You’ll see this structure all throughout Maths — No Problem! By offering students a learning experience just ahead of their development, Maths — No Problem! resources give learners a positive struggle. This approach helps move teachers organically towards a collaborative classroom, creating a learning environment that lets students switch easily and naturally between discussion with their peers and with teachers.
The Zone of Proximal Development
I recently watched a teenager in my class try to put a new protective cover on the screen of her phone. She was struggling to know exactly how to do it because it was the first time she was trying it. Along came her older brother who offered to help. He showed her how to put it on and she was able to learn the steps from someone a bit ‘further on’. She learnt from his experience. This is what Vygotsky means when talking about the ‘gap’ between the current developmental level of a student, and the potential level of where they could get to. He calls this ‘The Zone of Proximal Development’ (ZPD)— the level a learner is capable of reaching via the guidance of teachers or in collaboration with peers.
In practice, this means that as I plan for a lesson I might ask ‘what are they ready to learn now?’ That is, I want to design a lesson which broadly matches student readiness. I don’t want the lesson to be at their current cognitive level so that they stagnate, or offer something too far ahead so that they cannot grasp the concept. I have to guide the lesson knowing that the dialogue we share provides scope for most students to learn across their ZPD. For those struggling to grasp new concepts — they’re not at that developmental stage, or their learning intention is being reduced by social or affective factors — I’ll know that they’ve had the opportunity. And because of the spiral structure of Maths — No Problem! they’ll come back to it again, by which time they may be developmentally ready to grasp it.
A Collaborative Model
Students learn from and challenge one another when working collaboratively in diverse classrooms. Diverse and mixed ability settings can enhance learning — shifting from a model of teaching where teaching is something we do to a class, to a model where teaching/learning is something we do with the class. Maths — No Problem! invites us to create a learning environment which utilises talk and expression of thought rather than shutting it down.
The Language Instinct
One American educational thinker of the twentieth century, John Dewey, suggested even before Vygotsky that “the language instinct is the simplest form of the social expression of the child… and the greatest of all educational resources”. This might lead us to wonder if the collaborative classroom is worth developing beyond mathematics into other subjects where language and talk can also become a key model for learning.
So, I will leave you with some questions to reflect on.
- Firstly, can you recognise any collaborative situations in which you can see that your own learning thrived?
- Secondly, as you listen and observe in your maths classes this week, what do you notice about the kind of talk you hear when students work in pairs or groups?
- Thirdly, how does sharing the learning journey with your class in this way make you feel?
What I hope you’ll find is that a collaborative, “chatty” classroom is an enriching learning environment that will deepen all your students understanding and mastery of mathematics.