Paul Andrews
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Routine and adaptive experts: Individual characteristics and their impact on multidigit arithmetic strategy flexibility and mathematics achievement Open
Motivated by a curriculum privileging number-based strategies but national tests highlighting students’ reliance on standard algorithms, this study analyses 2,216 Danish Grade 3, 6 and 8 students’ solutions to various multidigit arithmetic…
Routine and adaptive experts: Individual characteristics and their impact on multidigit arithmetic strategy flexibility and mathematics achievement Open
Motivated by a curriculum privileging number-based strategies but national tests highlighting students’ reliance on standard algorithms, this study analyses 2216 Danish grade 3, 6 and 8 students’ solutions to various multidigit arithmetic …
English and Swedish year-one teachers’ number-related learning goals: the influence of intended and received curricula Open
In this paper, drawing on semi-structured interviews with generalist teachers of year-one children in England and Sweden, we examine comparatively the influence of the intended curriculum (teachers in both countries work within mandated na…
Grade six students’ multidigit arithmetic strategy adaptivity and flexibility: evaluating a novel tri-phase assessment tool Open
In this paper we present a novel adaptation of a tri-phase assessment tool, originally devised to investigate students’ linear equations-related strategy flexibility, to evaluate Danish grade-six students’ multidigit arithmetic-related str…
Danish third, sixth and eighth grade students’ strategy adaptivity, strategy flexibility and accuracy when solving multidigit arithmetic tasks Open
In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn…
Age- and gender-related differences in Danish students’ use of number-based strategies when solving multidigit addition tasks Open
International audience
Does solving arithmetic linear equations offer transferable algebraic competence? Open
International audience
Do students’ ways of solving linear equations influence their later mathematical learning? Evidence from a study of Swedish upper secondary students Open
International audience
The experiential construction of mathematics teacher identity and the impact of early mathematical failure Open
It is broadly accepted that teachers’ professional identities influence how they teach and what their pupils learn. In this paper, drawing on semi-structured interviews with 22 experienced primary teachers from the Republic of Cyprus, we e…
Estimation in the Primary Mathematics Curricula of Cyprus, Greece and Turkey: A Privileged or Prevented Competence? Open
Estimation is an essential competence with a developmental role in the learning of various mathematical topics. Yet, as previous studies highlight, this competence is either excluded or ambivalently included in intended curricula around th…
Two methods for quantifying similarity between textbooks with respect to content distribution Open
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 an…
Analysing English year-one mathematics textbooks through the lens of foundational number sense: A cautionary tale for importers of overseas-authored materials Open
In this paper we present analyses of three textbooks currently used in the teaching of mathematics to year-one children in England. One is an established English-authored textbook, while the others are Singaporean-authored imports promoted…
Norwegian and Swedish post-compulsory school students’ perspectives on the purpose of school mathematics: An exploratory study Open
Many countries’ educational aspirations are reflected in government-produced national curricula that specify, with varying degrees of prescription, what should be taught, when it should be taught, and even how it should be taught. These sy…
Swedish students' exploration of trigonometrical relationships: GeoGebra and protractors yield qualitatively different insights Open
Trigonometry, an important prerequisite for many advanced topics of school mathematics, links geometric, algebraic and graphical reasoning, but remains a difficult topic to teach and learn. The dynamic nature of many trigonometric function…
Parent-initiated activities in support of Swedish year-one children’s learning of mathematics: age-appropriate complements to school? Open
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 yea…
Content analysis of mathematics textbooks and adapted Lorentz curves Open
In this paper, we introduce an adaption of the Lorenz curve as a powerful tool for graphically presenting content analyses of mathematics textbooks. Three textbooks currently used with year-one children in Sweden, one Swedish-, one Finnish…
Swedish parents’ perspectives on homework: manifestations of principled pragmatism Open
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 homewo…
Computational Estimation and Mathematics Education: A Narrative Literature Review Open
Computational estimation, typically construed as an approximate mental calculation of an arithmetical problem, is an important skill in everyday life and a wide range of professional contexts. Despite its importance, textbooks and curricul…
Estimation in the Mathematics Curricula of Denmark, Norway and Sweden: Inadequate Conceptualisations of an Essential Competence Open
Acknowledging evidence that the ability to estimate has major consequences for both later mathematics learning and real-world functionality, this paper examines the national mathematics curriculum for compulsory school for each of Denmark,…
Estimation in the primary mathematics curricula of the United Kingdom: Ambivalent expectations of an essential competence Open
In this paper, we examine the national curricula for primary mathematics for each of the four constituent nations of the United Kingdom (England, Northern Ireland, Scotland and Wales) for the estimation-related opportunities they offer chi…
PISA, TIMSS and Swedish students’ knowledge of linear equations: A ‘telling’ case of a system fixing something that may not be broken Open
In this paper, we construct a ‘telling’ case to highlight a problematic inconsistency between the results of international large-scale assessments (ILSAs) and other studies of Swedish students’ knowledge of linear equations.In this context…
Teachers’ perspectives on homework: manifestations of culturally situated common sense Open
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 collea…
Estimation: An inadequately operationalised national curriculum competence Open
Research has highlighted the importance of estimation, in various forms, as both an essential life-skill and a significant underpinning of other forms of mathematical learning. It has also highlighted a lack of opportunities for learners t…
Two novel approaches to the content analysis of school mathematics textbooks Open
The analysis of the content of school textbooks, particularly in a time of cross-cultural borrowing, is a growing field restricted by the tools currently available. In this paper, drawing on the analyses of three English year-one mathemati…
Swedish primary teacher education students’ perspectives on linear equations Open
Linear equations, connecting arithmetic to the symbolism of formal mathematics, represent a key topic of mathematics. However, the understanding primary teacher education students bring to their studies has been rarely examined. In this st…
Time series analysis: Moving averages as an approach to analysing textbooks Open
In this study we introduce time series analysis, specifically moving averages, as a novel strategy for analysing mathematics textbooks. Such analyses show how different topics or mathematical processes are emphasised over different time pe…
Opportunities to learn foundational number sense in three Swedish year one textbooks: implications for the importation of overseas-authored materials Open
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 …
OPPORTUNITIES FOR YEAR-ONE CHILDREN TO ACQUIRE FOUNDATIONAL NUMBER SENSE: COMPARING ENGLISH AND SWEDISH ADAPTATIONS OF THE SAME SINGAPORE TEXTBOOK Open
We compare adaptations of a Singaporean year-one mathematics textbook for use in England and Sweden respectively. The texts were analysed in two different ways against the eight dimensions of Foundational Number Sense (FoNS), a set of core…