Article

A chronometric analysis of simple addition.

Psychological Review (Impact Factor: 9.8). 06/1972; 79(4):329-343. DOI: 10.1037/h0032950

ABSTRACT Considers a number of models that specify how children and adults solve single-digit addition problems. It is shown that the most adequate of these for children's response latencies is a model that assumes the existence of a counter with 2 operations: setting and incrementing. The child adds 2 digits, m and n, by setting this counter to max (m,n) and then incrementing it min (m,n) times. This model also accounts for adults' latencies, though with a drastically reduced incrementing time. Some theoretical issues raised by this reduced time are considered, and an alternative model is suggested which assumes that adults usually use a memory look-up process with homogeneous retrieval times, but occasionally revert back to the counting process used by children. (2l ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)

0 Bookmarks
 · 
71 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Recent evidence led to the conclusion that addition problems are biased towards overestimation, regardless of whether information is conveyed by symbolic or non-symbolic stimuli (the Operational Momentum effect). The present study focuses on the role of operands in the overestimation of addition problems. Based on the tie effect, and on recent evidence that the nature of operands biases addition problems towards an underestimation when operands are repeated, but towards an overestimation when different, we aim here to further elucidate the contribution of operands to addition problems. Experiment 1 replicates the underestimation of repeated-operand additions and overestimation of different-operand additions, with large numbers (around 50), and explores whether these effects also apply to small operand additions (around 10). Experiment 2 further explores the overestimation of different-operand additions by investigating the roles of operand order and numerical distance between operands. The results show that both factors have an impact on the overestimation size, but are not crucial for overestimation to occur. The results are discussed in terms of arithmetic strategies, spatial organization of numbers and magnitude representation.
    Psychological Research 04/2013; · 2.47 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A focus on mathematical understanding and problem solving in math education has developed a need to implement alternate ways of testing to better assess the students' understanding and problem solving kills. Furthermore, previous computer-assisted problem-solving systems designed for elementary school mathematical education have focused mainly on developing students’ cognitive skills and less interest is dedicated to related procedural skills. However, procedural and conceptual knowledge are highly correlated. This study proposes a computer-assisted system, whose design is based on Polya’s problem-solving model. The system is designed to help low-achieving second graders in mathematics with word-based addition and subtraction questions. The emphasis of using the specific model was on dividing the problem solving procedure into stages and the concentration on the students’ cognitive and procedural processes at each stage. In order to help students overcome procedural obstacles, we developed an agent oriented evaluation so as to give them a meaningful feedback to better monitor and support students learning performance.
    Interactive Environments and Emerging Technologies for eLearning 2013, IEETeL 2013 Utrecht, Utrecht, The Netherlands; 06/2013
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Trends in Neuroscience and Education,1-10. doi:10.1016/j.tine.2013.01.001
    Trends in Neuroscience and Education. 12/2012;