Search results for "word problem"
showing 10 items of 23 documents
Child-centered and teacher-directed practices in relation to calculation and word problem solving skills
2019
Abstract This study examined transactional associations between classroom-level math skills and teaching practices. Participants were 523 children from 31 classrooms. Math skills were assessed three times. Teaching practices were observed in Grades 1 and 3. Child-centered practices promoted subsequent calculation skills whereas teacher-directed practices were associated with a lower level of calculation skills. Higher problem-solving skills at Grade 2 predicted more child-centered practices and less teacher-directed practices in third grade. Moreover, calculation skills mediated the effect of child-centered practices on problem-solving skills. The results suggest that teaching practices and…
Words and forbidden factors
2002
AbstractGiven a finite or infinite word v, we consider the set M(v) of minimal forbidden factors of v. We show that the set M(v) is of fundamental importance in determining the structure of the word v. In the case of a finite word w we consider two parameters that are related to the size of M(w): the first counts the minimal forbidden factors of w and the second gives the length of the longest minimal forbidden factor of w. We derive sharp upper and lower bounds for both parameters. We prove also that the second parameter is related to the minimal period of the word w. We are further interested to the algorithmic point of view. Indeed, we design linear time algorithm for the following two p…
Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
1999
It is known that a number of algebraic properties of the braid groups extend to arbitrary finite Coxeter-type Artin groups. Here we show how to extend the results to more general groups that we call Garside groups. Define a Gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths, and where left and right lowest common multiples exist. A Garside monoid is a Gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition. A Gaussian group is the group of fractions of a Gaussian monoid, and a Garside group is the group of fractions of a Garside monoid. Braid groups and, more genera…
A decidable word problem without equivalent canonical term rewriting system
1989
We present a weak associative single-axiom system having the following property: the word problem is decidable with an efficient algorithm even though there does not exist any finite equivalent canonical term rewriting system.
Incremental termination proofs and the length of derivations
1991
Incremental termination proofs, a concept similar to termination proofs by quasi-commuting orderings, are investigated. In particular, we show how an incremental termination proof for a term rewriting system T can be used to derive upper bounds on the length of derivations in T. A number of examples show that our results can be applied to yield (sharp) low-degree polynomial complexity bounds.
A Hypergraph Based Framework for Intelligent Tutoring of Algebraic Reasoning
2013
The translation of word problems into equations is one of the major difficulties for students regarding problem solving. This paper describes both a domain-specific knowledge representation and an inference engine based on hypergraphs that permits intelligent student supervision of this stage of the solving process. The framework presented makes it possible to simultaneously: a) represent all potential algebraic solutions to a given word problem; b) keep track of the student’s actions; c) provide automatic remediation; and d) determine the current state of the resolution process univocally. Starting from these ideas, we have designed an intelligent tutoring system (ITS). An experimental eva…
Domain-specific knowledge representation and inference engine for an intelligent tutoring system
2013
One of the most challenging steps in learning algebra is the translation of word problems into symbolic notation. This paper describes an Intelligent Tutoring System (ITS) that focuses on this stage of the problem solving process. On the one hand, a domain specific inference engine and a knowledge representation mechanism are proposed. These are based on a description language based on hypergraphs, and the idea of using conceptual schemes to represent the student's knowledge. As a result, the system is able to simultaneously: (a) represent all potential algebraic solutions to a given word problem; (b) keep track of the student's actions; (c) univocally determine the current state of the res…
The role of literacy skills in adolescents' mathematics word problem performance – Controlling for visuo-spatial ability and mathematics anxiety
2014
Abstract The aim of the present study is to examine the relationship between eighth-grade adolescents' literacy skills and mathematics word problem performance. Moreover, visuo-spatial ability and mathematics anxiety were considered as covariates. According to the analyses of (co)variance, literacy skills were significantly associated with mathematics word problem skills among the 99 8th grade participants of the study. It is primarily for boys that reading comprehension skill predicts success in solving math word problems, while technical reading predicts both calculation skill and word problem solving skill across genders. Visuo-spatial ability was not a significant covariate in either of…
How upper secondary students solve algebraic word problems in the area of mathematical modelling : A case study of one group of Norwegian students
2019
Masteroppgave matematikkdidaktikk MA500 - Universitetet i Agder 2019 For å imøtekomme nye utfordringer på skolen, i jobb og i livet, kan elever ha behov for åtilpasse og utvide den matematikken de kan. Dette krever at elever evner, i noen grad, åsette skolematematikken i forbindelse med hverdagslige kontekster og motsatt. Matema-tisk modellering er en av de hensiktsmessige mediene for å støtte sammenhengen mellomskolematematikken og virkeligheten. Forskning har vist at det er en sterk tilbøyelighet ipensumet mot matematisk modellering og at i stedet høynivå matematikk er ansett somviktig, mest på videregående nivå. Igjen, forskning viser at elever har større utfordringermed abstrakte (fakta…
Why does placing the question before an arithmetic word problem improve performance. A situation model account.
2007
The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve arithmetic word problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. …