Thursday, April 18, 2013

HOT Tests - Student Created Assessments

I tried something new this week in Math Analysis... I had no idea how it would go, and it was far from perfect... but it is DEFINITELY something to do again (with several tweaks, but we all learn from experience!)

I had students each write their own version of the test for Unit S.  Then, they took each other's tests as the "real" assessment in class.

I would have to say this is the HOTtest (Higher-Order-Thinking) testing experience my students have participated in.  It wasn't about remembering, understanding, and spitting back out.  They truly had to apply their knowledge, analyze problems (the ones they wrote and the ones their classmates' wrote), evaluate not only the problem itself to see if it was valid and included all needed information appropriately but also their classmates work on the grading day, and of course - creating!

It was awesome!  Here's what a few of my students had to say about the experience of creating a test:

"It was interesting being in control and deciding which problems would be appropriate for a Math Analysis Honors Student. I learned to care about someone else’s grade and make sure that I made the test as best as I possibly could so that the test taker would not misjudge their understanding about the Unit. It also felt rewarding that I created a test and being in Mrs. Kirch’s shoes was not an easy task, but printing that test felt like such an accomplishment."
"I think it was really interesting to write our own problems and come up with a test. At first I thought it was going to be easy but once I started to write the test I realized that coming up with problems actually required a lot of thinking. It was a new experience and made me see what Mrs. Kirch goes through."
"By reverse solving as I like to call it, students are able to have a deeper understanding of what they’re learning. It’s one thing to solve. It is another thing to be able to create problems for someone else to solve, demonstrating more mastery the unit."

"I found that creating this test was really a great pro. It made me analyze and reflect on each concept of Unit S. This not only helped me in coming up with good questions but also to get an understanding of how to work out these types of math problems. It also gave me a sense of responsibility as another person's grade was technically in my hands."

So, here's basically what I did:

  1. Students were given a list of 7 types of problems they were to write.  I gave them specifics in terms of what the problems needed to include as well as level of difficulty that was expected. I graded them on a rubric in terms of what they included in their test and how well they met the expectations of difficulty and type of problems.
  2. Students made TWO copies of their assessment on a template they downloaded from the class website.  One copy had just the problems they wrote and directions to follow.  The other had the problems, directions, AND step-by-step work and a solution.
  3. Students brought their assessment to class on Wednesday.  After all of them were turned in, I randomly distributed them in partners.  I did use discretion and tried to partner up students at similar achievement levels in class so it was a little more "fair" in my opinion.
  4. Students had a class period to take their classmate's test.  If they found an error in the problem (like it didn't make sense, it was missing information, etc) they brought it to me and I fixed it or added information.  The person who wrote the test would receive deductions for errors like these.
  5. Students spent the period comparing work and answers,
    figuring out who was right and where errors were made.
    Today (Thursday), students came in and got in their partners.  They spent the period "grading" the tests.  They graded both the "answer key" and the test that was taken, comparing work and answers to decide who was correct - whether that be both of them, one of them, or neither of them.  They could only use red/purple/pink/green pen all period so any changes, edits, comments, etc they made on the tests were clearly visible.  They also decided on a point value for each problem, so they had to analyze how "big" the mistakes were and how many deductions should be taken.
Students were engaged with their partners the entire period - it was amazing!

Students critiqued each others work with the goal of helping each other understand where misconceptions may have happened
Some lessons learned:

  1. Plan ahead. You need to be specific and detailed of what you expect the problems to include.  I did this, but it was throughout the unit as I thought more about things.  Next time I want it to be 100% clear up front.
  2. Make sure the students understand that part of "taking" the test is also evaluating the validity of the problems.  If something doesn't seem right or is missing, they need to bring it to me so it can be fixed.
  3. Have clear expectations in terms of the writing of problems vs. solutions.  For example, some students wrote both the problem and their work in pencil, so it was very hard to tell what part was their "problem" and what part was their "work" when I looked at their answer key.  Problems = pen or typed. Solutions = pencil.
  4. (Possibly) Have students have a peer "proofread" their test the day before it is due to make sure it includes all needed information and looks ready to go.  This will avoid the small annoying things like, "She didn't write any directions", "I can't read her handwriting" (one student though a 24 was a 2i and solved an entire problem in the realm of imaginary numbers before mentioning it to me...), "This doesn't make sense for Quadrant IV", etc.

Other Student Comments about the process, both pros and cons...
(broken into the three stages of Creating --> Taking --> Grading)

It was difficult to wrap my head around having to trust someone else’s hard work as far as being in the shoes of a test taker. I am such a control freak and it was very hard to let that go. In the end, it turned out well (this part isn’t really a con, but I am happy the way things turned out).
I wasn’t sure that my questions were valid, much less the ones I was answering
I found it to be very difficult to come up with the questions, when in my mind I perfectly knew what I wanted, but then as soon as I began to write them they were not good as I thought. I do not think  that my questions followed the requirements.

The person whose test I took created a great test. The directions were clear, the level of difficulty was right on point, and her writing was clear.

The test I took in class was of appropriate difficulty. They really put some thought into creating their problems. I felt this was also a great trust exercise for the class.
Solving someone’s test and trusting that the problems are correct is like trusting a sashimi chef that there is no poison in the blowfish that the chef will give you
Some of the problems used on the test I took had the wrong signs and placed the numbers in the wrong side of the triangles (concept 5) which confused me.

I got to sit down with my partner and we explained to each other why a problem was done incorrectly. By further explaining this Unit, we got even more practice out of it.
Two brains are usually better than one. When two different people look at the same work and same problem, it is more likely one will spot the mistake made. Often, the person who makes the mistake retraces their wrong work and steps over and over again, so the whole partner thing is a plus for sure.

By sitting down with my partner I was able to realize what I actually did wrong, and it helped both of understand the concepts even more.
Me and my partner had a good laugh while helping each other on what our mistakes were and explaining why the problem they did was wrong and how to do them correctly. I think this Student test will help improve student’s understanding on how to do the math concepts in the future.  

Who wouldn't love a class period of students having discussions like this?


  1. I love this idea and am going to give it a try as my AP Eco students prep for their AP exam the next few weeks ... I'll report back how it goes. Thanks for sharing!

    1. Please let me know how it goes! It was such a great experience for me, I'm excited to try it a few more times next year!

  2. I tried a variation on your idea yesterday in my AP Macro class, the students had to create a FRQ (Free response Question) using certain guidelines that I couldn't answer. The feedback I have gotten today is that they loved the idea and challenge. It is defiantly something I will continue to use.


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