Math Word Problems Research Articles

ANALYSIS OF STUDENTS' ERRORS IN SOLVING WORD PROBLEMS ABOUT SOLID FIGURES IN FIFTH GRADE OF SDN TAMBAKREJO, PURWOREJO REGENCY, IN ACADEMIC YEAR OF 2020/2021.

<p><em>The study aimed: (1) to analyze the types of students’ errors of fifth grade in solving math word problems about solid figures, (2) to describe the factors causing students' errors in solving math word problems about solid figures, (3) to describe solutions to overcome students’ errors in solving math word problems about solid figures in fifth grade of SD Negeri Tambakrejo. The research was a qualitative case study method. The subjects were 24 fifth grade students. Data collection techniques included observation, tests, interviews, and documents. Data analysis techniques were data reduction, data presentation, and verification. The results showed that: (1) the types and the percentage of students’ errors were: reading error = 5.3%, comprehension error = 20.7%, transformation error= 24%, process skill error= 11%, encoding error= 20.5%. (2) The factors causing students’ errors were internal factors and external factors. (3) The solutions to solve students’ errors were (a) the students were discipline to do word problems step-by-step, (b) the teachers emphasized the students in order to write steps in solving word problems completely, (c) the teachers emphasized the students about the basic concept in doing word problems, (d) the teachers applied effective and creative learning models.</em></p>

Chinese Math Word Problems Generation Network

Aiming at the feature vector bottleneck problem and the high time cost of the training process in the automatic generation of Chinese math word problems under the end-to-end architecture, we proposed an automatic generation method of Chinese math word problems based on the pre-training model combined with the integration of encoder and decoder. We used a deep neural network to model the mathematical equation sequence and Chinese keyword information, and used the stepped attention matrix to generate word problems. For training and testing on the Ape210K data set, compared with the end-to-end method, the Rouge-1 and Rouge-L evaluation indicators in our method was increased by 14.1% and 12.5%, as well as the training time cost was reduced by nearly 50%.

Advancing math word problem instruction for English language learners to enhance their prospects in STEM disciplines.

Advancing math word problem instruction for English language learners to enhance their prospects in STEM disciplines.

Learning by Fixing: Solving Math Word Problems with Weak Supervision

Previous neural solvers of math word problems (MWPs) are learned with full supervision and fail to generate diverse solutions. In this paper, we address this issue by introducing a weakly-supervised paradigm for learning MWPs. Our method only requires the annotations of the final answers and can generate various solutions for a single problem. To boost weakly-supervised learning, we propose a novel learning-by-fixing (LBF) framework, which corrects the misperceptions of the neural network via symbolic reasoning. Specifically, for an incorrect solution tree generated by the neural network, the fixing mechanism propagates the error from the root node to the leaf nodes and infers the most probable fix that can be executed to get the desired answer. To generate more diverse solutions, tree regularization is applied to guide the efficient shrinkage and exploration of the solution space, and a memory buffer is designed to track and save the discovered various fixes for each problem. Experimental results on the Math23K dataset show the proposed LBF framework significantly outperforms reinforcement learning baselines in weakly-supervised learning. Furthermore, it achieves comparable top-1 and much better top-3/5 answer accuracies than fully-supervised methods, demonstrating its strength in producing diverse solutions.

HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem

Automatically solving math word problems is a crucial task for exploring the intelligence levels of machines in the general AI domain. It is highly challenging since it requires not only natural language understanding but also mathematical expression inference. Existing solutions usually explore sequence-to-sequence models to generate expressions, where the problems are simply encoded sequentially. However, such models are generally far from enough for understanding problems as similar to humans and lead to incorrect answers. To this end, in this paper, we propose a novel Hierarchical Math Solver (HMS) to make deep understanding and exploitation of problems. In problem understanding, imitating human reading habits, we propose a hierarchical word-clause-problem encoder. Specifically, we first split each problem into several clauses and learn problem semantics from the local clause level to the global problem level. Then, in clause understanding, we propose a dependency-based module to enhance clause semantics with the dependency structure of the problem. Next, in expression inference, we propose a novel tree-based decoder to generate the mathematical expression for the answer. In the decoder, we apply a hierarchical attention mechanism to enhance the problem semantics with context from different levels, and a pointer-generator network to guide the model to copy existing information and infer extra knowledge. Extensive experimental results on two widely used datasets demonstrate that HMS achieves not only better answers but also more reasonable inference.

SMART: A Situation Model for Algebra Story Problems via Attributed Grammar

Solving algebra story problems remains a challenging task in artificial intelligence, which requires a detailed understanding of real-world situations and a strong mathematical reasoning capability. Previous neural solvers of math word problems directly translate problem texts into equations, lacking an explicit interpretation of the situations, and often fail to handle more sophisticated situations. To address such limits of neural solvers, we introduce the concept of a situation model, which originates from psychology studies to represent the mental states of humans in problem-solving, and propose SMART, which adopts attributed grammar as the representation of situation models for algebra story problems. Specifically, we first train an information extraction module to extract nodes, attributes and relations from problem texts and then generate a parse graph based on a pre-defined attributed grammar. An iterative learning strategy is also proposed to further improve the performance of SMART. To study this task more rigorously, we carefully curate a new dataset named ASP6.6k. Experimental results on ASP6.6k show that the proposed model outperforms all previous neural solvers by a large margin, while preserving much better interpretability. To test these models' generalization capability, we also design an out-of-distribution (OOD) evaluation, in which problems are more complex than those in the training set. Our model exceeds state-of-the-art models by 17% in the OOD evaluation, demonstrating its superior generalization ability.

Αποτελεσματική διδασκαλία γνωστικού σχήματος προβλημάτων αφαίρεσης σε μαθητές με ειδικές μαθησιακές δυσκολίες με τη χρήση πολλαπλών τρόπων αναπαράστασης της γνώσης

The present research examines the construction and activation of cognitive schemata corresponding to subtraction-compare and subtraction-equalize math word problems by primary school students with specific learning disabilities. In order to facilitate the participants in developing their cognitive schemata, we utilized multiple ways of knowledge representation (manipulatives, pictures, and arithmetic symbols) in the context of an intervention based on the principles of effective instruction. In order to evaluate the results, assessments were conducted prior and immediately after the implementation of the intervention, as well as three weeks after its completion. It was found that participants performed significantly better in problem solving both after the intervention and at follow-up, proving that they benefited from the instruction they had received. Results are discussed in regard to organizing appropriate instruction for students with mathematical difficulties and disabilities.

Why and for whom does personalizing math problems enhance performance? Testing the mediation of enjoyment and cognitive load at different ability levels

In two context personalization studies, we examined (a) enjoyment and cognitive load as two potential mechanisms explaining the effects of context personalization on mathematical word problem performance, and (b) whether individual differences in math, reading and working memory ability moderated these effects. In both studies (Study 1: N = 238; Study 2: N = 149) primary school students from 6th grade completed math word problems in either a personalized condition or a control condition. Students rated their enjoyment and experienced cognitive load after each problem. Moderated mediation models showed that while ability, enjoyment and cognitive load significantly predicted performance, (a) personalization did not affect word problem performance, enjoyment or cognitive load, and (b) the three different abilities did not moderate these relations. The findings are discussed in light of three personalization principles (depth, grain size, ownership) and complexity in different steps of math problem solving.

RESEARCH ABILITY OF STUDENTS OF PEDAGOGICAL SCHOOL OF MONGOL STATE PEDAGOGICAL UNIVERSITY IN SOLVING THEIR PROBLEMS IN DIFFERENT WAYS

In this article, we tried to show the results of mastering by students of a pedagogical school Mongolian State Pedagogical University with the skills of solving word problems in different ways and methodological knowledge of teaching. Since 2012, students of the pedagogical school have been taking the elective «Mathematical Science». In the previous school, students did not solve math word problems in different ways, and therefore they faced difficulties and interesting cases, but after each training there were positive results.

Classifying and Solving Arithmetic Math Word Problems—An Intelligent Math Solver

Solving mathematical (math) word problems (MWP) automatically is a challenging research problem in natural language processing, machine learning, and education (learning) technology domains, which has gained momentum in the recent years. Applications of solving varieties of MWPs can increase the efficacy of teaching-learning systems, such as e-learning systems, intelligent tutoring systems, etc., to help improve learning (or teaching) to solve word problems by providing interactive computer support for peer math tutoring. This article is specifically intended to benefit such teaching-learning systems on arithmetic word problems solving by adding an interactive and intelligent word problem solver to assess an individual's learning outcome. This article presents arithmetic mathematical word problems solver (AMWPS), an educational software application for solving arithmetic word problems involving single equation with single operation. This article is based on a combination of a machine learning based (classification) approach and a rule-based approach. We start with classification of arithmetic word problems into four categories (Change, Compare, Combine, and Division-Multiplication) along with their subcategories, followed by the classification of operations (+, -, *, and /) related to different subcategories. Our system processes an input arithmetic word problem, predicts the category and subcategory, predicts the operation, identifies and retrieves the relevant quantities within the problem with respect to answer generation, and formulates and evaluates the mathematical expression to generate the final answer. AMWPS outperformed similar systems on the standard AddSub and SingleOp datasets and produced new state-of-the-art result (94.22% accuracy).

Environmental Health Education: From Museum Specimens and Math Word Problems to Virtual and Augmented Reality.

Environmental degradation and its severe impact on human health has revealed the necessity for effective educational interventions. Given the importance of “Environment,” “Health,” and “Education,” as key pillars for the achievement of sustainable development, the education for environmental health is evolving into a main component of current strategies against environmental health threats, such as climate change and urban air pollution. Environmental Health Education, which must be considered as a strategical response against environmental degradation, offers vast capacity for innovation alongside every educational stage. For instance, the application of new technologies, such as virtual and augmented reality applications, the adoption of innovative interdisciplinary educational approaches, and the incorporation of Arts are evolving into a new era’s educational perspectives. All the new trends in formal, non-formal and informal Environmental Health Education should be captured and assessed, in favor of protecting both local and global natural environment, human and animal health, and promoting sustainability.

Engagement and effectiveness of symbolic and iconic learning support for math problem representation: an eye tracking study

ABSTRACT Successful problem solving begins with constructing mental problem representations and the identification of problem characteristics to clarify the solution. The purpose of the current study is to examine the design principles of learning supports promoting mental problem representation in the math problem solving setting. We investigated the mental problem representations and problem solving performance influenced by the formats of the learning supports. Through the analysis of participants’ visual attention and solution notations, the current study found that problem solvers’ visual attention on symbolic learning support increases whereas their visual attention on iconic learning supports decreases during the problem representation stages. There is a significant difference in problem solvers’ visual attention on iconic learning supports between the successful and unsuccessful problem-solving groups. Unsuccessful problem solvers tended to disregard critical elements in the math word problem.

The reason why students are not successful to use diagrams, even if encouraged, when solving math word problems: Verification of diagram training effect based on behavioral and brain science

The reason why students are not successful to use diagrams, even if encouraged, when solving math word problems: Verification of diagram training effect based on behavioral and brain science

Solving arithmetic word problems: A deep learning based approach

This paper presents a novel deep learning based approach to solving arithmetic word problems. Solving different types of mathematical (math) word problems (MWP) is a very complex and challenging task as it requires Natural Language Understanding (NLU) and Commonsense knowledge. An application on this can benefit learning (education) technologies such as E-learning systems, Intelligent tutoring, Learning Management Systems (LMS), Innovative teaching/learning, etc. We propose Deep Learning based Arithmetic Word Problem Solver, DLAWPS, an intelligent MWP solver system. DLAWPS consists of a Recurrent Neural Network (RNN) based Bi-directional Long Short-Term Memory (BiLSTM) to classify operation among four basic operations {+ , - , * , /}, and a knowledge-based irrelevant information removal unit (IIRU) to identify the relevant quantities to form an equation to solve arithmetic MWPs. Our system generates state-of-the-art results on the standard arithmetic word problem datasets –AddSub, SingleOp, and a Combined dataset.

An investigation of the role of spatial ability in representing and solving word problems among engineering students

AbstractBackgroundSpatial ability is significantly related to performance in engineering education, and problem‐solving, an activity that is highly relevant to engineering education, has been linked to spatial ability.Purpose/HypothesisThis study investigated the following question: To what extent is spatial ability related to problem‐solving among engineering students and how do approaches to problem representation and solution vary with spatial ability level?Design/MethodA spatial ability test, a set of math word problems and an accompanying math ability test, was administered to two samples of first‐year engineering students in two countries. Data were analyzed at the test level to evaluate the relationship of spatial ability to problem representation and solution. A detailed item level analysis was conducted to compare approach to problem‐solving with spatial ability level.ResultsSpatial ability was found to be significantly related to problem‐solving but not to the math ability test, indicating the relationship was limited to the problem representation phase, not the solution phase. Key aspects of representation were identified for each problem to reveal a more pronounced relationship between representation and spatial ability than between problem‐solving (representation and solution) and spatial ability.ConclusionsProblem‐solving can be considered to consist of two cognitively distinct phases: problem representation and problem solution. It was found that spatial ability is significantly related to problem representation but not to problem solution. Hence, this study shows that spatial ability plays a key role in engineering education that is not limited to visualization of imagery but extends to thinking during problem‐solving, a nonroutine activity that requires mental representation.

Analisis Kesalahan Newman (Newman Error Analysis-Nea): Perbandingan Ketelitian Antara Siswa Yang Menghafal Dan Tidak Menghafal Alqur’an

Newman (1977) form Australia was defined five specific literacy and numeracy skills as crucial to performance on mathematical word problems: (1) reading error, (2) comprehension error, (3) transformation error, (4) process skills error, and (5) encoding error. The purpose of this study is to comparison Newman Error Analysis (NEA) between students are memorize and not memorize Al-Quran in solving word problem. This research is a qualitative research, and the subject of this research is students in grade 11th of MA in central lombok, with respectively six school in sub-district.. The result of this research is there are differences Newman’s Error Analysis (NEA) Between Students Are Memorize and Not Memorize Al-Quran in Solving Math Word Problems.

Automatic Generation of Amharic Math Word Problem and Equation

Math word problem uses a real word story to present basic arithmetic operations using textual narration. It is used to develop student’s comprehension skill in conjunction with the ability to generate a solution that agrees with the story given in the problem. To master math word problem solving, students need to be given fresh and enormous amount of problems, which normal textbooks as well as teachers fail to provide most of the time. To fill the gap, a few research works have been proposed on techniques to automatically generate math word problems and equations mainly for English speaking community. Amharic is a Semitic language spoken by more than hundred million Ethiopians and is a language of instruction in elementary schools in Ethiopia. And yet it belongs to one of a less resourced language in the field of linguistics and natural language processing (NLP). Hence, in this paper, a strategy for automatic generation of Amharic Math Word (AMW) problem and equation is proposed, which is a first attempt to introduce the use template based shallow NLP approach to generate math word problem for Amharic language as a step towards enabling comprehension and learning problem solving in mathematics for primary school students. The proposed novel technique accepts a sample AMW problem as user input to form a template. A template provides AMW problem with placeholders, type of problem and equation template. It is used as a pattern to generate semantically equivalent AMW problems with their equations. To validate the reality of the proposed approach, a prototype was developed and used as a testing platform. Experimental results have shown 93.84% overall efficiency on the core task of forming templates from a given corpus containing AMW problems collected from elementary school mathematics textbooks and other school worksheets. Human judges have also found generated AMW problem and equation as solvable as the textbook problems.

The Effects of Schema-Based Instruction on Solving Mathematics Word Problems

The purpose of this study was to investigate the frequency with which students use math word problem strategies during and after schema-based instruction. It examines the extent to which students increase their ability to correctly solve word problems. It compares students’ attitudes toward mathematics problem solving before and after schema-based instruction. The study was conducted in a resource class with seven second-grade students on individualized education programs (IEPs). A single-subject research design was used. The schema-based instruction was implemented by the special education teacher in a small group setting. Students showed an increase in attempted and correct strategy use during instruction. Three students increased their attempts of strategy use from pretest to posttest, but only one student used the strategy correctly on all attempts. The mean problem-solving accuracy increased from 22 percent to 34 percent from pretest to posttest. Students showed minimal change in their attitude toward math word problems.

Effectiveness of the Math Word Problem Intervention for Students with Math Underachievement: Case Studies on Word Problem Solving Strategies

This study examined and analyzed the effectiveness of the math intervention program with word problem solving strategies on 4th, 5th, and 6th grade elementary school students with math underachievement. A total of six students were selected as participants based on the screening test results and teachers’ recommendation and placed in either Tier 2 or Tier 3 according to the dynamic RTI model. All participants engaged in 14-16 intervention sessions with explicit instructions of math word problem strategies. Students’ progress monitoring evaluation was conducted through pre and posttests along with formative assessments in between, and analysis was done based on the students’ performance rate and percentile rank. As per the curriculum-based measurement (CBM) scoring guidance, the evaluation of the students included correct digit grading in addition to the formula and answer grading. Each student’s results are shown in these domains of correct digit, formula and answer. Further educational implications and study limitations are discussed.

Individuals development of the metacognitive thinking skills on solving math word problems

Metacognition as knowledge and cognition on cognitive phenomenon and one’s own knowledge on his self-cognitive processes and use of this knowledge in order to monitor cognitive processes. Metacognitive skills refer to a person’s procedural knowledge for regulating one’s learning activities including problem solving. Word problems in mathematics have been vastly included in educational literature mainly due to the fact that the issue is considered to be one of the most difficult in math lessons. This research aimed at investigating the contribution of students’ ability to metacognitive thinking to metacognitive thinking skills in the aspects of prediction, planning, monitoring, and evaluation through the provision of mathematical words problems. The data was collected through tests, Metacognitive Awareness Inventory (MAI-Jr-Modified) observation sheets and interviews. The results of the study showed that the score of students metacognitive ability was 75.80 which contributed to the level of students metacognitive thinking skills at 78.98% in the high category based on the four aspects of metacognitive skills namely 78.13%; 81.25%; 84.38% and 71.88%. Learning through the provision of mathematical problems in the form of words problems can develop students metacognitive skills.