Formative assessment is assessment that is ongoing. It is used during instruction. Summative assessment is assessment of learning, usually at the end of a unit of instruction.
Formative assessment is used to determine how students are progressing. Then, you can use the information to determine what action should be taken. You might re-teach a lesson, or move at a quicker pace. Formative assessment can be informal, or be something like a quiz or homework assignment that is used to see what students are learning.
Formative assessment is utilized to immediately determine whether students have learned what the instructor intended. (activelearning.uta.edu)
In an ESL classroom, a formative assessment will often be oral. You will determine how a child is doing by listening to him talk. Formative assessment is ongoing, and students can't be expected to get it right the first time.
Summative assessment is the kind you probably commonly think of when you consider assessment. It is the unit test, standardized test, essay or other assessment given at the end of the unit. These assessments are usually used to determine grades for report cards, or to determine a student’s achievement level.
Assessment is a huge topic that encompasses everything from statewide accountability tests to district benchmark or interim tests to everyday classroom tests. (amle.org)
There are important summative assessments in ESL classrooms that determine if the child can move on to a regular program. For example, the CELDT test is administered to determine a student's English proficiency.
Both formative and summative assessment are important in a classroom. Teachers need to continually assess in order to help students succeed.