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# Mathematics Matters Lesson Accounts 56 - Fluency in Recalling Facts and Performing Skills

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Created on 29 May 2008 by ncetm_administrator
Updated on 17 June 2008 by ncetm_administrator
 Mathematics Matters Lesson Accounts A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

# Lesson Account 56 - Fluency in Recalling Facts and Performing Skills

 Written by Watson Organisation Unknown Age/Ability Range Unknown

(a) What was the mathematical task(s)?
Constructing examples introduces sense of structure, characteristics, properties of new objects.  Also includes practice and fluency.  Also ‘big’ idea of conjugation is being introduced.  Also it builds on successful past tool use of the grid.  Also ownership, mystery, intrigue.  Also it feels do-able, but the difficulty adds to the motivation.  Also, you don’t have to tell students everything – or show them.

Having been just introduced to the idea that there are numbers of the form a + √b, and reminded of grid multiplication, find two such numbers which, when multiplied, you ‘lose’ the root part.  On your own or in pairs.  All rough working was kept and it is clear that most students shifted from some sort of ‘testing’ various integers’ approach to a ‘structural’ approach, e.g.: trying (2+√3)(3+√2) or (2+√2)(2+√2) etc.  Many started by using calculator, some abandoned this as they focused on structure.

Students trusted the teacher because of having done similar tasks in the past.  They were allowed to choose starting numbers and methods of working, except for grid multiplication.  Lots of talk.  Some ‘gossip’ method (distributed knowledge!).  Teacher says ‘why choose this, why choose that?’ and reminds them of purpose.  Some of the students carried on after class together or separately and the teacher was interested in their work!

(c) How could you tell that the task(s) achieved the intended purposes?  Do you have any evidence?
Saw the written work.  Some aspects of purpose achieved by all – (a+√b)(a-√b) = integer found by some.

It will be (special issue of ‘Educational Studies in Mathematics’ 2008)

(e) Can you say why you chose this example?  What criteria were in your mind?
To illustrate use of learner-generated examples to promote shifts between empirical and structural reasoning.

## Values & Principles

 Fluency in recalling facts and performing skills

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