Narrative:

Climbing out approximately 2 miles east of ZZZ we received a report of traffic at our 1:00 descending. We did not catch the altitude. Approximately 30 seconds later a second call stating 'traffic at your 1:00 one mile; descending through 8;400 ft.' at that moment I was also at 8;400 ft and could not see the [aircraft] likely due to the cowling blocking the view in my climbing attitude. I decided to make my climb more aggressive however approximately 5 seconds after the towers call; my friend and flight instructor saw the traffic inbound near our altitude [so he] pulled the yoke all the way back until [we received a] stall warning. [The aircraft] passed beneath us. I believe ATC began to ask for evasive maneuvers however the traffic had already passed and was no factor. ATC was behind the curve. Evasive maneuvers should have been asked for earlier.

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Original NASA ASRS Text

Title: A flight instructor and student pilot were advised by Air Traffic Control of another aircraft in their vicinity; but they were unable to acquire the traffic visually. While they were still climbing; and looking for the traffic; they were advised that the aircraft was descending through their altitude and within one mile. They pitched up aggressively and spotted traffic pass just beneath them.

Narrative: Climbing out approximately 2 miles east of ZZZ we received a report of traffic at our 1:00 descending. We did not catch the altitude. Approximately 30 seconds later a second call stating 'Traffic at your 1:00 one mile; descending through 8;400 FT.' At that moment I was also at 8;400 FT and could not see the [aircraft] likely due to the cowling blocking the view in my climbing attitude. I decided to make my climb more aggressive however approximately 5 seconds after the Towers call; my friend and flight instructor saw the traffic inbound near our altitude [so he] pulled the yoke all the way back until [we received a] stall warning. [The aircraft] passed beneath us. I believe ATC began to ask for evasive maneuvers however the traffic had already passed and was no factor. ATC was behind the curve. Evasive maneuvers should have been asked for earlier.

Data retrieved from NASA's ASRS site as of July 2013 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.