Can bitcoins be traced by pool workers? A lot of people doing bitcoin mining participate in pooled mining. When participating in pooled mining the workers perform some mathematical calculation (that I have actually not understood) and are rewarded payouts for their contribute to new block generation.

Is it possible that the workers, minining in a pool, can find out which bitcoin they are working on? If yes, I think they would be able to see to whome the bitcoin they worked on was transferred later to?
When a miner in a pool finds a valid block, the pool receives a reward (currently ~50 BTC) in a special generation transaction in the block. The address receiving the generation reward in a given block is known, and pools publish statistics on which blocks they found (and even if not, the miner who found it can in theory know which blocks he himself found if his mining software keeps a record of it), so the generation rewards can be tracked (to the same extent that any other Bitcoin transaction can be tracked).

The mathematical operation done when mining is calculating SHA-256 hashes of variants of a block header. You can learn more about mining for example at What exactly is mining?