Case
Correct or Incorrect Question

Mr. McKimm is teaching a unit on quadratic equations. He writes an equation and its solution on the blackboard and asks the class to vote on whether the solution is correct or incorrect. He chooses one student to explain why he or she thinks the solution is correct and one to explain why he or she thinks the solution is incorrect. After hearing both sides, the students vote again. Mr. McKimm makes a mental note of how many students appear to understand the problem. Does this illustrate an assessment being used for instructional feedback or for formative scores?

Solution #1
This form of assessment in my opinion would be for instructional feedback. I would take this information and base my group work on their responses. The students that were correct and understood the process would get work that would reinforce and stretch their understanding. One group would be set up with work to clarify and give practice to those that understood but was not as confident. The last group would be teacher led and that would be the one where we are able to work through where the disconnect lies.
Solution #2
Mr. McKimm is conducting a type of instructional feedback assessment. Because he is allowing students to vote, he is mentally taking note of who is voting for which problem. Mr. McKimm should then take this information and create groups to further understand quadratic equations based on what he sees. Because he is letting students explain their thinking, he is allowing them to explain to the class, as he would if teaching, to allow students to formulate their own thought process. Mr. McKimm could also create a formative assessment in which two problems are given, one is correct, one is not, and allow students to show the mistakes made if any in both. This would give more of a formative data score.
Solution #3
While I believe this is an important skill that the students need to be able to effectively complete, I do not think the way this activity is presented is a formative score activity. This is definitely an instructional feedback activity, and until you can focus on each student and if they understand is the math problem is completed correctly or an individual solution, a formative score should not be given.
Solution #4
This assessing method allows the teacher to gain instructional feedback and adjust their lesson to address any concerns. For students who understand/exceed at solving the problem, Mr. McKimm could provide additional problems that are more difficult. For students who are struggling, the teacher could work individually or as a small group with them and determine at what step they may lose their understanding. This assessing style allows the teacher to quickly determine any misconceptions that students are having and address them in a way that meets their needs.