Arithmetic Research Papers - Academia.edu (original) (raw)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an... more

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic.

Abstract-We describe a sequential universal data compression procedure for binary tree sources that performs the “double mixture.” Using a context tree, this method weights in an ef-ficient recursive way the coding distributions... more

Abstract-We describe a sequential universal data compression procedure for binary tree sources that performs the “double mixture.” Using a context tree, this method weights in an ef-ficient recursive way the coding distributions corresponding to all bounded memory tree sources, and ...

Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade = 82 months), children with IQ scores in the low-average to high-average range were classified as learning... more

Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade = 82 months), children with IQ scores in the low-average to high-average range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n = 42), a group of children who showed variable achievement test performance across grades (n = 16), and a control group of academically normal peers (n = 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children.

Groups of first-grade (mean age=82 months), third-grade (mean age=107 months), and fifth-grade (mean age=131 months) children with a learning disability in mathematics (MD, n=58) and their normally achieving peers (n=91) were administered... more

Groups of first-grade (mean age=82 months), third-grade (mean age=107 months), and fifth-grade (mean age=131 months) children with a learning disability in mathematics (MD, n=58) and their normally achieving peers (n=91) were administered tasks that assessed their knowledge of counting principles, working memory, and the strategies used to solve simple (4 + 3) and complex (16 + 8) addition problems. In all grades, the children with MD showed a working memory deficit, and in first grade, the children with MD used less sophisticated strategies and committed more errors while solving simple and complex addition problems. The group differences in strategy usage and accuracy were related, in part, to the group difference in working memory and to group and individual differences in counting knowledge. Across grade-level and group, the switch from simple to complex addition problems resulted in a shift in the mix of problem-solving strategies. Individual differences in the strategy mix and in the strategy shift were related, in part, to individual differences in working memory capacity and counting knowledge.

The fusion tree method is extended to develop a linear-time algorithm for the minimum spanning tree problem and an O(m +n log n/log log n) implementation of Dijkstra's shortest-path algorithm for a graph with n vertices and m edges. The... more

The fusion tree method is extended to develop a linear-time algorithm for the minimum spanning tree problem and an O(m +n log n/log log n) implementation of Dijkstra's shortest-path algorithm for a graph with n vertices and m edges. The shortest-path algorithm surpasses information-theoretic limitations. The extension of the fusion tree method involves the development of a new data structure, the atomic heap. The atomic heap accommodates heap (priority queue) operations in constant amortized time under suitable polylog restrictions on the heap size. The linear-time minimum spanning tree algorithm results from a direct application of the atomic heap. To obtain the shortest path algorithm, the atomic heap is used as a building block to construct a new data structure, the AF-heap, which has no size restrictions and surpasses information theoretic limitations. The AF-heap belongs to the Fibonacci heap family

SPASS is an automated theorem prover for full first-order logic with equality and a number of non-classical logics. This system description provides an overview of our recent developments in SPASS 3.5 including subterm contextual... more

SPASS is an automated theorem prover for full first-order logic with equality and a number of non-classical logics. This system description provides an overview of our recent developments in SPASS 3.5 including subterm contextual rewriting, improved split backtracking, a significantly faster FLOTTER implementation with additional control flags, completely symmetric implementation of forward and backward redundancy criteria, faster parsing with improved support for big files, faster and extended sort module, and support for include commands in input files. Finally, SPASS 3.5 can now parse files in TPTP syntax, comes with a new converter tptp2dfg and is distributed under a BSD style license.

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations,... more

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished learning opportunities. The consequences of poor mathematics achievement are serious for daily functioning and for career advancement. This article provides an overview of children's mathematics difficulties in relation to socioeconomic status (SES). We review foundations for early mathematics learning and key characteristics of mathematics learning difficulties. A particular focus is the delays or deficiencies in number competencies exhibited by low-income children entering school. Weaknesses in number competence can be reliably identified in early childhood, and there is good evidence that most children have the capacity to develop number c...

DOI: 10.1177/073724770503000202 2005; 30; 3 Assessment for Effective Intervention David J. Chard, Ben Clarke, Scott Baker, Janet Otterstedt, Drew Braun and Rachell Katz Preliminary Findings Using Measures of Number Sense to Screen for... more

DOI: 10.1177/073724770503000202 2005; 30; 3 Assessment for Effective Intervention David J. Chard, Ben Clarke, Scott Baker, Janet Otterstedt, Drew Braun and Rachell Katz Preliminary Findings Using Measures of Number Sense to Screen for Difficulties in Mathematics: