p> Montague considers the cognitive characteristics of children in deciding how they learn and so how they may be taught. Children use their natural mathematical abilities to begin acquiring mathematical concepts early through observation and spontaneous interactions with the environment. They then gain declarative or factual knowledge, through both informal and formal learning experiences, and use this declarative knowledge as they learn algorithms and become proficient in computational procedures. As children experience more, they draw on their cumulative conceptual, declarative, and procedural knowledge to construct a fourth type of knowledge, strategic knowledge, which is demonstrated by an individual's ability to describe or apply mnemonic or problem solving strategies that are either domain specific or universal in nature.
Strategic knowledge is crucial to proficient problem solving and is acquired naturally by most children as they are exposed to problem solving. Montague says that children only need the opportunity to solve problems and so
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