Conducting the Jazz Band
The standard conducting patterns were designed to mirror the stress patterns in classic time signatures. In 4/4 time the strongest beat is beat one and is conducted with the strongest movement - the downbeat. Beat three is the next strongest beat and is conducted with the next strongest movement - across the body. Beats two and four are weaker beats and are conducted with weaker movements.
In Jazz, beats two and four are the strongest beats. Therefore, most Jazz Band directors don't use the standard conducting patterns. They generally start the band by snapping their fingers or clapping on beats two and four to set the tempo and counting the measure before the band starts. After the band begins to play, the director steps to the side of the band leaving the responsibility of maintaining a steady tempo, and so forth, to the musicians. He typically steps back in front of the band to adjust the microphone stand for soloists, to conduct fermatas or changes in tempo, and to end the piece.
For me this method of conducting worked well at the high school but not so well at the junior high. The junior high students seemed to play with more confidence when I stayed in front of the band and continued to help with dynamic changes, entrances, and so forth. In addition, our band was much larger than a standard jazz band which made it more difficult for them to stay together without a conductor.