The mathematical underpinnings range from low-level tasks such as the identification of properties,to medium-level tasks such as the explanation of the significance of a property,to high-level tasks such as proof-writing. It is still the case today that many mathematicians will say that a person does not really understand arithmetic until he or she knows the mathematical underpinnings behind it. many if not most conrses for elementary school mathematics teachers are taught to convey this aspect of understanding.little more is done.