Quasigroup

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative.

A quasigroup with an identity element is called a loop.

Definitions

There are at least two equivalent formal definitions of quasigroup. One defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. We begin with the first definition.

A quasigroup (Q, ∗) is a set, Q, with a binary operation, ∗, (that is, a magma), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that both

hold. (In other words: Each element of the set occurs exactly once in each row and exactly once in each column of the quasigroup's multiplication table, or Cayley table. This property ensures that the Cayley table of a finite quasigroup is a Latin square.)

Loop (knot)

In reference to knots, loop may refer to:

References

Loop (education)

Looping, in education, refers to the practice of a teacher remaining with the same group of students for more than one school year. For example, a teacher who teaches a third grade class and then goes on to teach the same students, the following year, for the fourth grade.

This is distinct from the teacher of a multi-age class, who teaches a specific range of school grades together. In this case, although each child remains with the same teacher for multiple years, the group of students being taught changes annually as older children leave the group and are replaced by younger students entering.

Looping is usual in Waldorf education, where the traditional goal has been for a primary teacher to remain as the lead teacher of a class for eight consecutive years, though in conjunction with numerous specialized teachers; over the last decades, many schools have been reducing the loop to a shorter interval.

Benefits

Educational advantages to having a single teacher have been found, including: