First, you have to realize that different actresses/directors could have a different take on this particular moment, but I will speak of the theatrical release of The Miracle Worker which stars Patty Duke. This should be fairly accurate, though, because the two lead in this production also played the leads in the Broadway version.
It's also important to keep in mind that Annie is truly "using" this moment to impress upon the Kellers the importance of Annie taking "complete charge" of Helen for a while as well as the desperation with which Annie does NOT want Helen to end up in that asylum.
Let's approach the text first. "Miss Annie, before you came we spoke of putting her in an asylum. (Annie turns back to regard her. A pause.)" You see, sometimes saying nothing says even more than saying something. There is a slight, almost imperceptible eye-close here, and a silent sigh. Annie knows what's coming. She knows what she will have to do in order to keep Helen out of that horrid place. She is using that moment to compose her thoughts. Then, out they come:
Rats--why my brother Jimmie and I used to play with the rats because we didn't have toys. Maybe you'd like to know what Helen will find there, not on visiting days? One ward was full of the--old women, crippled, blind, most of them dying, but even if what they had was catching there was nowhere else to move them, and that's where they put us. There were younger ones across the hall, prostitutes mostly, with TB and epileptic fits, and a couple of the kind who--keep after other girls, especially young ones, and some insane. ... But the babies stayed and we played with them, too, though a lot of them had--sores all over from diseases you're not supposed to talk about, but not many of them lived. the first year we had eight, seventy died. the room Jimmie and I played in was the deadhouse, where they kept the bodies till they could dig--the graves. ... No, it made me strong. But I don't think you need send Helen there. She's strong enough.
This is spoken both in desperation for Helen NOT to go there, but also as an admonishment for the Kellers NOT to send Helen there. As a result, her tone is one of stubborn rigidity with a hint of desperation. Annie is firm when she says these line with great strength. They are spoken at first with determination as her voice gets louder and louder, becoming more frantic as the danger to Helen becomes more apparent. She also begins slow and ends quite quickly, getting all the words out as fast as she can, ... but ending with a pause right before (and after) "No, it made me strong." As Annie doesn't WANT compassion from the Kellers, only for them to know the horrors that Helen would experience in an assylum.
Therefore in summation, here is an easy-reference bullet point list for you:
- tone/attitude: stubborn rigidity (with a bit of disgust & desperation)
- volume: soft to loud, reaching a creshendo near the end.
- fluency: slow to fast, significant pause before the line, "No, it made me strong."