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