A Year of Mathematical Freedom
Replacing stress and conformity with enjoyment and creativity
I hated maths at school.
As a student, mathematics was a confusion of disjointed concepts to be memorised from page upon page of joyless, sterile and seemingly endless textbook problems. It was about speed and rules and conformity. Correct answers were currency. Every test score, grade and report comment only served to reinforce that I wasn’t a math person. My experience never deviated from the traditional.
Fast forward to today, I love teaching maths. Love it. My approach is pretty simple; I try to be the teacher I needed in school. If I could go back in time and give advice to my younger self, I’d let that little kid know he is a maths person. He needn’t feel dumb because eventually, he would begin to connect the dots rather than merely collect them. I’d tell him, absurd as it might seem at the time, that one day he’d be teaching the class.
Still, I feel a little imposter syndrome when I write about maths because I’m not a specialist. When I hit the publish button on Self-Reporting Grades in Maths early last year, I didn’t expect anyone to read it. I certainly didn’t expect it to be my most read post of 2018. What this post’s popularity tells me is many others have shared similar experiences and/or connect with the idea of reducing math anxiety.
In Self-Reporting Grades, I made this claim:
“Taking grades, scores, percentages, and competition out of our maths lessons has had a significant impact. And I’m not just talking about growth and achievement; I’m talking enjoyment. Students like learning maths in this environment. They don’t avoid “the struggle”, there is less fear of failure, in fact, we rely on it. Failing forward is the common factor in our room; if we aren’t struggling and making mistakes, then we probably aren’t learning.”
Nearly a year later, I stand by this statement and I put it down to one thing; mathematical freedom. But before I dig into that, I want to acknowledge the elephant in the room. Social media is replete with highlight reel success stories about the impactful and empowering learning that happens in classrooms but rarely do we hear from students. So for this post, I’ve weaved in some student responses from end of year conferences (with permission). As always, I share this in the hope that someone, somewhere, will find it useful.
“I’ve definitely found Maths different to previous years because before it was sitting down and simply filling in a worksheet and waiting for a score, but this year we’ve been given more choice over what we do and how we choose to do it. I’ve enjoyed doing more hands-on activities and collaborations.” — C.H.
According to Dr Jo Boaler — Professor of Mathematics Education at Stanford University- mathematical freedom involves creating environments where learning is more highly valued than performing. Boaler expands this concept in the 2017 article “Math Class Doesn’t Work. Here’s the Solution.”
In my classroom, mathematical freedom looks like:
- No grading day-to-day learning
- Formative feedback
- Regular self-assessment
- Open problems
- Authentic assessments
- Student controlled evidence of learning portfolios
Pedagogy aside, the hidden curriculum of mathematics has a huge impact on the attitudes and beliefs of students before a single lesson has been taught. Unlearning the performance culture that has stripped creativity, joy and wonder from an essential life subject might be the biggest challenge for educators who, like me, only experienced maths as highlighted in the left-hand column of the Freedom Scales featured above.
For educators contemplating change, I would say this: creating a culture of mathematical freedom is greater than the sum of its parts. While collaboration, flexible learning spaces, technology and assessment are also important parts of the whole in our classroom, this post focuses on the impact of mindset, open problems and organisational flexibility, and de-emphasising grades.
Believe You Can And You’re Half Way There…
“In previous years I doubted myself in maths thinking I wasn’t good enough. But when I came into this classroom my teacher understood me and helped me realise that I was pretty good at maths.” — P.J.
“I enjoy learning maths more now because I feel that if I try hard enough, I can learn it (eventually).” — A.T.
Helping students find their mathematical strengths is a big part of the job. How important is a little belief? Priceless. All kids bring something to the table, taking the time to help them identify their math qualities and strengths, rather than focusing on deficits, is time well spent. And it does take time, there is no quick fix. As Carol Dweck points out, one of the biggest misconceptions about growth mindset is,
“That it’s easy to implement. It isn’t. It’s really hard to pass a growth mindset on to others and create a growth mindset culture. It’s not about educators giving a mindset lecture or putting up a poster — it’s about embodying it in all their practices.”
Are we teaching mathematics to kids or teaching kids to be mathematicians? If it’s the latter, then we need purposely help students to understand themselves as mathematical thinkers. The speed + fluency = excellence stereotype is difficult to overcome, particularly when many parents with fragile math identities unknowingly perpetuate the same messages at home as a result of their own maths trauma experiences in school. The diversity of skills and thinking that students bring to the classroom is something to be celebrated, and that starts with us.
If you have quick mental recall in maths that’s great, but it doesn’t make you superior to others. Some very famous mathematicians are slow in figuring out answers” — D.S.
Open = Trust
I like that I can find different ways of getting an answer instead of just finding the answer “the right way.” — C.K.
Open — or low floor/high ceiling- problems are similar to essential or non-googleable questions because they encourage the use of diverse strategies and pathways to arrive at a variety of answers depending on the learner’s understanding. We frequently use open problems — DESMOS, Open Middle, Youcubed and 3-Act problems are our go-to sources right now- and students love them. Why? I think it boils down to trust.
When I look at the right-hand column of the Freedom Scales, I see trust. Working on problems as long as it is useful; collaborating; sharing thinking; valuing different interpretations and methods and answers. Open problems and organisational flexibility provide students with the opportunity to have a sense of control over learning, seek to learn and improve for intrinsic reward, and the ability to connect learning with their own goals or interests, what Dan Pink describes as autonomy, mastery and purpose.
The Depth Of Knowledge (DOK) required to solve open problems also plays an important role.
“Depth Of Knowledge is like the depths of the sea. You have shallow stuff like DOK1 problems which can be worksheets or simple math problems that have a right or wrong answer. You don’t really have to think about them too much. DOK2 & 3 is the deeper stuff when you need to dive deep and put a lot of thought into your answer. There are lots of different ways of doing it and somebody else might have a different point of view.” — E.K.
“To me, depth of knowledge is about how much you have to think when trying to solve a problem. I like doing Open Middle questions because I can collaborate with other people and we can share our thinking with each other.” — P.J.
Problems with a high DOK ask students to demonstrate conceptual understanding, low DOK problems often require procedural skills and fluency. Again, this can be demonstrated by the differences between the two columns of the Freedom Scales. Low DOK tasks can be done alone, sitting at a desk, following a procedure. High DOK tasks encourage collaboration, discussion, and creative solutions. Both have value, but which one do you think learners enjoy doing most?
Learning > Performing
It doesn’t explicitly rate a mention on the Freedom Scales, but arguably, de-emphasising grades has had the biggest impact on learning in our room. Freedom from the constant judgement of scores and grades is something that I can offer in my room.
“Giving people grades isn’t always a good thing because if they get a bad score it can lower their self-confidence. Removing tests has definitely been positive and lifted the stress off my shoulders.” — C.K.
In the past, I’ve been guilty of pushing through content at breakneck speed to ensure we covered as much of the curriculum map as possible. Didn’t quite grasp that concept? Sorry kiddo, maybe next year.
But last year, I gave myself permission to slow down. In turn, this gave my students the time and space to struggle, wonder, explore and create rather than “learn and burn” to pass a test. In fact, we pretty much stopped testing at all. When test scores are off the table, standardised norms, competition, and cheating become redundant. Opportunity replaces compliance.
We do still use a few diagnostic tests as formative feedback to inform future teaching and learning rather than as a summative score to go in the gradebook because as Alfie Kohn points out,
“There’s a difference between using them to figure out who needs help — or, for more thoughtful teachers, what aspects of their own instruction may have been ineffective — and using them to compel students to pay attention and complete their assignments.” — Alfie Kohn, Why the Best Teachers Don’t Give Tests
Students are willing to take on and persevere with challenging tasks at the edge of their understanding because there is no point scoring to be done, no punishment for failed attempts, only progress to be made.
“Removing tests has impacted me in a good way because knowing I couldn’t answer all the questions used to make me feel like I suck at maths.” — A.T.
So was our year of mathematical freedom a success? I observed students become more confident, persistent, collaborative, and engaged in the learning. For the quantitative data crowd, our standardised testing results showed student growth of achievement was among the highest in our partnership. Interestingly, everyone passed. Even the ones who school normally says shouldn’t; the learner with attendance issues, the students with disabilities and difficulties, the kids with test anxiety, all of them. Not because I lowered the bar, because they deserved to.
But the data I trust the most? Kids. Listen to them, they know.
A couple of questions I have moving forward:
- Can mathematical freedom ever really exist in traditional schools?
- Wouldn’t true mathematical freedom require the learner to be intrinsically driven to purposefully pursue answers to a problem of personal interest?
I’d love to hear your opinion. Hit me up in the comment section or tweet @arbay38 on the Twitter.