Something like the "Empty Outlines", "Muddiest Point" or "One-Minute Paper" are not only extremely simple to describe, but easy to use. Better than that, they are educational! Other simple, educational assessments are One Sentence Summary, RSQC2, or exam post-mortem (return students' exams and go through each question in class).
The answer is both yes and no.
'Yes,' you must assess how students perform. Yes, you should assess your teaching. But note that because students are being graded on homework, class participation, tests, performances, etc., you are already assessing them. Also, if you're like most teachers, you already constantly assess your own teaching and make course corrections as you go. So 'yes', you are doing assessment.
And 'No,' you need not write up every assessment you do. Pick a few each semester that you'd like to study - problem areas that you'd like to investigate, then spend some time really thinking and writing about what you found. We teach that writing about what students are learning is one of the best ways to construct understanding; here is our opportunity to practice what we preach!
Lord Kelvin said
When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind.
to which Ernest Rutherford counters
If your experiment needs statistics, then you ought to have done a better experiment.
So the answer is no, numerical data is not absolutely mandatory, but academic culture does lean more toward Kelvin than Rutherford.
A rubric is a complete specification of an assignment: what is required and how, exactly, it will be graded. Writing the rubric when an assignment is first conceived helps everyone. It helps the instructor focus on specific outcomes and what, exactly, is most important. It helps the student because it specifies expectations for any grade value the student may desire to earn. Some sample rubrics are arts and humanities embedded essay, early childhood, gunsmithing, manufacturing technology, science 6-Trait Writing. The following is an article written my Colorado Schools of Mines Mathematics professor Barbara Moskal on writing rubics Scoring Rubrics: What, When and How?
At the most basic level, the 'Assessment Cycle'