Investigation and Scaffolding

"…mathematics is a cultural activity that should not be reduced to correctly performing mathematical operations." (Oers cited in Carruthers and Worthington, 2006)

Real engagement in mathematics involves mathematical thinking and this is best achieved by investigation and problem solving activities.

Realistic Mathematics Education (RME) is one pedagogical approach which originated in Holland. Realistic refers not only to connections to the real world but also to problem situations that children can imagine and engage with. This does not mean that the connection to real life is not important. It only implies that the contexts are not necessarily restricted to real-world situations. The fantasy world of fairy tales can be very suitable contexts for problems, as long as they are ‘real’ in the students’ minds.

Instructional scaffolding is the provision of sufficient support to

promote learning when concepts and skills are being first introduced to students. These supports may include: resources, a compelling task, working walls, templates and guides.

These supports are gradually removed as students develop autonomous learning strategies, thus promoting their own cognitive and affective learning skills and knowledge.

Scaffolding instruction, as a teaching strategy, originates from Lev Vygotsky’s sociocultural theory and his concept of the zone of proximal development (ZPD). “The zone of proximal development is the distance between what children can do by themselves and the next learning that they can be helped to achieve with competent assistance” (Raymond, 2000, p.176).

The scaffolding teaching strategy provides individualised support based on the learner’s ZPD (Chang, Sung, & Chen, 2002). In scaffolding instruction a 'more knowledgeable other' provides scaffolds or supports to facilitate the learner’s development. The scaffolds facilitate a student’s ability to build on prior knowledge and internalize new information. The activities provided in scaffolding instruction are just beyond the level of what the learner can do alone (Olson & Pratt, 2000). The 'more capable other' provides the scaffolds so that the learner can accomplish (with assistance) the tasks that he or she could otherwise not complete, thus helping the learner through the ZPD (Bransford, Brown, & Cocking, 2000).