American English: /ɪr/ /hIr/ If you are familiar with Spanish, ear = ir. Your teacher is correct. However, I find that "ear" and "hear" are pronounced with more stress in the tongue where it touches the mid-portion of the palate. "Sheep" seems more relaxed to me. These words: beer, here, dear, ear, hear, near, queer, fear, shear all have the same vowel sound to me.

In this situation written answers are useless unless you know the IPA. Go to forvo and type the words in, and you will hear them pronounced by native speakers. If not, get text-to-speech working on your computer and listen to them that way. They are both pronounced the same except one has a 'h' sound at the beginning.

Which dictionary did you use? Just speaking as a native U.S. speaker, not a phonologist or teacher, the vowel sounds in "sheep," "here," and "ship" are fairly close to each other, but not quite the same as each other. OxfordDictionaries online is showing sheep/iːp/, here/hɪə/, ship/ʃɪp/. American Heritage using an old non-IPA system is showing shēp, hîr, shĭp, three different vowel sounds. To my ears, if I try to say "here" using the vowel sound of "ship," it is not what I say but it is close enough. If I try to say it using the vowel sound of "sheep," again, it is not what I say but it is close enough. Since the "r" is sometime regarded as a semivowel, what I say has a definite "diphthong" nature to it--I'm sliding from an "ee" sound to an "ur" sound. In any case, however it is pronounced, I agree with Richard that "beer, here, deer, dear, ear, hear, near, queer, fear, shear, sheer" are all perfect rhymes and have the same vowel sound in them. The normal reaction of grade school children learning to read, or people who aren't good at spelling, is that the "ea" spellings are odd and that logically and phonetically these words "should" be spelled "beer, heer, deer, eer, heer, neer, feer..."