Sunday, January 24, 2010

Formative Assessing to the Extreme

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.


  1. I'm admittedly jumping in a bit late to know your system, but a few questions come to mind:
    1) Why not just post your answers and have students check their own? From my experience, a good chunk of the students can figure out what they did wrong after they see the correct answer and are given some time to re-work the problem. It may shorten you line for questions a bit at the very least. Maybe you have an alternate rationale for making yourself the answer provider, again, I'm jumping in here without having read any of your other posts.
    2) This post describes what your classroom looks like on a daily basis, I'm assuming. What do your more formal (tests, quizzes, etc.) look like? Are you doing assessments weekly? by chapter? How are you reporting these scores? Using a 100 point scale? 4 point lykert scale by learning target?

    Looking forward to learning along with you. I'm working on tweaking my system this semester a bit. It looks like you've been keeping up over at meta musings. Keep up the good work yourself!

  2. Matt,

    Ok...let me see if I can answer everthing...

    (1) Good question. I have just hung up the answers, but I was not able to see who is doing what. I found that a few of my students might just copy down may answers and not give a hoot. The way I am doing it right now (and it could change in a week), I feel I can see exactly what my students can and can't do with respect to the current content. I am ok with a group of kids around me. It is typically no more than four or five, and as long as they are all paying attention to any feedback I am giving, I am ok with it. I do not give daily homework, so this is their chance to practice. If there is something they do not complete in class, then they need to complete it and show me the next day.

    (2) For the most part, this is a daily thing. I usually give a formal quiz every Friday. Last Friday's quiz was two right triangles - one with two sides, one with a side and an acute angle - that they had to solve. I essentially looked to see if they could find angles when needed or find sides when needed (my learning targets).

    We do have a text book (Discovering Geometry) that we follow (sort of). I try to get as much of the geometry done by March so my students are ready for the state graduation tests given to 10th graders in March.

    I report the scores as a raw scores, but I try to fudge them to reflect their understanding of the content. So if a student could not find the sides of the triangle, but could find the angles, I considered that to be average or a 70%. Of course, they can come in and retake the quiz any time.