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A Learning Episode: Straight Line

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Summative Exams as Formative Devices with Implications

Let's begin with what I mean by the following: 
Summative assessment – is normally based upon a sample of a domain.  This is used for looking at the distribution of pupil attainment at a point in time.
Formative assessment – is normally used for identifying what do next.
I’ve previously written at length about the mastery learning model and how fundamental formative assessment is to this.Teachers need to use formative assessment to make judgments about pupil performance and attempt to make inferences about pupil learning. We can never know what has been learned at the point of teaching, as learning takes place over time.
In my experience, formative assessment has been almost unanimously accepted as being a good thing by the profession.Summative assessment, on the other hand, can be a topic of much debate:When should it happen?What should the format be?Are exams a fair way of awarding qualifications?What about coursework?
Something that I feel that is often missed out is that summative …

Short Reflection: Decimals, Division and Place Value

I’ve shared a couple of lessons in recent blog posts that went well.  The following is a lesson which I'm much less sure about.
With my S2 class who, historically, would be likely borderline National 5 candidates in S5 I’ve been trying to develop their “sense” and “feel” for mathematics.  Much of their appreciation of the subject seems to be in the form of procedures and algorithms.  They are not fluent with many of these procedures, but more, I have the sense that there is a weak conceptual foundation on many ideas.  
I know these young people have the capacity to reason, but in the first couple of weeks working with them I’ve witnessed many errors in lesson starters due to a lack of fluency with procedures they’ve tried to memorise.  I argue that if the learners had a stronger conceptual understanding of this previous work then they would have the capacity to make sense of their answers and identify that they make sense. 
I normally begin lessons with a mix of content from previou…

Revelations in Right Angle Trig – A Learning Episode