A pointer or pointing stick is a solid rod

Switch (rod)

A switch is a flexible rod, typically used for corporal punishment of the birching type, called switching after it, especially when using a single branch: multiple branches are rather called a rod, a less flexible single rod is rather called a cane, an inflexible one a stick; a paddle is broader...

 used to point manually, in the form of a stick, but always finished off or artificially produced.

The typical pointer is simply a long, slender, often flexible stick made in a strong material, designed to indicate places on maps, words on blackboard

Blackboard

A chalkboard is a reusable writing surface.Blackboard may also refer to:* Blackboards are synonymous with "boards of infamy", an element of agitation-propaganda in the Soviet Union in 1930s, coincidental with Holodomor...

s etc.
In addition it may be used like any ordinary stick for other purposes, e.g. for punitive caning

Caning

Caning is a form of corporal punishment consisting of a number of hits with a single cane usually made of rattan, generally applied to the offender's bare or clothed buttocks or hand . Application of a cane to the knuckles or the shoulders has been much less common...

 (compare rulering).

Some are telescopic

Telescoping (mechanics)

Telescoping in mechanics describes the movement of one part sliding out from another, lengthening an object from its rest state. In modern equipment, this is often done by hydraulics....

and can be carried in a pocket like a pen.