Document Type


Publication details

Dineen, A 2014, 'Use of grouping strategies to solve addition tasks in the range one to twenty by students in their first year of school : a teaching experiment', PhD thesis, Southern Cross University, Lismore, NSW.

Copyright A Dineen 2014


The participants in this PhD study were Australian students in their first year of school. This study followed a design research methodology. Videotaped pre- and post- assessments were conducted as clinical interviews. Video records were made of each lesson and case studies were constructed for three students.

This teaching experiment focused on students’ use of grouping strategies to solve addition tasks. Extensive use was made of settings designed to engender students’ additive reasoning. Results indicate that part-part-whole knowledge of numbers can support additive reasoning strategies. The introduction of formal arithmetic notation appeared to support students’ conception of addition tasks as binary operations.

Additional information

teaching approach, number knowledge, pre-numerical counting, basic addition combinations, habituating knowledge, addition tasks, one-digit addition tasks, counting, counting based strategies, grouping strategies, additive reasoning, binary operations, Phases of Early Grouping Strategies, PEGS, one-digit addends.