Maths ARA Analysis 1

Lately there’s seems to have been a lot more discussion about the need for critical feedback and reflection as journey towards a learning renaissance. @geoumouldey and @mattynicoll in particular talk about this on Twitter. Personally I couldn’t agree more, but it was this week that everything seemed to click into place.

I was lucky enough to have my awesome syndicate leader Louise come and observe me teaching maths at the beginning of the week. One of the things I really like about having someone come in when you are teaching is that they notice all the things you don’t – all the awesomeness but also the things that could be improved, and I particularly value the detailed feedback Louise gives.

We use a framework called ARA – Aims, Reality, Actions to discuss and reflect on our practice, and target these around observations of teaching and learning so that we have a second person to discuss our ideas with.

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In this lesson we were using lego to build Aztec pyramids and then recording the patterns we noticed as part of algebra.

Lesson Context

Students were using Aztec pyramids as a context for building understanding of number patterns and algebraic rules. We were practicing tabling the patterns we noticed in a square-based step pyramid using a 3D model built out of lego. We worked together as a group with a shared model and recorded the information together. Students were then given opportunity to create their own pyramid and identify the patterns they could see within these. Once they’d identified the pattern they had to figure out the rule. The follow up lesson the next day was then on how to encode the rule use algebraic norms.

 

Aims

All students are given support and opportunity to share, collaborate and engage with learning.

Students are given opportunity to make connections between practical and abstract ideas.

This will be evident when:

  • Students build, create and notice patterns
  • Students can explain changes to a pattern in mathematical language and record these ideas using algebraic concepts
  • Students interact with each other and work collaboratively to share ideas

 

Reality

Students were highly engaged by the maths warm up game and were all involved in discussion about it. Students made choices about they level they worked at and were able to self-evaluate as they worked to ensure it was a good challenge but not too hard. Student would have benefited from some more feedback time to discuss strategies beyond their own group. The main teaching was highly engaging, all students were actively involved in the task. Discussion and practical hands on materials that weren’t traditional ‘maths’ materials drew students into the problem. I used questioning to build the understanding slowly and to encourage students to notice and make connections to other areas of maths. We discussed misconceptions so that we were all on the same page. Students enjoyed a short burst of discussion followed by time to get ‘stuck in’ to the task.

The observed reality was verified by student feedback that Louise recorded and also her notes and feedback from the observations as well as my own reflection. I think the lesson was successful. Students were all engaged and very motivated (never underestimate the power of lego!). They were active in both discussion and practical tasks and were challenged to find the links themselves.

 

Actions

Although the lesson was successful, I can still see a number of next steps and ways to tweak it. Firstly I want to continue the hands on approach but try different materials – maybe toothpicks and plasticine. I think this really benefited the students as they could take an abstract idea and represent it visually. I want to continue to focus on this for a bit longer even though they got it once to make sure the conceptual understanding is really embedded and understood at a deeper level. I also want to continue get students to work together on their maths, as this seems to provide far deeper learning. I need to provide scope for challenge by extending the context (or having a extension of the context ready to go – perhaps a ‘how might…?’ question). And finally I want to end the lesson with more opportunity to reflect on what made learning successful and draw more explicit links to Building Learning Power – i.e. actually commenting on the skills as I see them being used.