Options
Examining a teacher's use of multiple representations and noticing in the teaching of percentage : a commognitive perspective
Author
Chia, Su Ngin
Supervisor
Choy, Ban Heng
Abstract
The use of multiple representations is prevalent in mathematics teaching. However, many studies suggest that using multiple representations would not automatically lead to mathematics teaching and learning. Teachers’ lack of awareness of the transitions among the different representations is one of the common factors which affect teachers’ use of multiple representations. Percentage, an important but challenging topic for primary school pupils, presents opportunities for teachers to use multiple representations and to deliberate on the use of mathematical language to support pupils’ learning. However, not many studies have explored the use of multiple representations in the teaching of the percentage topic. Using an exploratory qualitative case study, this study explores how a teacher, Mrs Hannah, used multiple representations in the teaching of percentage in Singapore through the lens of commognition and teacher noticing.
More specifically, this study introduces and demonstrates how the use of a mediation flowchart and a theoretical model created from a FOCUS framework can be used to study teachers’ use of multiple representations in the teaching of percentage. Hence, using the lens of commognition and teacher noticing, Mrs Hannah’s use of multiple representations were analysed to shed light on the interplay among representations in the teaching of percentage.
The participants of the study include the researcher, the teacher participant, Mrs Hannah, and her class of seven Primary 5 pupils. A total of six lessons were recorded using a Swivl® robot. After a process of data condensation and data analysis, an episode which reflected Mrs Hannah’s rich use of multiple representations was presented in this dissertation as a case study. The episode was divided into three segments, which will be analysed and presented through the lens of commognitive framework and teacher noticing. A mediation flowchart was created to analyse Mrs Hannah’s use of representations from a commognitive perspective in each segment. Using the four characteristics of mathematics discourse (keywords, visual mediators, narratives and routines), the study discovered that the fluent transition among multiple representations depends on a few factors. Firstly, use of keywords and gestures can mediate representations together, thus improving representational fluency. Next, the use of an elaborated realising procedure during the creation of signifiers-realisation pairs in a discourse and the types of routines used also improves representational fluency. The study suggests that the interplay of the different characteristics of a discourse also affects representational fluency.
Next, a theoretical model created from FOCUS framework was also used to analyse Mrs Hannah’s use of multiple representations in each of the three segments. The FOCUS framework highlights two important characteristics of productive noticing which includes explicit focus of noticing (What to notice) and focusing noticing of pedagogy reasoning (How to notice). With reference to Mrs Hannah’s explicit focus which includes the identification of the concepts that pupils have to learn (Key point), how she made sense of pupils’ difficulties in learning of the concepts (Difficult point) and how she had decided to respond to pupils’ difficulties (Critical point), and focusing noticing through justification of her teaching actions, this study demonstrates how a teacher’s noticing on the use of multiple representations in the teaching of percentage may be productive and non-productive.
More specifically, this study introduces and demonstrates how the use of a mediation flowchart and a theoretical model created from a FOCUS framework can be used to study teachers’ use of multiple representations in the teaching of percentage. Hence, using the lens of commognition and teacher noticing, Mrs Hannah’s use of multiple representations were analysed to shed light on the interplay among representations in the teaching of percentage.
The participants of the study include the researcher, the teacher participant, Mrs Hannah, and her class of seven Primary 5 pupils. A total of six lessons were recorded using a Swivl® robot. After a process of data condensation and data analysis, an episode which reflected Mrs Hannah’s rich use of multiple representations was presented in this dissertation as a case study. The episode was divided into three segments, which will be analysed and presented through the lens of commognitive framework and teacher noticing. A mediation flowchart was created to analyse Mrs Hannah’s use of representations from a commognitive perspective in each segment. Using the four characteristics of mathematics discourse (keywords, visual mediators, narratives and routines), the study discovered that the fluent transition among multiple representations depends on a few factors. Firstly, use of keywords and gestures can mediate representations together, thus improving representational fluency. Next, the use of an elaborated realising procedure during the creation of signifiers-realisation pairs in a discourse and the types of routines used also improves representational fluency. The study suggests that the interplay of the different characteristics of a discourse also affects representational fluency.
Next, a theoretical model created from FOCUS framework was also used to analyse Mrs Hannah’s use of multiple representations in each of the three segments. The FOCUS framework highlights two important characteristics of productive noticing which includes explicit focus of noticing (What to notice) and focusing noticing of pedagogy reasoning (How to notice). With reference to Mrs Hannah’s explicit focus which includes the identification of the concepts that pupils have to learn (Key point), how she made sense of pupils’ difficulties in learning of the concepts (Difficult point) and how she had decided to respond to pupils’ difficulties (Critical point), and focusing noticing through justification of her teaching actions, this study demonstrates how a teacher’s noticing on the use of multiple representations in the teaching of percentage may be productive and non-productive.
Date Issued
2017
Call Number
QA137 Chi
Date Submitted
2017