We have a team who benchmark test most of our students. However, in Kindergarten, we do most of that ourselves. The benchmark team mainly keeps track of those students who will be taking state tests during the year.

Our formal, universal screeners are with NWEA MAP and Cambium ATLAS. We use district created progress monitoring tools for things like fact fluency.
For assessments that are administered across the whole school, we use a team of support staff like our interventionists, academic coaches, SPED, and ESL to help classroom teachers.
For progress monitoring, the classroom teacher is primarily responsible. Intervention, ESL, and SPED will progress monitor the students they serve.

We use our intervention team when possible especially at the beginning of the year. We use star phonics, NWEA MAP for reading and math and then common assessments k-5. The classroom teacher completes the common assessments every nine weeks. The other tests are given on chrome-books and usually a grade level at a time. We have a few additional tests for those below benchmark. Sometimes it seems like a lot, but I also get different useful information from each assessment. I try to motivate my students with a lunch club for any growth. We celebrate all gains.

We have progress monitoring meetings every month to review the data of or diagnostics. For third grade we have benchmark testing. For those students who receive services, the resource teacher also monitors student progress through their programs.