Mathematical word problems

Solving mathematical word problems is a difficult, complex and intellectual activity. The formation of problem solving skills is much more difficult than calculation skills because the problems are related to many concepts and a lot of mathematical relationships. Therefore, students are inevitable to commit errors to deal with them. This study shows the errors of 160 3rd grade students regarding some kinds of word problems in Mathematics 3 in Vietnam. The results indicate that children commit many errors due to many different reasons such as: subjectivity, carelessness, wrong application of the calculation rules, incorrect identification of problem kinds and wrong calculation. Article visualizations:

Deixis is the method of relating to the spatio-temporal context of an utterance. Deictic expressions or indexicals are among the first forms to be spoken by very young children, and are thus very fundamental to our notion. Deictic concepts are most easily understood by people. Among the various types of deixis, this paper focuses on application of Temporal and Spatial deixis concepts in solving mathematical word problems. A deictic expression is anchored to a deictic center, such that the evaluation of the meaning of the expression leads one to the relevant point. As deictic expressions are frequently egocentric, the center often consists of the speaker at the time and place of the utterance. Also, the deictic center may be transferred to other participants in the exchange, or to persons / places / etc. being described in a narrative. In language, we talk about time in terms of space. From the perspective of conceptual grounding, abstract temporal cognition is grounded in a more concrete spatial cognition. On a similar ground, this paper aims to apply these fundamental concepts of temporal deixis and deictic temporal elements, and project them to a spatial structure, and use the concept of deictic center shifting for solution of mathematical word problems which involve equations based on time-dependent variables. The projection of the temporal problem into a spatial structure simplifies the comprehension process for the student. This deictic approach improves the student's understanding of the problem at hand and increases the student's accuracy in solving such numericals of the same genre.

ABSTRACT
Hafsah B. Mama and Johanisa M. Dibagulun. “Difficulties encountered in solving word problems in Mathematics”. An Undergraduate Thesis, Secondary and Elementary teaching Department, College of Education, Mindanao State University, Marawi City, June 2016.

Thesis Adviser: Prof. Teodoro M. Drilon

Word problems are consistently used as practice exercises and illustrations throughout Mathematics curriculum. However, problem solving is a difficult task as it involves a lot of steps. People have to hurdle the challenges in going from one step to another although the steps may not necessarily have to take in sequential manner. This study employed the mixed method design, a combination of quantitative and qualitative research methods. It aims to determine the difficulties encountered in solving word problems in Mathematics by the Grade six pupils in Amai Pakpak Central Elementary School. There were forty seven (47) pupils who participated in the study. Data were gathered through administering 10-item researchers’ made test regarding word problems. The test were administered right after it was statistically proven to be reliable using Richard-Kurson with value 0.84. Moreover, one-on-one interview with the respondents also took place. The interview questions were based on the three problems which most of the pupils answered incorrectly. Results showed that most (55.3%) of the respondents have satisfactory grades in English. Moreover, almost the same number of percentages (48.9% &46.8%) had passing and satisfactory grades in Mathematics. In addition, more than half of the respondents failed the test. It is also found that there is a significant relationship between English grade, Mathematics grade and performance in solving word problems. Findings revealed that pupils have difficulties in solving word problems in Mathematics. Some difficulties were lack of comprehension, lack of strategy, incorrect use of operations, inability to translate the problems in Mathematical equation, interchanging values and computational errors. After thorough analysis, it is suggested that students should enhance their skills in solving and vocabulary to understand the problem so that they could carry out the required solution. Furthermore, future researchers may consider the comprehension level of the pupils perhaps administering comprehension test simultaneously.

Keywords: English Grade, Mathematics Grade, Difficulty, Solving, Word problem

In this article, we discuss the approach adopted within the Vanderbilt University Learning Disabilities Innovation Hub, which focuses on students with higher-order comorbidity: students with concurrent difficulty with reading comprehension and word-problem solving. The aim of the Hub' s Research Project is to test what we refer to as the higher-order comorbidity hypothesis: that language comprehension plays a critical role in reading comprehension and word-problem solving. In the Hub' s study, we test the hypothesize that language comprehension offers a coordinated approach for improving both outcomes and that this approach thus provides direction for understanding higher-order comorbidity and support for the validity of reading comprehension and word-problem solving

Since 1975, researchers have conducted interventions to improve the word-problem performance of elementary school students facing mathematics difficulties. The current study reports a meta-analysis of 52 studies that examined the effect of these interventions. We estimated multivariate, random-effects models (REM) with robust variance estimation (RVE) with and without outliers. Results showed a large, positive, and significant mean weighted effect size ( g = 1.01 for the model with outliers; g = 0.81 for the model without outliers). Findings of meta-regression analyses showed several moderators, such as sample composition, group size, intervention dosage, group assignment approach, interventionist, year of publication, and dependent measure type, significantly explained heterogeneity in effects across studies. A sensitivity analysis showed these results were generally robust to outliers. We offer possible explanations for the findings and discuss study limitations. Finally, we propo...

This article addresses the problem of understanding mathematics described in natural language. Research in this area dates back to early 1960s. Several systems have so far been proposed to involve machines to solve mathematical problems of various domains like ...

Since 1975, researchers have conducted interventions to improve the word-problem performance of elementary school students facing mathematics difficulties. The current study reports a meta-analysis of 52 studies that examined the effect of these interventions. We estimated multivariate, random-effects models (REM) with robust variance estimation (RVE) with and without outliers. Results showed a large, positive, and significant mean weighted effect size (g = 1.01 for the model with outliers; g = 0.81 for the model without outliers). Findings of meta-regression analyses showed several moderators, such as sample composition, group size, intervention dosage, group assignment approach, interventionist, year of publication, and dependent measure type, significantly explained heterogeneity in effects across studies. A sensitivity analysis showed these results were generally robust to outliers. We offer possible explanations for the findings and discuss study limitations. Finally, we propose recommendations for future research and classroom practice.

Solving mathematical word problems is a difficult, complex and intellectual activity. The formation of problem solving skills is much more difficult than calculation skills because the problems are related to many concepts and a lot of mathematical relationships. Therefore, students are inevitable to commit errors to deal with them. This study shows the errors of 160 3rd grade students regarding some kinds of word problems in Mathematics 3 in Vietnam. The results indicate that children commit many errors due to many different reasons such as: subjectivity, carelessness, wrong application of the calculation rules, incorrect identification of problem kinds and wrong calculation.

The aim of this paper is to formulate a method for solving mathematical word problems by using the concept of deixis in language. The main focus is to understand the pattern of the question presented and thereby correlating the deictic aspects in the problem formulation with the solution strategy. This paper particularly focuses on school-level mathematics problems, particularly those involving the concept of time.

Bu araştırmanın amacı, ilkokul dördüncü sınıf öğrencilerinin problem çözme sürecinde oluşturduğu görsel temsillerin türlerinin ve görsel temsil türlerinin problemin doğru çözülmesi temelinde nasıl bir dağılım gösterdiğinin incelenmesidir. Bu amaçla çalışma bir tarama araştırması olarak tasarlanmıştır. Araştırma verileri Ordu ilinde öğrenim görmekte olan 162 dördüncü sınıf öğrencisinden elde edilmiştir. Verilerin toplanmasında 12 matematik probleminden oluşan bir envanter kullanlmıştır. Çalışmaya katılan 162 öğrencinin cevap kâğıdından elde edilen toplam 1909 görsel temsil analiz edilmiştir. Verilerin analizinde betimsel analiz ve içerik analizi yöntemleri kullanılmıştır. Araştırma sonucunda; dördüncü sınıf öğrencilerinin problem çözme sürecince oluşturduğu üç temsil türü (şematik, resimsel ve işlemsel) tanımlanmıştır. Problem çözme sürecinde şematik temsil oluşturan öğrencilerin %87.4 oranında probleme doğru cevap verdiği görülmüştür. Resimsel temsil oluşturulan durumlarda problemin yanlış çözülme oranının %91.9 olduğu ve işlemsel temsil oluşturulan durumlarda ise %67.5 oranında probleme yanlış cevap verildiği görülmüştür. // In this research, it is aimed to examine the types of representation that primary school students created during the problem solving process. For the purpose of the research, this study designed as a survey research which is a qualitative research model. The research data were collected with 12 word problems. The study group consist 162 fourth grade students. A total of 1909 visual representations obtained from the working paper of 162 students participating in the study were examined. Content analysis method was used in the analysis of the data. It is aimed to understand and explain the use of visual representations in the problem solving process and to reach the basic patterns related to them. As a result of the research, three kinds of representations (schematic, pictorial and computational) that the fourth grade students created in the problem solving process are defined and the representation types evaluated in terms of correct solution of the problem. As a result of this evaluation, 87.4% of the students who created a schematic representation in problem solving process were found to respond correctly. In cases where pictorial representation was created, the rate of wrong solution of the problem was 91.9%, and in case of computational representation, 67.5% of the problem were answered incorrectly

Math word problems are difficult for students to start with since they involve understanding the problem? s context and abstracting out its underlying mathematical operations. A visual understanding of the problem at hand can be very useful for the comprehension of the problem. We present a system VisualMath that uses machine learning tools and crafted visual logic to automatically generate appropriate visualizations from the text of the word-problems and solve it. We demonstrate the improvements in the understanding of math word-problems by conducting a user study and learning of meaning of relevant new words by students.

This paper is devoted to the study of a free-convective boundary-layer flow modeled by a system of nonlinear ordinary differential equations. We apply a modified variational iteration method (MVIM) coupled with He's polynomials and Padé approximation to solve free-convective boundary-layer equation. It is observed that the combination of MVIM and the Padé approximation improves the accuracy and enlarges the convergence domain.

This study explored oral retellings used as a problem solving strategy for compare word
problems in mathematics. The research involved 29 sixth graders (14 boys and 15 girls) from two classes who took a pretest, participated in four 30-minute instructional periods, and completed a posttest and delayed posttest. Results showed no statistically significant change in overall success in problem solving or in the number of computational errors students made. However, students made fewer operational errors following instruction in oral retellings. This finding suggests that students may more accurately select operations based on their retelling of the word problem, thus benefiting from instruction in oral retellings as a strategy for solving compare word problems.

The first part of this column is devoted to work of David Tall and Bernard Cornu on students' understanding of the derivative and limits, more generally. It then goes on to discuss J. Michael Shaughnessy's article, “Misconceptions of Probability: An Experiment with a Small-Group, Activity-Based, Model Building Approach to Introductory Probability at the College Level." After that, it discusses the article of Hall, Kibler, Wenger, and Truxaw, “Exploring the episodic structure of algebra story problem solving,” on algebra students word problem solving.

In this work, two numerical methodologies are proposed for the solution of unilateral contact problems between a structural member (beam or arch) and an elastic foundation. In the first approach, the finite element method is used to discretize the structure and elastic foundation and the contact problem is formulated as a constrained optimization problem. Only the original variables of the problem are used, subjected to inequality constraints, and the relevant equations are written as a linear complementary problem (LCP). The second approach is based on the Ritz method, where the coordinates defining the limits of the contact regions are considered as additional variables of the problem. The contact problem here is treated as an unconstrained optimum design problem. These proposed methodologies are then tested and compared using results from specific problems involving structures under unilateral contact constraints.

An integrated equilibrium model for tactical decisions in network design is developed. We consider a decentralized supply chain network operating in markets under uncertain demands when there is a rival decentralized chain. The primary assumption is that two chains provide partial substitutable products to the markets, and markets' demands are affected by tactical decisions such as price, service level, and advertising expenditure. Each chain consists of one risk-averse manufacturer and a set of risk-averse retailers. The strategic decisions are frequently taking precedence over tactical ones. Therefore, we first find equilibrium of tactical decisions for each possible scenario of supply chain network. Afterwards, we find optimal distribution network of the new supply chain by the scenario evaluation method. Numerical example, including sensitivity analysis will illustrate how the conservative behaviors of chains' members affect expected demand, profit, and utility of each d...