Session 5: Number Sense

This was an important session in that it confirmed so much of what I consider best practice in mathematics education.  The observations in the earlier section that low achievers over-rely on counting resonates with my experience.  the over-arching idea here is flexibility in approach to calculation and that one size does not fit all.  The multiple ways of approaching a calculation are important for students to see and give essential validation to individual students' methods.   However, not all strategies are equal and I disagree with Jo's dismissal of the separation of conceptual and procedural.  Whilst the separation may be artificial from a teaching point of view, from an assessment perspective, identifying errors that are conceptual or procedural is important in gauging the students' level of understanding.

I was interested in the William Thurston quote regarding compression and that without conceptual learning such compression was impossible!  The examples of number talks shown in the video clips often gave examples of the teacher framing the calculation talks within deeper concepts, such as the rules of arithmetic and seeking to explain a problem algebraically.

For ISZL, much of this session should serve as a positive reinforcement of what we already do.  I have recently seen examples of number talks in G1 and G4 that were very productive and pivotal in developing the flexibility we should aim for in approaches to calculation.  Our students learn a repertoire of mental strategies and written methods but we should not be complacent.  How consistent is our approach across grades for instance?  My recent foray into G7 was interesting in that so many of the students showed evidence of the kind of compression that Thurston talks about; they had assimilated strategies, number sense, knowledge of operations etc and were applying them to a range of problems.  What was significant to me was the variety of calculation methods successfully used.

A key feature of the examples of number talks in the session was the teacher modelling the spoken strategy using standard notation, and checking with the student that the recording was an accurate representation of their method.

The visual models employed were sometimes effective but at times I didn't think they accurately represented the strategy discussed, however, the message here is important: visual models are an essential component of helping students develop number sense...and we need to use a wide variety.