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Editorial
(2008)
Although the general development of mathematical abilities in primary school has been the focus of many researchers, the development of place value understanding has rarely been investigated to date. This is possibly due to the lack of conceptual approaches and empirical studies related to this topic. To fill this gap, a theory-driven and empirically validated model was developed that describes five sequential conceptual levels of place value understanding. The level sequence model gives us the ability to estimate general abilities and difficulties in primary school pupils in the development of a conceptual place value understanding. The level sequence model was tried and tested in Germany, and given that number words are very differently constructed in German and in the languages used in South African classrooms, this study aims to investigate whether this level sequence model can be transferred to South Africa. The findings based on the responses of 198 Grade 2-4 learners show that the English translation of the test items results in the same item level allocation as the original German test items, especially for the three basic levels. Educational implications are provided, in particular concrete suggestions on how place value might be taught according to the model and how to collect specific empirical data related to place value understanding.
In this study, we investigated effects of morphological processing on handwriting production in beginning writers of German. Children from Grades 3 and 4 were asked to copy words from a computer screen onto a pen tablet, while we recorded their handwriting with high spatiotemporal resolution. Words involved a syllable-congruent visual disruption (e.g., "Golfer"), a morpheme-congruent visual disruption (e.g., "Golfer"), or had no disruption (e.g., "Golfer"). We analyzed productions in terms of Writing Onset Duration and Letter Duration at the onset of the second syllable ("f" in "Gol.fer") and the onset of the suffix ("e" in "Golf_er"). Results showed that durations were longer at word-writing onset only for words with a morpheme-congruent visual disruption. Also, letter durations were longer at the onset of the second syllable (i.e., "-fer") and shorter at the onset of the suffix (i.e., "-er") only for words with a syllable-congruent visual disruption. We interpret these findings within extant theories of handwriting production and offer an explanation for the observed effects before and during trajectory formation.
Language skills and mathematical competencies are argued to influence each other during development. While a relation between the development of vocabulary size and mathematical skills is already documented in the literature, this study further examines how children's ability to map a novel word to an unknown object as well as their ability to retain this word from memory may be related to their knowledge of number words. Twenty-five children were tested longitudinally (at 30 and at 36 months of age) using an eye-tracking-based fast mapping task, the Give-a Number task, and standardized measures of vocabulary. The results reveal that children's ability to create and retain a mental representation of a novel word was related to number knowledge at 30 months, but not at 36 months while vocabulary size correlated with number knowledge only at 36 months. These results show that even specific mapping processes are initially related to the acquisition of number words and they speak for a parallelism between the development of lexical and number-concept knowledge despite their semantic and syntactic differences.
Teachers, as role models, are crucial in promoting inclusion in society through their actions. Being perceived as fair by their students is linked to students' feelings of belonging in school. In addition, their decisions of resource allocations also affect students' academic success. Both aspects underpin the importance of teachers' views on justice. This article aims to investigate what teachers consider to be just and how teacher characteristics and situational factors affect justice ratings of hypothetical student-teacher-interactions. In an experimental design, we randomly varied the description of the interacting student in text vignettes regarding his/her special educational need (SEN) (situational factor). We also collected data on teachers' attitudes toward inclusion and experiences with persons with disabilities (individual factors). A sample of in-service teachers in Germany (N = 2,254) rated randomized versions of two text vignettes. To also consider the effect of professional status, a sample of pre-service teachers (N = 275) did the same. Linear mixed effect models point to a negative effect of the SEN on justice ratings, meaning situations in which the interacting student is described with a SEN were rated less just compared to the control condition. As the interacting student in the situations was treated worse than the rest, this was indicative for the application of the need principle. Teachers with more positive attitudes toward inclusion rated the vignettes as significantly less just. Professional status also had a negative effect on justice ratings, with in-service teachers rating the interactions significantly lower than the pre-service teachers. Our results suggest that the teachers applied the principle of need in their ratings. Implications for inclusive teaching practices and future research are discussed further.
In this intervention study, we investigated how we could teach university students who were majoring in education to teach reading strategies. The goal of the study was to analyze whether and to what extent students would benefit from the intervention with respect to their own learning. Did their own reading skills improve after they attended the intervention? The sample consisted of n = 61 students who were assigned to one of two conditions: (a) an adaption of reciprocal teaching; and (b) a control group that was not taught how to teach reading strategies. The evidence-based teaching method used in the intervention condition consisted of three elements: modeling, scaffolding, and repeated practice. Training success was assessed in a pre-posttest control group design with standardized reading comprehension and reading speed tests. To compare the development of the students in the two conditions, repeated measures ANOVAs were used. At posttest, intervention students outperformed control students in reading comprehension as well as in reading speed.
The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during mathematics problem-solving, (2) to describe their multi-method interview approach developed to study student mathematical metacognition, and (3) to empirically evaluate the utility of their model and the adaptation of their approach in the context of grade 2 and grade 4 mathematics problem-solving. The results are discussed not only with regard to further development of the adapted multi-method interview approach, but also with regard to their theoretical and practical implications.
This chapter provides an overview of methods to capture developments and changes in motivational beliefs. Motivational research has recently begun to venture beyond just examining average developmental trends in motivational variables by starting to investigate how developmental changes in motivational variables differ between and within individuals in different learning situations and across contexts. Although studies have started to uncover differences in motivational changes, a systematic overview of suitable methods for capturing motivational differences in developmental processes is still missing. In this chapter, we review key methods of change modelling, bringing together variable-centred approaches, such as growth modelling and true intraindividual change (TIC) models, and person-centred approaches, such as latent transition and growth mixture models. We illustrate the value of the reviewed statistical methods for the analysis of context-specific motivational changes by reviewing recent empirical studies that identify different patterns and trajectories of such motivational beliefs across time. Our focus is thereby on research grounded in situated expectancy-value theory as a core theory in motivational research.
Germany is continuously expanding its inclusive education system. Research provides evidence that students with special educational needs (SEN) in inclusive school settings show lower academic achievement and come from lower socioeconomic backgrounds than their peers without SEN. Identifying to what extent the disadvantages originating from both characteristics are confounded in predicting academic achievement, has been neglected in the German educational context. Using data of 1711 primary and secondary school students from a longitudinal study in the state of Brandenburg, this study evaluates to what degree SEN (in the areas of learning and emotional-social difficulties) and socioeconomic background (SES) are confounded in predicting academic initial achievement in reading and mathematics as well as their development over time. Using multilevel modelling techniques that nest three measurement points into students and students into classes, results identify SES and SEN as relevant predictors of achievement status and growth in both subjects. Only few and small mediation effects of SES were found, indicating that both SES and SEN remain independent risk factors for achievement. Understanding the origins of student disadvantage can help teachers to make better informed choices for designing support measures and aid policymakers' reasoning for resource allocations.
Nonsymbolic numerical magnitude processing skills are assumed to be fundamental to mathematical learning. Recent findings suggest that visual–spatial skills account for associations between children’s performance in visually presented nonsymbolic numerical magnitude comparison tasks and their performance in visually presented arithmetic tasks. The aim of the current study was to examine whether associations between children’s performance in visually presented tasks assessing nonsymbolic numerical magnitude processing skills and their performance in tasks assessing early mathematical skills, which do not involve visual stimulation, may also be mediated by visual–spatial skills. This line of reasoning is based on the assumption that children make use of mental visualization processes when working on tasks assessing early mathematical skills, such as knowledge of the sequence of number words, even when these tasks do not involve visual stimulation. We assessed 4- to 6-year-old children’s performance in a nonsymbolic numerical magnitude comparison task, in tasks concerning knowledge of the sequence of number words, and in a developmental test to assess visual–spatial skills. Children’s nonsymbolic numerical magnitude processing skills were found to be associated with their number word sequence skills. This association was fully mediated by interindividual differences in visual–spatial skills. The effect size of this mediation effect was small. We assume that the ability to construct mental visualizations constitutes the key factor underlying this mediation effect.
This study investigates the effect of bilingualism on learning English as a foreign language (L3), examining the impact of manner and sequence of bilingual acquisition and learning as well as language use practices in language minority children. With a sample of 1295 German eighth and ninth graders (bilingual: n = 456, monolingual: n = 839), we examined if certain aspects of bilingualism present an advantageous condition for learning English as a foreign language in bilingual language minority students. Controlling for socio-economic status, indicators of cultural capital, and gender, the regression analyses revealed higher L3 listening and reading outcomes for bilinguals who received formal instruction in their minority language, had acquired both languages in their first three years, and switched more often between their two languages, when compared to their other bilingual and monolingual peers. The discussion focuses on the importance for bilingual children in immigrant communities to have high proficiencies in both majority and minority languages in order to develop advantages in foreign language learning.
This article describes architectural extensions for a dynamically scheduled processor to enable three different operation modes, ranging from high-performance, to high-reliability. With minor extensions of the control path, the resources of the super-scalar data-path can be used either for high-performance execution, fail-safe-operation, or fault-tolerant-operation. Furthermore, the online error-correction capabilities are combined with reconfiguration techniques for permanent fault handling. This reconfiguration can take defective components out of operation permanently, and can be triggered on-demand during runtime, depending on the frequency of online corrected faults. A comprehensive fault simulation was carried out in order to evaluate hardware overhead, fault coverage and performance penalties of the proposed approach. Moreover, the impact of the permanent reconfiguration regarding the reliability and performance is investigated.
In this classroom intervention study, reciprocal teaching (RI) of reading strategies was combined with explicit instruction in self-regulated learning (SRL) to promote the reading comprehension of fifth-grade students (N = 306). Twelve intact classes were randomly assigned either to an RT + SRL condition or to an RI condition without explicit instruction in self-regulation. Three additional classes served as a no-treatment comparison group. Strategies instruction was delivered by trained assistants in conventional German language lessons. Students practiced the application of these strategies in small groups. Both at posttest and at maintenance (8 weeks after the intervention), students in the two intervention conditions (RT and RI + SRL) outperformed comparison students in measures of reading comprehension, strategy-related task performance, and self-efficacy for reading. Relative to RI students, students in the RI + SRL condition were better able to maintain training-induced performance gains over the follow-up interval. A moderated mediation analysis revealed that this difference in the sustainability of the two treatments was (a) mediated by the successful mastery of the learned strategies and (b) most evident among students with poor reading fluency skills.
The goal of this research was to highlight the role social regulatory processes play in making students’ teamwork in reciprocal teaching (RT) groups (a classroom activity in which students take the teacher’s role in small group reading sessions) effective. In addition to teamwork quality, we expected peer feedback to be a key factor in enhancing students’ reading comprehension achievements. Because previous research (Schünemann et al. in Contemp Educ Psychol 38:289–305, 2013) has shown that procedures of self-regulated learning (SRL) augment the effects of RT methods, we further assumed that such procedures would promote the quality of students’ collaborative efforts. In a cluster-randomized trial, students in 12 fifth-grade classes practiced a strategic approach to reading either in a RT condition or in a RT + SRL condition. In one of the 14 sessions, students’ interactive behavior was videotaped. Strategy use and reading comprehension were assessed at pretest, posttest, and maintenance. Performance differences between conditions were reliable only at maintenance. A multilevel mediation analysis showed that relative to RT students, RT + SRL students were better able to provide their teammates with informative feedback and organize their group work in a task-focused manner. Only feedback quality mediated the sustainability of treatment effects on strategy use and reading comprehension. In essence, this research suggests that effective reading comprehension trainings should integrate explicit instruction and practice in reading strategies, SRL, and focus on supportive peer processes in small groups with extensive instruction and practice in peer feedback.