Monitoring Student Progress

Whenever you listen and provide feedback to student explanations of their problem-solving strategy, you're monitoring the progress of their learning. Such assessments:

  • Determine whether or not your students are progressing adequately toward achieving the content standards of the unit of study.
  • Answer the questions:
    • Do I need to adjust how/what I am teaching?
    • Do students need re-teaching?
    • Are they progressing adequately?
    • To what degree are my students achieving the content standards I am teaching?

One way to assess students' explanations is to utilize a rubric. The rubric could be used only by the teacher as a quick way to identify verbal feedback OR it could be scored and given to students as a more formal assessment of their explanation. The specific use of the rubric needs to serve the purpose and circumstance of the lesson.

Here's a rubric that Ms. Barney could use to assess the quality of student explanations. This could be printed with multiple copies on a page, then cut up, and a teacher could quickly highlight the quality indicators and give it to students. Highlighting indicators would allow the teacher to select criteria from different levels (i.e., a student might have an explanation that "demonstrates strong understanding of concept" yet it may also be "nearly complete but some gaps exist.")

Rubric for Student Explanation
  • Explanation demonstrates strong understanding of concept.
  • Student uses an appropriate strategy and there are no errors.
  • Student completely explains each step using appropriate vocabulary.
  • Explanation demonstrates good understanding of concept.
  • Student uses an appropriate strategy but there are minor errors in notation or labels.
  • Explanation is nearly complete but some gaps exist; vocabulary is appropriate.
  • Explanation demonstrates some understanding of concept, but there are significant computational or algebraic errors.
  • Student uses an appropriate strategy but application is inconsistent and there are significant errors in notation or labels.
  • Explanation is vague or inconsistent with missing or inappropriate vocabulary.
  • Explanation demonstrates limited understanding of concept and includes significant computational and algebraic errors.
  • Student uses an inappropriate strategy or uses irrelevant information.
  • Minimal explanation is provided and explanation is unclear with missing and inappropriate vocabulary.
  • Student is unable to offer any explanation.


With practice, students will become more adept at explaning their mathematical thinking. And, they'll be able to use these skills in small groups as well as whole-class discussion!

Review the explanation given by the second student and apply the above rubric.