Car sometimes starts in third gear not first gear?

At a stop sign, on three different occasions, I shifted into the first gear "slot", but the car was in third gear. Other times in between it would shift normal meaning the first gear slot was first gear, second gear slot was second, etc.
But on three different occasions that night after coming to a stop, despite putting the stick all the way to the left where first gear would normally be found, the engine was in third gear.
After slowly accelerating to a normal third gear speed, I could slow down, and downshift without problems all the way down to first gear. And again, it would shift normally for a time. My mechanic says I need a whole new transmission, but I am skeptical.