8ccb22b7_Math_Maturity___IAE_Pedia__Math_Cognitive_Developments
[Stage & Name] Level 3. Piagetian and Math concrete operations. Age 7 to 11. [Math Cognitive Developments] 
During the concrete operations stage, children begin to think logically. This stage is characterized by 7 types of conservation: number, length, liquid, mass, weight, area, and volume. Intelligence is demonstrated through logical and systematic manipulation of symbols related to concrete objects. Operational thinking develops (mental actions that are reversible). While concrete objects are an important aspect of learning during this stage, children also begin to learn from words, language, and pictures/video, learning about objects that are not concretely available to them. For the average child, the time span of concrete operations is approximately the time span of elementary school (grades 1-5 or 1-6). During this time, learning math is somewhat linked to having previously developed some knowledge of math words (such as counting numbers) and concepts. However, the level of abstraction in the written and oral math language quickly surpasses a student’s previous math experience. That is, math learning tends to proceed in an environment in which the new content materials and ideas are not strongly rooted in verbal, concrete, mental images and understanding of somewhat similar ideas that have already been acquired. There is a substantial difference between (1) developing general ideas and understanding of conservation of number, length, liquid, mass, weight, area, and volume, and (2) learning the mathematics that corresponds to these concepts. These tend to be relatively deep and abstract topics, although they can be taught in very concrete manners.
Math Maturity - IAE-Pedia
Math Cognitive Developments