A few weeks ago the teachers from the Kahui Ako Maths Workstream went to Mayfield School to observe the way that they do maths across the school. At Mayfield School, they plan collaboratively across the school using the Upside Down Teaching approach. Strands are not taught in isolation. They entwined with problem-solving. Problem-solving is about open-ended questions - questions that have lots of possibilities for answers
In the Upside Down Teaching approach, the children work in mixed ability groups to do problem-solving. The pedagogy around the upside-down teaching approach is that it is a shift from 'I – we – you'
To
'You – we – I'
Which will create a shift to the children teaching each other and working collaboratively to work through problems.
What I Observed
Planning:
The teachers plan collaboratively across the school. Once a week they get together and design and plan the problems they are going to use to teach their maths that week. The teachers work collaboratively and design problems that can be adapted to be used across the school for a range of learner ability and age.
In Action:
The teacher would share a problem with a small group at a time (mixed ability to an extent). The rest of the class works independently on 'must do's, can do's' that are not only maths but a range of independent work across the learning areas. Problem is printed out and put up on the whiteboard. The teacher would read through the problem with the group and work out together what information was important from the problem and what kind of problem they are solving eg addition, multiplication etc. The children were given some time to solve the problem - some children chose to work independently while others worked in buddies or groups of three. The teacher would then go around and observe the children - discuss with them how they are going to solve the problem and she wrote down the strategies that each group used to solve the problem so that they could discuss them in share back time. After some time when it looked as though most children had an answer they all came back together to the mat. The teacher asked children to share back the way they had solved the problem and the other children listened and discussed what they liked about that strategy/ what they didn't understand about it/ if they did it another way and worked through the problem together. The teaching and learning was the same across the school with slight adaptations to suit each level of learner.
My Thoughts:
I thought that this was a really interesting and effective looking approach to teaching numeracy. The children all seemed really engaged in the problems and keen to find the answer, which I liked as I find that my class struggles to be engaged and excited by maths learning.
The Research Behind The Upside Down Approach To Teaching
The Traditional Right-Side Up Model
"One way to characterize this teaching approach is I-We-You. In other words, I (the teacher) will present the mathematical concepts and rules for the lesson; then We (students and teacher) will do some guided practice, where we walk through some examples of those concepts and rules, perhaps including word problems involving these same concepts and rules; finally You (students) will practice on your own and later do homework on what you have learned. This method is too often accompanied by several hurdles. First, some students don’t learn well from a teacher-delivered explanation; many become bored and, thus, disengage from what’s going on. Some students also see an error-free teacher explanation as further proof that they (the students) simply don’t have the “math gene.” They believe that mathematics is something only some people can do, as demonstrated by their teacher’s explanation and by the few students who seem to be able to master the particular concept or procedure being demonstrated. Most of all, when we primarily present students with problems for which they come to expect that they will apply the procedure they have just learned, we withhold perhaps the most important experience students need. We deny them the opportunity to dig into a problem, get a sense of what mathematics might be involved, constructively grapple with the underlying mathematical ideas, try out possible solutions and learn from mistakes they make in the process of coming to actual solutions." Smarter Than We Think by Cathy L. Seeley (Scholastic, 2014).
The Upside-Down Model
"Teaching upside down involves choosing to first present to students a problem they are expected to mess around with for a while, without having first taught them the particular rules or procedures they could use to solve the problem. Engaging students in this way helps them interact with the mathematics and sets them up to learn the mathematical content the teacher intends. Rather than the I-We-You structure used in many mathematics classrooms today, this model could be characterized as You-We-I: You (students) will mess around with a task for a while, ideally engaging in some thinking, trying things out, and generally wrestling with or constructively struggling with mathematics arising from the problem; then We (students and teacher) will discuss the different approaches students tried, with students explaining, questioning, clarifying, and further grappling with the mathematics; fi nally, I (the teacher) will connect this work and the class’s productive discourse around the problem and related mathematical ideas, facilitating the whole process and ensuring that students come away with the intended mathematics learning. "
Smarter Than We Think by Cathy L. Seeley (Scholastic, 2014).
Working in mixed groups and solving problems in peers - collaboration in learning
Working together to solve a problem will generate important social learning and life skills. Research evidence suggests that collaborative learning is associated with higher performance. Collaboration involves solving something greater together than we would have achieved separately. Communication is central and also the key to learning.
Problem Solving and The Importance of Reporting Back.
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