One of the things that I changed most about my teaching approach at my previous school (I’m joining a new one this fall) is an expansion of my approach to summative assessment. Our curriculum there was a collaborative problem solving curriculum based on the Exeter materials. Students would work together in class discussing and debating about ideas, and exploring the problems presented to them, so by giving traditional, sit-down, silent, period-long individual tests, we found that we weren’t really assessing them in the way we were teaching. Due to a scheduling snafu one winter, we were left without a midterm during our exam period (lollll), but we were all like… oh well, who cares? Let’s do creative things! We all tried oral exams that winter in class, and then our minds were open from there…

Here are some of the different things that I have in my toolbox now:

The Oral Assessment

Good for: Areas of math with layered conceptual ideas underpinning them

How it could work: This was a staple for our math department. We would assign a set of problems (maybe 6-8 meaty problems) and students would have the couple of days beforehand to complete them (either with or without each other, I preferred with!). They could use whatever materials they wanted, but knew that they not only needed to solve a problem, but needed to understand it deeply, so there in essence was no way to cheat (just having the correct work on the paper didn’t really help!). Then students would come in one at at time for a 5-10 minute oral where we would roll a dice and randomly pick a couple of the problems to talk through. I preferred students just to show me work they had already completed to save time, but some colleagues had students re-do the problems for them on the board. Then I would ask questions like, “Hmm, how do you know that?” and “Does that work all the time?” or “Was that the only way to do that?” For each problem we discussed, I would give them a grade on the accuracy of their work, their mathematical discourse with me, and then a completion/accuracy grade for the rest of the assessment we didn’t get to talk about it.

I loved this because it’s pretty immediately clear who knows what they’re talking about and who doesn’t. How often do we try to assess this on written tests and get stuff like this that seem to go viral all the time (usually attacking Common Core, which is not why I’m sharing this):

Instead, you can ask specific questions, and just rephrase a bit until students understand what you are asking. I also loved when a student would have incorrect work, and I would ask a question, and they would figure out a mistake and correct their work – learning happens DURING the assessment!

If you’re wondering, “when do you have time to do something like this?” I would often do it DURING a normal written test, or give them problems to work on and try to power through my whole class in one period. I trust my students, and I know that is a luxury, but that works for me.

The Group Assessment

Good for: When you want to assess something that takes slow thinking, or is too complicated for a written test, or when you just want to get your students sharing knowledge and ideas with each other

How it could work: There are some things that students just need to know how to do individually (how to factor, how to take a derivative etc), but problem solving skills are amplified by others, and *real* mathematicians work together.  I would have the students work on a problem together on a big whiteboard and then whenever they felt ready, they would erase their work, and then silently and individually solve the problem on their own, and this is what their grade would be based on. Some colleagues just had them do the problem together and grade that product, and my way takes longer, but I preferred not having students’ work determine each other’s grades. This was often great evidence to help people see that their way of learning and collaborating wasn’t working (if their group mates got a problem that they totally didn’t).

A fun modification is to give them the problem with the values blacked out, like this example:

They can then discuss HOW they would go about the problem, focusing on ideas, instead of specific numbers. And then, when they felt like they were done with the group, I would give them the problem with the numbers included to complete individually.

I usually would combine this with a standard test (maybe the first question) and found that it really cut the tension in the room around an assessment (it was exciting!).

The Screencast

Good for: Presenting challenge problems, assessing understanding with homework, doing oral tests without taking up class-time, assessing understanding with coding

How it could work: This is an idea taken from Andy Rundquist (@arundquist) and many other science teachers that do this – students would take a picture of their work, upload it and record a brief 2-3 minute explanation of their work. They talked through the WHAT of their work, but also the WHY. Similar to the oral assessment, it was always super easy to tell who really understood what was going on and who was faking it. I would watch the videos and give them feedback, sometimes even requesting another video or a written response to my feedback. I especially loved this as a way to change up homework, and as a way to assess students’ understanding of the really tricky problems that we went over in class, or solved collaboratively. It was also great for assessing code because, again, it didn’t matter if everyone had the same code, I was assessing their understanding of it.

You really need an LMS, and to insist students do it the way that makes it easy for you to grade them in order for this to work, because otherwise it’s a technological hassle. I found students figured out the easiest way to do this, but would suggest Screencast-O-Matic if they needed a suggestion for an easy way to do this.

The Toolbox Assessment

Good for: Reviewing many learning objectives, forcing students to find their own examples of things and do the art of “problem-finding”

How it could work: When I have taught Statistics, I have used coding, which makes a lot of things quicker, and generally “get through” most of the material with 3-4 weeks to go at the end of the year. I found that students struggled with APPLYING the ideas though, so came up with the toolbox assessment. I had a list of standards and skills that covered the whole year (“Running a t-Test”, “Using a Boxplot” etc.), and they needed to design small, quick statistical studies that showed proficiency on these ideas. I had 13 of them, but they could check off multiple with a single study. They would complete a study and then “present” to me and have a conversation to show me their work and understanding. I told them not to worry too much about what their product looked like (i.e. no need for tri-fold poster presentations) and would sometimes send them back to fix or re-do something. Their grade at the end was about how many of the objectives they checked out. I loved this because it put the onus on them to really figure out where something applied, instead of just regurgitating problems I made up. Though it’s not as applicable to other math classes, I could totally see this working as a review activity before a final exam.