Solving General Arithmetic Word Problems

This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional annotations or predefined templates. We develop a theory for expression trees that can be used to represent and evaluate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combining these with world knowledge through a constrained inference framework. Our classifiers gain from the use of {\em quantity schemas} that supports better extraction of features. Experimental results show that our method outperforms existing systems, achieving state of the art performance on benchmark datasets of arithmetic word problems.Comment: EMNLP 201

Solving General Arithmetic Word Problems

Abstract This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional annotations or predefined templates. We develop a theory for expression trees that can be used to represent and evaluate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combining these with world knowledge through a constrained inference framework. Our classifiers gain from the use of quantity schemas that supports better extraction of features. Experimental results show that our method outperforms existing systems, achieving state of the art performance on benchmark datasets of arithmetic word problems

Contribution of flexibility in dealing with mathematical situations to word-problem solving beyond established predictors

To solve mathematical word problems, students need to build appropriate models of the described situations, which they can describe with mathematical operations. Various studies have confirmed the importance of general cognitive skills, basic arithmetic skills, and language skills for word-problem solving. Beyond these, we investigate flexibility in dealing with mathematical situations, a new construct that describes the skill to re-interpret everyday situations from various perspectives. In a study with N = 113 second graders, an instrument to measure this flexibility construct has been developed and investigated. We find that the construct explains word-problem solving skills beyond the established predictors. Being able to flexibly re-interpret everyday situations may be beneficial for word-problem solving

The effects of instruction in problem-solving strategies including reading word problems on student achievement in solving word problems, 1986

The purpose of the study was to determine if there was a significant difference between the traditional method and the experimental or structured method of instruction in word problem solving and translating them into almost word less sentences. Two groups of ninth graders in a general mathematics course on reading and solving word problems were selected for the study. At the beginning of the study a pre test for achievement differences was administered. The test results indicated there were no significant achievement differences between the groups when the test was initiated. Word problem solving instruction was given to the experimental group, but the control group was allowed to ask. questions only for clarification of the problems which possibly enabled them to pick up ideas on how to analyze word problems during the questioning session. The treatment consisted of problems on how to find discounts, commission, interest and sales tax. The t statistic and a .05 level of significance were used. A posttest was administered to both groups after the treatment, and the findings of the test results indicated that there was no significant difference in achievement. Therefore, teaching the reading of word problems did not affect the experimental method more than the use of the conventional method. of data indicated that there was no significant differ ence in achievement between the two groups. It was suggested that because the control group was permitted to ask questions, students in that group may have learned how to analyze word problems during the questioning sessions. It was recommended that there should be more inter action between students and teachers through questions and answers during word problem-solving instruction. Teaching word problem solving should begin early in the elementary school and sequentialized in the middle and high school. In-service teaching on word problem solv ing should be provided. Calculators should be used by students only after they have mastered the basics of arithmetic

The contributions of language and literacy skills to mathematical performance in children learning English as an additional language

In recent years, research has demonstrated that children learning English as an Additional Language (EAL) show a weakness in reading comprehension, and its underlying language comprehension skills, relative to children whose first language is English (FLE). Despite this, relatively little attention has been paid to how this disadvantage might affect performance in other areas of education, such as mathematics. Indeed, national performance data from England shows a mathematical achievement gap between EAL and FLE children. A growing body of research has suggested that EAL children struggle with mathematical word problem solving relative to their FLE peers, given its reliance on reading comprehension. However, research seeking to clarify the relationships between linguistic abilities and mathematical performance in EAL and FLE children within the UK context is scarce. The current study compares the linguistic and mathematical abilities of EAL and FLE children in Key Stage 2 and investigates the linguistic and cognitive predictors of reading comprehension, arithmetic computation and mathematical word problem solving ability in both groups. A sample of 28 EAL and 44 FLE children from Year 3 and Year 5 were assessed on a battery of measures, and a sub-sample were reassessed one year later. In comparison to their FLE peers, the EAL children showed weaknesses in language comprehension and struggled with the contextualisation of arithmetic problems into mathematical word problems, but displayed comparable decoding and arithmetic skills. Overall, the predictors of reading comprehension and mathematical performance were comparable between the language groups, though general vocabulary knowledge was found to be a stronger predictor of both reading comprehension and mathematical word problem solving for the EAL children. The relevance of these findings to our understanding of academic achievement in EAL children are discussed, as well as their educational implications

A bibliography of six years (1951-1956) research in arithmetic

Thesis (Ed.M.)--Boston Universit

Individual differences in children’s understanding of inversion and arithmetical skill

Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children’s understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. Sample. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6–7 and 8–9 years). Methods. Children’s accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Results. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the ‘high ability’ and ‘low ability’ groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. Conclusions. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children’s conceptual understanding and problem-solving skills