For the past couple of weeks, I have been taking How Math Must Assess to an extreme, literally checking every problem every student does in class, providing constructive feedback to each student who needs it, and placing a check next to their names if they demonstrate to me that they can "do" whatever it was they were doing on that day. And it really is easy.
For example, this past week was a short week, having Monday off. My goal for this week was to have students solve right triangles. I really began last week by reviewing the Pythagorean Theorem the Friday before after a very short quiz, checking off on every student who demonstrated to me in class that they could actually find any side of a right triangle when given any two of them, providing constructive feedback for those students who needed it and checking them off after they could demonstrate to me that they could do it. Tuesday, I introduced the three trig ratios and how to use them to find any side of a triangle. Wednesday, we went from sides to angles. Thursday, we put everything together.
What I do is this: After some sort of a "mini-lesson" of fifteen minutes or less, I provide the remaining thirty minutes or so for students to apply the ideas learned during the mini-lesson on a problem set containing somewhere around fifteen to twenty problems, broken up into groups of four or five problems. I do NOT circulate around the room. I pull up my chair and sit next to an empty student desk somewhere in the room, and I ask my students to get up, walk to where I am sitting, and check their work with me after each group of problems. This seems to provide my students just enough movement-with-a-purpose that they can work rather diligently for the entire class.
When a student comes up to me, I can quickly scan their work and answers and provide specific feedback ("If you are going to use this angle in your calculations, then this side is the adjacent side"). If, after looking over their work for a group of problems, I am satisfied that a student can do things correctly, I place a check next to their name. For some students, this may not occur until after they have received feedback from me and re-worked some of the problems. For other students, if it looks like some sort of a calculation error on their part, I may send them back to their seats and have them shout out the answer to me without making the trip back up and standing around my desk ("It looks like you divided 4.3 by the tan(5) instead of the tan(55). Go back and double check that you end up with something around 4, and shout out your answer to me when you get it.").
I have 28 students in three of my four classes that I have been doing this with (the fourth class has 13 kids). I may have a group of four or five students waiting around me to have their work checked, but I ask them to listen carefully to any feedback given to another, because it may apply to them and their work.
My hope is that by the end of the week, every student will have demonstrated that they can meet the objectives for the week before we ever have a quiz. The results from last week? Fifty-eight students in the four classes combined could solve the right triangles perfectly. Only eleven students out of the four class could not solve the right triangles. Of these eleven, nine of them did not demonstrate to me during the week that they could do the work anyway, so this was not a surprise.
Anyway, I plan on continuing my extreme formative assessment this week as work with special right triangles and their trig ratios. We'll see how it goes.