Search results for "arithmetic"

Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge

2013

Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are …

Naming speed and Effortful and Automatic Inhibition in Children with Arithmetic Learning Disabilities

2009

Abstract We report a two-year longitudinal study aimed at investigating the rate of access to numerical and non-numerical information in long-term memory and the functioning of automatic and effortful cognitive inhibition processes in children with arithmetical learning disabilities (ALDs). Twelve children with ALDs, of age 9.3 years, and twelve gender–age-matched controls were involved in the study. Rate of access was measured through digit- and letter-naming tasks, automatic cognitive inhibition was measured using a negative priming paradigm, and effortful cognitive inhibition was measured rating intrusion errors in a working memory task. Children with ALDs suffered from a deficit in the …

Adult counting is resource demanding.

2004

Several recent studies on both the development of counting and working-memory span tasks have provided results that could be interpreted as ruling out any cognitive resource model for counting. The aim of this study was to test the hypothesis that, even in adults, counting is a demanding task that requires the allocation of cognitive resources. In a first experiment, we asked adults to count arrays of dots while maintaining 5 items in memory (either digits or letters). As we predicted, the concurrent memory load did not increase the rate of errors but induced longer counting times. In a second experiment, we asked adults to count using either the numeric chain or the alphabet while they mai…

Training of Attention in Children With Low Arithmetical Achievement

2014

This study focuses on the role of attentional processes in arithmetical skills and examines if training of basic attentive skills may improve also working memory abilities reducing arithmetic difficulties. In order to study the efficacy of attentional treatment in arithmetic achievement and in enhancing working memory abilities a test-treatment-retest quasi experimental design was adopted. The research involved 14 children, attending fourth and fifth grades, with Arithmetical Learning Disabilities (ALD) assigned to experimental and control conditions. The numerical comprehension and calculation processes were assessed using the ABCA battery (Lucangeli, Tressoldi, & Fiore, 1998). Attenti…

Block Sorting-Based Transformations on Words: Beyond the Magic BWT

2018

The Burrows-Wheeler Transform (BWT) is a word transformation introduced in 1994 for Data Compression and later results have contributed to make it a fundamental tool for the design of self-indexing compressed data structures. The Alternating Burrows-Wheeler Transform (ABWT) is a more recent transformation, studied in the context of Combinatorics on Words, that works in a similar way, using an alternating lexicographical order instead of the usual one. In this paper we study a more general class of block sorting-based transformations. The transformations in this new class prove to be interesting combinatorial tools that offer new research perspectives. In particular, we show that all the tra…

The linear diophantine problem of Frobenius for subsets of arithmetic sequences

1997

Let A k = {a 1,. . . , a k } $ \subset \Bbb N $ with gcd (a 1,. . . , a k ) = 1. We shall say that a natural number n has a representation by a 1,. . . , a k if $ n =\sum \limits_{i=1}^{k}a_ix_i,\; x_i\in \Bbb N_0 $ . Let g = g (A k ) be the largest integer with no such representation. We then study the set A k = {a,ha + d,ha + 2d,..., ha + (k - 1) d} h,d > 0, gcd (a,d) = 1). If l k denotes the greatest number of elements which can be omitted without altering g (A k ), we show that ¶¶ $ 1-{4 \over \sqrt k} \le {l_k\over k} \le 1 - {3\over k}, $ ¶¶ provided a > k, or a = k with $ d \ge 2 h \sqrt {k} $ . The lower bound can be improved to 1 - 4 / k if we choose a > (k - 4) k + 3. Moreover, we…

A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics

2011

International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…

2018

Early number skills underlie success in basic arithmetic. However, very little is known about the skill profiles among children in preprimary education and how the potential profiles are related to arithmetic development. This longitudinal study of 440 Finnish children in preprimary education (mean age 75 months) modeled latent performance-level profile groups for the early number skill components that are proposed to be key predictors of arithmetic (symbolic number comparison, mapping, and verbal counting skills). Based on three assessment time points (September, January, and May), four profile groups were found: the poorest-performing (6%), low-performing (16%), near-average-performing (3…

Responsive home numeracy as children progress from kindergarten through Grade 1

2020

The aim of the present study was to investigate longitudinal associations between formal home numeracy activities and children’s arithmetic fluency skills. Children were followed during the transition from the end of kindergarten (T1; Mage = 6.87 years) to the beginning of Grade 1 (T2), and again at the end of the Grade 1 (T3). Participants were Lithuanian children (n = 341) and their parents. At each time point, parents reported the frequency of the formal home numeracy activities they engaged in with their children; the children completed addition and subtraction tasks at the same three time points. Using a cross-lagged analysis, we found that parents adjusted the frequency of their home …

A question in the theory of saturated formations of finite soluble groups

1993

This paper examines the following question. If\(\mathcal{H}\) and\(\mathcal{F}\) are saturated formations then\(\mathcal{H}_\mathcal{F} \) is defined to be the class of all soluble groups whose\(\mathcal{H} - normalizers\) belong to\(\mathcal{F}\). In general\(\mathcal{H}_\mathcal{F} \) is a formation, but need not be a saturated formation. Here the smallest saturated formation containing\(\mathcal{H}_\mathcal{F} \) is studied.