Students try to use what they already know to make sense of new mathematical concepts. A good teacher makes these connections explicit, determining what their students already know and helping students see how the new concept is related to that knowledge.
For example, students may understand area as the number of squares required to cover a region or figure and understand perimeter as the length of string required to surround the region. A teacher can approach the concept of volume as a natural extension of the concept of area; it is the number of cubes required to fill an object or open figure such as an open box. Similarly, surface area is the three-dimensional equivalent of the two-dimensional concept of perimeter; it is the amount of material needed to surround the object. Students will remember and have a stronger conceptual understanding because the teacher built on prior knowledge.
A teacher can make this connection even stronger by using objects that students are familiar with (such as a cereal box) and by introducing the concepts as part of a problem ("How much cereal will fit in the box and how much paper is needed to cover the cardboard?"). Because it is difficult to transfer knowledge from one discipline to another, students should be given practice in applying mathematical knowledge to other disciplines. This will also motivate the need for learning mathematics.
Integrating mathematics and science or mathematics and art instruction is an excellent way to facilitate teaching in context. Small group work that asks students to investigate a concept or explore possible solutions to a problem encourages them to discuss what they already know and communicate mathematically how this knowledge could be applied in a new situation. Clustering ideas is another way of helping students see connections within mathematics.
