Disclaimer: This post is purely about my own experience about teaching maths without worksheets. This isn’t an attempt to discredit the validity of all worksheets… just most of them.
This semester, I set a challenge to myself to refrain from handing out any worksheets during lesson or for homework. I did this because I felt like there was a disconnect between how I was teaching and how I was expecting my students to work during class time. The topics that I was teaching this semester included Exponents & Logarithms (index and log laws), Polynomials (big focus on Quadratics/Parabolas), and Rates of Change (introduction to Differential Calculus). Around the same time, I was working with some primary (elementary) schools about creative ways to develop students’ fluency in mathematics. When they asked about what I did in my own classroom, I felt uncomfortable admitting that I resorted to handing out worksheets, expecting students to develop a deep level of understanding through practice. I came to the realisation that handing out worksheets wasn’t solely the issue, rather the purpose that I expected it to serve. So, I went cold turkey – no worksheets. Ever.
Thankfully, I had plenty of magnificent people to steal ideas from, ask questions of, and share thoughts with. These people, The Global Math Department (if you don’t know them, you need to meet them #MTBoS), transformed the way I teach and how my students learn. My aim was to help students develop a stronger, broader, and deeper conceptual understanding of the mathematics they were learning. For me, as a teacher, it is the exploration of mathematical concepts (often through efforts to find ways to engage my students to learn them) that has allowed me to develop a strong understanding. I didn’t practice problem after problem to try and master procedures, or become super-quick through doing so. So, I don’t expect my students to do the same, nor do I think that they will become better learners if they do.
It was tough though. Resources that I had previously printed off and used as gap-fill in my lessons were now obsolete. When teachers handed me spare copies of their worksheets, which I would have previously photocopied for my students, I now awkwardly took them and added them to my scrap paper pile face down on my desk. Initially, my students were expecting and even asking for worksheets in class, assuming that it was the next part of the lesson or the homework to be completed. With the students, at least, I was able to have an open conversation with them about why they wanted a worksheet and it often led to reasons centered on being ready for a test. This is what kept me motivated.
More work. That’s usually what change initially feels like and boy, it did. Instead of planning the first 40% of the lesson before serving the three-course set menu of worksheets, I was thinking more critically about where the students needed to be in order to be ready to push their understanding to the limits and discover the next concept or key idea. One blog post that I’ve been quite significantly influenced by is Jon Orr’s Hero’s Journey in Math Class. He writes at length about two really important aspects of learning that I spend a lot of time trying to get right as a teacher. Productive Struggle and the Development of a Need to Learn. My efforts to do this in my class can best be followed by reading some of my blog posts over the past couple of months, but here are some more specific examples of what took place of worksheets in my sessions:
A big reason that many students feel practice is important is to ready themselves for a test scenario. Can you do the maths in isolation under a certain amount of time? Why is that so important? Unfortunately, this has been the main focus for many students, and perhaps even more unfortunately, some teachers too. Our assessments needed to also challenge the status-quo. Not because new is always good, but because old didn’t match up with what we wanted the students to understand about mathematics. I try to help my students connect their understanding from topic to topic, subject to subject, and year to year. I do this by making them feel like there is a clear purpose for why they need the maths before actually learning how to “do it”. I would emplore you (especially if you’re still reading the post all the way down here) to read my post on Ditching Tests for Desmos. Then, try it in your class. Here were our four tasks this semester:
- Exponents & Logarithms Test (boo)
- Quadratics Desmos task (see Ditching Tests for Desmos)
- Polynomials folio task – based on graphing out narrative tension in films or books
- Mathematicians commentary (Rates of Change) – justification / motion analysis of a film students made for another subject
Apart from the first test, which the students nailed by the way, the assessment tasks focus on students’ ability to communicate their understanding of mathematical concepts.
Teachers are always looking for something to quantify the effect pedagogy has on student learning. Usually, this is done by handing out and analysing tests, surveys, and other formative work (e.g. check quizzes). I’m not sure if we can ever expect to find a clear-cut answer to justify our choice to educate in a certain way, but I think reflection is incredibly important. Here are some things that I noticed in my class when I stopped handing out worksheets:
- More discussions. Like, heaps more.
- More questions. Better questions.
- More students asking for re-explanations or clarity on their thoughts.
- More collaboration and arguments (good ones – based on maths).
- Less sheets left on tables at the end of lesson.
- A greater sense of community amongst the class. More group-based problems helped with this.
- More use of graphing tools, such as Desmos.
- Less stress about skill development for test preparation.
- More a-ha moments. Louder ones too.
Do you think I’m crazy? Please comment below, I’d love your thoughts, challenging questions, or any other comments that you have!
9 thoughts on “Maths Without Worksheets”
Great post. I’ve been working on getting rid of “worksheets”, or at least transforming them. Getting easier to assess Desmos activities as they add features. I think what you’re doing is great, and can’t wait to hear more about it.
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Thanks Jonathon. I think it’s really quite a commitment to maintaining and following through with inquiry based pedagogy. Sometimes it can be easier to slip back into old habits (especially because we’re so time poor as teachers). Have a look at my post on reversing the question, I claim that it’s the best worksheet I’ve re-written/transformed.
Excellent post! You are challenging my thoughts on teaching with worksheets. I need to do this in physics!
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Thanks Jen! Worksheets aren’t necessarily bad. In maths, it is common to see a list of 20-30 questions given to students to complete, with little direction or pedagogical basis.
Great post John, thank you! As a primary school leader who is passionate about helping students develop a real love of learning, I often engage in rigorous two-way dialogue with our middle school teachers about how they approach teaching Maths for deep understanding… I will certainly be alerting them to your blog and look forward to reading more about your work in this area.
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Hi Josh, thanks for your comment! The work I have done this year with PS teachers has impacted my own practice significantly. There’s so much to be learnt and shared, the more teachers are able to connect with each other, the better it will be for the students’ learning journeys.
Hi John! I really dig this post. I think it’s always productive to think about how we align our teaching purpose to classroom practice. Sounds like you successfully got more about what you value (discourse, thinking, questions…) by shifting student focus toward thinking about problems rather than focusing on completing worksheets.
At the end of my classroom career, I had it dialed in where my (alg2, precalc, call) handouts were half filled in notes, partial examples, pair-share-table discussion prompts. I found it helpful for me to see them express their individual thinking using white space i had created in a general format. It also greatly reduced notetaking time where kids would copy crap. Such a waste!
Anyway, i’m curious to see how your pendulum moves to find that sweet spot of student learning and the role that teacher generated content plays in the classroom!
Thanks for the inspiration!
Thanks for your insight, Chase! It’s a funny thing (teaching), I’m sure that I’ll never be completely satisfied about the way I’m working with my students but I guess that’s what keeps us motivated to change what we do to continue meeting the needs of the students. I’ve just signed up for your newsletter and I’m looking forward to checking out your stuff! Cheers!
about that newsletter.,.. i need to get on that. 🙂