Abstract
Research focusing on algebra from primary to early secondary school level has
made several major advances over the past decades. Students’ difficulties have been identified
and supportive teaching and learning environments have been set up (Cai & Knuth, 2011;
Kieran, 2007; Radford, 2008, Mathematics Education Research Journal, 26, 257–277, 2014).
The effectiveness of these environments relies on the teachers’ ability to pay careful attention
to students’ thinking, which then guides their instructional decisions. This inevitably raises the
crucial question of the teachers’ knowledge for managing these types of situations in the
classroom. In this context, this paper focuses on the mathematical knowledge for teaching
figural pattern activities of 100 teachers at the primary and early secondary school levels. The
results show that many primary teachers lack the essential knowledge for teaching these types
of activities: they do not have a clear idea of their goal, they do not consider non-standard
algebraic generalisations to be correct and they generally seem unable to help students to
improve their arithmetical generalisation. Secondary school teachers also seem unable to give
adequate feedback to improve students’ arithmetical generalisation. Although they seem to
recognise that these activities are intended to improve algebraic thinking, they do not have a
clear perception of the role that primary school learning can play in the development of this
algebraic thinking.
