"The bear is playing."
Translation:Der Bär spielt.
The best translation is "Der Bär spielt." "Der Bär ist am Spielen.", while literally correct too (see below), is uncommon and its usage dependent on context.
"Der Bär ist am Spielen." literally is "The bear is at the playing", meaning the bear is in the course of playing, or the bear is at play right now.
The verb has to be spelled with a capitel S as it is a verb turned into a noun by adding a neutral article ("am" is a contraction of "an dem" - dem is the 3rd case of das). You can do this with every German verb , e.g. spielen (to play) - das Spielen (the playing, the act of playing) gehen (to walk) - das Gehen (the walking, the act of walking) waschen (to wash) - das Waschen (the washing, the act of washing) etc.
Das Spielen war toll. - The playing was great. Das Gehen war schwierig. - The walking was difficult.