Exploring the transition into Year 3 of Year 2 students who use counting on to solve mathematics problems
Matthews, M. J. (Jo). (2014). Exploring the transition into Year 3 of Year 2 students who use counting on to solve mathematics problems (Thesis, Master of Education (MEd)). University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/9222
Permanent Research Commons link: https://hdl.handle.net/10289/9222
This research project examined how five Year 2 students, at stage 4 on the Number Framework (counting on), experienced mathematics as they transitioned into a Year 3 and 4 classroom. It investigated the support structures put in place to shift students from counting on to part-whole thinking, as part of the Numeracy Development Projects (NDP) approach to teaching mathematics. An additional transition of two teachers into Year 3 and 4 (one up from Year 2 and one down from Year 5 and 6) provided evidence of teacher transition experiences when shifting teaching levels. The setting, role of the teacher, and external influences were examined. This research was a qualitative investigation framed within a case study approach. The main source of data was classroom observations and semi-structured interviews. The teachers’ interviews focused on their approach to teaching and learning, attitude, student ability, assessment, and knowledge of the mathematics curriculum from Level 1 to Level 2. The combination of classroom observation and student interviews demonstrated the current level students were operating at and any signs of shift in their knowledge, as well as attitude towards mathematical learning. The thesis illustrates how classroom practices and teaching approaches encouraged students to count on instead of shifting into part-whole thinking. The findings highlight possible barriers, student experience, the importance of teacher knowledge and understanding, and the impact of teaching practices that support and undermine the shift. The findings also show that teachers are still following the NDP material very closely, without a full understanding of the pedagogy of number knowledge which can bridge Level 1 to Level 2 of the New Zealand Curriculum. The findings also indicate that the NDP teaching model is not being fully incorporated into classroom teaching, with a decrease of manipulatives used over the transition, a limited use of visualisation through diagrams and pictures, and students experiencing abstract representations without a full understanding of their meaning. The findings also show that the current reform in mathematics is only operating at a surface level. Teacher practices reflected an instrumental, procedurally-based approach to the teaching and learning of mathematics. The evidence contained within this thesis points to the link between knowledge and strategy not being made explicit, with limited experiences of exploring relationships between numbers and quantity. It considers a critical aspect of student understanding is to develop a full understanding of number relationships through the concept of subitising, part-whole relationships, and more-and-less relationships. Continuing Professional Learning and Development is needed for teachers to develop a deeper understanding of these relationships and how they support student shift from ‘counting on’ to part-whole thinking.
University of Waikato
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