264 research outputs found
Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge
While preschool-aged children display some skills with quantitative relations, later learning of related fraction concepts is difficult for many students. We present two studies that investigate young children's tendency of Spontaneous Focusing On quantitative Relations (SFOR), which may help explain individual differences in the development of fraction knowledge. In the first study, a cross-sectional sample of 84 kindergarteners to third graders completed tasks measuring their spontaneous recognition and use of quantitative relations and then completed the tasks again with explicit guidance to focus on quantitative relations. Findings suggest that SFOR is a measure of the spontaneous focusing of attention on quantitative relations and the use of these relations in reasoning. In the second (longitudinal) study, 25 first graders completed measures of SFOR tendency and a measure of fraction knowledge three years later. SFOR tendency was found to predict fraction knowledge, suggesting that it plays a role in the development of fraction knowledge.</p
Preschool spontaneous focusing on numerosity predicts rational number conceptual knowledge 6 years later
Recent evidence suggests that early natural number knowledge is a predictor of later rational number conceptual knowledge, even though students’ difficulties with rational numbers have also been explained by the overuse of natural number concepts—often referred to as the natural number bias. Hannula and Lehtinen (Learn Instr 15:237–256, 2005) have shown that children’s tendency to spontaneously focus on numerosity (SFON) predicts the development of natural number and arithmetic skills. The present study follows 36 children from the age of 6 years to the age of 12 years in order to determine how preschool SFON tendency and number sequence skills are related to rational number conceptual knowledge at the age of 12 years. The results show that children’s SFON tendency before school age is a strong predictor of later
rational numbers conceptual knowledge, even after controlling for preschool number sequence skills. This finding has implications for the understanding of how the transition from reasoning about natural number concepts to reasoning about rational numbers may be influenced by children’s self-initiated practice with numbers in everyday situations.</p
Spontaneous mathematical focusing tendencies in mathematical development
Children's own spontaneous mathematical activities are crucial for their mathematical development. Mathematical thinking and learning does not only occur in explicitly mathematical situations, such as the classroom. Those children with higher tendencies to recognize and use mathematical aspects of their everyday surroundings, both within the classroom and without, appear to have an advantage in learning formal mathematical skills and knowledge. In this introduction to the special issue, we provide an overview of the existing literature on spontaneous mathematical focusing tendencies. We then provide a brief overview of the contributions to the special issue
Young children’s recognition of quantitative relations in mathematically unspecified settings
Children have been found to be able to reason about quantitative relations, such as non- symbolic proportions, already by the age of 5 years. However, these studies utilize settings in which children were explicitly guided to notice the mathematical nature of the tasks. This study investigates children’s spontaneous recognition of quantitative relations on mathe- matically unspecified settings. Participants were 86 Finnish-speaking children, ages 5–8. Two video-recorded tasks, in which participants were not guided to notice the mathe- matical aspects, were used. The tasks could be completed in a number of ways, including by matching quantitative relations, numerosity, or other aspects. Participants’ matching strategies were analyzed with regard to the most mathematically advanced level utilized. There were substantial differences in participants’ use of quantitative relations, numerosity and other aspects in their matching strategies. The results of this novel experimental set- ting show that investigating children’s spontaneous recognition of quantitative relations provides novel insight into children’s mathematical thinking and furthers the understand- ing of how children recognize and utilize mathematical aspects when not explicitly guided to do so.</p
Maternal sensitivity in responding during play and children’s pre-mathematical skills: a longitudinal study from infancy to preschool age
This longitudinal study explored how mothers’ sensitivity in responding to their child’s cognitive and emotional needs in infancy and toddlerhood predicts children’s pre-mathematical skills at early preschool age. The sample consisted of 65 mother-child dyads (N = 130 individuals) videotaped during joint play at ages 1;0 and 2;0. The children’s pre-mathematical skills were tested at age 3;0. The path analyses showed that, in infancy, mothers’ autonomy support and scaffolding are more strongly related than emotional support to children’s later performance on spatial and numerical tasks. The findings are discussed in relation to how maternal sensitivity in responding fosters children’s pre-mathematical development in an optimal way.</p
Spontaneous focusing on quantitative relations as a predictor of rational number and algebra knowledge
Spontaneous Focusing On quantitative Relations (SFOR) has been found to predict the development of rational number conceptual knowledge in primary students. Additionally, rational number knowledge has been shown to be related to later algebra knowledge. However, it is not yet clear: (a) the relative consistency of SFOR across multiple measurement points, (b) how SFOR tendency and rational number knowledge are inter-related across multiple time points, and (c) if SFOR tendency also predicts algebra knowledge. A sample of 140 third to fifth graders were followed over a four-year period and completed measures of SFOR tendency, rational number conceptual knowledge, and algebra knowledge. Results revealed that the SFOR was relatively consistent over a one-year period, suggesting that SFOR is not entirely context-dependent, but a more generalizable tendency. SFOR tendency was in a reciprocal relation with rational number conceptual knowledge, each being uniquely predictive of the other over a four-year period. Finally, SFOR tendency predicted algebra knowledge three-years later, even after taking into account non-verbal intelligence and rational number knowledge. The results of the present study provide further evidence that individual differences in SFOR tendency may have an important role in the development of mathematical knowledge, including rational numbers and algebra.</p
Recommended from our members
Creative professional users musical relevance criteria
Although known item searching for music can be dealt with by searching metadata using existing text search techniques, human subjectivity and variability within the music itself make it very difficult to search for unknown items. This paper examines these problems within the context of text retrieval and music information retrieval. The focus is on ascertaining a relationship between music relevance criteria and those relating to relevance judgements in text retrieval. A data-rich collection of relevance judgements by creative professionals searching for unknown musical items to accompany moving images using real world queries is analysed. The participants in our observations are found to take a socio-cognitive approach and use a range of content and context based criteria. These criteria correlate strongly with those arising from previous text retrieval studies despite the many differences between music and text in their actual content
Spontaneous focusing on quantitative relations as a predictor of the development of rational number conceptual knowledge
Many people have serious difficulties in understanding rational numbers, limiting their ability to interpret and make use of them in modern daily life. This also leads to later difficulties in learning more advanced mathematical content. In this study, novel tasks are used to measure 263 late primary school students’ spontaneous focusing on quantitative relations, in situations that are not explicitly mathematical. Even after controlling for a number of known predictors of rational number knowledge, spontaneous focusing on quantitative relations is found to have a strong impact on students’ learning of rational number conceptual knowledge. This finding opens new possibilities for developing pedagogical solutions to one of the most difficult challenges of mathematics education. The findings suggest that students’ own focusing tendency and self-initiated practice may have on important role in the long-term development of complex cognitive skills.</p
Does document relevance affect the searcher's perception 0f time?
Time plays an essential role in multiple areas of Information Retrieval (IR) studies such as search evaluation, user behavior analysis, temporal search result ranking and query understanding. Especially, in search evaluation studies, time is usually adopted as a measure to quantify users' efforts in search processes. Psychological studies have reported that the time perception of human beings can be affected by many stimuli, such as attention and motivation, which are closely related to many cognitive factors in search. Considering the fact that users' search experiences are affected by their subjective feelings of time, rather than the objective time measured by timing devices, it is necessary to look into the different factors that have impacts on search users' perception of time. In this work, we make a first step towards revealing the time perception mechanism of search users with the following contributions: (1) We establish an experimental research framework to measure the subjective perception of time while reading documents in search scenario, which originates from but is also different from traditional time perception measurements in psychological studies. (2) With the framework, we show that while users are reading result documents, document relevance has small yet visible effect on search users' perception of time. By further examining the impact of other factors, we demonstrate that the effect on relevant documents can also be influenced by individuals and tasks. (3) We conduct a preliminary experiment in which the difference between perceived time and dwell time is taken into consideration in a search evaluation task. We found that the revised framework achieved a better correlation with users' satisfaction feedbacks. This work may help us better understand the time perception mechanism of search users and provide insights in how to better incorporate time factor in search evaluation studies
- …