Introducing Surds (Year 10/11)

This activity is inspired first by Dylan Wiliam’s chapter on “Eliciting Evidence of Learner’s Achievement” in Embedded Formative Assessment. My approach to the task is inspired by Danny Brown’s (@dannytybrown) posts on noticing and listening (http://www.squeaktime.com/).

Instead of setting a pre-test before going into our unit on surds – which can deter students and also be difficult for teachers to draw meaningful evidence from – I gave year 11 the group based task below (groups of four). Very little input from me with the exception of a few guiding questions here and there.

surds22

After 25 minutes I had a huge amount of rich, qualitative data from student comments and I now feel that I can teach the entirety of surds from what they currently know. I can use their comments as a starting point for most discussions we’ll have over the next week. (It was also a good chance to revise a few topics from last year as well – indices and standard form).

You’ll notice that I stuck a few questions in there that might reveal a few misconceptions (not just with surds). Can you identify where some of the students may have gone wrong due to a misconception?

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4 Responses to Introducing Surds (Year 10/11)

  1. dannytybrown says:

    I really like this Dan, not just because you referenced my blog!

    In particular, I like the thoughts around pre-testing, It is problematic to base choices around what to teach on performance on a test; I much prefer your approach on basing it on a range of responses and conversations with students – as you say, rich qualitative data.

    It is interesting to me that by opening the task and your approach you now have much more information on which to base your pedagogical decisions; there is something profound in this.

    Thanks for this, Danny

  2. mikeollerton says:

    Very interesting approach you describe here and much that could be generalised and used by yourself and others for teaching a wide range of topics/units of work. I really like the way you asked your classroom work in groups of fours.

    I am also intrigued by your statement about very little input from you – this is because such a statement can be misconstrued, particularly by people who believe teachers should take the lead role. I suggest you performed key teaching roles before the lesson began through a) the quality of the task you planned b) the grouping strategy you used c) by actively choosing to step back in the lesson and d) what you will plan to do as an outcome of the analyses you carry out on the work produced.
    Finally I shall be very interested in what task(s) you plan for subsequent lessons in the unit. BTW one exploration involving surds is to prove why the length of a diagonal of a rectangle with lengths root a and root b is root a + root b.

    Regards
    Mike

  3. dannytybrown says:

    I agree with Mike – would love to know what happens next…

    Also I would add that when you are taking a step back, in actual fact you are carefully listening to the students and planning for next steps in response to what they are saying – A crucial part part of the process…

  4. Thanks Mike and Danny for your comments. You’re right to correct my informal language about ‘little input for me’. As you say, it’s in the careful planning of a task, the specific groupings of the students, the way that you listen and draw from student comments and the language you use to guide learners towards greater collective understanding. The majority of the time I was simply pointing out things to students, such as, “Do you think everyone understood your explanation?” or “Is everyone in agreement that…?” or “Is that an argument or a guess?”.

    I have blogged about the way in which I tend to approach surds in the past so much of my approach will be similar although arranged in a different order and focusing on slightly different things due to the data collected from student responses to this task. (https://danpearcymaths.wordpress.com/2013/11/16/allowing-students-to-discover-the-mystery-of-square-roots-surds/)

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