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

A geometry tutor has a particularly difficult job. Whileas well as the volume of certain solids (spheres, cones,
algebra is often said to be the first truly abstractcubes, etc.).
mathematical discipline that most students encounter,Whereas a calculus student could calculate these
geometry (which is usually taught the year aftervalues on the fly by applying the principles of
algebra is taught) requires that the student beginintegration, the average geometry student has not yet
learning to apply the relatively abstract conceptsbeen exposed to calculus and must commit to
learned in algebra to real life problems involving shapesmemory the formulae for all of the shapes and solids.
and volumes.A good idea for the geometry tutor is to use flash
Geometry is a very applied mathematical science and,cards and mnemonics to help the students retain the
as such, any college or university program in themany formulae that they must memorize. Another
natural sciences or engineering will require students tohelpful tip for the geometry tutor is to make sure that
be well versed in geometry as well as its morethey are familiar with the many geometrical proofs that
advanced cousin, trigonometry.the student will have to learn. Geometrical proofs are a
The effective geometry tutor must be able to help thefundamental component of geography, and the
math student bridge the chasm between the abstractgeography teacher should make sure that his or her
and the concrete. Geometry in many ways is astudent has a firm grasp of this important part of the
precursor of trigonometry and calculus in that itstudy of geometry.
requires students to think both in the abstract as wellGeometry is a notoriously difficult subject for some
as the concrete. The effective geometry tutor muststudents to learn since it combines the concrete and
also deal with the fact that students who are studyingthe abstract. It is also very difficult because there is
geometry must use formulae that they are not yetmore memorization involved in geometry than in
able to derive (most of the formulae used in geometryperhaps any other mathematical subject. A good
can only be derived using calculus).geometry tutor will help the student overcome both of
This means that geometry requires much morethese difficulties by focusing on both the concepts as
memorization than any other mathematical discipline,well as the formulae of geometry.
with the possible exception of trigonometry. AAs far as the calculating goes, geometry is no more
fundamental part of learning geometry is committing todifficult than algebra. The hard part for the geometry
memory the formulae for calculating the area oftutor is teaching the student how to learn exactly what
(shapes, square, rectangles, triangles, rhombuses, etc.)should be calculated.