Feedback in the class

An assessment that I have recently done with my students was a "pre-assessment" of finding the roots of a polynomial of third degree. It was some guided questions that would inform me of where they were at based on the past few lessons that we've had (finding real and double roots and using the quadratic formula) and whether or not they were able to apply these concepts learned to more conceptual questions and problems. I did not give an actual number/letter grade for this but rather a participation grade: if they did it and attempted it then they got an 8, if they didn't attempt it or didn't take it then I did not give a grade.

Most students did well but their way of showing their work and thinking was presented differently. For instance, the following student was very throughout with their work and the way they presented their thinking. They were very detailed and expressive so I didn't give much feedback in the paper itself, my feedback was spoken which was "Now that you understand how to use the quadratic formula to find the roots of a polynomial of degree three, I challenge you to begin thinking how you can find the roots for a polynomial of degree 4 or higher (which will be our next topic."

This next student seemed like they understood what they were doing but they were not as throughout expressing their work and how they obtained their answer. Even though I knew where their thinking was coming from, I wanted to know more about the thought process so that I could  support them better in the areas where help was needed. I left some questions in order to get their thinking going and I asked the same question orally to receive their answer which allowed me to see that they were confused on the +/- symbol in the quadratic formula but we worked through it and now she was able to explain it back to me.