Search results for "word problem"
showing 10 items of 23 documents
PreGarside monoids and groups, parabolicity, amalgamation, and FC property
2012
We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin–Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parabolic subgroups in terms of these presentations. Afterwards we prove that the amalgamated product of two preGarside groups along a common parabolic subgroup is again a preGarside group. This enables us to define the family of preGarside groups of FC type as the smallest family of preGarside groups that contains the Garside g…
“How Real People Really Need Mathematics in the Real World”—Authenticity in Mathematics Education
2018
This paper discusses authenticity from the perspective of mathematics education. Often, school mathematics offers students inauthentic word problems, which don’t show the authentic usefulness of mathematics in real life. In some tasks, authentic aspects are combined with inauthentic ones (e.g., an authentic context, but the question is artificial and different from what people within that context would ask). Several studies show that students are more motivated by authentic questions than by authentic contexts. Embedding these findings, I discuss issues associated with defining authenticity in education. A first issue is that philosophers use the term to characterize a person’s existential …
Efectos de la similitud superficial y estructural sobre la transferencia a partir de análogos en problemas de alta y baja familiaridad : primeros res…
2013
Se desarrollan dos estudios exploratorios para analizar el éxito en la transferencia en resolución de problemas a partir de análogos. Las diferentes analogías entre problemas «ejemplo» y «propuestos » se suponen construidas a partir de dos variables: la superficie y la estructura. Los resultados muestran que cuando los contextos de los problemas son familiares para los estudiantes, las analogías superficiales pueden ocultar las diferencias estructurales. Sin embargo, cuando los contextos de los problemas son no familiares para los estudiantes, el único efecto significativo procede de la igualdad/diferencia estructural. El efecto global de la familiaridad de los problemas es una reducción si…
Analysis of Word Problems in Primary Education Mathematics Textbooks in Spain
2021
A textbook constitutes the hegemonic material of the educational institution. It acts as a mediator between the official curriculum and the educational practice. Given its potential influence in the classroom, this study analyzes the treatment of word problems included in the mathematics textbooks published by the publishing houses with the greatest diffusion in Spain at every primary education grade. Three variables were analyzed: their semantic structure, their degree of challenge, and their situational context. The results indicate that most of the problems included in textbooks are characterized by low complexity and variability regarding their semantic structure. They are also characte…
Domain Specific Knowledge Representation for an Intelligent Tutoring System to Teach Algebraic Reasoning
2012
Translation of word problems into symbolic notation is one of the most challenging steps in learning the algebraic method. This paper describes a domain-specific knowledge representation mechanism to support Intelligent Tutoring Systems (ITS) which focus on this stage of the problem solving process. The description language proposed is based on the concept of a hypergraph and 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) unequivocally determine the current state of the resolution process. An experimental evaluation with students at a public school su…
The association between mathematical word problems and reading comprehension
2008
This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9–10 (Grade 4). The children’s text comprehension and mathematical word problem‐solving performance was tested. Technical reading skills were investigated in order to categorise participants as good or poor readers. The results showed that performance on maths word problems was strongly related to performance in reading comprehension. Fluent technical reading abilities increased the aforementioned skills. However, even after controlling for the level of technical reading involved, performance in maths word problems was still related to rea…
Primary school text comprehension predicts mathematical word problem-solving skills in secondary school
2014
This longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9–10 years old at the baseline). The children’s text-reading fluency, text comprehension and basic calculation ability were tested in grade four. In grade seven and nine, their skills in solving mathematical word problems were assessed. Overall, the results showed that text comprehension in grade four of primary school predicts math word problem-solving skills in secondary school, after controlling for text-reading fluency and basic calculation ability. Among …
Gui-driven intelligent tutoring system with affective support to help learning the algebraic method
2017
Despite many research efforts focused on the development of algebraic reasoning and the resolution of story problems, several investigations have reported that relatively advanced students experience serious difficulties in symbolizing certain meaningful relations by using algebraic equations. In this paper, we describe and justify the Graphical User Interface of an Intelligent Tutoring System that allows learning and practising the procedural aspects involved in translating the information contained in a story problem into a symbolic representation. The application design has been driven by cognitive findings from several previous investigations. First, the process of translating a word pr…
Transferencia inter-dominios en resolución de problemas : una propuesta instruccional basada en el proceso de «traducción algebraica»
2009
Understanding a science and math word problem means constructing mental representations at different levels of abstraction. Secondary students have dificulties solving algebraic word problems due to the transition from the concrete representation to the mathematic representation. In order to facilitate the «algebraic translation» of the problems, we adapt a «rule to put a problem into equations» by Puig (1998) and insert it in an experimental methodology devoted to improving the inter-domain transfer in science. Results show the power of the instructional methodology to overcome most of the students’ dificulties, no matters their average academic performance.
Analysis of the psicometric properties of a multiplication and division processes assessment scale
2019
Esta comunicación se encuentra disponible en la siguiente URL: http://www.infad.eu/RevistaINFAD/OJS/index.php/IJODAEP/article/view/1464/1321 Este número está dedicado a la "Psicología de la Educación y Saberes Originarios". The domain of multiplication and division operations depends on both algorithm management and the ability to identify the semantic structure of the problem and to translate it into mathematical language. Many students present difficulties in identifying the semantic structure of the problem but not applying the algorithm when the problem is presented numericaly. The aim of the study is to validate an assessment tool of the processes involved in multiplication and divisio…