Page 14 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 1
specific roles of child and teacher factors in children’s mathematical development and to examine the extent to which dynamic math interviews facilitate the identification of math learning needs and promote teachers’ mathematics teaching and children’s mathematics learning.
Mathematical development
In the early years of elementary school, children develop an understanding of numbers, counting, and simple arithmetic (Geary, 2004). Children learn different solution methods, such as use of doubles, splitting, and deriving an answer from a known number combination. Considerable attention is paid to basic arithmetical skills and, over the years, accuracy improves and calculation processes speed up (Ostad, 2000). From about fourth grade (children aged 8-10 years), the transition is made to new domains of mathematics with increasingly abstract and complex problems (Geary, 2011).
Mathematics in elementary school involves various domains — such as number, number sense, operations, measurement, and ratios, which all require a conceptual understanding, procedural knowledge, and factual knowledge (National Research Council, 2001). Two particularly relevant aspects of mathematical development are arithmetic fluency and mathematical problem-solving (Fuchs et al., 2008).
Children are arithmetically fluent when they are able to add, subtract, multiply, and divide both quickly and accurately. And arithmetic fluency has been found to be essential for overall mathematics achievement (Fuchs et al., 2006). To become arithmetically fluent, conceptual understanding in combination with selection and application of appropriate strategies and extended practice is needed. In grade 4, it is to be expected that most children are arithmetically fluent.
Mathematical problem-solving is the ability to apply mathematical knowledge and skills to solve actual real-world or hypothetical problems using mathematical notation, text, and/or pictures (Polya, 1957). Mathematical problem-solving promotes analytical thinking and mathematical reasoning, which are skills that are obviously useful in later life and therefore required learning at school (Gravemeijer et al., 2017).