Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Andrews, Paul; Sayers, Judy

doi:10.1007/s10643-014-0653-6

Cited by 46 publications

(49 citation statements)

References 77 publications

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“…Our constant comparison analysis (Strauss & Corbin, 1998) of the literature, a process which has been described extensively in Andrews & Sayers (2014b), has identified three distinct conceptions. The first, an innate or preverbal number sense (Butterworth, 2005;Ivrendi, 2011;Lipton & Spelke, 2005), comprises an understanding of small quantities that allows for comparison.…”

Section: Three Conceptions Of Number Sensementioning

confidence: 99%

“…This second, literature-based, paper offered a detailed account of the development of the seven components. More recently (Andrews & Sayers, 2014b), we have presented a stronger explanatory narrative for the eight component FoNS framework and provide, through the examination of excerpts drawn from the teaching of exemplary teachers in England, Hungary and Sweden, further evidence of the analytical power of the FoNS framework. These eight components are summarised thus:…”

Section: Defining Foundational Number Sensementioning

confidence: 99%

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The Role of Conceptual Subitising in the Development of Foundational Number Sense

Sayers

Andrews

Boistrup

2016

Mathematics Education in the Early Years

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INTRODUCTIONOver the last fifteen years since the publication of Clements' (1999) well-known paper, various scholars, particularly in the United states, have been encouraging teachers to attend to the development of young learners' conceptual subitising (See, for example, Clements & Sarama, 2009;Conderman et al., 2014); where conceptual subitising is the ability to recognise quickly and without counting relatively large numerosities by partitioning these large groups into smaller groups that can be individually subitised (Clements & Sarama, 2007;Geary, 2011). Various claims, which we discuss below, have been made with respect to the efficacy of conceptual subitising-focused instruction. In a related vein, our own recent work has focused on a conceptualisation of foundational number sense (FoNS), which we describe as those number-related competences expected of a typical first grade student that require instruction (Back et al., 2014;Andrews & Sayers, 2014a). FoNS is characterised by eight components, which we describe below. The purpose of this paper, drawing on excerpts from grade one lessons taught by a case study teacher in each of Hungary and Sweden, is to examine the extent to which conceptual subitising-focused activities have the propensity to facilitate students' acquisition of the various FoNS components and, in so doing, examine the warrant for their claimed efficacy. WHAT IS SUBITISING?Subitising refers to being instantly and automatically able to recognise small numerosities without having to count (Clements, 1999;Jung et al., 2013;Moeller et al., 2009;Clements & Sarama, 2009). Children as young as three are typically able to subitise numerosities up to three (Fuson, 1988, Moeller et al., 2009), while most adults are able instantly to recognise without counting the numerosity represented by the dots on the face of a die (Jung et al. 2013). This process, innate to all humans, is typically known as perceptual subitising (Gelman & Tucker, 1975) and forms an element of the preverbal number sense we describe below. In short, perceptual subitising is recognizing a numerosity without using other mathematical processes (Clement, 1999). Conceptual subitisingHowever, a second form of subitising, conceptual subitising (Clements, 1999), which is not unrelated to FoNS, has been shown to have considerable implications for teaching and learning. Conceptual subitising relates to how an individual identifies "a whole quantity as the result of recognizing smaller quantities... that make up the whole" (Conderman et al., 2014, p.29). More generally, it can be summarised as the systematic management of perceptually subitised numerosities to facilitate the management of larger numerosities (Obersteiner et al., 2013). For example, when a child is confronted by two dice, one showing three and another showing four, each is perceptually subitised before any sense of seven can emerge.Subitising can be construed as having a synonymity with the spatial structuring of numbers (Battista et al., 1998). In this case, the ability to ...

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Section: Three Conceptions Of Number Sensementioning

confidence: 99%

Section: Defining Foundational Number Sensementioning

confidence: 99%

The Role of Conceptual Subitising in the Development of Foundational Number Sense

Sayers

Andrews

Boistrup

2016

Mathematics Education in the Early Years

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“…Son diversos los autores que apoyan esta subdivisión del sentido numérico, haciendo referencia a un sentido numérico más temprano, que los niños normalmente adquieren de manera informal (Ivrendi, 2011;Jordan y Levine, 2009) antes de iniciarse en el sistema educativo, siendo éste un importante prerrequisito para el posterior logro matemático (Andrews y Sayers, 2015;Gersten y Chard, 1999).…”

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“…Un cuerpo amplio de bibliografía científica aporta evidencia de que las medidas basadas en el sentido numérico tienen el potencial de proveer de indicadores técnicamente adecuados para la evaluación del logro académico en matemáticas de los estudiantes (Andrews y Sayers, 2015;Foegen, Jiban, y Deno, 2007;Lembke y Foegen, 2009). De forma más específica, se ha encontrado que las medidas basadas en el currículo (del inglés, Curriculum Based Measurement, CBM) han demostrado adecuación técnica para detectar la mejora del logro académico del alumno (Fuchs y Fuchs, 1986;Stecker, Fuchs, y Fuchs, 2005) y predecir el estatus de riesgo (Lembke y Foegen, 2009).…”

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Análisis factorial confirmatorio de Indicadores de Progreso de Aprendizaje en Matemáticas (IPAM) en escolares de primer curso de Primaria

Jiménez¹,

León²

2017

Ejihpe

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En este estudio se pretende poner a prueba un modelo hipotético para profundizar en la dimensionalidad del sentido numérico utilizando la técnica del Análisis Factorial Confirmatorio (AFC). Se ha llevado a cabo un estudio longitudinal con una muestra de 176 alumnos de primer curso de Educación Primaria de las Islas Canarias, a los que se les administró el instrumento Indicadores de Progreso de Aprendizaje en Matemáticas (IPAM) en tres momentos diferentes del curso escolar. El IPAM es un instrumento CBM compuesto por tres medidas alternativas o paralelas (A, B y C) que tratan de medir una misma estructura latente (i.e., sentido numérico). Estas medidas se aplican en tres momentos diferentes a lo largo del año escolar (i.e., noviembre, febrero, mayo). Su principal objetivo es el cribado universal y la evaluación del progreso de aprendizaje en matemáticas del alumnado de educación primaria mediante la evaluación de la fluidez en la resolución de diferentes tareas (i.e., comparación de magnitudes, operaciones de un dígito, operaciones de dos dígitos, series numéricas, y valor de posición). La fluidez es medida contabilizando el número de respuestas correctas que da el alumno en un tiempo dado. Los resultados del AFC confirman un buen ajuste del modelo propuesto para los distintos momentos de medida.Palabras clave: Sentido numérico, educación primaria, matemáticas, análisis factorial confirmatorio, medida basada en el currículo. Confirmatory factor analysis of Mathematics Progress Indicators (IPAM) in first-grade students.This study analyses the factorial structure of Mathematics Progress Indicators (IPAM), by using Confirmatory Factorial Analysis (CFA) techniques. For this purpose, a longitudinal study was carried out with a sample of 176 first-grade students from the Canary Islands, IPAM was administered to the study sample three times throughout the scholar year. The IPAM is a Curriculum-Based Measurement (CBM) instrument composed of three alternative or parallel measures (A, B and C) that try to measure the same latent structure (i.e., number sense). The IPAM measures were administered three times per year (i.e., fall, winter, spring). Its main objective is the universal screening and evaluation of students' mathematics learning progress in the elementary grades through the evaluation of fluency for different tasks (i.e., magnitude comparison, one-digit operations, two-digit operations, missing number, and position value). Fluency is measured by counting the number of correct answers given by the student at a given time. The results of the CFA confirm a good fit of the proposed model for the different moments of measurement.

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“…One is a Swedish-authored series of long-standing, while two are imports, one from Finland and the other from Singapore, countries generally acknowledged as successful on international tests of mathematics achievement, particularly PISA. Analyses are framed against the eight categories of foundational number sense (FoNS) (Andrews & Sayers, 2015), each of which is a literature-derived competence necessary for the later learning of mathematics.…”

Section: Textbook Borrowingmentioning

confidence: 99%

Opportunities to learn foundational number sense in three Swedish year one textbooks: implications for the importation of overseas-authored materials

Sayers

Petersson

Rosenqvist

et al. 2019

International Journal of Mathematical Education in Science and

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In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded against the eight categories of foundational number sense, which are the number-related competences literature has shown to be essential for the later mathematical success of year one learners. Two analyses were undertaken; the first was a frequency analysis of the tasks coded for a particular category, the second was a time-series analysis highlighting the temporal location of such opportunities. The frequency analyses identified statistically significant differences with respect to children's opportunities to acquire foundational number sense. Additionally, the time series showed substantial differences in the ways in which such tasks were located in the structure of the textbooks. Such differences, we argue, offer substantial didactical challenges to teachers trying to adapt their practices to the expectations of such imports.

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Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Cited by 46 publications

References 77 publications

The Role of Conceptual Subitising in the Development of Foundational Number Sense

The Role of Conceptual Subitising in the Development of Foundational Number Sense

Análisis factorial confirmatorio de Indicadores de Progreso de Aprendizaje en Matemáticas (IPAM) en escolares de primer curso de Primaria

Opportunities to learn foundational number sense in three Swedish year one textbooks: implications for the importation of overseas-authored materials

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