Date: 202101
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Weather elements / visibility: 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Other Flight School
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Takeoff / Launch
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Reporter organization: Other Flight School
Reporter function: Instructor
Reporter qualification: Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Human factors: Fatigue; Situational Awareness; Training / Qualification; Confusion
Second reporter function: Pilot Flying; Trainee
Anomaly: Deviation / Discrepancy - Procedural Clearance; Ground Incursion Taxiway
Detector: Person Air Traffic Control
When detected: Taxi
Result: Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: I was soloing a new student pilot at ZZZ. After completing several warm-up laps in the pattern dual; I informed Tower that my student was about to solo and had my student drop me off in the non-movement area of the east ramp. On my student's first attempt at a landing; he flared high and initiated a go-around. On his second attempt he landed; stopped; and then initiated a takeoff roll. I realized that my student had mistaken the command 'Cleared to Land' for 'Cleared Stop-And-Go.' I used a handheld radio to call out my student by name and told him to discontinue the takeoff. He stopped on the runway; and he was switched to Ground for taxi instructions. I asked Ground to instruct my student to return to my location and discontinue the flight. While taxiing back to my location on south end of the east ramp; my student missed a left turn from A to F; stopped; and was directed by Ground to complete a 180 turn and return to his original taxi instructions. If had continued forward there was the possibility of crossing Runway XX-XY and committing a runway incursion.There were several contributing factors to both of these new runway incursions/violations.1) My student's confusion about ATC clearances. We had previously been issued 'stop-and-go' and 'cleared to land' clearances earlier that morning; but I did not confirm that my student understood the difference.2) Poor Aeronautical Decision-Making: My student informed me after the flight that he had only slept four hours the night before. I believe this contributed to both errors he made during his solo.3) Unfamiliarity/Lack of Training on Towered Airport Operations: We had one previous flight at ZZZ; but it did not involve extensive taxi instructions or various ATC clearances. Even that morning my student had the same repetitive taxi clearance after each of our landings completed together.Corrective Actions (To be completed with this student and future students).1) My student and I are going to have an extensive ground covering various ATC clearances; communication procedures; and possible taxi instructions at unfamiliar airports. I will require my student to complete a FAASafety.gov course on runway incursions.2) While I have my students use an ADM (Aeronautical Decision Making) checklist before each flight; I will audibly confirm the 'IMSAFE' checklist is complete before each flight.3) We will conduct another dual flight or two and ask for various different taxi instructions to diversify my student's experience.


Second narrative: I made a call on the downwind 'Full Stop Touch and Go' and was cleared for landing. Did not correctly understand that Cleared For Landing does not allow for 'Touch and Go' unless given that prompt. Also missed a taxi-way.Not properly understanding 'Cleared for Landing' in full. After given Instructor not to take off; I missed my taxi-way; thus entering a different taxiway from Instructor. Unfamiliar with map + going too fast; missed the taxiway. Ultimately; challenged with receiving tower communications at their rate of communications.My Instructor realized I was not stopping and told me to not take off. I saw that I was about to cross a runway and realized I was missing something. I realized it and then was given Instructor to 180. My Instructor told me to not take off so I didn't take off. We exited the lesson and went back to our home airport. Need to slow down on taxiways. Mostly just incorrect decisions on incorrect understanding of definition 'cleared to land'. Will role-play / simulate communications and different scenarios to ensure I'm understanding and communicating properly with the tower.


Synopsis: C172 Flight Instructor reported students confusion with ATC instructions on initial solo flight.