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Showing posts from December, 2012

Constructivist Intervention

For a long time, Constructivism seemed to me to be a theory of learning that didn't have any direct implications for the way that I taught.

Then I read "Evidence Based Learning" by Geoff Petty and the penny dropped.

Constructivism is now the lens through which I view everything that happens in the maths classrooms in my department (on good days!).  Our rooms are full of young people constructing their own versions of maths.  They do this with the support of the environments, inputs and activities which we offer them.  They do it together with those around them, and they do it, in large part, by attempting to connect new learning to their pre-existing model of maths.

I get a kick from seeing this happening. My S4 class today was looking at extending sine and cosine beyond 90ยบ.  It involved playing with a Geogebra applet that showed how the sine and cosine of an angle can be represented by the y and x coordinates of a point moving round a unit circle.

I used show-me board…

Success and Failure

My S3 class sat an important test yesterday.  It was set at level 4, and was designed to ascertain whether or not they would be able to pass a National 4 unit assessment.  The class have known about the test for several months, and have known that failure to gain 50% in the test would mean moving to a different class - to focus on passing National 4 by the end of S4 instead of moving beyond level 4 to start working toward National 5.I've written about this class before in Notes for Future Self and Aww. I put in place a major program of support for all those pupils who were not reaching the standard back in September - almost half the class.  Yesterday's test was where we found out whether or not all the hard work had paid off - and there was a lot of hard work!  I contacted the parents of every pupil who had underperformed; the pupils attended support sessions after school from 4-5pm on Wednesdays and Thursdays, completed substantial homeworks every week and spent time correc…

Flying with Geese

I was very lucky to have the opportunity to attend the "Flying with Geese" masterclass in Glasgow today.  Dylan William and Graham Donaldson spoke. It would be futile to attempt to summarise the day, but here are some interesting points that stuck in my head:

Having identified the strengths and weaknesses of a teacher, the research shows that the best way to elicit improvement in their professional performance is to focus on trying to further improve their strengths, rather than trying to fix their weaknesses (unless the weaknesses are really bad!)Creativity, problem solving and critical thinking are not generalisable. Rather than trying to teach these (or any other) skills separately, we should use these terms as audit tools within disciplines.Content from disciplines must be strong within topic work, and be directed by teachers.  Left to their own devices, learners will not bring worthwhile levels of disciplinary content into their project work.There is no correlation betwe…

A Feedback Idea that Didn't Stick

Last year, I tried giving feedback to pupils - about their homework - using a detailed marking scheme, highlighted to show successes and failures.  A pupil's feedback would look something like this:



Question Step Comment 1a differentiate sin to cos use the chain rule to produce an extra multiplier of 2 (the derivative of the function inside sin) keep 3 as a multiplier of the derivative know to evaluate f’ at x=0 perform evaluation correctly 1b realise that rearranging to tan(x)=... is the first step take square root to give tan(x)=... remember to use +/- square roots find building block angle from exact values choose correct quadrants for solutions
work with fractions of pi correctly not available, as you did not consider other solutions state solution clearly My hope was that the pupils would use the feedback to see where they had "gone right" as well as where they had gone wrong, and would be able to use it to help with corrections.
As it turned out, these feedback forms (returned to the…

Video Homeworks?

Just thinking aloud...

I'm not the only one with a video camera in my phone.  Most of my pupils have the same technology in their pockets.  I wonder if I could convince some of them to record a video explaining their thinking as they solve one of the questions in their homework?

That would be really interesting. I would receive so much more information about their thinking processes, which would in turn allow me to provide higher quality feedback to them.

Sometimes the language that pupils use highlights misconceptions that are not apparent from their written work. For example, I was working with an advanced higher pupil on Friday, who asked me, when tackling the step below,  "what happens to the dy?"

$\int dy = \int x^2 dx$

I asked her what happens to the dx in a regular integration, and she said "it turns into +c?".  Further discussion showed that she had not grasped the fact that the integration symbol, plus the "dx", represent an instruction to pe…