ERO’s June 2010 report Promoting Success for Māori students: Schools’ Progress highlighted the importance of good classroom teaching and better relationships for raising achievement expectations and enhancing outcomes for Māori students.
The students at ROSCOMMON SCHOOL are mostly Māori and Pacific; historically, many had experienced little success with mathematics. Teachers enjoyed good relationships with the students but realised that this was not enough: they needed to start expecting more of them mathematically. They saw that it was only by changing and/or improving their teaching practices that they were going to raise mathematical achievement.
This narrative describes how the school improved the effectiveness of its mathematics teaching with the support of an extensive professional learning and development (PLD) programme. We show how the leaders worked with the external providers to ensure that the PLD matched the strengths and needs of teachers, and how they monitored what was and was not matching a teacher’s needs or working for children. Finally, we share observations from mathematics lessons and include children’s perspectives on the strategies they had been newly introduced to.
In discussions about classroom practice, leaders and teachers agreed that they wanted to put in place teaching practices that would more effectively engage students in problem solving, deep thinking and learning. These aims were to become major emphases in a redevelopment of the school’s mathematics programme.
During staff meetings leaders asked teachers to look at mathematics achievement data and identify children’s strengths and weaknesses. They were then asked to think about possible reasons for the weaknesses they had identified. This challenged teachers to think about how their own teaching practices could be a contributing factor in underachievement.
Careful scrutiny of the data revealed that, while some parts of the number strand were evidently well covered, many children had little understanding of geometry, fractions and algebra. Teachers revealed that these topics were in their long-term plans, but often near the end of a term, so they would run out of time to teach them.
Sensitive questioning by leaders supported teachers to think more deeply about their practice. Many had the courage to recognise that they had not been taught mathematics well themselves and, as a result, avoided some parts of the curriculum or rushed through concepts without appreciating connections that children needed to make for their future understanding. Following honest and challenging discussion, teachers and leaders identified three priorities:
To improve mathematics achievement, the school applied for Ministry-funded PLD in numeracy. An associate principal, who had previously participated in Accelerating Learning in Mathematics (ALiM) PLD, argued what was needed was more intense, school-wide PLD that would simultaneously strengthen both content knowledge and pedagogical knowledge.
The leadership team worked closely with the external provider to ensure that the PLD would promote culturally responsive pedagogies. They discussed the strengths, needs, sensitivities and preferred ways of working of the different teachers, as well as cultural considerations to be kept in mind when working in a school with Māori and Samoan immersion classes. They stressed the importance of knowing the teachers as learners, just as teachers are expected to know their students.
“We had to build a trusting relationship with the PLD provider. We knew that it had taken a lot of courage for so many of our teachers to reveal that they weren’t confident with mathematics so we wanted them to be supported to learn rather than be embarrassed by their knowledge gaps. Group work was key so teachers could use their combined knowledge to solve things and they could see how their children might like to learn in their classes.”
“The first time the facilitator put a maths problem on the white board, almost everyone looked away. You could see that they didn’t want to be chosen to answer it in front of their colleagues.”
In team and staff meetings, maximum time was spent on collective inquiry into the effectiveness of teaching practices. Teachers collaboratively analysed their student achievement data to see the impacts of their changes. They discussed the strategies they used that were working or not working for children.
Many staff meetings and teacher-only days became mathematics workshops for the whole staff. To meet the teachers’ extensive content needs some workshops were held during the weekends or holidays. The PLD put the teachers in their students’ shoes as they worked together to solve mathematical problems. They were shown strategies and approaches they could master and then use with the children. In time, mathematics leaders and school leaders were able to take some workshops without the help of external experts.
School leaders closely monitored the teachers’ progress and confidence. At the end of each PLD session or workshop they discussed with the providers what was working and for whom, who was disengaged, what needed to change, and what the next steps were for teachers. This helped ensure that all teachers were getting to grips with the new strategies and approaches.
This practice of debriefing was also observed after sessions facilitated by teachers or school leaders. An algebra workshop led by school mathematics leaders highlighted for them some of their own less successful teaching practices.
“It is interesting watching and being the learner in the workshops because we learn about content and teaching practices. Even last night, when we had a maths workshop as a staff, my own behaviour taught me something about how my students may feel. We looked at a problem and I had worked out a different way to solve it. I was just about to show my group when the teacher running the workshop came and told the group my different way. I almost felt angry because it was the way I was going to show and I didn’t get the chance. It taught me about ‘wait time’ and resisting interfering too early when my kids are working on a problem.”
In the whole-staff workshops the teachers practised voicing their thinking, asking questions and expressing their ideas in mixed-ability groups – the very skills they wanted the children to develop.
Teachers did the bulk of their PLD as a whole staff, in their teams, or in house groups that included teachers from across the year levels. In staff meetings they were able to workshop new content and approaches. In team meetings they were able to reflect on and respond to assessment information. In house groups they were very aware of what had gone before for the students, and what they learned next.
The PLD was also designed to give teachers the capabilities to develop mathematical inquiry communities (MICs). In MICs, children work in mixed-ability groups to discuss, negotiate and solve problems. Like the reading PLD that Year 5 and 6 teachers were already engaged in, MICs emphasise voicing thinking, asking questions and expressing ideas – pedagogies the teachers were keen to explore further.
The fact that the mathematics PLD involved a major financial commitment made leaders even more determined to make sure it would have a positive impact on achievement.
Leaders carefully managed the two different types of mathematics PLD occurring at the same time. In practice, this meant varying the time and resources allocated to the one or the other. While focusing on learning about the MIC approach, teachers would put less time and energy into building content knowledge.
Leaders and teachers elected to keep some of the practices that had been used previously. These had to be justified on the grounds that they were working well and having a positive impact on achievement.
“We still do warm ups at the beginning of a lesson as a quick revision and sometimes we do rotations, where kids go to every teacher in the team. At first, the facilitator didn’t like that but when we explained why we wanted to do it they said it was OK.”
“When we had done some work on fractions we checked how the kids were going and saw that many still didn’t understand fully. So we went back and did more workshops and only gave them two problems to solve a day in their mixed-ability groups. We will see how that works.”
Children learning mathematics through the MIC approach told us they understood what their friends knew and didn’t know. They saw each other as learners and valued the opportunities to work together with other children. When solving mathematics problems with a buddy, they were happy for the teacher to come to them and help at times when they were at an impasse and needed ‘just in time’ teaching.
ERO observed a lesson where Year 3 and 4 children were working in twos or threes to solve problems. One group was working out how many containers they needed to make 18 cups of smoothies when their container held four and a half cups. When children felt they had an answer, others in the group reminded them to share what they did with the others.
The children explained they were still learning how to share and ask questions of each other and they showed us cards they had to help remind them (shown below).
They also told us they have to take responsibility for understanding things. “We have workshops and if you don’t understand, you stay on the mat. The teachers will explain it again or get us to explain what we understand and then go over it with us.”
Children explained the norms they practise every day. “We talk about how we did with it at the end of the lesson so you have to keep it in your head. Today’s norm was ‘when someone is talking we give them our full attention’.”
Reminder cards the children used to help them question their peers.
In another classroom, children told us they understood the teacher was there to help them with their learning. They also knew that their peers were there to help them and that they were there to help their peers. Teachers encouraged these mindsets by avoiding immediately offering solutions, asking children to explain their thinking so far, and reminding children to listen carefully to the ideas of others in the group.“I like explaining to others if they ask. This helps me understand and helps the other person.”
“Everyone is good at maths ‘cause we work to their standard. They take risks and never give up. Our teacher encourages us to keep trying.”
“If I don’t understand I ask a question. I don’t feel embarrassed.”
“Teachers care about your learning. They want us to move up to a higher stage and want us to be at a better standard. They tell us to never give up – it doesn’t matter if the answer is wrong as long as we have given it a go.”
Year 5 and 6 children
When we visited the school, teachers were still consolidating new strategies and practices but many changes were already evident. Long-term overviews had been modified to make sure the children experienced the full curriculum. Concepts and skills that the children found hard to grasp with confidence (for example, fractions) were now taught several times during the year. Teachers varied the amount of direct instruction and ran workshops to address specific gaps while making sure the children had frequent opportunities to solve problems in mixed-ability groups.