The Shape of Things--The Skills Required to be a Great Geometry Tutor

A geometry tutor has a particularly difficult job. While algebra is often said to be the first truly abstract mathematical discipline that most students encounter, geometry (which is usually taught the year after algebra is taught) requires that the student begin learning to apply the relatively abstract concepts learned in algebra to real life problems involving shapes and volumes.

Geometry is a very applied mathematical science and, as such, any college or university program in the natural sciences or engineering will require students to be well versed in geometry as well as its more advanced cousin, trigonometry.

The effective geometry tutor must be able to help the math student bridge the chasm between the abstract and the concrete. Geometry in many ways is a precursor of trigonometry and calculus in that it requires students to think both in the abstract as well as the concrete. The effective geometry tutor must also deal with the fact that students who are studying geometry must use formulae that they are not yet able to derive (most of the formulae used in geometry can only be derived using calculus).

This means that geometry requires much more memorization than any other mathematical discipline, with the possible exception of trigonometry. A fundamental part of learning geometry is committing to memory the formulae for calculating the area of (shapes, square, rectangles, triangles, rhombuses, etc.) as well as the volume of certain solids (spheres, cones, cubes, etc.).

Whereas a calculus student could calculate these values on the fly by applying the principles of integration, the average geometry student has not yet been exposed to calculus and must commit to memory the formulae for all of the shapes and solids.

A good idea for the geometry tutor is to use flash cards and mnemonics to help the students retain the many formulae that they must memorize. Another helpful tip for the geometry tutor is to make sure that they are familiar with the many geometrical proofs that the student will have to learn. Geometrical proofs are a fundamental component of geography, and the geography teacher should make sure that his or her student has a firm grasp of this important part of the study of geometry.

Geometry is a notoriously difficult subject for some students to learn since it combines the concrete and the abstract. It is also very difficult because there is more memorization involved in geometry than in perhaps any other mathematical subject. A good geometry tutor will help the student overcome both of these difficulties by focusing on both the concepts as well as the formulae of geometry.

As far as the calculating goes, geometry is no more difficult than algebra. The hard part for the geometry tutor is teaching the student how to learn exactly what should be calculated.