- Teachers' use of instructional examples in the teaching of mathematics

###### Options

# Teachers' use of instructional examples in the teaching of mathematics

Loading...

Type

Thesis

Author

Ng, Lay Keow

Supervisor

Dindyal, Jaguthsing

Abstract

This study set out to examine the use of instructional examples by teachers in the mathematics classrooms. The research questions were: (1) What kinds of instructional examples do teachers use? (2) How do teachers use instructional examples? (3) Why do teachers use these instructional examples?

To identify the factors involved in teachers’ planning and enactment of examples, the Mathematics Teaching-via-Examples Cycle (MTEC), an adaption of the Mathematics Teaching Cycle framework (Simon, 1995), was developed and used. A qualitative multiple-case study (Merriam, 1998) approach was adopted, where three secondary school teachers, each with over ten years of teaching experience, were selected to participate. The three teachers were selected based on their responses to a questionnaire which surveyed 121 teachers’ opinions on example use, mathematics knowledge and beliefs. The main research design involved lesson observations of each teacher’s teaching of a lesson sequence for a mathematics topic. The data sources comprised lesson observation videos, teacher interview audios, lesson artefacts and field notes.

The research findings were derived using the constant comparative method which surfaced the need to parse the lessons. Repeated video viewing of the lessons identified four lesson phases namely, Introduction, Engagement, Application and Integration, and eight activity segments. Detailed analysis hinted at common classroom practices too where teachers began most lessons with the Introduction phase and were also observed to follow the Introduction-Engagement-Application phase cycle when introducing new content which occasionally continued into the Integration phase to enhance students’ mathematical understanding. Despite the commonalities, the main classroom activity that each teacher focused on was different.

To answer the first research question, teachers were found to have two key example sources where one was their personal example space (Watson & Mason, 2005). The other major sources were the prescribed textbook, stipulated assessment book, or online mathematics portal. Very few examples were generated by students. Four categories concerning the origin, purpose, enacted form and structure of the instructional examples also emerged to provide multiple descriptions of examples.

The instructional examples were then situated within the lesson phases and activity segments to address the second research question. Teachers tended to rely on their own example space in the Introduction and Engagement phases, used examples primarily for entry or formative purposes, and enacted them mainly as expository examples. On the other hand, they used examples residing in instructional materials in the other two phases largely as formative or enhancing tasks.

To focus on the “why” behind teachers’ example use, as reflected in the third research question, eight reasons and seven guiding principles were surfaced. The reasons behind teachers’ example use included the need to make connections or to provide practice, whereas the guiding principles involved focusing on structure or including a wide range of examples. The research findings complemented the literature where subject matter knowledge, pedagogical content knowledge, and craft knowledge have been associated with teachers’ use of examples in mathematics instruction.

To identify the factors involved in teachers’ planning and enactment of examples, the Mathematics Teaching-via-Examples Cycle (MTEC), an adaption of the Mathematics Teaching Cycle framework (Simon, 1995), was developed and used. A qualitative multiple-case study (Merriam, 1998) approach was adopted, where three secondary school teachers, each with over ten years of teaching experience, were selected to participate. The three teachers were selected based on their responses to a questionnaire which surveyed 121 teachers’ opinions on example use, mathematics knowledge and beliefs. The main research design involved lesson observations of each teacher’s teaching of a lesson sequence for a mathematics topic. The data sources comprised lesson observation videos, teacher interview audios, lesson artefacts and field notes.

The research findings were derived using the constant comparative method which surfaced the need to parse the lessons. Repeated video viewing of the lessons identified four lesson phases namely, Introduction, Engagement, Application and Integration, and eight activity segments. Detailed analysis hinted at common classroom practices too where teachers began most lessons with the Introduction phase and were also observed to follow the Introduction-Engagement-Application phase cycle when introducing new content which occasionally continued into the Integration phase to enhance students’ mathematical understanding. Despite the commonalities, the main classroom activity that each teacher focused on was different.

To answer the first research question, teachers were found to have two key example sources where one was their personal example space (Watson & Mason, 2005). The other major sources were the prescribed textbook, stipulated assessment book, or online mathematics portal. Very few examples were generated by students. Four categories concerning the origin, purpose, enacted form and structure of the instructional examples also emerged to provide multiple descriptions of examples.

The instructional examples were then situated within the lesson phases and activity segments to address the second research question. Teachers tended to rely on their own example space in the Introduction and Engagement phases, used examples primarily for entry or formative purposes, and enacted them mainly as expository examples. On the other hand, they used examples residing in instructional materials in the other two phases largely as formative or enhancing tasks.

To focus on the “why” behind teachers’ example use, as reflected in the third research question, eight reasons and seven guiding principles were surfaced. The reasons behind teachers’ example use included the need to make connections or to provide practice, whereas the guiding principles involved focusing on structure or including a wide range of examples. The research findings complemented the literature where subject matter knowledge, pedagogical content knowledge, and craft knowledge have been associated with teachers’ use of examples in mathematics instruction.

Date Issued

2018

Call Number

QA14.S55 Ng