It has been called Manichaeism, and there is in much of O'Brien's and Myles's writing a sense of the arcane, a cabalistic insistence on number, knowledge as gnosis, as ritual.
Three 18-session design experiments were conducted, each with 6 9 7th and 8th grade students, to investigate relationships between students' rational number knowledge and algebraic reasoning.
The study examined effects of playing number games (linear number board game, circular number board game, and nonlinear numerical activities) on the development of number knowledge and early arithmetic.
They argued that some of the variations in students' number knowledge of number words and symbols appeared to be associated with "differential exposure to the language and symbol systems of mathematics (p. 64)".
Once a child decides what strategy to use, he or she must then mentally perform the requisite arithmetical operations that follow from the selected strategy, which also rely on number knowledge, such as basic facts and place value [24, 40].
Other areas activated to a greater degree in the children included the left precentral sulcus, which may mediate number knowledge and, for EA, the head of the caudate nucleus, which is part of a fronto-subcortical circuit involved in the behavioral execution of sequences.
