When one Te Toi Tupu maths facilitator worked alongside a Lead Teacher (DP) in mathematics, she observed the teacher demonstrated the skills of an effective practitioner. The teacher had a sound understanding of mathematics, a strong relationship with her Year 7 and 8 students and was very organised with task boards and support material around textbook work. At the time, the teacher felt the best approach to the teaching and learning mathematics - was ability grouping.
During the professional learning and development, the teacher began working through a problem solving approach with mixed ability groupings. Her thinking shifted dramatically. Problems were pitched at a challenging level and students worked independently, then collaboratively in different pods or groups that catered for students with varying degrees of ability.
This problem solving approach was based on a Framework of '5 Practices for Orchestrating Productive Mathematics Discussions’ (Smith & Stein, 2012). The process has been captured as follows:
Launch the problem
- Students spend time reading the problem and identifying key information.
- Those students who need materials to support solving the problem work in the same area. The class moto at this phase is, "Working by yourself for yourself”. This video shows students working through the problem independently with the support of equipment.
- Other students work around the classroom in independent spaces. Looking for different ways to solve the problem.
- Students work in large scrapbooks so they can write and draw their different ways of working and thinking.
- While students work independently, the teacher roams and monitors different ways students are solving the problem.
|Small Group Sharing
- To expose students to a range of thinking: There may be more than one way to solve the problem. Children will learn to use new strategies when they see what other children have used.
- To foster mathematical communication skills: This in itself is an important process. However, it does have the valuable by-product of increasing understanding. In verbalising their own solutions, children will understand them better themselves. Students are placed in pods of 4 students with a range of abilities.
- Student voice: Hika, The pods - working with high people we have someone that can step us up and we understand the strategy more. It’s getting easier with the support of the teacher. In the video below, the high ability students are incorrect and the low ability students are correct. A follow-up discussion was led by the teacher to discover who in fact was correct. Devon went on to share his mistake with the whole class at the end of this session.
- Student Voice on mixed ability grouping: Aron: Gives harder work and we work in maths pods if we need help. Brainy kids in the group help you. Sophie: They tell their thinking. I try to follow their track but my ideas go on another track most of the time. Sometimes I learn from others or the teacher. Ben Group of different abilities sometimes people who would have been in lower groups get the right answer because I didn’t understand the problem properly. Ben Usually we have arguments over who is right sometimes majority rules or we ask another groups opinion. I sometimes have to take the lead. Sometimes I mini teach students to catch them up.
Whole class reporting back
- To increase students’ confidence: Students are selected or volunteer to share their way of working. In a friendly classroom atmosphere we have seen many students’ confidence increase, both in themselves and in their mathematical ability, by reporting back to the class. The teacher observes, I have a high flier who loves the process and has made huge shift in his ability to lead a group showing perseverance and patience.
- To highlight the mathematics inherent in the problem: Time is taken to point out any new strategies that a group has found and to show how this fits with other strategies used. The ideas produced can also be related to the problems that have been attempted, and to other aspects of the curriculum. Any generalisations and extensions can be developed to show that mathematics is about big ideas that cover many problems.
Mistakes / misconceptions
- To clarify common misunderstandings: At times mistakes are discussed and used as learning opportunities. Verbalising seems to help many children see their errors more quickly than writing their answers out on paper. By discussing points of difference, valuable learning can be achieved.
- Students are happy to share mistakes: Hika, I am willing to stand up and share and am not scared. Being wrong isn’t so important. I am still trying to get the right answer and share my ideas. Sometimes it helps me understand where I went wrong. Aron, I struggled last year. In here I am brainer. I didn’t know what to do last year. Doing better at maths. Willing to make mistakes and keep trying.
At the end of this problem solving session, the teacher constructs follow-up workshops from the needs identified while monitoring students in the problem solving session. Planning is responsive and with a flexible group structure, the programme becomes differentiated to meet the current needs of all students.
The students now want to talk about their learning, share their learning and have become much better at articulating their thinking. They have become more aware of the importance of sharing and working collaboratively. For most of the students, it has made a big impact on their learning. One high-flier in particular loves the process and has made huge shifts in his ability to lead a group. His skills of supporting others that struggle have demonstrated the skills of patience and perseverance. There are still some issues to work through, meeting the needs of those that are special needs and planning, but the teacher comments that the PLD has made a big impact and it has change her way of thinking and approach to mathematics. As the teacher observes, I feel they want to talk about their learning, share their learning and articulate their thinking. They are aware that they need to share.
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