08 Undertaking an inquiry to build and extend teachers’ mathematics teaching capabilities

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ERO’s July 2012 report Teaching as Inquiry: Responding to Learners found that, although many teachers were engaging in classroom-based inquiries, they were less likely to reflect moment by moment on how changes to their teaching practice were impacting on learning, or to adjust them accordingly.

Four teachers at WAIPAHIHI SCHOOL undertook inquiries into practices designed to accelerate mathematics achievement. They used a variety of strategies to improve their teaching approaches and outcomes for children.

In this narrative we describe the strategies that the teachers introduced and the children’s responses to them. We also describe the processes used by the teachers for reflecting on and responding to the emerging outcomes. The collaboration between the four teachers enabled the practices to spread more widely across the school.

In Waipahihi School well over 85 percent of students meet the expected level for mathematics by the end of Year 6. This result follows improvements that can be attributed to the school’s recent involvement in Accelerated Learning in Mathematics (ALiM) professional learning and development (PLD).

As part of their involvement in the ALiM PLD, four teachers undertook an inquiry into how they could accelerate the progress of some of the students in their classes. The target group for the intervention consisted of 20 children from across the four classes. Each teacher worked with their group of target students in the classroom for 30 minutes four times a week. By the end of the 11 weeks of the intervention all but two of the students had made considerable progress.

To accelerate achievement, two of the teachers introduced peer mentoring while the other two concentrated on increasing the children’s ownership of their own learning. The teachers also explored ways to extend the use of visual aids and other technologies in their mathematics programmes.

Increasing children’s ownership of their learning

In the two classes that were working on peer mentoring, teachers used multi-ability pairs or small groups to ensure that each target child always had the support of a more confident peer, plus access to more sophisticated strategies. Simple measures such as requiring the two children to use only one book, worksheet or device meant they got used to working together and developed a shared sense of responsibility for the learning. As the children began to rely more on each other, teachers found they had more time to notice where children were succeeding and where they were confused.

To enhance the target students’ ability to engage in mathematical discourse, the four teachers introduced them to the five ‘talk moves’. Using this tool, the students sharpened their ability to think mathematically, explain their mathematical ideas and seek clarification of others’ ideas. The teachers asked the children to repeat and rephrase each other’s thinking to show they were actively listening. The teachers found that, by increasing ‘wait time’, they could reduce the anxiety experienced by children when asked to explain their reasoning or solve a problem. The children learned that they could not opt out of mathematical discussions when in a larger group with the teacher, so they listened more closely to their peers.

This is a set of two images one using a chart to solve problems the other a child using online resources

Children get direct instruction from online resources before working with teacher or peers

The peer mentoring worked well for both the target children and their mentors. At the end of the intervention the target children said they liked being taught strategies by their peers because they found it easier to understand their language. The mentors said they felt more confident to explain their ideas and strategies to others, and by the end of the intervention were enthusiastically offering to ‘be the teacher’.

Using visual prompts and other technologies

Teachers used visual prompts such as sentence starters to explain a process that reminded children of the discussion and mathematical strategies to apply.

Using the ‘flipped learning’ principle, the teachers trialled making instructional videos available to students online. They found the website www.teachertools.co.nz to be a valuable source of videos that explicitly explain different mathematics strategies. The students would watch the selected videos before the lesson and then apply what they had learned in class with the teacher.

The teachers found apps such as Explain Everything and Maths Shake useful for getting children to identify the steps in a solution, manipulate digital materials and record thinking. The playback function was particularly useful when it came to reflecting on recent learning.

Improving teaching practices

Early in the ALiM PLD the four teachers had formed an inquiry team, with the intention of meeting regularly and sharing their reflections. However, they had not always found time to meet. They knew they had to increase the level of collaborative activity and do more to sustain collective decision making.

In the second year, leaders gave them two hours of classroom release time every fortnight so that they could meet to plan and reflect. The team used the Effective Pedagogy in Mathematics/Pāngarau Best Evidence Synthesis to inform their changing practice, focusing particularly on the use of mathematical language and the implications of the ‘ethic of care’ principle. Over time the emphasis of their discussions shifted from their teaching to the children’s learning.

The four teachers regularly communicated about changes they had observed in the children and about inquiry processes that had benefitted their learning. Prior to their regular meeting they would do short, formal observations that they could share with their colleagues.

Over the two years of the intervention, the level of collaboration, an integral part of the inquiry process, increased. Supported by regular coaching conversations, the teachers were able to:

  • plan effectively for their target group
  • guide each other through the challenges
  • reflect on their own professional learning.

Following the end of the ALiM intervention, the number of teachers working collaboratively in pairs to look at data and reflect on their teaching practices continued to increase across the school. With the encouragement of school leaders, ‘talk moves’ and learning buddies in multi-ability groups became widespread classroom practices.

As they redeveloped their mathematics curriculum, the teachers looked closely at what they believed and whether their actions were consistent with their beliefs. If they noticed misalignments, they investigated how they could change their practice. Leaders also asked the children what they felt their teachers did that helped them with their learning. The end result was a curriculum that promoted more authentic learning and which was more seamlessly connected to the other learning areas of the curriculum.

By improving how teachers worked together and inquired into their teaching practice, the ALiM PLD improved outcomes for students.