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Measures of association, which typically require pairwise data, are widespread in many aspects of educational research. However, due to the need to reduce their content to equal numbers of units of analysis, they are rarely found in the analysis of textbooks. In this paper, we present two methods for overcoming this limitation, one through the use of disjoint sections and the other through the use of overlapping moving averages. Both methods preserve the temporal structure of data and enable researchers to calculate a measure of association which, in this case, is the complementary Euclidean average distance, as an indicator of the books' similarity. We illustrate these approaches by means of a comparative analysis of three commonly-used English and Swedish mathematics textbooks. Analyses were focused on individual tasks, which had all been coded according to the presence or absence of particular characteristics. Both methods produce nearly identical results and are robust with respect to both densely and sparsely occurring characteristics. For both methods, widening the aggregation window results in a slightly increased level of quantified similarity, which is the result of the 'smoothing effect'. We discuss the relation between the window width and the choice of research question.

Motivated by earlier research highlighting Swedish teachers' beliefs that the setting of homework compromises deep-seated principles of educational equity, this paper presents an exploratory study of Swedish parents' perspectives on homework in their year-one children's learning. Twenty-five parents, drawn from three demographically different schools in the Stockholm region, participated in semi-structured interviews. The interviews, broadly focused on how parents support their children's learning and including questions about homework in general and mathematics homework in particular, were transcribed and data subjected to a constant comparison analytical process. This yielded four broad themes, highlighting considerable variation in how parents perceive the relationship between homework and educational equity. First, all parents spoke appreciatively of their children receiving reading homework and, in so doing, indicated a collective construal that reading homework is neither homework nor a threat to equity. Second, four parents, despite their enthusiasm for reading homework, opposed the setting of any homework due to its potential compromise of family life. Third, seven parents indicated that they would appreciate mathematics homework where it were not a threat to equity. Finally, fourteen parents, despite acknowledging homework's potential compromise to equity, were unequivocally in favour of mathematics homework being set to their children.

This paper presents an exploratory study of English and Swedish teachers' perspectives on the role of homework in year-one children's learning of number. In order to ensure cultural integrity, data were analysed independently by two colleagues in each context. Analyses yielded three broad but cross-culturally common themes reflecting culturally situated notions of common sense. These concerned the existence of homework, the purpose of homework and the role of parents in homework's completion. While homework was unproblematic for all English teachers, half the Swedish cohort spoke against it, arguing that variation in home background would compromise principles of equity. All teachers who set homework, whether English or Swedish, spoke of homework as a means of supporting children at risk of falling behind their peers, a process by which children practice routine skills. English teachers' homework-related justifications were located in a discourse of target setting that was invisible in the Swedish.

In this paper, motivated in part by evidence that Swedish teachers are sceptical of parents' abilities to offer appropriate support, we present an exploratory investigation of the activities Swedish parents initiate to facilitate their year-one (first grade) children's learning of mathematics. Data, derived from 25 semi-structured interviews conducted with parents from three demographically different schools, were subjected to constant comparison analyses and yielded three broad categories of activity. These concerned the use of games in the learning of mathematics, contextualised mathematics activities like cooking and shopping, and decontextualised mathematics activities like systematic counting. Collectively, the results indicate that while parents of year-one children are confident supporting their children's learning of mathematics, they are also conscious of the need to avoid both undermining schools' efforts and exacerbating educational inequity. With few exceptions, the activities parents described were age-appropriate and more likely to complement teachers' actions than not.

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.

This paper presents an exploratory study of English and Swedish teachers' perspectives on the role of parents in year one children's learning of number. Drawing on the results of semi-structured interviews, data from each cohort were analysed independently to ensure the cultural integrity of any response categories and the results of this process compared. Two broad themes were identified concerning implicit and explicit forms of parental involvement. The former, manifested similarly across the two cohorts, concerned the importance of parents presenting children with positive attitudes towards mathematics. The latter, incorporating three comparable subthemes, focused on the creation of number-rich home environments, home-school communication and parents' role in the completion of homework. All three subthemes differentiated the cohorts in ways that highlighted teachers' culturally situated perspective on teaching and learning. Some implications are discussed, particularly with respect to the challenge this study poses for developers of cross-cultural survey instruments.

It is known that an appropriately developed foundational number sense (FONS), or the ability to operate flexibly with number and quantity, is a powerful predictor of young children's later mathematical achievement. However, until now not only has FONS been definitionally elusive but instruments for identifying opportunities for children to acquire its various components have been missing from the classroom observation tools available. In this paper, drawing on a constant comparison analysis of appropriate literature, we outline the development of an eight dimensional FONS framework. We then show, by applying this framework to three culturally diverse European grade one lessons, one English, one Hungarian and one Swedish, that it is both straightforwardly operationalised and amenable to cross cultural analyses of classroom practice. Some implications are discussed.

Motivated by earlier research highlighting Swedish teachers' beliefs that the setting of homework compromises deep-seated principles of educational equity, this paper presents an exploratory study of Swedish parents' perspectives on homework in their year-one children's learning. Twenty-five parents, drawn from three demographically different schools in the Stockholm region, participated in semi-structured interviews. The interviews, broadly focused on how parents support their children's learning and including questions about homework in general and mathematics homework in particular, were transcribed and data subjected to a constant comparison analytical process. This yielded four broad themes, highlighting considerable variation in how parents perceive the relationship between homework and educational equity. First, all parents spoke appreciatively of their children receiving reading homework and, in so doing, indicated a collective construal that reading homework is neither homework nor a threat to equity. Second, four parents, despite their enthusiasm for reading homework, opposed the setting of any homework due to its potential compromise of family life. Third, seven parents indicated that they would appreciate mathematics homework where it were not a threat to equity. Finally, fourteen parents, despite acknowledging homework's potential compromise to equity, were unequivocally in favour of mathematics homework being set to their children. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]