Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance
Human Factors; Procedure
Climbing out of EWR on a heading of roughly 300 and around 10;000ft we were given instructions that I heard as 'climb to 13;000 and fly heading'. We continued the climb to 13;000 and started a left turn to 230. Shortly thereafter the controller says it should be a RIGHT turn to 320. I apologized and said I must have reversed the numbers but we would correct it and start turning back. He was polite and said something like 'Oh maybe I gave you the wrong heading'. We had maybe turned half way to the incorrect heading.
Pilot reported flying towards an assigned heading only to be promptly queried and redirected by ATC.