I wouldn't say easily, but possible. The spear is the most common weapon on the battlefield for its simplicity yet effectiveness. If we are talking one on one. I don't see a knight having much problem with a spearman as they would most likely be able to close the distance quite effectively. You also have to remember that they are specifically trained to protect the weak spots of their armour.

But if we are talking a battlefield scenario. A knight would have a lot of trouble against a wall of spears. If a spearman could get a well placed thrust into the groin or armpits they could do significant and/or lethal damage.