Supporting teachers in the development of young children’s mathematical thinking: Three large scale cases

The Impact and Challenges of Early Mathematics Intervention in an Australian Context

“…The growth points do not represent an assessment score, but rather describe a child's current knowledge in reference to the set of research-informed progressions in children's developing knowledge. This is a common approach in Australia (Bobis et al 2005). The idea is that the growth points guide teachers about how they might respond to a child's current knowledge, and then provide the resources and teaching to extend their learning.…”

Invited Lectures from the 13th International Congress on Mathematical Education

“…But this, I argue, is relevant not only for the U.S., but for any country that is faced with educating children whose home language(s) is different from the language of instruction. As it has been pointed out, discussion on language policy in schools are closely related to issues around immigration and the education of immigrant students (e.g., Alrø et al 2009;Barwell et al 2016;Civil 2012;Gándara and Orfield 2012;Wright 2005).…”

Rethinking the role of counting in mathematics learning

“…New Zealand, along with other western countries responded to its relatively poor results on the Third International Mathematics and Science Study (TIMSS) by developing an initiative designed to strengthen students' understanding of mathematics and numeracy. Most initiatives in mathematics focused initially on the early years of school (Bobis et al, 2005;British Columbia Ministry of Education, 2003;Commonwealth of Australia, 2000;Department for Education and Employment, 1999;Ministry of Education, 2001; National Council of Teachers of Mathematics, 2000). These initiatives have several features in common, including professional development programmes for teachers to enhance their capacity to teach mathematics, the construction of developmental frameworks that describe progressions in the learning of mathematics, individual taskbased interviews to assess students' thinking and reasoning in mathematics, and a constructivist/ socioconstructivist view of mathematics teaching and learning, so that instruction builds on the existing knowledge of the learner (Bobis et al, 2005).…”

“…At the core of many numeracy initiatives are the learning frameworks, consisting of progressions of increasingly sophisticated strategies in particular mathematical domains (Bobis et al, 2005). Most initiatives include a sequence of stages outlining progressions in number, reflecting the perceived importance of number in the curriculum, and the comprehensive foundation of research that is available to support this (Kilpatrick, Swafford, & Findell, 2001).…”

“…Many of the learning frameworks constructed as part of reform in mathematics education begin with the development of counting skills (e.g., Bobis et al, 2005;Ministry of Education, 2008). Such frameworks have taken the work of Gelman and Gallistel (1978), who documented the progression from saying number names in order (rote counting), to assigning number names to items while maintaining one toone correspondence between the number name and the item (object counting), and finally recognition of the cardinal principle-the idea that the last number name used when counting a collection of objects tells how many items are in the collection in total.…”