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The improvement of arithmetic calculation skills in General Basic Education (EGB) students is fundamental for their academic and cognitive development. The present study investigated the impact of a strategy based on active learning on the development of arithmetic skills in students in the fourth year of General Basic Education (EGB). A sample of 25 students and five teachers from the "15 de Abril" Intercultural Bilingual Community Education Center of Basic Education was selected. A pretest-posttest analysis was carried out to evaluate emotional and motivational elements of learning, as well as the students' performance before and after the implementation of the strategy. Tests of the relationship between variables were applied using IBM SPSS Statistic software. The results indicated a significant increase in students' motivation and satisfaction, as well as in their arithmetic calculation skills. As a complement, a survey of teachers was conducted to evaluate their perception of the usefulness and viability of the strategy in the classroom. The teachers' assessment revealed a positive perception regarding the relevance of the proposed strategy to promote active learning and the development of arithmetic and higher order cognitive skills in students. [ABSTRACT FROM AUTHOR]

It is currently known that problems in mathematics teaching are present in teachers' school teaching processes, official documents, and textbooks. However, is it possible to say that the problems have always been present in educational practices and official documents linked to teaching? Based on these initial considerations, this production is affiliated with the research field of the history of mathematics education. It aims to scrutinize the permanence and changes, at different historical moments, of the meanings and purposes of problems for mathematics teaching from a literature review based on the state of knowledge methodology. From the survey of works such as dissertations, theses, and scientific articles in different digital repositories, it is clear that there have been changes in the conception of problems over time. Between the transition from traditional teaching periods to the intuitive method, the term problems is not mentioned. Subsequently, the term is presented as a synonym for exercises, for teaching arithmetic. In New School times, however, problems became dissociated from exercises. They gained both a teaching support character and are also structured as a teaching method to be followed. Finally, problem solving is gaining ground in research in mathematics education field. [ABSTRACT FROM AUTHOR]

This study explores how elementary and secondary school students solve multiplicative structure problems (multiplication, partitive division, and measurement division). A questionnaire was used with nine problems involving natural numbers and fractions, and the research examined both the level of success of students and the strategies employed for each type of problem (by grade level). The results show a lower level of success in problems with fractions than with natural numbers, with students having difficulty recognizing that the structure of the problems was the same. Algorithms were the most commonly used strategy, but other strategies also emerged, depending on the type of number involved (natural numbers or fractions). [ABSTRACT FROM AUTHOR]

This article deals with the transition from arithmetic to algebraic instruction. We will try to highlight, in a specific and necessarily limited way, the extent of the upheaval that teachers had to face. But above all, we will try to show how the structural modifications made at the time in the didactic text impose their effects even today, in an often hidden but very real way, despite the "reform of the reform" that the 1978 programs were supposed to symbolize for the eighth grade. [ABSTRACT FROM AUTHOR]

In this third part on the "Transition from arithmetic to algebraic in the teaching of mathematics in high school" we reflect on the term modeling: modeling, in the sense that we use this word, can be based on a non-mathematical system as well as on a mathematical system. The didactic analysis of the curricular perspectives we have outlined reveals problems in the didactics of mathematics that underline the need for very close links, for a tenacious dialectic, which should be everyone's concern, between fundamental research in didactics and the development activities of the teaching system. In contrast, the present situation reveals the great superficiality of which the empirical and dogmatic tradition has made us unfortunate heirs. It is not enough to weaken, decide, and act to solve the problems we are and continue to be faced with. As in other fields, research is no longer that part of the dream in which high-growth societies could offer themselves as a bonus. It is up to it to explore on behalf of all, the avenues of the possible. [ABSTRACT FROM AUTHOR]

The objective of the article is to discuss the epistemological and didactic dimensions of the curriculum reforms carried out in the 1960s. Among them, the Chevènement reform that aimed to rescue the arithmetic to the detriment of the algebraic. This look at the numerical was seen as something destabilizing of the curriculum in the French education system in the late 1960s. This reform understood the numerical as something practical and coming from reality, that did not need such abstract ideas, as algebra demanded. The Chevènement reform relegates the algebraic aspects in second place but does not exclude them; the use of letters is seen as a preceding generalization of the studies of numerical calculations. The problems posed in the teaching of arithmetic and algebra in the French education system are revealed, they involved the process of didactic transposition established in the official college program. The didactic transposition, which modifies the operation of the objects of knowledge, gives a certain specificity to the official program that the prodigal school proposes to the student. This official program engenders in the student a personal program that, as it is in the official program, will enjoy limited adequacy as the said object of knowledge, which will no longer be a pure didactic stake, will only be a tool of the student's didactic-mathematical activity: for example, the factoring of an algebraic expression may no longer be the goal of his activity, becoming the means to solve a third degree equation, knowing one of its roots. [ABSTRACT FROM AUTHOR]

A Phenomenological Reading. In this article I will present a working hypothesis that combines Edmund Husserl's and Immanuel Kant's stances on the dimension of the transcendental schema. I will offer a reading that, based on the interpretative proposal of the Argentinian philosopher Martín Arias Albisu, will show how schemata, understood as schema-procedure and schema-product, exhibit a certain similarity to the work that Husserl presented in Philosophy of Arithmetic. In other words, I will describe, on the one hand, how the schema-procedure functions as a representation that encompasses the successive addition that constitutes the unity of one to one, while, on the other hand, the schema-product synthesizes (phenomenologically) empirical multiplicity, i.e., it generates a phenomenal order in accordance with understanding. [ABSTRACT FROM AUTHOR]

The present study aimed to investigate the relationship between bilingualism and numerical cognition, more specifically, the way English-Portuguese bilinguals solve simple mathematical problems when these are presented in different formats (digits, English, and Portuguese) and whether their language history background has any effect on such behavior. The main results suggest that bilinguals are faster and more accurate in solving mathematical problems presented in digit format and in solving those problems presented in the written format when the language of the stimuli was the one in which they learned basic arithmetic. Also, the participants' language background experience did not have any significance in their task performance. [ABSTRACT FROM AUTHOR]

This paper aims to compare the neuropsychological and educational profiles of Brazilian children with dyscalculia (n = 8), dyslexia (n = 13) and without learning disabilities (n = 12). The neuropsychological profile was composed of: (a) intelligence - assessed by the Wechsler Intelligence Scale for Children (WISC-III); (b) attention - WISC-III Coding and Symbol Search subtests; (c) executive functions - Digit Span (backward order) and WISC-III Arithmetic subtests, Pseudoword Repetition Test for Brazilian Children, Stroop Test and Wisconsin Card Sorting Test; (d) memory - WISC-III Digit Span subtest (forward order) and Rey Complex Figures. The educational profile was composed of reading, writing and mathematics, assessed by the Academic Performance Test and the Arithmetic Test. It was found that the groups with dyscalculia and dyslexia did not differentiate in any of the neuropsychological abilities, only in the reading and writing abilities. Neuropsychological variables that could explain these results were discussed. [ABSTRACT FROM AUTHOR]

The mastering of single-digit multiplication is a challenge for many children. Recent research has suggested that some basic numerical skills, such as those measured in Arabic numeral comparison tasks (i.e. access to numerical representations from symbols), are good predictors of children's performance on single-digit multiplication. On the other hand, emotional variables, such as math anxiety, play a role in learning arithmetic facts. The aim of the current study was to study the role of several basic numerical cognitive skills and emotional factors in single-digit multiplication solving in a longitudinal study including school-age children. Math anxiety, trait anxiety, non-symbolic numerical comparison, Arabic numeral comparison, and subtraction fluency were assessed in first-, second-, and third-grade Spanish children, (N = 141; boys = 66, girls = 75; age range: 6 - 9 years). We assessed multiplication fluency 3 years later. The results showed that performance on Arabic numeral comparison and subtraction tasks significantly predicted performance on multiplication tasks. This finding supports previously published results. Regarding anxiety factors, it was also found that the participant's score in trait anxiety, but not math anxiety, was a marginally significant predictor. The results highlight the relevance of access to numerical semantic codes from symbolic representations and fluency in combining these representations in subtraction in predicting children's performance in single-digit multiplication. Anxiety factors seem to be of less relevance. [ABSTRACT FROM AUTHOR]

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez (2000), I propose one particular conceptual metaphor, the Process → Object Metaphor (POM), as a key element in understanding the development of mathematical thinking. [ABSTRACT FROM AUTHOR]

This study sought to verify the relationship between attention (selective and sustained visual) and school performance (reading, writing and arithmetic). We evaluated 258 students from the 1st to the 9th year of elementary school in Brazilian public and private schools, with a mean age of 10.33 years (SD=2.52). The students were evaluated by the Bells Test - children's version (BT) and by the School Performance Test - second edition (SPT-II). Test scores were correlated by the Pearson correlation coefficient, considering the level of significance of p<0.05. There were significant positive correlations of weak intensity between BT and SPT-II total scores and significant negative correlation of weak intensity between BT errors and omission scores and total SPT-II scores. An observable relationship between the constructs studied exists; however, it is suggested that future investigations use different methods to evaluate other skills related to school performance and attentional processes. [ABSTRACT FROM AUTHOR]

Executive functions (FE) have been considered one of the main predictors of school performance, however, little emphasis has been placed on the role of EF in more basic levels of writing, reading, and arithmetic. The objective of this study was to analyze whether these three academic domains are influenced by the components of inhibition, cognitive flexibility (CF), working memory (WM) and initiation / processing speed. We evaluated 302 students from 1st to 9th grade of elementary school with tasks to evaluate the mentioned constructs. Linear regression analysis indicated that phonological WM and lexical access velocity are predictors for reading, writing and arithmetic from the first to the last grade of elementary school. In addition to these abilities, inhibition, CF, and processing speed were strong predictors, but with variations throughout school life. In order of decreasing impact of EFs on learning, the following stand out: mathematics, writing and reading. This study emphasizes the importance of cognitive flexibility for the processing of the three academic domains and provides evidence of the involvement of executive processing with the writing ability, a relation still little explored in the literature. [ABSTRACT FROM AUTHOR]

This text aims to analyze, from the perspective of the History of Mathematics Education, the arithmetic instructions present in the work Escola Nova, Christã, e Politica, Na qual se ensinão os primeiros rudimentos, que deve saber o Menino Christão, e se lhes dão regras para com facilidade, e em poucotempo aprender a ler, escrever e contar. Originally published in Portugal in 1756, the work by Francisco Luiz Ameno (1713-1793) was registered under the pseudonym of D. Leonor Thomasia de Sousa e Silva. This manual was one of the first printed educational works in Portuguese America. Printed in Bahia in 1813, the treatise contained numerous prescriptions, interrelated to Christian precepts, considered necessary for the complete mastery of letters, numbers and the Portuguese language. In this sense, this research focuses on identifying how the author of the work privileged certain mathematical knowledge, highlighting the methodological instructions used in the construction of the number. [ABSTRACT FROM AUTHOR]

Following a quantitative and descriptive approach, we analyze the variety of mathematical topics treated by word problems in mathematics textbooks from two Spanish series. Also, we examine whether the problems are contextualized in real and familiar situations to the students. Results showed that there were more problems about numbers and less about geometrical compared to the suggestions of TIMSS. Add to this, the problems about topics in the higher grades--fractions, geometry, data display--were the worst contextualized. [ABSTRACT FROM AUTHOR]

La proposition de cet article est d'analyser un aspect peu exploré dans l'oeuvre du psychologue français Alfred Binet: l'aspect arithmétique. Érudit de la psychologie expérimentale, Binet a noté que les tests de calcul permettent un aperçu de l'intelligence et en même temps, la puissance de l'attention et la méthode du sujet. En ce qui concerne cet article, intéressé à savoir que ces observations scientifiques psychologue fait sur l'apprentissage de l'arithmétique? Les expériences de Binet lui ont permis de critiquer la façon dont les premiers contenus arithmétiques ont été enseignés les enfants. Par ailleurs, Binet a souligné l'importance de la mémoire et les exercices répété dans le développement de la capacité du calcul. [ABSTRACT FROM AUTHOR]

Os cursos de licenciatura em Matemática possuem em sua estrutura curricular, disciplinas de Álgebra abstrata cujos primeiros semestres, contemplam tópicos da Teoria dos números, com os primórdios da noção de divisibilidade nos números inteiros. Objetivando auxiliar os alunos iniciantes para um bom aproveitamento do curso, o grupo PETMAT, Programa de Educação Tutorial, vinculado ao curso de Licenciatura em Matemática da UFMS - Campus de Três Lagoas (CPTL), realiza atividades regulares de monitoria e oficinas. Neste trabalho descrevemos a experiência do PETMAT com a utilização de critérios de divisibilidade não convencionais. [ABSTRACT FROM AUTHOR]

This article discusses the use of images in mathematics textbooks written by George Augusto Büchler and Karl Sölter, in a cultural historic perspective. Büchler's first work, written in 1919, was aimed at the school public of school groups and German-Brazilian schools, while the second by Solter, published in 1932, was aimed at primary school. We conclude that the insertion of images in the two books analyzed, based on the intuitive method, had an instructional role but some of the images had ideological and aesthetic roles. Both authors included the images, more attractive to children's eyes, moving away from the abstraction so criticized by Pestalozzi and mathematical content presented in both books are focused on basic concepts of arithmetic, in a close connection between the child's life and the child's school life. [ABSTRACT FROM AUTHOR]

The relationship between school achievement and cognitive mechanisms stated by neuropsychology may help understanding assessment validity of formal education domains. However, this interface remains not fully explored regarding mathematical, linguistic and executive ability. Thus, the present study aimed to investigate convergent validity of Arithmetic Subtest from School Performance Test - Second Edition (TDE-II), towards the relationship between arithmetic and executive functions (EF). Therefore we analyzed the refined scores of TDE-II subtests (theta scores) based on Item Response Theory (IRT). A study comprising 111 elementary students (ES), from the first to the ninth year, half from public schools, paired by gender. Each sample comprising 10 to 14 students. Both A version of Arithmetic subtest (from first to fifth year of ES) and B Version ( from sixth to ninth year of ES) were high correlated to WISC-IV Arithmetic Subtest. A Version had high correlation to reading and writing and moderated correlation with EF working memory and inhibitory control, while version B had low correlation to Reading, writing and EF scores. Thus, EF appear to contribute with the initial learning process of mathematics learning. We conclude that Arithmetic Subtest from TDE-II has proper convergent validity and may be used as a school performance assessment in educational and clinical context. Future studies with children with learning disabilities and other neurodevelopmental disorders may contribute in a more accurate view of the relationship between mathematical and executive development. [ABSTRACT FROM AUTHOR]

Executive functions (EF) are a set of higher cognitive skills especially relevant in new situations that require adaptation, as in the school context. There is still few understanding about the developmental trajectories of such functions, and lack of adequate developmental measures for pediatric populations. This study aims to establish the developmental profile in executives components in childhood using NEPSY-II battery. It's about a correlational study, comparative, cross-sectional, of predominantly quantitative nature. Were evaluated eighty children, between five and eight years, of both genders, from Natal's public and private schools. The sample was divided into six-month intervals. The data collection instruments are the subtests of the NEPSY-II "Attention and Executive Functioning" domain that evaluate selective attention, motor and cognitive inhibitory control, categorization, cognitive flexibility, organization and planning. Analyzes of multivariate and univariate variance and post hoc tests (Tukey and Games-Howell) were performed to check the effect of gender, age and type of school. Was identified a significant difference in the type of school on tasks that assess cognitive inhibitory control and categorization. The one-way ANOVA was significant in the six months interval for performance improvement on tasks that assess auditory attention and inhibition. The evaluation of flexibility, especially in tasks that require maintaining two or more rules, showed remarkable variability. For this function, a long trajectory of development was observed, represented by an upward curve of performance and no peak at all age groups. The remaining searched components have significant differences only between the extremes of the sample. Significant correlations were identified between all subtests of the instrument, which suggests that the skills evaluated are part of the same function. Understanding the development of FE can assist in identifying predictive factors in the acquisition of reading, writing and arithmetic skills. [ABSTRACT FROM AUTHOR]

Whereas the introduction of algebraic language in math classes can be quite traumatic and cause disruption to the student, accustomed only with Arithmetic studies, we noted the need for discussion on the language involved in this transition, sometimes with formality and excesses rigor and other impregnated the colloquial language. We noted the need to propose didactic situations enabling and ensuring the understanding of the early algebraic concepts and a reflection of linguistic action practiced in the classroom. We also discuss the effectiveness of the language of the textbook that has its own set of symbols in the production of meanings. We emphasize the importance of investigating the relationship between language and Mathematics, and until point the everyday language interferes in Mathematics the teaching learning process. [ABSTRACT FROM AUTHOR]

This study analysed the effectiveness of presenting mathematical problems as ‘authentic’, which simulated the main aspects of situations in which students are usually involved. To do so, four independent variables were considered: level of mathematical difficulty (easy or difficult); rewording: standard problems (similar to those presented in textbooks), authentic and containing irrelevant situational information; mathematical ability (measured by means of the BADyG test); and reading comprehension level (measured with the comprehension task from the PROLEC-R test). The dependent measure was the success rate of a sample of 156 primary education children (grades four, five and six) in solving each kind of word problem. The results showed that the authentic versions of difficult problems were solved more successfully than other versions by students with high levels of mathematical aptitude and reading comprehension. That means that authentic wording is useful when children are able to understand the added information and have the mathematical knowledge necessary to interpret it. [ABSTRACT FROM PUBLISHER]

Textbooks are frequently used as a resource to teach children how to solve word problems in mathematics classes. The solving models explicitly proposed by textbooks, and the kind of problems they propose, can therefore have a decisive influence on the way in which students learn to solve them. This paper analyses the extent to which the problem solving models proposed by the books include reasoning as one of the steps needed to solve a problem. To do this, the processes and steps articulated in the models proposed in the books by Anaya, SM and Santillana are categorized according to data, reasoning, choice of operation, strategies, execution of operations, expression of results, checking and inventing. The results indicate that reasoning processes are hardly ever found in the models, especially in lower year courses. It is concluded that mathematical textbooks provide incomplete solving models that fail to promote reasoning. [ABSTRACT FROM AUTHOR]

The objective of this work is to build a didatic proposal for teaching methods to fing the integer or racional roots of polynomials of degree greater than two by using properties of integers learned on the studies of Arithmetic and the relations between coeficients and roots of polynomials known as Relations of Girard, with minimal application of formulas. Thus the student is given the opportunity to exercise simultaneously and dynamically the basics of algebra and arithmetic present in basic education. [ABSTRACT FROM AUTHOR]

Taking as premises some reasonable principles about the essences of natural numbers, pluralities and sets, the paper offers two types of argument for the conclusions that the natural numbers could not be the Zermelo numbers, the von Neumann numbers, the "Kripke numbers", or the positions in the ω-structure, among other things. These conclusions are thus Benacerrafian in form, but it is emphasized that the two kinds of argument offered in the paper are anti-Benacerrafian in substance, as they are perfectly compatible and in fact congenial with some views on which the numbers could be things of certain other kinds. [ABSTRACT FROM AUTHOR]

The objective of this work is to build a didatic proposal for teaching methods tofing the integer or racional roots of polynomials of degree greater than two by using properties of integers learned on the studies of Arithmetic and the relations between coeficients and roots of polynomials known as Relations of Girard, with minimal application of formulas. Thus the student is given the opportunity to exercise simultaneously and dynamically the basics of algebra and arithmetic present in basic education. [ABSTRACT FROM AUTHOR]

The importance of the arithmetical proportion is unquestionable from two points of view: school mathematics and its practical application. Its importance is reflected in a series of works in the Mathematics Education field, which is our main topic. In this article we show an historical review of some of the main concepts related to the arithmetical proportion, such as ratio and proportion. Besides its importance, as an historical study, we believe that the conclusions that follow this research may be useful in order to improve the teaching of ideas, concepts and techniques involved. [ABSTRACT FROM AUTHOR]

The article presents the theory of variations in G.W. Leibniz's De arte combinatoria as a theory of science. Their relation is suggested by the text in terms of that human reason can justify the validity of all the propositions belonging to empirical sciences that have been acquired by single observations or by an observation plus a universal law. Human reason finds through the analysis the way in which the variety of things are related among them. This allows that reason completes deductively the system of sciences by a combinatorial synthesis whose laws are the laws of inventive logic which is founded on the principles of combinatory and arithmetic. [ABSTRACT FROM AUTHOR]

Education is in general the basis for development in any country in the world. In the education al field, several international assessments (Pisa, 2006) reflect the great gap that yet subsists among developing countries, in which the case of Peru is not an exception. There have been many national and international academic achievement evaluations that examine the skills and knowledge of students not only in Peru but also in other Latin American countries in different academic domains. One of these examples is the Regional Comparative and Explanatory Study (LLECE), in which Peru participated, in order to evaluate and compare the performance achieved by Latin American students of 3rd and 6th grade in core areas like Language, Mathematics, and Natural Sciences. Peru ranks, together with other Latin countries, with scores below the average (Regional Office for Education of UNESCO, 2008). The low ranking of the Peruvian educational system carries heavy implications and consequences, especially to the intellectual and social development of learning disabled Peruvian children. Understanding the relation between academic performance and child development is of paramount importance. The present study examines how spelling, reading and arithmetic performances are associated to various child variables (gender, intelligence, and age), and distal variables such as Socio-Economic Status (SES) or type of school. The subjects in the study were 1.129 elementary school children who were in the 6th grade (11 - 12 years old) in Metropolitan Lima, Perú. Children complet - ed four different tests: In the reading area, the subtest of Procesos Lectores (PROLEC-SE; Cuetos & Ramos, 1999), Reading of Word and Pseudo-word; in the Arithmetic domain, the Number Facility from the Kit of Factor Referenced Cognitive Tests of Ekstrom, French, and Harman (1979) and in the spelling domain, the Spelling Achievement Test from Dioses (2001) was used. The Intelligence Quotient (IQ) was measured using Raven's Progressive Matrices Test (Raven, J., Raven, J.C., & Court, 2004, updated edition). Some preliminary analyses were conducted beforehand in order to overview and examine the structure of the data. Following this, and because of the hierarchical structure of the data (students within classes within schools) multilevel analyses were conducted. Results showed, first and foremost, a great impact of (a) type of school, private schools performed better than in the public sector; (b) intelligence, another essential variable (the higher the IQ the better the academic achievement), and partially of (c) gender, girls showed prevalence over boys in spelling. Likewise, we did not encounter any significant results of socioeconomic status in the multilevel analysis. Based on these results, some practical and pedagogical implications were discussed, such as the fundamental effort to bring the lower achievement group into average levels of learning with remedial work, otherwise these students will lack the requisite skills needed to fulfill their secondary school academic expectations. Notwithstanding, we have to point out some limitations such as the lack of data from rural zones that could prevent us from comparisons between rural and urban zones. Future work is necessary in order to investigate academic performance associated with other variables that might influence the child's development, such as parenting behavior or psychosocial factors. [ABSTRACT FROM AUTHOR]

A sample of 30 subjects, 10 with Attention Deficit and Hyperactivity Disorder (ADHD) and 20 non-ADHD children, statistically controlled by age, gender, academic grades and normal full scale intelligence quotient, was selected. To measure cognitive inhibitory control, a math problem solving ability test containing four problems for each level with verbal and numerical irrelevant content was administered. ADHD children exhibited significantly inferior performance in choosing correct answers (p = 0.011) with a large effect size (d = 1.00) and a significantly superior number of irrelevant answers (p = 0.004) with a very large effect size. In conclusion ADHD children showed a cognitive inhibitory control disorder, measured by math problem solving ability. [ABSTRACT FROM AUTHOR]

We describe a curricular proposal, based on the integration of algebraic ways of thinking in the elementary curriculum, which is currently aim of numerous research studies. In this context and by using the construct relational thinking, we present some results from a teaching experiment based on working with number sentences. It exemplifies the potential of this proposal and allows us to evidence third grade students' capacity to work algebraically in arithmetic. [ABSTRACT FROM AUTHOR]

We present the results of two tests performed by primary school students. The first one was on finite numeric inductive reasoning and was performed by 400 students. According to its results, we selected 28 students to whom we clinically interviewed aiming to determine the evolution of the logic relations that they can establish in the field of finite natural numbers. This study originates on historic problems of the logical foundation of arithmetic. We aim to empirically determine the extent to which logic plays a key role in the origin of arithmetic or, on the contrary, if the origins of logic are predetermined by arithmetic and other fields. [ABSTRACT FROM AUTHOR]