualizations of learners’ problem-posing processes from the data obtained through the practical use of MONSAKUN, including the states in which many learners had difficulties finding the correct answer. In this study, we refer to such states as “trap states.” In MONSAKUN, a trap state is a combination of simple sentences where many learners tend to make and need relatively more actions to obtain the correct answer. As the result of the visualization and analysis of the data, some trap states have been identified, and they changed for each trial in the same problem.