[Maths-Education] Research on number in secondary / high school - help sought

[Ernest, Paul]

Dear Colleagues

I'm putting together a doctoral seminar on research on number in secondary / high school / advanced school maths
I wondered if anybody has suggestions about research publications (your own or otherwise) illuminating different aspects of number 

My first brianstorming of different aspects of number came up with this far from final list:
• Place value – including errors, both conceptual & procedural
• Rationals (fractions)
• Ratios & percentages
• Integers – negative numbers
• Real numbers
• Infinite decimals and convergence / divergence
• Estimation, rounding, number sense
• Equivalence between different number signs (0.5, ½, 1 / 2, 1:2, etc)
• Use of calculators
• Number operations, exponents, order of operations, brackets, etc
• (number patterns --> algebra)
• (number axioms)

Any criticisms (of this), suggestions, attachments, references, etc. gratefully received

With thanks
Paul
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Paul Ernest
Emeritus Professor
Graduate School of Education
University of Exeter
St Lukes, Heavitree Road
Exeter  EX1 2LU, UK
+44-(0)1392-264796
http://www.people.ex.ac.uk/PErnest/

Visiting Professor, HiST-ALT College, Trondheim, Norway
Visiting Professor, University of Oslo, Norway
Adjunct Professor, Hope University, Liverpool

See http://www.people.ex.ac.uk/PErnest/  for Philosophy of Mathematics Education Journal - No. 24 on theme 'Mathematics and Art' -- (out since December 2009)

Papers for No. 25 on theme Critical Mathematics Education -- now sought (intended for August 2010)
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