B737-700
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 206
Situational Awareness; Distraction
Deviation - Speed All Types; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Became Reoriented
Human Factors
While in the climb regime; we were initially in VNAV mode at FL380. We experienced some turbulence; therefore; I; being the Pilot Flying; changed the mode to Vertical Speed (VS) to increase the pitch in hopes of leaving the rough air. During the climb in VS mode; I diverted my attention to the pages regarding SJC; since I'd never been there. At the same time; the First Officer was inputting [computer] data. In other words; neither pilot was monitoring the aircraft's operation. The airspeed decelerated to just above the amber airspeed warning. I immediately changed the VS pitch to much lower angle by disconnecting the autopilot; leveling the pitch attitude and even descended from the climb through the horizon to a momentary descent to increase airspeed.  No alert or warning was experienced and no inquiry from ATC. The remainder of the flight was non-eventful.In order to prevent this situation from occurring in the future; I believe one pilot should have the responsibility of monitoring the aircraft at all times while the other pilot is involved in any duties outside of flying the aircraft. Neither pilot should ever be performing non-flying [or] administrative actions at the same time. The aircrew should voice the transfer of control prior to performing any non-flying actions.  Also; I suggest the VS mode of accelerating or decelerating should be the LAST mode selected since it provides no protection of pitch control.
A B737-700 Captain reported noticing aircraft speed had slowed to just above the airspeed warning area during climb in Vertical Speed mode at FL380 when the flight crew was distracted.