[AnE] Ordered Pair Assessment - formative, summative, and evaluative

I've talked a lot about assessments (Thoughts and practice on Assessment for inquiry-based approaches (Standards Based Grading) Part 1, Part 2), so I thought I'd share some examples.

Here is an assessment method that I like to use from time to time.  This particular method primarily functions formatively, but I also use video evidence for evaluative purposes.

The task: Ordered Pair Assessment

The idea is fairly simple.

The room is set up like this - where the students face off each other

They have to find their ordered pair and then sit down.  I personally arranged all the pairing so that good conversations could ensue between the pairs.  On their table they get the following sheet:

The assessment takes over two days.  The first day is where they get the opportunity to explore all the questions with their partner.  They then get to take it home to review the ideas that they've connected together.

On day 2, each group gets assigned a number where they focus on preparing to present their discussions.  

If a pair has been assigned #2, for example, student x would tackle:

"what is the difference between direct and partial variation in the context of a table, a graph, and an equation?" 

and student y would tackle:

"what would be a linear function that goes through the first and third quadrant? are there more than one?"

Throughout day 1 and day 2 they have the use of a white board where they can record whatever they like on there.

Then on day 2 they would present their explanations to their classmates.  Most of them use the blackboard to describe their findings.  Some of them decided to pass their own white boards around.  Other students decided to just speak to their question.

What worked well

• The questions were open and required explanation (which then requires understanding)
• students used this opportunity the refresh their conceptual understanding
• the task had multiple entry points for different levels of understanding.  I was happy with most of the questions.
• this effectively incorporated assessment as learning (where students were reinforcing and extending their understanding through the task), assessment for learning (since both the students and I were getting a good sense of what they understand), and assessment of learning (since I was able to use the video evidence of their understand to inform my evaluations)
• students were engaged! All of them were talking math.  Some were more effective than others with certain questions, but all of them had something tangible to work with, and they were allowed to review their notes to inform their understanding.

What needs improvement

• Time was a huge issue. There was not enough time for presentation. May need to reconsider this task for multiple days (more than 2).  Perhaps embedding new materials if I am concerned about course time.  In my opinion, this was too valuable to be cut short.
• The instructions had to be changed multiple times as we went along.  Sometimes because of time restraints, others because I change my mind... a lot.
• While I am happy with most of the questions, some of them dug too deep.  It was good that I was able to choose numbers for pairs that were more suited to answer the question, but day 1 was definitely challenging for some of them.  I am unsure how I should address this.  On the one hand, I like the fact that all of the students had all the questions.  On the other hand, I am wary of students who were stuck on questions that demanded too much depth.