Page 38 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews
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Chapter 2
math self-efficacy, and math anxiety of fourth grade children and 2) the actual mathematics teaching behavior, mathematical knowledge for teaching, and mathematics teaching self-efficacy of their teachers.
Mathematical development
During early elementary school, children are expected to develop an understanding of numbers, counting, and simple arithmetic (Geary, 2003). With increasing arithmetic speed and accuracy, a solid foundation is assumed to be laid for the development of more advanced mathematical problem-solving abilities (Gersten et al., 2005). Geary (2004) has provided a theoretical framework in which mathematical development is assumed to relate to the combined functioning of the visuospatial and language systems, the central executive functioning of the brain, conceptual development, and procedural knowledge (e.g., knowledge of rules and algorithms). Knowledge of basic arithmetic combinations is stored in long-term memory and easily retrieved for the solution of mathematical problems using short-term memory information (Baddeley, 2000). The development of arithmetic fluency and mathematical problem-solving can thus be seen as distinct aspects of children’s mathematical development (Fuchs et al., 2008).
Arithmetic fluency is the ability to add, subtract, multiply, and divide with basic number combinations accurately and quickly. The development of arithmetic fluency starts with the onset of formal mathematical education. As part of early elementary education (children aged 6-8 years), considerable attention is paid to the promotion of arithmetic knowledge and fluency. The speed and accuracy of children’s performance on arithmetic fact problems increases between the first and seventh grades (Ostad, 2000) with attention and processing speed identified as key factors (Fuchs et al., 2008). And the later mathematical development of children who have difficulties retrieving basic arithmetic facts from long-term memory has been shown to be hampered (Duncan et al., 2007; Geary, 2004; Geary & Hoard, 2005).
Mathematical problem-solving can be defined as the ability to apply mathematical knowledge and skills to solve actual or imagined “real life” imaginable problems using mathematical notation, text, and/or
 



























































































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