By Sue Southward (July 2020)
I’ve been on an IT journey. It’s been a rollercoaster ride, and I wasn’t expecting it.
I found myself using this expression “…from novice to expert”, which I had previously used for reasoning, based on an article by nrich: https://nrich.maths.org/11336
Those of you who have been part of the “Mathematical Thinking” work group will have seen this before. Those of you who know me well will know that I’ve also used this progression to frame colleagues’ discussions following lesson study. I started to see parallels between the learning I was doing and the learning we hope pupils will do in a problem-based class lesson.
The progression looks like this: nrich reasoning stages My online developmentStep one: Describing: simply tells what the pupil did.Getting in: Working out how to log on, switch video and audio on, use the chat.Step two: Explaining: offers some reasons for what they did. These may or may not be correct. The argument may yet not hang together coherently. This is the beginning of inductive reasoning.Exploring: Experimenting with recorded PowerPoints, live lessons, Desmos, Whiteboards, breakout rooms. Lots of time spent on help pages and asking colleagues for support.Step three: Convincing: confident that their chain of reasoning is right and may use words such as, ‘I reckon’ or ‘without doubt’. The underlying mathematical argument may or may not be accurate yet is likely to have more coherence and completeness than the explaining stage. This is called inductive reasoning.Sharing: showcasing ideas with others and demonstrating how they work through work groups and my own lessons. This involves a level of bravery and inevitably mistakes happen. It does offer others the opportunity to take up the ideas and run with them.Step four: Justifying: a correct logical argument that has a complete chain of reasoning to it and uses words such as ‘because’, ‘therefore’, ‘and so’, ‘that leads to’ …Choosing the right platforms: Making decisions about which tools will be used for which activities, with some pedagogical reasoning behind it.Step five: Proving: a watertight argument that is mathematically sound, often based on generalisations and underlying structure. This is also called deductive reasoning.Being the expert: Knowing you have the expertise to switch between platforms with ease and being the one people come to for help.
(I can only dream of reaching this stage!)
When we tried to use the five steps to describe pupils’ reasoning development, we had some issues; it depended on the task they were doing. In some tasks they started at step one and progressed through, whilst in others they were able to “jump in” at the justifying stage. Lots of the tasks we give pupils don’t lend themselves to a proof and some can’t be generalised. We found there are some young children who can articulate logical arguments and older pupils who struggled to move beyond ‘describing’. It does, though, describe a pathway we would like pupils to follow over their time in school, and we have spent many happy hours discussing how we can accelerate their journey. We talked about the necessity of “flounder time”, where pupils appear to be making no progress, but are taking stock of their thinking and may then move forward without prompts.
My IT journey has been much faster, by necessity. In the first week of lockdown I grappled with all sorts of platforms, depending on who I was talking to. I felt that same helpless, powerless feeling that pupils get when they are faced with a problem they can’t solve. I felt the pressure to get an answer quickly, to focus on getting it done, not looking at the process of getting there, and I experienced that same frustration followed by pride when I managed to achieve a good lesson or work group.
My colleagues have been amazing; offering advice, allowing me to experiment on them, giving me time to think.
This lockdown has forced me to learn some useful skills very quickly. I have definitely moved beyond the logging-on stage but aspire to become an expert in the future.
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