An Iceberg Model for Improving Mathematical Understanding and Mindset or Disposition: An Individualized Summer Intervention Program

This study describes 3 years of mathematics intervention research examining the effectiveness of a summer individualized tutoring program for rising fourth-, fifth-, and sixth-grade students with low mathematics achievement. Based on an iceberg model of learning, an instructional framework was developed that identified and targeted students’ specific mathematical needs, developed number sense flexibility, and encouraged positive mindset or disposition. Students participated in eight one-on-one tutoring intervention sessions. Pre- and posttest results indicated that students made moderate to large effect size gains in each targeted area of instruction. Additionally, the intervention proved to produce positive results across three different contexts for delivering tutoring instruction

Biennale d'art performatif de Rouyn-Noranda 2014

Providing an appropriate education for exceptional students in mathematics is mandated in educational policy in Australasia (Australian Curriculum, Assessment and Reporting Agency (ACARA), 2010; Ministry of Education, 2009, 2011) but a challenge for teachers and schools. ‘Exceptional students’ refer to two distinct populations, namely those who are gifted in mathematics and have the capability to perform very highly compared to age peers and those who experience learning difficulties in mathematics and may underperform (Diezmann, Lowrie, Bicknell, Faragher, & Putt, 2004)

Oral counting sequences: a theoretical discussion and analysis through the lens of representational redescription

Empirical research has documented how children’s early counting develops into an increasingly abstract process and initial counting procedures are reified as children develop and use more sophisticated counting. In this development, the learning of different verbal counting sequences that allow children to count in steps bigger than one is seen as an essential skill that supports children’s mental calculation strategies. This paper proposes that the reification or refinement of the counting process that results to increased-in-sophistication use of counting is underlaid by the process of knowledge explicitation that the model of Representational Redescription postulates. The paper uses a case study to provide insight into the pathway that a 6-year-old child followed from learning how to verbally count in 2s and 10s to being able to use this knowledge for calculation purposes. The proposal is that knowledge of verbal sequences is redescribed in more explicit and accessible formats before children are able to connect their knowledge of the verbal counting with the goal of using the sequence for calculation. The discussion presented here queries the notion of spontaneity as an inherent element of the theory and discusses the role that social interaction may play in supporting knowledge redescription. If it is the case that children’s knowledge of verbal counting sequences is redescribed into increasingly explicit formats before it can be applied for calculation then children need to be provided early in their education with structured activities that trigger knowledge redescription and support the necessary connections between counting, number structure and calculation