Mathematics

One usual name for providers of such PD is ‘multipliers’. This term stresses
the ‘multiplying’ feature of scaling up: For example, in order to reach 8,000
teachers, and following a simple multiplication model, 20 × 20 ‘multipliers’ are
needed if each PD educates 20 participants. Of course, several challenges of
this scaling-up strategy should be taken into account. For example, it is
obvious that in each step the PD participants can hardly reach the knowledge
of the PD providers. In addition, it is likely that the interest of PD participants
decreases in each cascade, whereas their scepticism (e.g., towards the reform
ideas) increases 2 .
Large-scale PD design and research is a complex endeavour. It has at least
three dimensions that afford critical consideration: PD design, research design,
and time & number (see Figure 1).
Figure 1: Large-scale PD design and research
The PD design includes several cascades. However, in order to aim at an
impact on all students, at least the last cascade needs to deal with practising
teachers. These teachers have the challenge to cope both with the PD idea,
and the complexity of their classroom (sketched as a triangle comprising the
teacher, the student/s, and the content/s). The PD can be designed in various
forms regarding the content. To sketch only two very different forms: a) All
cascades are dedicated to a specific mathematical content (big C), like
fractions (e.g., referring to grades 5-6); here, the challenge is that only a part
of all teachers (those teaching in grades 5-6) are reached, and also regarding
these teachers the question remains how they get support in further
developing their teaching in all other mathematical areas and grades. b) The
content of the cascades is varying, which means that no specific content is
2 Due to these challenges of disseminating knowledge in a top-down-manner, other approaches follow bottom-up (or mixed)
strategies where the starting point of innovations are teachers’ own ideas for improving their teaching, supported by “critical
friends” (e.g., colleagues or university staff). For example, in Japan, the lesson study approach has a long tradition, meanwhile
widespread all over the world, recently more often combined with the learning study approach. There is an increasing claim to
regard teachers as relevant stakeholders in research (see e.g., Kieran, Krainer & Shaughnessy 2013).
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