Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth graders (12-year-olds) use shortcut strategies in solving multidigit addition, subtraction, multiplication, and division problems, to what extent student factors and task instructions affected this frequency of shortcut strategy use, and to what extent the strategies differed in performance. A sample of 648 sixth graders from 23 Dutch primary schools completed a paper-and-pencil task of 12 multidigit arithmetic problems, designed to elicit specific shortcut strategies such as compensation. Based on the students’ written work, strategies were classified into whether a shortcut strategy was used or not. Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies. An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems. Finally, the use of shortcut strategies did not yield higher performance than using standard strategies. All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common.Article / Letter to edito

Aftrekopgaven: rijgen of aanvullen

Education and Child Studie

Explanatory latent variable modeling of mathematical ability in primary school : crossing the border between psychometrics and psychology

This thesis focuses on primary school students’ mathematical ability in the Netherlands. Starting with a systematic research synthesis of performance outcomes of different mathematics programs in Chapter 1, the remaining Chapters 2 to 7 report the results of six empirical studies. These studies address the determinants of students’ ability in the domain of arithmetic (addition, subtraction, multiplication, and division). Moreover, they can be said to cross the border between the academic fields of substantive (educational and cognitive) psychology on the one hand, and psychometrics on the other. Chapters 2 and 3 report on the results of secondary analyses on data collected for CITO’s national mathematics assessment in grade six (12-year-olds) focusing on the strategies students used to solve the problems. Chapters 4 and 5 aimed to more systematically investigate the distinction between mental and written solution strategies for solving division problems. Finally, Chapters 6 and 7 address the role of realistic contexts in mathematics problems, both for students in early grades as well as in grade six. The data analyzed in the empirical studies are complex, requiring advanced psychometric modeling. It is argued that latent variable models incorporating explanatory variables are appropriate to analyze data on solution strategies and performance.LEI Universiteit LeidenCito, National Institute for Educational MeasurementMultivariate analysis of psychological dat

The effects of presenting multidigit mathematics problems in a realistic context on sixth graders' problem solving

Mathematics education and assessments increasingly involve arithmetic problems presented in context: a realistic situation that requires mathematical modeling. This study assessed the effects of such typical school mathematics contexts on two aspects of problem solving: performance and strategy use. Multidigit arithmetic problems presented in two conditions-with and without a realistic context-were solved by 685 sixth graders from The Netherlands. Regarding performance, the same (latent) ability dimension was involved in solving both types of problems, and the presence of a context increased the difficulty level of the division problems but not of other operations. Regarding strategy use, strategy choice and strategy accuracy were not affected by the presence of a problem context. In sum, the presence of a typical context in multidigit arithmetic problems had no marked effects on students' problem-solving behavior, which held for different subgroups of students with respect to language ability and gender.Multivariate analysis of psychological dat

Flexibility and adaptivity in arithmetic strategy use: what children know and what they show

Central elements of adaptive expertise in arithmetic problem solving are flexibility,flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflectreflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from the Netherlands completed a comprehensive assessment of adaptive expertise in the domain of multidigit subtraction, designed to measure, first, the strategies students know and use to solve subtraction problems (potential and practical flexibility).flexibility). Second, it measured to what extent students know which strategy is optimal and to what extent they use the optimal strategy (potential and practical adaptivity). Findings for flexibilityflexibility showed that most students consistently used the same strategy across all problems: practical flexibilityflexibility was low. When prompted, students knew more strategies than they used spontaneously, suggesting hidden potential in flexibility.flexibility. Findings for adaptivity showed that students hardly ever spontaneously used the task-specifictask-specific strategy that is efficient for specificspecific problems since it has the fewest and easiest steps. However, almost half of the students could select this strategy from a set of given strategies at least once. Furthermore, an innovative, personalized version of the choice/no-choice method showed that the task-specifictask-specific strategy was usually not the optimal strategy (fastest strategy leading to a correct answer) for individual students. Finally, students used the strategy with which they performed best more often than the other strategies, but there is hidden potential for the adaptive use of task-specifictask-specific strategies.NWO016.Veni.195.166/6812Education and Child Studie

Clustering nominal data with equivalent categories: A simulation study comparing restricted GROUPALS and restricted latent class analysis

Multivariate analysis of psychological data - ou

Fourth graders’ adaptive strategy use in solving multidigit subtraction problems

sing the choice/no-choice methodology we investigated Dutch fourth graders’ (N = 124) adaptive use of the indirect addition strategy to solve subtraction problems. Children solved multidigit subtraction problems in one choice condition, in which they were free to choose between direct subtraction and indirect addition, and in two no-choice conditions, in which they had to use either direct subtraction or indirect addition. Furthermore, children were randomly assigned to mental computation, written computation, or free choice between mental and written computation. One third of the children adaptively switched their strategy according to the number characteristics of the problems, whereas the remaining children consistently used the same strategy. The likelihood to adaptively switch strategies decreased when written computation was allowed or required, compared to mandatory mental computation. On average, children were adaptive to their own speed differences but not to the accuracy differences between the strategies. Education and Child Studie

Flexibility and adaptivity in arithmetic strategy use: what children know and what they show

Central elements of adaptive expertise in arithmetic problem solving are flexibility,flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflectreflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from the Netherlands completed a comprehensive assessment of adaptive expertise in the domain of multidigit subtraction, designed to measure, first, the strategies students know and use to solve subtraction problems (potential and practical flexibility).flexibility). Second, it measured to what extent students know which strategy is optimal and to what extent they use the optimal strategy (potential and practical adaptivity). Findings for flexibilityflexibility showed that most students consistently used the same strategy across all problems: practical flexibilityflexibility was low. When prompted, students knew more strategies than they used spontaneously, suggesting hidden potential in flexibility.flexibility. Findings for adaptivity showed that students hardly ever spontaneously used the task-specifictask-specific strategy that is efficient for specificspecific problems since it has the fewest and easiest steps. However, almost half of the students could select this strategy from a set of given strategies at least once. Furthermore, an innovative, personalized version of the choice/no-choice method showed that the task-specifictask-specific strategy was usually not the optimal strategy (fastest strategy leading to a correct answer) for individual students. Finally, students used the strategy with which they performed best more often than the other strategies, but there is hidden potential for the adaptive use of task-specifictask-specific strategies.NWO016.Veni.195.166/6812Education and Child Studie

The demands of simple and complex arithmetic word problems on language and cognitive resources

Education and Child Studie