Number sense in early and elementary mathematics education

no abstractNumber sense is crucial in daily life and therefore an important aspect of education. The development of number sense recently attracted the attention of an increasing number of researchers in the domains of cognitive and developmental (neuro)psychology, (psychology of) mathematics education, special education, and educational neuroscience. In this article, we integrate and discuss the major results of these numerous studies on children’s acquisition of number sense. We start with the definition of the concept of number sense. Afterwards, we summarize the major findings on children’s acquisition of number sense from infancy to the early school years. Next, we provide an overview of recent intervention studies aiming at stimulating the development of number sense in young children. We end with a summary of the major findings and future issues for studies in this domai

Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks

[EN] The success or failure of education systems in promoting student problem-solving skills depends on attitudinal, political, and pedagogical variables. Among these variables, the design of mathematics textbooks is thought to partially explain why students from highachieving countries show better problem-solving ability in international assessments. In the current study, we delved into this question and compared the frequency and characteristics of arithmetic word problems (AWPs) contained in primary school math textbooks in two countries with diferent levels of performance in international assessments—Singapore and Spain. In our analyses, we focused on (1) the quantity of arithmetic word problems, (2) the variety of problems in terms of their additive or multiplicative structures and semantic-mathematical substructures, and (3) the quantity and nature of illustrations that were presented together with arithmetic word problems. Although a larger proportion of AWP activities was found in Singaporean textbooks, the results showed a similar variety of AWPs in both Singaporean and Spanish math textbooks. Furthermore, in both countries, math textbooks emphasized the structures classifed as (additive) combine 1 and (multiplication) simple rate in AWPs. Notably, the Singaporean textbook contained a larger percentage of illustrations that refected the semantic-mathematical structures of the problems and helped students learn how to solve AWPs (e.g., bar models). The fndings are discussed in light of theories that posit that textbooks constitute a fundamental part of the teaching–learning process in the classroom.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE

Influence of situational and conceptual rewording on word problem solving

Se analiza la doble naturaleza semántica y textual de la tarea de resolver un problema matemático en el aula.Background: Studies on rewording word problems can be grouped into two main groups: situational rewording, in which the situation denoted by the text is described more richly, and conceptual rewording, in which the underlying semantic relations are highlighted. Aims: Our aims are to define and distinguish these two kinds of rewording and to test empirically their relative effectiveness in two different studies. Sample: In the first study, 79 third graders, 64 fourth graders and 65 fifth graders took part; the sample for Study 2 was similar. Method: In Study 1, children were asked to solve both easy and difficult two-step change problems in three different versions: standard, situational and conceptual rewording. In Study 2, three different versions of the situational version were compared: one with only temporal elaborations, one with only causal elaborations and a "complete" version combining both elaborations. Results: In Study 1, conceptually reworded problems elicited the best results, especially among younger children and for difficult two-step problems. Neither in Study 1 nor in Study 2 did the situationally reworded problems yield better performance than standard items. Conclusion: Only conceptual rewording has proved to be useful for improving children's performance, especially among younger children and for difficult problems. The lack of impact of situational rewording cannot be explained in terms of the length of the resulting text

Preschool teachers’ selection of picture books for mathematics instruction: an interview study

Various studies pointed to the potential of picture book reading (PBR) for supporting preschoolers’ mathematical development. The features of picture books vary greatly, and these features contribute to the effectiveness of PBR. It is therefore important to adequately select picture books for mathematics instruction. We analyzed the general and mathematical PB features preschool teachers take into account when selecting picture books for this aim. Interviews with 66 preschool teachers indicated that they rate general features and features related to basic mathematical skills as most important, and explain their importance based on instructional goals rather than preschooler characteristics. Our results point to the need for professional development initiatives on the selection of picture books for mathematics instruction

Desenvolvimento numérico de pré-escolares equatorianos: o papel do nível sócio econômico, da qualidade da educação matemática inicial e do tipo de escola

Este estudo teve como objetivo analisar o desenvolvimento de habilidades numéricas iniciais entre crianças equatorianas durante a pré-escola, em relação a seu status sócio econômico (SES), à qualidade da sua educação matemática inicial e ao tipo de escola frequentada. 179 pré-escolares equatorianos (18 classes, sendo 6 por tipo de escola) responderam um teste padronizado sobre numeramento inicial, tanto no começo quanto ao final do ano escolar. Em todas as salas de aula a qualidade da educação matemática inicial foi medida duas vezes por meio do instrumento COEMET. Em primeiro lugar, os resultados mostraram pontuações bastante baixas no teste de numeramento inicial, com apenas 50% (no início) e 70% (no final) dos itens resolvidos corretamente, ao lado de grandes diferenças interindividuais nesses escores. Em segundo lugar, a qualidade da educação matemática inicial nas salas de aula participantes também foi bastante baixa. Em terceiro lugar, as habilidades numéricas iniciais das crianças na entrada da pré-escola, o nível socio econômico (SES) e o tipo de escola foram preditores das habilidades numéricas das crianças no final do ano letivo. A qualidade da educação matemática inicial não contribuiu para o desenvolvimento das crianças em numeramento. Discutimos criticamente nossas descobertas com vistas a otimizar a qualidade da educação matemática inicial equatoriana, como um passo para melhorar o desenvolvimento das habilidades numéricas.This study aimed at analyzing the development of Ecuadorian children’s early numerical abilities during the Kindergarten year in relation to their SES, the quality of their early mathematics education, and the attended school type. 179 Ecuadorian Kindergartners (18 classrooms, 6 classrooms per school type) were offered a standards-based early numeracy test at both the start and the end of the Kindergarten year. In all classrooms, the quality of early mathematics education was assessed twice via the COEMET instrument. Results first showed rather low scores on the early numeracy test, with only 50% (at the start) up to 70% (at the end) of the items solved correctly, along with large inter-individual differences in these scores. Second, the quality of early mathematics education in the participating classrooms was also rather low. Third, children’s early numerical abilities at Kindergarten entry, SES, and school type predicted children’s early numerical abilities at the end of the school year. The quality of early mathematics education did not contribute to children’s numerical development. We critically discuss our findings in view of optimizing the quality of Ecuadorian early mathematics education as a stepping stone towards enhanced numerical development

The acquisition of preschool mathematical abilities: theoretical, methodological and educational considerations

The acquisition of preschool mathematical abilities: theoretical, methodological and educational consideration

Do students confuse dimensionality and “directionality”?

The aim of this research is to understand the way in which students struggle with the distinction between dimensionality and “directionality” and if this type of potential confusion could be a factor affecting students’ tendency toward improper linear reasoning in the context of the relations between length and area of geometrical figures. 131 9th grade students were confronted with a multiple-choice test consisting of six problems related to the perimeter or the area of an enlarged geometrical figure, then some interviews were carried out to obtain qualitative data in relation to students’ reasoning. Results indicate that more than one fifth of the students’ answers could be characterized as based on directional thinking, suggesting that students struggled with the distinction between dimensionality and “directionality”. A single arrow showing one direction (image provided to the students) seemed to strengthen the tendency toward improper linear reasoning for the area problems. Two arrows showing two directions helped students to see a quadratic relation for the area problems.The research reported here has been financed in part by Ministerio de Educación y Ciencia, Dirección General de Investigación, Spain, under Grant no. EDU2011-27288 and in part by the University of Alicante under the birth project GRE10-10