Sunday, June 3, 2018

End of year celebration of knowledge

Dan Meyer started a discussion on Twitter recently about the unnecessary stress that final exams cause for students at the end of the year, questioning how much insight they really give into student learning. It’s been a helpful reminder that while I definitely agree that high-stakes final exams are terrible, I really don’t have a great system yet for wrapping up the year.

We certainly don't want students feeling like this:

But what makes for a good alternative?

It seems challenging to balance the goal of ending the year with celebration and anticipation of more learning, while also gaining information about retention and content synthesis. I want students to end the year on a high note, feeling positive about their progress and provided with the opportunity to dig deeply into a particular topic, but it would also be great to be able to identify topics from the entire year that would benefit from review and work with them to do that.

In some ideal universe where time doesn't exist and Firefly is still on the air, I would be able to do both: a meaty project in which students can shine and review and an assessment of all of the things. However, even given this bounty of time, I'm not sure that a timed, paper and pencil, silent, individual assessment would really promote the most learning and information for me and students.

So I spent a bunch time the last few weeks reading up on various ideas and here is my current compilation.

  • A group whiteboard assessment that looks at problem solving and tying together big concepts from the year, something like what @AlexOverwijk does with his classes:
    This would require careful teacher observation to untangle individual understanding and contribution to the group product, but seems like a much closer fit to what students do in class every day and therefore a more accurate picture of their understanding, as well as obviously being less stressful.
  • An annotated portfolio of work throughout the term, which would require students to find evidence of learning for previous topics, identify important connections, revise work, and identify topics that need further attention themselves. I really like this option as it puts the student in the driver's seat. However, this would be fairly time-consuming and likely need students to have been tracking their work throughout the semester. It's something I'm strongly considering for next year. If you do this, I'd love more information - directions, rubrics, advice for someone who wants to try it. How do you make this work in large classes?
  • An oral final exam in which each student has a one-on-one interview and discusses their process and reasoning for one or two problems, which @JadeMohrWhite proposed:

    This seems great for digging deep into mathematical practices and student thinking, but would only give limited content knowledge information due to time constraints. Building in class time for every student to have a 20 minute interview or so also seems a bit daunting in the end-of-year crunch, but could potentially complement a final project or portfolio assignment, during which students are working relatively independently.
  • Final individual project and group presentation. This is the model I'm trying this year in one of my classes. Students selected a topic of personal interest to them that is related to the content in the course and did research and Math work related to this topic. They were then placed into groups based on some possible common threads between projects and created a presentation that highlighted their individual work AND the connections between them, as well as how what they learned related to their Math course this year. Detailed directions are here.

    I like how positive and forward-looking the projects have been this year - it does feel like a celebration and memorable opportunity for students to shine. However, because projects are typically looking at a single topic in a great deal of depth, this way of ending the year misses out on the whole cumulative, wrapping everything up feeling that I like to have. 
  • Bring back the final exam, but have it be extremely low stakes by focusing on retention, connections, and structured so that it can only help a student's grade, not hurt it. This is how I've done final exams before - as a final opportunity for a student to show understanding of a topic from a previous unit and a place to look at cumulative retention and synthesis. It's efficient and serves that purpose well, but isn't the kind of experience I want students to take away with them as their last memory of my class, so if I brought it back, I would definitely want to pair it with one of the above ideas.
  • Edited to add:

    Take-home final exams, as described by @benjamin_leis below, seem like another way to get more comprehensive information about content knowledge in a less-stressful setting. I like the idea of removing time pressure from the equation and letting students assess in a more comfortable and familiar setting where they can take breaks and dig deeper into problems. Again, because this more closely replicates the ways that students do math in my class during the year, it should be a better assessment of what they know. I also think questions on a take-home final should be more interesting and less routine than what I would ask on an in-class timed assessment. 

I would love to know of other ideas people have for alternatives to high-stakes final exams or any feedback on these still-cooking ones. Share them in the comments or send out a tweet.


  1. In most of my courses the final is just a last SBAR opportunity. I ask everyone to do at least one problem, and I try to have a fun synthesizing problem as that choice. But I love the courses where we can end with a project and student presentations. And the more choice the better.

    1. Yes! Why do we have to choose? I feel like projects and presentations complement some of the other options so well. It means there are multiple ways to show understanding, which lowers the stakes on each individual component.

  2. I like the idea of multiple pieces to the end assessment. They all cover different things and allow more opportunities for ss to demonstrate understanding. As an aside, as a student I strongly disliked projects and presentations so a choice would have been my vote back then. Also I'm just at an event today at UW that is using oral solution presentations. So that's on my mind. They're doing 5 problems over 3 hours with multiple chances to reexplain. The nice thing is that if the problems are meaty enough you can proctor a whole room without everyone bunching up for the oral portion. One other format I like is a take home problem set with some kind of honor code about doing it without outside help.

    1. Do you think that doing projects and presentations would have been less useful as a learning opportunity for you because you disliked them? I think a lot about the tension between choice, which usually means students pursuing deeper things they're already interested in or believe themselves to be good at, and pushing students (gently) to work on aspects of their thinking and learning that are more challenging for them.

      Thanks for the addition of take-home problem sets. I'll go ahead and add it to the list above. I haven't used this strategy much, but know lots of people have. It seems like a way to save time and make a final exam feel less stressful for students. Would you give problems at the same or a higher level of difficulty for a take-home assessment as for an in-class timed one?

    2. I love all these ideas! At my last school, in addition to a final exam in each class the students had to do a portfolio assignment. The basic idea was that students had to describe one learning objective and how their work at some point in the semester demonstrated their understanding of the objective. It was really cool, but definitely had some kids scrambling at the end who had procrastinated. I also was not super familiar with what it should have looked like so I could have done better at making them think about it more throughout the semester. Most students chose a project that they did but some did different things like quizzes or random assignments. I think a portfolio could be a great replacement to a final exam, as long as it's organized enough.

    3. I did a three part final in my post Algebra 2, College Readiness class: 10% a do now/take home Quadratic anchor problem set, 40% Delta Math 12 problems, 6 concepts--no penalty for incorrect answers, and 50% THEY made a Desmos Activity Builder that the other student had access to of the semester's review topics. (One concept per two people).
      It was wonderful. My students worked so hard during their final bc they could see their Delta Math Progress.

    4. For me, presentations always made me nervous. I still to this day occasionally get a case of nerves despite having to talk in front of groups fairly often. Also while I love Math, I'm not very keen on graphic design or slide creation. So the pressure of the presentation did always outweigh the learning opportunity part. But you could easily make a claim that it was a life skill I needed to practice.

      Also, although this can be corrected for, I often see projects devolve to either take a survey, graph some data and do some cursory analysis OR do a simple probability experiment. So I think the key is to vet the ideas.

    5. Re ensuring appropriate depth of projects, I think that this can’t be the first time the students are doing a big Math project because then they don’t really have a frame of reference for what makes for a good project and what is a reasonable question to bite off in the amount of time provided. My students this year tended to overshoot and be overly ambitious so we talked a lot about backup plans and more achievable goals on the way to the Really Amazing But Super Hard Question they were interested in exploring, just in case the giant, ambitious goal didn’t work out or took too long.

      I think that you make some very valid points about the disconnect between presentations and some students. The big positive for presentations in my book is the creation of an authentic audience to whom results must be communicated. Rather than saying, “explain your thinking so that an imaginary peer who hypothetically could read your writing would understand,” it’s patently clear that the presentation, which has an audience of very real peers, needs to make sense to them. I am thinking more now, however, about coaching or helping students for whom public speaking is stressful or who would not shine in that medium.

    6. Amy, I really like the idea of students collaborating to make a class review activity for each other. It seems like another great complement for an individual assessment. I haven’t used Delta Math, but it’s on my list of resources to check out over the summer. What do you like about it? How does it compare/contrast to Khan Academy?

    7. Marissa, did students select the learning objective for which they provided evidence of understanding? Was it looking at a single assessment (project, quiz, etc) or at growth in understanding that objective over time? I think that if I do portfolios, I would like to heavily focus on the mathematical practices or growth over time, but that definitely seems to require a lot of advance planning and a clear idea of what I’m looking for from students.