The role of *language in early childhood mathematics

Math literacy is imperative to succeed in society. Experience is key for acquiring math literacy. A preschooler's world is full of mathematical experiences. Children are continually counting, sorting and comparing as they play. As children are engaged in these activities they are using language as a tool to express their mathematical thinking. If teachers are aware of these teachable moments and help children bridge their daily experiences to mathematical concepts, math literacy may be enhanced. This study described the interactions between teachers and preschoolers, determining the extent to which teachers scaffold children's everyday language into expressions of mathematical concepts. Of primary concern were the teachers' responsive interactions to children's expressions of an implicit mathematical utterance made while engaged in block play. The parallel mixed methods research design consisted of two strands. Strand 1 of the study focused on preschoolers' use of everyday language and the teachers' responses after a child made a mathematical utterance. Twelve teachers and 60 students were observed and videotaped while engaged in block play. Each teacher worked with five children for 20 minutes, yielding 240 minutes of observation. Interaction analysis was used to deductively analyze the recorded observations and field notes. Using a priori codes for the five mathematical concepts, it was found children produced 2,831 mathematical utterances. Teachers ignored 60% of these utterances and responded to, but did not mediate 30% of them. Only 10% of the mathematical utterances were mediated to a mathematical concept. Strand 2 focused on the teacher's view of the role of language in early childhood mathematics. The 12 teachers who had been observed as part of the first strand of the study were interviewed. Based on a thematic analysis of these interviews three themes emerged: (a) the importance of a child's environment, (b) the importance of an education in society, and (c) the role of math in early childhood. Finally, based on a meta-inference of both strands, three themes emerged: (a) teacher conception of math, (b) teacher practice, and (c) teacher sensitivity. Implications based on the findings involve policy, curriculum, and professional development.

Functional near infrared spectroscopy study of language, joint attention and motor skills

Near infrared spectroscopy (NIRS) is an emerging non-invasive optical neuro imaging technique that monitors the hemodynamic response to brain activation with ms-scale temporal resolution and sub-cm spatial resolution. The overall goal of my dissertation was to develop and apply NIRS towards investigation of neurological response to language, joint attention and planning and execution of motor skills in healthy adults. Language studies were performed to investigate the hemodynamic response, synchrony and dominance feature of the frontal and fronto-temporal cortex of healthy adults in response to language reception and expression. The mathematical model developed based on granger causality explicated the directional flow of information during the processing of language stimuli by the fronto-temporal cortex. Joint attention and planning/ execution of motor skill studies were performed to investigate the hemodynamic response, synchrony and dominance feature of the frontal cortex of healthy adults and in children (5-8 years old) with autism (for joint attention studies) and individuals with cerebral palsy (for planning/execution of motor skills studies). The joint attention studies on healthy adults showed differences in activation as well as intensity and phase dependent connectivity in the frontal cortex during joint attention in comparison to rest. The joint attention studies on typically developing children showed differences in frontal cortical activation in comparison to that in children with autism. The planning and execution of motor skills studies on healthy adults and individuals with cerebral palsy (CP) showed difference in the frontal cortical dominance, that is, bilateral and ipsilateral dominance, respectively. The planning and execution of motor skills studies also demonstrated the plastic and learning behavior of brain wherein correlation was found between the relative change in total hemoglobin in the frontal cortex and the kinematics of the activity performed by the participants. Thus, during my dissertation the NIRS neuroimaging technique was successfully implemented to investigate the neurological response of language, joint attention and planning and execution of motor skills in healthy adults as well as preliminarily on children with autism and individuals with cerebral palsy. These NIRS studies have long-term potential for the design of early stage interventions in children with autism and customized rehabilitation in individuals with cerebral palsy.

Parsing mathematical constructs:results from a preliminary eye tracking study

The semantic model described in this paper is based on ones developed for arithmetic (e.g. McCloskey et al. 1985, Cohene and Dehaene 1995), natural language processing (Fodor 1975, Chomsky 1981) and work by the author on how learners parse mathematical structures. The semantic model highlights the importance of the parsing process and the relationship between this process and the mathematical lexicon/grammar. It concludes by demonstrating that for a learner to become an efficient, competent mathematician a process of top-down parsing is essential.

THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

Using blogs to enhance the capacity of mathematical communication in High School

The aim of this investigation is to analyze the use of the blog as an educational resource for the development of the mathematical communication in secondary education. With this aim, four aspects are analyzed: organization of mathematical thinking through communication; communication of mathematical thinking; analysis and evaluation of the strategies and mathematical thought of others; and expression of mathematical ideas using mathematical language. The research was conducted from a qualitative approach on an exploratory level, with the case study method of 4 classrooms of second grade of secondary education in a private school in Lima. The observational technique of 20 publications in the blog of the math class was applied; a study of a focal group with a sample of 9 students with different levels of academic performance; and an interview with the academic coordinator of the school was conducted. The results show that the organization of mathematical thinking through communication is carried out in the blog in a written, graphical and oral way through explanations, schemes and videos. Regarding communication of mathematical thinking, the blog is used to describe concepts, arguments and mathematical procedures with words and examples of the students. The analysis and evaluation of the strategies and mathematical thinking is performed through comments and debates about the publications. It was also noted that the blog does not facilitate the use of mathematical language to express mathematical ideas, since it does not allow direct writing of symbols nor graphic representation.

Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Funtional Near Infrared Spectroscopy Study of Language, Joint Attention and Motor Skills

Near infrared spectroscopy (NIRS) is an emerging non-invasive optical neuro imaging technique that monitors the hemodynamic response to brain activation with ms-scale temporal resolution and sub-cm spatial resolution. The overall goal of my dissertation was to develop and apply NIRS towards investigation of neurological response to language, joint attention and planning and execution of motor skills in healthy adults. Language studies were performed to investigate the hemodynamic response, synchrony and dominance feature of the frontal and fronto-temporal cortex of healthy adults in response to language reception and expression. The mathematical model developed based on granger causality explicated the directional flow of information during the processing of language stimuli by the fronto-temporal cortex. Joint attention and planning/ execution of motor skill studies were performed to investigate the hemodynamic response, synchrony and dominance feature of the frontal cortex of healthy adults and in children (5-8 years old) with autism (for joint attention studies) and individuals with cerebral palsy (for planning/execution of motor skills studies). The joint attention studies on healthy adults showed differences in activation as well as intensity and phase dependent connectivity in the frontal cortex during joint attention in comparison to rest. The joint attention studies on typically developing children showed differences in frontal cortical activation in comparison to that in children with autism. The planning and execution of motor skills studies on healthy adults and individuals with cerebral palsy (CP) showed difference in the frontal cortical dominance, that is, bilateral and ipsilateral dominance, respectively. The planning and execution of motor skills studies also demonstrated the plastic and learning behavior of brain wherein correlation was found between the relative change in total hemoglobin in the frontal cortex and the kinematics of the activity performed by the participants. Thus, during my dissertation the NIRS neuroimaging technique was successfully implemented to investigate the neurological response of language, joint attention and planning and execution of motor skills in healthy adults as well as preliminarily on children with autism and individuals with cerebral palsy. These NIRS studies have long-term potential for the design of early stage interventions in children with autism and customized rehabilitation in individuals with cerebral palsy.

Influence of English language in the number of citations of articles published in Brazilian journals of Ophthalmology

PURPOSE: To determine the association between language and number of citations of ophthalmology articles published in Brazilian journals. METHODS: This study was a systematic review. Original articles were identified by review of documents published at the two Brazilian ophthalmology journals indexed at Science Citation Index Expanded - SCIE [Arquivos Brasileiros de Oftalmologia (ABO) and Revista Brasileira de Oftalmologia (RBO)]. All document types (articles and reviews) listed at SCIE in English (English Group) or in Portuguese (Portuguese Group) from January 1, 2008 to December 31, 2009 were included, except: editorial materials; corrections; letters; and biographical items. The primary outcome was the number of citations through the end of second year after publication date. Subgroup analysis included likelihood of citation (cited at least once versus no citation), journal, and year of publication. RESULTS: The search at the web of science revealed 382 articles [107 (28%) in the English Group and 275 (72%) in the Portuguese Group]. Of those, 297 (77.7%) were published at the ABO and 85 (23.3%) at the RBO. The citation counts were statistically significantly higher (P<0.001) in the English Group (1.51 - SD 1.98 - range 0 to 11) compared with the Portuguese Group (0.57 - SD 1.06 - range 0 to 7). The likelihood citation was statistically significant higher (P<0.001) in the English Group (70/107 - 65.4%) compared with the Portuguese Group (89/275 - 32.7%). There were more articles published in English at the ABO (98/297 - 32.9%) than at the RBO (9/85 - 10.6%) [P<0.001]. There were no significant difference (P=0.967) at the proportion of articles published in English at the years 2008 (48/172 - 27.9%) and 2009 (59/210 - 28.1%). CONCLUSION: The number of citations of articles published in Portuguese at Brazilian ophthalmology journals is lower than the published in English. The results of this study suggest that the editorial boards should strongly encourage the authors to adopt English as the main language in their future articles.

Conteudo curricular para crianças de creche de dois a tres anos : teoria e pratica

Universidade Estadual de Campinas. Faculdade de Educação Física

Health Related Quality of Life Assessment questionnaire for children aged 5 to 11 years with HIV/AIDS: cross-cultural adaptation for the Portuguese language

The objective of this study is to describe preliminary results from the cross-cultural adaptation of the Quality of Life Assessment Questionnaire, used to measure health related quality of life (HRQL) in Brazilian children aged between 5 and 11 with HIV/AIDS. The cross-cultural model evaluated the Concept, Item, Semantic and Measurement Equivalences (internal consistency and intra-observer reliability). Evaluation of the conceptual, item, semantic equivalences showed that the Portuguese version is pertinent for the Brazilian context. Four of seven domains showed internal consistency above 0.70 (α: 0.76-0.90) and five of seven revealed intra-observer reliability (ricc: 0.41-0.70). This first Portuguese version of the HRQL questionnaire can be understood as a valuable tool for assessing children's HRQL, but further studies with large samples and more robust analyses are recommended before use in the Brazilian context.

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.

Biologically Plausible Connectionist Prediction of Natural Language Thematic Relations

In Natural Language Processing (NLP) symbolic systems, several linguistic phenomena, for instance, the thematic role relationships between sentence constituents, such as AGENT, PATIENT, and LOCATION, can be accounted for by the employment of a rule-based grammar. Another approach to NLP concerns the use of the connectionist model, which has the benefits of learning, generalization and fault tolerance, among others. A third option merges the two previous approaches into a hybrid one: a symbolic thematic theory is used to supply the connectionist network with initial knowledge. Inspired on neuroscience, it is proposed a symbolic-connectionist hybrid system called BIO theta PRED (BIOlogically plausible thematic (theta) symbolic-connectionist PREDictor), designed to reveal the thematic grid assigned to a sentence. Its connectionist architecture comprises, as input, a featural representation of the words (based on the verb/noun WordNet classification and on the classical semantic microfeature representation), and, as output, the thematic grid assigned to the sentence. BIO theta PRED is designed to ""predict"" thematic (semantic) roles assigned to words in a sentence context, employing biologically inspired training algorithm and architecture, and adopting a psycholinguistic view of thematic theory.

Numerical study of a model for nonequilibrium wetting

We revisit the scaling properties of a model for nonequilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point.

Proposal of a High-Level Language for Writing Self Modifying Programs

This paper proposes a simple high-level programming language, endowed with resources that help encoding self-modifying programs. With this purpose, a conventional imperative language syntax (not explicitly stated in this paper) is incremented with special commands and statements forming an adaptive layer specially designed with focus on the dynamical changes to be applied to the code at run-time. The resulting language allows programmers to easily specify dynamic changes to their own program`s code. Such a language succeeds to allow programmers to effortless describe the dynamic logic of their adaptive applications. In this paper, we describe the most important aspects of the design and implementation of such a language. A small example is finally presented for illustration purposes.

Deterministic mathematical model for the prediction of the as-cast macrostructure

A multiphase deterministic mathematical model was implemented to predict the formation of the grain macrostructure during unidirectional solidification. The model consists of macroscopic equations of energy, mass, and species conservation coupled with dendritic growth models. A grain nucleation model based on a Gaussian distribution of nucleation undercoolings was also adopted. At some solidification conditions, the cooling curves calculated with the model showed oscillations (""wiggles""), which prevented the correct prediction of the average grain size along the structure. Numerous simulations were carried out at nucleation conditions where the oscillations are absent, enabling an assessment of the effect of the heat transfer coefficient on the average grain size and columnar-to-equiaxed transition.