Last Friday, we took a massive leap in what we hope is a forward direction. The Maths coordinator (@Jason_Loke) and I gave our students a summative assessment task that could potentially change the way we assess students in maths.

In South Australia, we have two main types of assessment in mathematics: Folio Tasks (Mathematical Investigations) and Skills and Applications Tasks (typically – Tests). The main difference between these two types of assessment is that students can complete Folios unsupervised whereas SATs must be supervised, hence why 99.9% of teachers give their students a test. No surprise about which assessment type counts for more of the students’ final overall grade.

This semester, we have made a particular focus on teaching our students through Problem Based Learning activities. These have been a great way to get students engaged and learning mathematics purposefully. Problem and Inquiry Based Learning strategies have allowed teachers to develop a need for the learning of maths, structuring their lessons to promote inquiry as the driver for learning and embracing productive struggle. Further to this, we took it to the next level by creating tasks that were interdisciplinary so that the learning didn’t stop when it became more “sciencey”.

Traditionally, we handed out tests to students at the end of the unit to measure their ability to pay attention in class, learn the content we were required to teach them, and answer problems that scaled their understanding in a way that allowed us to label that student with a grade. The “high end” students found it too easy, the “lower end” students found it too hard, and it was a waste of time for at least 40% of the students. It also reinforced the idea that mathematics is something that should be memorised in case you encountered that weird situation when you can’t research anything or ask anyone else for help, and you need to solve some mathematical problems. As well as this, our students seem to finish every topic across their subjects at the same time, which produces a tsunami of tests and deadlines, further pushing the message that the purpose of learning is to be assessed.

These weren’t the messages we wanted our students getting. In fact, they’re the ones that we’re fighting against on a daily basis. So, we felt that it didn’t really make much sense to give students a topic test at the end of the unit. Here’s what we did instead:

### We gave it to them before the end of the unit

We didn’t assess them on what we expected them to already know. Most students had an awareness of the different forms that quadratics/parabolas are represented in (standard, vertex, and factored/intercept form), but few had much experience in coming up with these based on key coordinates (vertex, roots/zeros). Much of what they were being assessed on was to be learnt from working through the task. Students were then required to explain their strategy and thinking behind it.

### We assessed them using a Desmos Classroom Activity

(this activity can be found here)

I had personally been using Desmos activities a lot in my lessons. The main aspect that makes Desmos so different from other graphing tools is its accessibility to all students. They don’t need to overcome the hurdle of operating the graphing tool, nor do they need to follow a strict input process. Students are able to operate the graphing tool with ease and can explore the mathematics sooner, with less stress and anxiety (let’s be real, input error codes on calculators are the cause of death of 83% of all graphics calculators).

Without harping on too much more about the awesome benefits of Desmos and the cool features it has, I can honestly say that it made the task what it was. The level of mathematics that the students were able to engage with and the difficulty of the problems through which they learnt it was of a much higher and conceptually deeper level than what was possible in a test. The interactivity and scope to question students’ thoughts before posing a problem allowed us to scaffold the task in a way that promoted inquiry as the driver for learning. We used interactive graphs to hook students and make the maths seem less abstract and more real.

### Students could work in pairs or groups of three

This was an uncomfortable situation for the teachers and students who still thought this task was a test – which it wasn’t. For everyone else, it was the main strength of the lesson. Teachers didn’t have to sit back and watch their students stare blankly at the wall while they waited for the time to finish, and students weren’t peering at each other’s papers when they didn’t know what to do. Instead, students *asked questions*. They asked their friends first, then they asked their teacher. The teacher then responded with a question, which got them discussing and trying different approaches. Some students were arguing, while others were explaining. All students were communicating their mathematical understanding in some way. The noise level was high, but so was the cognitive demand and learning outcomes.

Disclaimer: All students were required to sign into Desmos and complete the task on their own computer. One of the questions required them to input their partners names. Students also submitted their own handwritten notes to show their working out to specific screens of the Desmos activity.

### Teachers could monitor how the students were going – all at the same time

Jason in particular loved this feature of Desmos. In real-time, the teacher has the ability to see which screen each student is currently viewing, as well as their responses. Through the dashboard, the students’ responses are collected and viewable on the teacher’s screen as the student types their answer or graphs a function. This allows the teacher to quickly spot a student or group of students who have been stuck for too long. This feature allowed our teachers to realise that there was not enough time given for the task, and we were able to let other maths teachers know that the students would need to have more time than what was initially given.

### Final thoughts

I personally think that this online tool could be a massive step in the right direction for providing more authentic and challenging assessment tasks in maths. If Desmos were to build an “export” feature to allow teachers to download individual student responses, I think many more teachers would be more willing to use tasks like these instead of a topic test here and there.

What are your thoughts? Would you be willing to run a Desmos Classroom Activity instead of a test? Why? I’d really love to hear your thoughts!

I love this – I would be happy to assess using Desmos; I do need to assign grades, and I wonder about the feasibility of reviewing all the work with over 100 students in Algebra 2. But it’s a wonderful idea to ponder.

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Thanks Wendy, there was a fair bit of discussion about this at the Maths meeting. I had 50 students to mark across two Year levels. We assessed it using a rubric (performance standards) and gave whole grades rather than + and -. If it’s any consolation, they were more interesting to mark than a test?

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And much more revealing of student understanding, I am sure. Going to keep it in mind, for sure – thanks!

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What a great idea to use Desmos for assessment! I’m not sure how open my school would be to using it. I would probably have to make up a complex rubric to justify the grades. How many of these assessments have you done? How many class periods did students have to complete this? Did all work need to be done in class? What did you do if students didn’t want a group?

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Thanks Jennifer, we use rubrics to mark any task, so it was great that the teacher judgement of the work against the rubric allowed for grades to be assigned more authentically. This is the first one we have tried. We initially thought it would take 100 minutes but took about 120 instead, which is pretty long. Had they already learnt the content prior to the session, they would’ve been much quicker. All work technically needed to be done in class as it was a task that was under direct supervision. We had some students who didn’t want to be in a group and they were allowed to work individually. Hope that helps! 🙂

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