The term aspiration refers to a turbulent puff of air that accompanies certain speech sounds in certain contexts (e.g., the initial sounds in the words top, post, cake). In the International Phonetic Alphabet, aspiration is represented by adding a a small symbol (i.e., a diacritic), in this case a superscript h (e.g., [tʰ] [pʰ] [kʰ]).
In every introductory class, instructors must name the phonemes that are assigned to handshapes. For example, handshape 5 represents /m f t/. Often, instructors who are working with hearing students choose to say the aspirated versions when referring to handshapes. In other words, the /t/ that is spoken in front of a class is generally going to be [th]. This is because it is easy for hearing people to hear and recognize the familair sound. It is less likely that instructors word cues to say the "t" sound found in the word Batman. While that sound is also reresented by handshape 5, it is unreleased and would be hard to recognize in isolation.
Understanding that instructors choose aspirated versions to refer to handshapes is important. New cuers may believe tht handshape 5 refers only to /t/ when it is spoken as [th]. They announce, "But I don't say Ba[th]man!", "I don't say [th]ree!" These students should be praised for recognizing these subtle differences, but must be reassured that hadshape 5 represents all versions of /t/ – aspirated for not.
The problem with /t/ is that some of its versions sound like other phonemes. People want to cue the different allophones with different handshapes. Instructors can help student understand the concept of phonemes and aspirated allophones with a simple test.
You should see that the tissue is propelled by a puff of air on the /p/ in pot, but not in spot. That is because the aspiration of the /p/ disappears when the /p/ is between /s/ and a vowel. Do you need to know these rules? No. But the key idea that that although they sound different to hearing people, they are both cued with handshape 1. And eventhough some people might notice that the /p/ in spot might resemble /b/, it is certainly not cued that way. These simple demonstrations can help cuers realize that phonetic differences like aspiration may affect how words sound, but they are not cued.