Early Childhood Mathematics Education: Research, Curriculum and Educational Practice

This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines

Codeship: Financing growth: Case study and Teaching note

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Notebook concerning mathematical equations : manuscript, 1769-1774

Notes on measuring height and distance, trigonometry, spherical projection, and other mathematical equations. Probably William Winthrop (1753-1825; Harvard AB 1770).

Of the invention of theorems : manuscript, [17--]

Mathematical notes, equations, theorems, and definitions. Probablynot by William Winthrop (Harvard AB 1770) as it is different handwriting and language habits from other of his manuscript.

Arithmetic copybook : manuscript, [17--]

Arithmetic copybook containing mathematical rules, problems, proofs, and charts of weights and measures.

Talking everyday science to very young children: a study involving parents and practitioners within an early childhood centre

The acquisition of everyday scientific concepts by 3-6 year old children attending early childhood institutions has been widely studied. In contrast, research on science learning processes among younger children is less extensive. This paper reports on findings from an exploratory empirical study undertaken in a ‘stay and play’ service used by parents with children aged 0-3 and located within an East London early childhood centre. The research team collaborated with practitioners to deliver a programme of activities aimed at encouraging parents’ confidence in their own ability to support emergent scientific thinking among their young children. The programme generated children’s engagement and interest. Parents and practitioners reported increased confidence in their ability to promote young children’s natural curiosity at home and in early childhood provision. The authors see no reason for positing qualitative differences between the way children acquire scientific and other concepts in their earliest years.

Association of free amino acids with caries experience and mutans streptococci levels in whole saliva of children with early childhood caries

Objective: The aim of the present study was to identify the free amino acid content in whole saliva of children with (CE) and without early childhood caries (CF) (ECC), correlating these findings with caries experience and mutans streptococci (MS) levels in saliva.Design: Seventy-eight healthy children, both genders, 6-71 months age, were selected to participate in the study. Following examination for dmft scores calculation, unstimulated whole saliva was collected from all 78 participants, stored at -80 degrees C, and used for amino acid analysis, on a Biochem 20 plus amino acid analyzer. Stimulated whole saliva was collected from 52 children, transported, diluted and plated on MSB agar medium for detection of MS in cfu/mL.Results: Forty different free amino acids were identified in whole saliva, with great variation in their concentration. A statistically significant relation was found between caries experience and the presence of free proline and glycine. While proline (p = 0.0182) was more frequently absent in the CF group, the absence of glycine (p = 0.0397) was more often observed in the CE group. In the presence of higher levels of MS, free glycine reduced the risk of experiencing dental caries (p = 0.0419). Conversely, the presence of proline was found to increase the risk of experiencing the disease (p = 0.0492).Conclusions: The presence of free proline and absence of free glycine in children with ECC, highly contaminated with MS, increased the chances of experiencing dental caries in the present population. Further studies are needed to better understand this phenomenon. (C) 2008 Elsevier Ltd. All rights reserved.

Algebra, or universal mathematics: revived 1738 with notes and additions : manuscript, [after 1738]

Instructional book in algebra with exercises.

Peer interaction in mixed age groups: a study in the computer area of an early childhood education center in Portugal

The study was developed as a teacher-research project during initial teacher education – Masters Degree of Early Childhood and Primary Education, in Portugal. It analysed the interactions between children of 3 to 6 years old, during the use of the computer as a free choice activity, confronting situations between peers of the same age and situations between peers of different ages. The focus of the analysis was the collaborative interactions. This was a qualitative study. Children could choose the computer, amongst other interest areas, and work for around an hour in pairs. In the computer, children used mainly educational games. During four weeks, the interactions between the pairs were audio recorded. Field notes and informal interviews to the children were also used to collect data. Eleven children were involved in the study with ages ranging from 3 to 6 years old. Baseline data on children’s basic computer proficiency was collected using the Individualized Computer Proficiency Checklist (ICPC) by Hyun. The recorded interactions were analysed using the types of talk offered by Scrimshaw and Perkins and Wegerif and Scrimshaw: cumulative talk, exploratory talk, disputational talk, and tutorial talk. This framework was already used in a study in an early childhood education context in Portugal by Amante. The results reveal differences in computer use and characterize the observed interactions. Seven different pairs of children's interactions were analysed. More than a third of the interactions were cumulative talk, followed by exploratory talk, tutorial talk and disputational talk. Comparing same and mixed age pairs, we observed that cumulative talk is the more present interaction, but in same age pairs this is followed by exploratory talk whereas in the mixed age pairs it is tutorial talk that has the second largest percentage. The pairs formed by the children were very asymmetrical in terms of age and computer proficiency. This lead to the more tutorial interactions, where one children showed the other or directed him/her on how to play. The results show that collaboration is present during the use of a computer area in early childhood education. The free choice of the children means the adults can only suggest pairing suited to specific interactions between the children. Another way to support children in more exploratory talk interactions could be by discussing the way the older children can help the younger ones beyond directing or correcting their work.

La Enseñanza de los sistemas externos de representación matemáticos y lingüísticos en la educación infantil

El objetivo de este estudio es identificar factores que contribuyen a mantener un enfoque básicamente instrumental para enseñar los sistemas externos de representación matemáticos y lingüísticos en las primeras edades de escolarización. En el estudio han participado 123 maestros de Educación Infantil de diversos centros escolares públicos de Andalucía, Asturias, Cataluña y Navarra que han asistido a cursos de formación permanente del profesorado. El análisis cualitativo realizado se basa en grupos de discusión a partir de tópicos. Los resultados evidencian la influencia de diversos factores: el currículo de Educación Infantil; las concepciones del profesorado; las presiones entre etapas educativas; y, finalmente, la presión social. La identificación de los factores asociados a una enseñanza instrumental de los sistemas externos de representación puede entenderse como un tipo de información relevante acerca de las condiciones de la enseñanza de estos sistemas que, además, pueden servir de base para reconstruir las prácticas educativas

El aprendizaje reflexivo en la formación inicial del profesorado: un modelo para aprender a enseñar matemáticas = Reflective learning in the early formation of teachers: a model to learn to teach maths

In this study we analize the application of the reflective learning during initial formation mathematics teachers. This model is based on the sociocultural theories of the human learning and assumes that the interaction and the contrast make possible the coconstruction and the active reconstruction of knowledge.In order to make the study, it was left from a sample of 29 teaching students. The qualitative analysis allowed to identify factors that facilitate the incorporation of the reflective learning in university teaching, as well as the degree of effectiveness of this model to learn to teach mathematics

La estadística y la probabilidad en Educación Infantil conocimientos disciplinares, didácticos y experienciales

This article presents an approach to disciplinary knowledge, and experiential learning necessary for the Early Childhood Education teachers can teach statistics and probability significantly, effective and systematic. First, are specified a set of basic knowledge about the discipline and exposed the contents sequenced by level; secondly, provides guidance on how they learn and how they should be taught the knowledge of statistics and probability in the first ages; and, finally, are some examples of activities implemented in kindergarten classrooms

Una visión actualizada de la didáctica de la matemática en educación infantil = An up-to-date vision of pre-school mathematics teaching

This article aims to investigate pre-school mathematics teaching from an uptodate perspective. To pursue this contemporary vision we focus on four key questions: what kind of maths is being worked on, who is doing it, how it is being done, and why it is being done

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

The impact of integrated programming on student attitude and achievement in grade 9 academic mathematics and science

This research studioo the effect of integrated instruction in mathematics and~ science on student achievement in and attitude towards both mathematics and science. A group of grade 9 academic students received instruction in both science and mathematics in an integrated program specifically developed for the purposes of the research. This group was compared to a control group that had received science and mathematics instruction in a traditional, nonintegrated program. The findings showed that in all measures of attitude, there was no significant difference between the students who participated in the integrated science and mathematics program and those who participated in a traditional science and mathematics program. The findings also revealed that integration did improve achievement on some of the measures used. The performance on mathematics open-ended problem-solving tasks improved after participation in the integrated program, suggesting that the integrated students were better able to apply their understanding of mathematics in a real-life context. The performance on the final science exam was also improved for the integrated group. Improvement was not noted on the other measures, which included EQAO scores and laboratory practical tasks. These results raise the issue of the suitability of the instruments used to gauge both achievement and attitude. The accuracy and suitability of traditional measures of achievement are considered. It is argued that they should not necessarily be used as the measure of the value of integrated instruction in a science and mathematics classroom.