Kate,
Do you ride with a heart rate monitor? It's pretty important to climb within your ability, at a heart rate you can susatain. If you go anaerobic, i.e. near your max heart rate, your lungs will fee like they're coming out of your chest, your eyes will cross and you'll have to slow down and "give up," but probably not stop.
I've been working with a trainer who has you do a fitness test at the beginning of your season: Pick a flat section of road with as little wind as you can muster. Warm up well first, at least 10-15 minutes. Then start at one end of your course from a standstill, and hammer as hard as you can sustain for 8 minutes. Stop, record all your data: distance, average speed, average heart rate and max heart rate. Spin back to the start and repeat. What he's looking for is your max heart rate on this test, which will tell him your trainable max. Then he builds "zones" below this like 60 percent of max, 70-75 percent, 80 percent, 90 percent plus.
The idea is to occasionally train at 90 percent plus in intervals to try to raise your sustainable max heart rate and make it "easier" to cycle that hard.
With all that being said, if you don't ride with a monitor, pick a gear you think you can push all the way up the hill and keep a steady cadence to try to keep your heart rate steady. If it feels like you can't sustain it, drop down a gear or two and try to keep the same cadence. Don't worry about "keeping up" with anybody when you're first starting out on hills, just get up them and they WILL get easier!
Johanna in the rocky, rocky mountains of Wyoming...



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