We have been back at school for 4 days. The first day was dedicated to exam analysis, exam corrections, and peer editing. The second day we talked briefly about graphing simple exponential function and negative exponents and then worked more on their exams. After school the usual crew worked in my room to complete their homework. I was really surprised to be asked “Ms. Gough, what level are these questions?” In an earlier blog post, Deep Practice, Leveling, and Communication, I wrote about the formative assessment with levels that is my team’s current assessment experiment. On day 3, we decided to go ahead with a formative assessment on computational fluency with negative exponents and then have students investigate exponential growth with an investigation using M&Ms. We were hesitant to give this assessment so early, but we thought it might serve as a diagnostic assessment too.
Let me stop here and offer our current thinking about the scoring and levels on this type of formative assessment. These assessments are not graded. They are taken individually as if taking a test. The assessments are self-scored, and then our learners complete a table of specifications to help us all determine their level of proficiency and where they need support. They are to work together to correct any problems up through level 3 and are encouraged to work on level 4 if they are moderately successful with level 3.
Level 1 – We try to target the most basic of the prerequisite skills necessary for this learning target.
Level 2 – We try to assess a prerequisite area that might cause our learners to stumble based on our history and experience with learners of this age.
Level 3 – This is the target level. Can our learners function at the desired level?
Level 4 – This is an enrichment level. If you are functioning on target, can we challenge you to learn more? These questions generally come from either the Honors Algebra I or the Algebra II learning targets.
If formative assessment informs the teachers and learner and causes a change in practice or behavior, then this was definitely formative assessment. The M&Ms were out on the table ready to be tossed and counted. As I looked through their tables of specifications, I learned that hardly anyone was working confidently at level 3. So, we took a poll. Do we postpone the M&M lab to work more on negative exponents? Rarely do I get 100% agreement, but today I did. “Yes, please Ms. Gough. We need to work more on negative exponents. And, will you teach us about exponents that are fractions?”
It was great! DD, my friend and teammate, was there to observe the M&M experiment. We agreed with our learners that the best decision was to stop and teach more about negative exponents; how often are we asked to teach something?
Here are three examples of my learners work and reflections from this formative assessment.
Isn’t it interesting that VB still puts a score on her paper, but MC and CL do not? We can quickly see that VB needs pay attention to a few details and needs to be challenged to move to level 4. MC needs to read the directions more carefully as well as correct her work and complete the table of specifications correctly. She understands whole number exponents, but needs a little coaching on how to write her answers. She may not understand the term evaluate, or she may need to read the directions. MC also needs help with fractions and arithmetic, but she understands negative exponents. CL is unclear when the exponent is zero and might need a refresher with fractions. She needs to pay attention to parentheses and should be encouraged to investigate fractional exponents.
One other thing to notice…CL reported 50% at level 3 and marked that this is the level where the work is most consistently correct. I just had to ask. Her response “yeah, if you look at my work, I messed up multiplying fractions and the zero exponent. I got negative exponents. You don’t have to worry about me.” I spend about the same amount of time with these formative assessments as I did when I gave quizzes, but now my job is more interesting. It is problem-solving, coaching, and having conversations with my learners. They have the opportunity to critique their work and report back to me. I feel like I’m coaching rather than judging. My learners talk to me about what they can do and what they need.
Does the formative assessment and table of specifications help these learners identify where they are and where we want them to be by the end of the unit? Will it help us know how to plan and teach? Does it tell us all where gaps are that need to be filled? Can we work together to close each gap?
Don’t you love CL’s reflection? “I think I need more help with Integers and exponents with rational numbers. With rational numbers, I feel like I had no idea what was going on, and like I hadn’t learned that stuff yet.”
It is about learning.