The level of arithmetic knowledge of a high school student was explored when solving additive word problems considering the semantic structure and syntactic component. The methodology was qualitative and developed in four stages: the first is the selection of the participant, the second is the design of a questionnaire with twenty additive…

Arithmetic word problems are a staple in mathematical curricula yet give individuals of all ages difficulty. Successful word problem solving requires translating the problem into a symbolic arithmetic format. However, the linguistic component may make problem solving more complex and increase cognitive load, specifically the processes that…

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…

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…

In this study we investigated word-problem (WP) item characteristics, individual differences in text comprehension and arithmetic skills, and their relations to mathematical WP-solving. The participants were 891 fourth-grade students from elementary schools in Finland. Analyses were conducted in two phases. In the first phase, WP characteristics…

Despite decades of research on the close link between eye movements and human cognitive processes, the exact nature of the link between eye movements and deliberative thinking in problem-solving remains unknown. Thus, this study explored the critical eye-movement indicators of deliberative thinking and investigated whether visual behaviors could…

This study explored the effectiveness of external representations presented together with compare word problems, and whether such effectiveness was moderated by working memory. Participants were 49 secondary school students. Each participant solved 48 problems presented in 4 presentation types that included 2 difficulty treatments (number of steps…

The Organization for Economic Cooperation and Development [OECD] is a global policy organization that includes the United States and about half of the Western Europe countries. It administers international comparison tests, called Programme for International Student Assessment (PISA), for 15 year-old students in Mathematics and other subjects. I…

Research shows that the greatest gains in student learning in mathematics classrooms occur in classrooms in which there is sustained use of high cognitive demanding tasks throughout instruction (Boston and Smith 2009). High cognitive demanding tasks, which this article will refer to as rich tasks, are mathematics problems that are complex, less…

Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing…

This study was designed to determine a word problem difficulty classification in children with arithmetic learning disabilities (ALD; n = 104) in comparison with typically achieving students (n = 44). We tested variables such as (a) semantic structure (Change, Combine, Compare, and Equalize), (b) operation (subtraction and addition), and (c)…

An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…

Urban Canadian sixth-graders (n=84) were tested on 80 arithmetic word problems developed as part of a larger set to reflect individual differences in problem solving. Problems varied in complexity of language and amount of extraneous information present. Results indicated substantial internal consistency and concurrent validity relative to…

Simple arithmetic word problems are often featured in elementary school education. One type of problem, "compare with unknown reference set," ranks among the most difficult to solve. Differences in item difficulty for compare problems with unknown reference set are observed depending on the direction of the relational statement (more than vs. less…

Six experiments with 42 kindergartners, 190 first graders, and 15 second graders in Germany investigated why arithmetic word problems with an unknown reference set are more difficult for children than are problems with an unknown compare set. Lack of access to flexible language use makes these problems so difficult. (SLD)