Welcome the official blog of the Alcoa Maths Enrichment Program. Here you will find ideas and stories to inspire you in implementing powerful practises for engagement and learning in primary mathematics. I’m Shyam Drury, professional learning consultant for Scitech, and I currently run the Alcoa Maths Enrichment Program (AMEP).
AMEP runs three different programs in Australia: Champions of Maths (WA) that focuses on developing expert primary maths teachers; Real World Maths (WA) that supports teachers to implement curriculum aligned, real-world maths projects; and Portland Maths Network (VIC) that supports a teacher-led professional learning community. This blog will focus mainly on the Champions of Maths program, as we work with 8 teachers over the course of the year to develop them as leaders in maths education for primary teaching.
Champions of Maths teachers attend a series of workshops drawing on the most qualified and up-to-date research, and they train in how to teach maths for deep learning and engagement through a number of activities. I follow up the workshops with classroom visits to each of the teachers. Teachers work in pairs at a school, and will each teach a lesson with the other observing, while I am there. Following this we meet for an hour and a half to debrief the lessons. Teachers are also coached to deliver a number of workshops to other teachers, their school staff, and parents of their schools.
In this blog, you will hear directly from the teachers themselves, as they share their successes in implementing the strategies they’ve learnt in their classes. You will be able to take inspiration and lessons from these and apply them to your own practice.
We begin the Alcoa Champions of Maths program exploring the idea of teacher orientation as defined by Askew et al in the 1997 paper, Effective Teachers of Numeracy. This paper defines three different teacher orientations: transmission, discovery and connectionist; and demonstrates a strong link between high student gains in numeracy and a connectionist teacher orientation. I’ll give a brief characterisation of the three orientations, as I understand them. You can also refer to the table below for a more in-depth overview.
Transmission teachers believe that the teacher’s role is to dispense information and the students’ role is to receive this information, repeatedly, if the student does not understand at first. Discovery teachers believe that students only gain knowledge when they are ready and should be allowed to discover ideas, connections and strategies for themselves. Connectionist teachers believe that students must be given the opportunity to apply their own ideas to problems, but the teacher must help them compare and assess different solutions and strategies and guide them to greater accuracy and efficiency. One of the important aspects of a connectionist orientation is that teachers with this orientation believe that learning happens in the interaction between student and teacher.
Based on these ideas, we have targeted the development of effective problem solving lessons and powerful classroom discussions. Teachers in the program consistently focus discussions with students on comparing the efficiency of different strategies, as well as making connections between different strategies, solutions and representations. Our lessons typically follow a 3-part format:
1) Introduce the problem.
2) Students work on the problem in groups of 4. Groups are chosen randomly, in front of the students and groups are each given a vertical whiteboard to work at – here we’ve followed recommendations from Peter Liljedahl’s, Building Thinking Classrooms. Here’s a snapshot of a class working in this way:
3) Whole-class discussion of solutions. (Selected student groups will present ideas here).
Really good discussions require the right type of planning, and to do this we have chosen to use the 5 Practises for Orchestrating Productive Mathematics Discussions: anticipating, monitoring, selecting, sequencing and connecting. In essence this means to plan for a problem solving lesson by:
- Solving the problem yourself and predicting the different ways students will try to solve the problem correctly and incorrectly. Thinking about how you will respond to their different approaches – questions you will ask to progress them or get them back on track.
- While the students working on the problem, you pay attention to which groups use which type of strategy and make a note. You help bring them back on track, or move forward with extending questions (made much easier and more effective by the preparation in step 1)
- You choose which students you want to present, and in which order, based on the ideas you want the class to discuss and the connections you want them to make.
- You use carefully crafted questions to bring out the mathematical ideas, making them explicit, and making connections between them, between the different strategies and solution types.
Through the use of these strategies and the personal coaching with teachers, I have already seen remarkable changes in both the teachers and the students involved. For example, we’ve had a great success in the class that had the most problems with student collaboration – because of a culture of competition and shaming. Students in this class worked together to develop sentence stems they could use to engage in productive discussion with each other such as, “I disagree with that idea because….”, “I agree with that idea because….” and “I’m confused by…”. I’ve heard students now using these sentences while working in groups, I’ve seen them ask for clarification without shame when they are confused, and I’ve seen them genuinely engage with each other’s ideas and support each other in learning. I’ve also seen, in another class where the teacher had really emphasised the analysis of efficiency, students discussing and asking about efficiency without solicitation.
You will hear about these stories and many more through the course of the year as you follow this blog. In future posts, I will go into more detail about the approaches outlined above, adding more specific advice on how to plan, and what to do and say in class, to encourage deep thinking and engagement in your maths lessons. I will also (in future posts) go into more detail about our research methodology and how we evaluate the effectiveness of our program. I hope you enjoy reading the Alcoa Maths Enrichment Program blog and that it helps you build on your own classroom practice.
Keep thinking and enjoy the struggle!
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