Manurewa Intermediate School (TLIF2-008) - Innovative teacher practice using materials in mathematics to support learning new concepts Publications
Teachers at Manurewa Intermediate School believed in the importance of having a culture of high expectations for their students but were disappointed that this was not translating into academic success.
Author(s): (Inquiry Team) Richard George, Ben Hutchings and Suman Shara
Date Published: February 2019
They knew that there is a wealth of research to support the use of problem-solving, hands-on activities, and learning materials to support students to develop and apply their understandings about mathematical concepts, but this was not being translated into their practice. They hoped that by developing their capability to use materials in innovative ways in their classrooms, they would combat student underachievement in mathematics and help their students perceive themselves as successful mathematicians.
T. Held the clock up and asked, “What’s the time?” [Diagnostic]
T. What type of clock is this?
T. The other type is …?
[Ss asked to translate analogue time into digital. … Two minutes into workshop, every child had contributed something to conversation, except for Jelly and Julie. … T. handed out problem. Ss jumped straight into reading. T held Ss back from jumping to the answer by applying the following question thread.]
T. What type of question is this?
S. Problem-solving question.
T. What are the steps to solving problems?
S. We read it. Then we read it again.
[Deliberate acts of teaching. T. reinforced importance of focusing on the comprehension.]
T. Next step?
S. Look for the math words and information – numbers.
S. To read out whole problem. [Julie! Awesome.]
[T. Asked who wants to talk about what the main maths information in the problem.]
S. It’s about how much time the watch adds on.
T. Who does not understand the question? Okay, talk in twos or threes about the information in the question and what it is asking you to do.
Excerpt from a teacher observation. Observer’s comments in square brackets.
The excerpt above provides a glimpse into what these teachers learned and what they achieved. We see a teacher colleague conducting a peer observation informed by mutual understandings of the goals for teacher practice and student learning. The collaborative approach taken by the teachers is mirrored in the discussions the students have with each other and their teacher – their teacher is prompting them to engage in mathematical talk and to focus on the strategies they need to use to solve a problem together. He uses a material object to help them think through and talk about the problem. And – in a surprise outcome from this project – he takes action to support the students to address the literacy demands of the task.
The initial project lead was Richard George. After six months, he departed, and deputy principal Ben Hutchings took up the role. Suman Sharan was the practice leader. A small pilot group at the start of the project later grew to include all members of the school’s mathematics team.
Facilitation services were provided by Cognition Education, first by Fiona Fox, then (briefly) Sean Heanaghan, and finally Dr Pip Arnold.
Further support came from Jeanette Saunders (St Cuthbert’s College) and Bina Kachwalla (CORE Education).
The inquiry story
Manurewa Intermediate School is a large school that is organised into departments within which teachers teach to their specialities. This innovation began with a pilot group of teachers who taught, between them, around 180 students. Their approach meant that they had a natural control group, not only with previous student year groups but with other classes taking a more traditional approach to mathematics teaching and learning.
What was the focus?
Manurewa Intermediate School has an ongoing problem with year seven students entering the school significantly behind expectations for mathematics. The school’s achievement data showed some accelerated progress for students in their time at the school, but it was not enough, particularly for Māori and Pacific students. There was a need for further acceleration and to change students’ mindsets so that they could see themselves as mathematicians.
The project sought to help students to develop new conceptual understandings in mathematics by using materials to promote high-level thinking and rich mathematical dialogue. The team asked, “Does innovative teacher practice using materials in mathematics support students to learn new concepts?”
An initial inquiry phase helped the team better understand their practice and its impact on students. The team realised that the traditional approach of frontloading concepts, providing opportunities for practice, and offering remedial workshops for students who needed it meant that they were focused more on ‘filling gaps’ than supporting students to explore mathematical concepts and make progress. Lessons were planned in blocks, with a lack of connection between different mathematical concepts, and this made it difficult for students to retain what they had learned. While teachers connected in their weekly meetings and sometimes cooperated, they didn’t collaborate. Concrete learning materials, such as beans, counters, dice, and tens frames were available, but teachers rarely used them of made them available.
What did the teachers try?
As the pilot group moved into the first phase of the inquiry, the teachers realised that they needed to move from a teacher-directed approach to one that was based more on inquiry and discourse. To support this work, they engaged in professional learning about the ‘talk moves’ (Kazemi & Hintz, 2014) required to engage in productive, learning-focused conversation. They developed their content knowledge and reviewed their understandings of what materials are and how they can be used.
The team had initiated their project with the assumption that their students thought concrete materials were babyish. When they asked students, they discovered that this was not so. Students said they liked using materials to help them think through problems and explain their solutions. They were interested in learning how to use materials for this purpose and felt that working in groups and being able to explain thinking would help them to make progress in mathematics.
Teachers began introducing more learning materials to the classroom. For example, they used Spinners to introduce probability and ratios, Deci-mats to develop student understandings about decimal place value, and a Cartesian puzzle for exploring parallelograms and coordinates. The team noticed that when students explored new concepts with the resources, they were more engaged with the learning and their conversations became more exploratory. They were forming their own groups and, because the concepts were quite often new, and the activities had ‘low floors and high ceilings’, the breadth of access meant fewer management issues.
As the inquiry deepened, so did the team’s questioning. The teachers focused their attention on the word ‘practice’ in their central inquiry question and began exploring a more open, problem-solving approach, in which control would shift more to the students. Returning to their original student voice data, they realised that their students did not have a clear understanding of what materials are. To aid clarity, the teachers used the Mathematics/Pāngarau Best Evidence Synthesis to classify materials into the following categories: symbols, diagrams, models, notation, stories, technologies, and concrete materials.
Teacher observation revealed that students typically use materials:
- to aid their thought processes; and
- to communicate their methods.
This was an ‘aha’ moment. The teachers realised that using relevant and engaging materials within the context of a collaborative problem-solving approach could help students not just to learn a new concept, but to retain what they had learned. The focus shifted to the creation of a classroom community of learners in which it was the teacher’s role to scaffold students to make connections between theoretical concepts and their application in realistic scenarios that the students understood.
The team sought pre-existing resources for facilitating a problem-solving approach, as well as developing some of their own. They found that careful planning was needed and developed a set process for scaffolding groups of students through their approach for inquiring into a particular mathematical idea. This was effective, but time-consuming, including, as it did, the need to work through problems themselves and identify potential misconceptions. Collaboration deepened as meeting time was set aside each week for teachers to work together in twos or threes to gradually develop a bank of co-constructed plans for inquiry. Meeting time was also spent on reflection and on helping each other through the deep learning required when making significant changes to long-standing practice.
To participate in mathematical conversations, the students themselves needed to let go of negative self-talk and develop a ‘growth mindset’. Teachers found they needed to communicate that while efficiency is desirable, what matters most in the first instance is that they find problem-solving strategies that work for them.
The problem-solving approach involves the use of scenarios in which students have to ‘find the maths’ and identify the clues that will help them come to a solution. This takes literacy skills. Teachers realised they couldn’t leave literacy learning to the humanities department. They needed to identify the literacy challenges in the tasks they were designing and plan how to support students to deal with them.
As the project was extended across the wider mathematics department, new teachers and pilot group teachers buddied up to work in each other’s classrooms. A process was developed for this. Processes were also developed to deal with the disruption caused when teachers left the school or department and were replaced by others.
What happened as a result of the innovation?
Attempts were made to connect with whānau, but these were of limited success and is the subject of further inquiry. However, the results for students and teachers have been significant. Students were confidently and flexibly attacking mathematical problems after just a few months of the new approach. Students in the first cohort – those taught by the pilot group teachers – enjoyed accelerated progress at a rate considerably higher than those whose teachers were not yet involved.
Teachers feel they know their students better and have a greater appreciation of the prior knowledge they bring with them to school. They understand that at times, assessment can blind students to what they can do by highlighting the areas where they struggle. They want to use these insights and the other learning from the project to continue their inquiry, looking, for example, at the use of digital materials in classrooms and video analysis as a professional learning tool.
What did they learn?
Learning from the project included the following:
- When students are a part of a classroom that uses innovative practice based around a collaborative problem-solving approach to mathematics, they will experience success, both academically and in their sense of themselves as learners of mathematics. Problems and inquiry ideas that work are context specific, culturally appropriate, and incorporate the deliberate use of materials for aiding thinking or communicating solutions.
- It is important to take time carefully constructing classroom cultures of learning that foster students’ identity as mathematicians and their ability to take part in mathematical discourse. Creating such an environment requires the construction of shared norms and expectations and the implementation of a clearly structured discussion framework.
- Literacy skills are vital to making sense of mathematical problems and communicating mathematical ideas. They need to be fostered through deliberately planned learning opportunities.
Anthony, G., & Walshaw, M. (2007). Effective pedagogy in mathematics/pāngarau: Best evidence synthesis iteration. Wellington: Ministry of Education.
Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics. Educational Practices Series, no. 19. Brussels: International Bureau of Education.
Boaler, J., & Dweck, C. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages, and innovative teaching. San Francisco, CA: Jossey-Bass.
Clark, M. (2002, December). Some problems with the emphasis on numeracy. Paper presented at the New Zealand Mathematics Colloquium 2002. Auckland University, Auckland.
Dweck, C.S. (2006). Mindset: the new psychology of success. New York: Ballantine Books.
Hunter, R., & Anthony, G. (2010). “Developing mathematical inquiry and argumentation”. In Teaching Primary School Mathematics and Statistics: Evidence-based Practice, ed. R. Averill and R. Harvey, Wellington: NZCER.
Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Steinhouse.
Watson, J.M. (2006). Statistical literacy at the school level: Growth and goals. Mahwah: Erlbaum Associates.
For further information
If you would like to learn more about this project, please contact the project leader, Ben Hutchings at email@example.com
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