Perhaps, If you can find the energy and time engage with other families and work on a collaborative project together. I think that a small group with parents and children of different ages on say a Saturday or Sunday afternoon for about four weeks might be fun and help with the communication. I have a resource if this idea appeals. My email is kbolmanahaa@gmail.com
And you can find me on google Katherine Bolman

I HAD THE SAME PROBLEM,
BUT MY DAUGHTER WAS SO SHY SHE WOULD CRY BECAUSE SHE WAS AFRAID OF THE KIDS AND WHAT THEY WOULD THINK OF HER ,THAT WAS K-THUR 2ND GRADE(SHES IN 7TH NOW)I STARTED HELPEN OUT IN EVERY WAY I COULD AT THE SCHOOL,FIELD TRIPS,CHRISTMAS PLAYS,TEACHERS HELPER.SHE FELT SAFER KNOWNING I WAS AROUND,HER GRADES WENT UP,SHE BECAME HONOR ROLL.NOW IN MIDDLE SCHOOL SAME THING HAPPENED,SO I NEW WHAT I NEEDED TO DO,SO NOW IM ON THE SIP/RESTRUCTURING TEAM,IM NOT IN HER CLASS HELPEN,BUT SHE KNOWS IM THERE,SHE DOING VERY WELL ,MORE PARENTS NEED TO GET INVOLVED WITH THERE SCHOOLS , AND MEKE SURE ARE CHILDREN GET A GOOD EDUCATION ,GOD BLESS

Children usually begin to speak up when they feel comfortable speaking up. It's not easy or even always possible to force them to speak up before they're comfortable doing so. In fact, pressure placed on them to speak up can sometimes make them even more quiet.
Is your daughter naturally quiet? Does she speak her mind in any setting? At home? At play? If she does, then she likely will do the same at school as she finds her comfort level.
I dislike the practice of grading students for their participation - I particularly dislike it when very young students are graded on participation. People have personalities and for some of us speaking up comes naturally and for others it doesn't. In these early years of school, grading a child on spoken participation has always felt to me as if the child's personality is what's being graded and even found wanting.
Good luck with this - it's a fine line between fostering freer expression in a child and fostering their fear of doing so.

HI. Did your daughter attend preschool? If so, did her teachers express any concerns then? I'm wondering if the kindergarten classroom setting with so many other children is somehow intimidating to her, and it may just take time for her to "come out of her shell." Could she be a perfectionist, who is afraid to answer questions in a group setting, or sing if she's afraid her voice isn't on key or she doesn't know all the words to the song?
I'd like to invite you to join the Kindergarten Parents Group at community.greatschools.net/groups/11535 for more support.