Does she enjoy looking at books? Does she respond to listening to read alouds? Does she draw or color? Does she interact with other kids? Maybe using some of these skills can get her involved in Daily 5 activities.

I have had 2 children who chose not to speak (elective mute). I always expected they would draw at writing time and expressed confidence to them and the rest of the class;e.g. “When Sue is ready to talk she’ll tell us all about her picture.” If she ponts in response to a question like “I wonder if you are in this picture?” Simply label it and move on. Don’t spend a lot of time lingering to beg for verbal responses.For word work have her copy or make high interest words with various materials. if she is not disruptive but does not make a move to do the task, leave it in front of her saying " When you’re ready, I know you’ll begin." If she doesn’t by the end of the time given simply say " I see didn’t begin today." Do not try to make her speak or write - entice , express confidence, and the leave her alone - if nothing else she is watching you to see what the worst is that can happen in your class.

Hello! I understand your frustration and feel how difficult it can be to have students who refuse or choose not to speak. I have two interesting cases I think would be worth while sharing:
First Case: Last year I had a Vietnamese ESL boy in my first grade class that did not speak. This was an interesting case because when he was with me he would only whisper answers or short phrases or shake his head, or say a little word to acknowledge his understanding of something we were working on. It seemed much more than him going through the silent period with language learning. After working with Child Study and probing deeper into the situation, we found out from the parents that he just started taking medicine for an unusual issue he had with his vocal chords, where his vocal chords had been inflamed since he was a child and they didn’t find out until the summer before first grade. It would hurt him when he spoke so he never spoke, only whispered on occasion. After taking the medicine from the doctor to limit the inflammation, he was physically capable of talking, but the psychological and emotional ramifications of not speaking for so many years took a toll. He felt embarrassed to speak because others had already expected him not to speak and he felt intimidated by and uncomfortable with his own voice. Here’s some simple things we did with him that proved successful:
-He worked three times a week with the school speech therapist on language and making sounds
-An instructional aide came in daily to work with him. First he was pulled out of the room with her to work on fun games that would require talking and yelling out things. These games included games like sight word games to call out the words, BINGO, and repeating aloud fun and silly phrases. He also got to verbally choose which classmates he wanted to go with him (up to 4 others) so this helped him socially too and to ease his way into speaking. By mid-year, we had the aide come into the classroom to play the games with him and the other students he chose. This got a little loud, but it was all good! He got to use his voice for choosing classmates (and calling out their names by saying in a complete sentence, “I choose ____”). This intervention was ESSENTIAL for his success because it let others know that he could speak and he didn’t feel embarrassed to use his voice because everyone had already heard it already. He started to feel more comfortable to speak.
-In guided reading group, we did lots of oral language activities, book walks, and I provided lots of who, what, where, why, how questions with sentence structure assistance. For example, I would ask questions like, “Where did the boy go in the story?” and would help him with the sentence structure by providing him with the sentence formation, “He boy went…” He saw other students participate and this encouraged him along.
-In guided reading groups, he could use the “talk-a-phone” (made of PVC pipe) to hear his own voice.
-Use of lots of songs, poems, chants in the classroom during whole group instruction.
By the end of the year, he was talking in the classroom, raising his hand to speak on his own, and talking more with his friends. It was an AMAZING day when we first heard his voice!
Second Case: My second year teaching (15 years ago) I had an ESL refugee boy from Afghanistan in my class. He refused to speak ever. He would only shake his head and on a rare occasion would whisper. He was extremely, extremely shy and his older siblings would do ALL the speaking for him in every situation at home. We tried to speak with the family to get his siblings not to talk for him, but this was a work in progress. He was actually with me for two years since he repeated first grade. We thought he was experiencing a silent period, but after a whole year in first grade it became more evident that it was a psychological issue that was blocking him from wanting to speak because he was not given the opportunity to speak at home because everyone spoke for him, so he refused to speak. By the end of first grade the second time, he began whispering more but never really spoke. He did the same thing at him in his home language and in English. Looking back, I think getting him to play games aloud in a small group and then in the classroom would have helped his verbal and psychological development tremendously.
Be sure to check to have your student tested to make sure she doesn’t have any thing physically wrong with her vocal chords or anything else that may be preventing her from writing or speaking. Be sure to have a thorough hearing test done on her to omit any problems with hearing. You may be surprised. When I taught kindergarten I had another ESL student we found out was partially deaf and the parents and teachers had no idea and this is what was hindering his progress in language development.
Good luck with your student that does not speak or write, and I hope that doing lots of verbal and calling out games, songs, and poems will help. I realize this is a lengthy post, but hopefully something can help you in some way!

Thanks to everyone. We have discovered since that this child suffers from selective mutism which is an anxiety disorder rather than a physical difficulty in speaking. Although the cause is different - all of your advice is helpful for her as well. Thank you for taking the time to post; it is appreciated!