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  • 13

    Lesson Study: Improving Teachers

    Conceptions of Students

    Understanding in Place Value

    Emilie Dawson

  • ii

    Contents 1. Introduction .................................................................................................................................... 1

    1.1 Research Background .............................................................................................................. 1

    1.2 Purpose for Research .............................................................................................................. 1

    1.2.1 Problem of Practice ......................................................................................................... 2

    1.2.2 Research Questions......................................................................................................... 2

    1.3 Definitions of Key Terms ......................................................................................................... 2

    1.4 Report Outline......................................................................................................................... 3

    2 Literature Review ............................................................................................................................ 4

    2.1 Background of Place Value...................................................................................................... 4

    2.2 Base Ten Materials .................................................................................................................. 5

    2.3 Lesson Study ........................................................................................................................... 7

    3 Methodology ................................................................................................................................... 8

    3.1 Outline and Justification ......................................................................................................... 8

    3.2 Participants ............................................................................................................................. 9

    3.3 Data Collection Tools .............................................................................................................. 9

    3.4 Lesson Study Stages .............................................................................................................. 11

    4 Results ........................................................................................................................................... 12

    4.1 Kylies Class ........................................................................................................................... 12

    4.2 Mirandas Class ..................................................................................................................... 13

    4.3 Pablos Class .......................................................................................................................... 15

    5 Discussion ...................................................................................................................................... 17

    5.1 Teacher Practice .................................................................................................................... 17

    5.1.1 First Implementation .................................................................................................... 17

    5.1.2 Second Implementation ................................................................................................ 18

    5.1.3 Third Implementation ................................................................................................... 19

    5.2 Teachers Conceptions of Students Understanding in Place Value ..................................... 19

    5.3 Student Understanding of Place Value ................................................................................. 21

    5.3.1 Kylies Class ................................................................................................................... 21

    5.3.2 Mirandas Class ............................................................................................................. 22

    5.3.3 Pablos Class .................................................................................................................. 23

    5.4 Conclusions ........................................................................................................................... 24

    5.5 Implications ........................................................................................................................... 24

    6 References .................................................................................................................................... 26

    7 Appendices .................................................................................................................................... 29

  • 1

    Abstract

    This research examines Lesson Study and its potential to improve students misconceptions

    in place value by targeting teacher Pedagogical Content Knowledge. It aims to test whether a

    single, collaboratively planned lesson has the potential to improve teachers scaffolding

    practices by better understanding students misconceptions in place value. Qualitative and

    quantitative data were collected as evidence to measure improvement in students

    understanding of place value through the implementation of place value related tasks.

    Interviews were used to monitor teachers perceptions of their practice. The research

    highlighted that Lesson Study enhanced teachers conceptions of student understanding of

    place value, enabling them to design, implement and review lessons to implement scaffolding

    that resulted in improved student outcomes. It was found that Lesson study can be used to

    promote shared practice that, if sustained, could create a culture of powerful student

    intervention in the development of foundational place value concepts.

    1. Introduction

    1.1 Research Background

    The underperformance of Australian students in mathematics is marked by a decrease in the

    number of students achieving high results on PISA and TIMMS testing (Stephens, 2009).

    Student disengagement from mathematics is occurring at a younger age as a result of the

    development of poor mathematical identities (Marshman, Pendergast, & Brimmer, 2011,

    p.500). Australian students are increasingly likely to resign from formal mathematical

    education in secondary school to pursue less demanding disciplines (Council of Australian

    Governments [COAG], 2008).

    The issue of disengagement resides in students lack of robust foundational knowledge,

    which is needed to assist students to transition into abstract thinking (Department of

    Education and Early Childhood Development [DEECD], 2012). This highlights the

    importance of teachers having the necessary Pedagogical Content Knowledge (PCK) to

    effectively scaffold students understanding in Mathematics (COAG, 2008).

    Place value is an important foundational area of Mathematics that underpins the development

    of more complex skills, including addition and subtraction, decimals and multiplicative

    thinking (Hiebert & Wearne, 1992; Steinle & Stacey, 2004; Siemon et al., 2011). Students do

    not always have the place value knowledge and skills to apply learning to more abstract

    contexts (DEECD, 2012).

    1.2 Purpose for Research The research evaluates the effectiveness of Lesson Study for improving students

    understanding of place value by strengthening the Instructional Core of teaching and learning

    (City, Elmore, Fiarman, & Teitel, 2009).

    Lesson Study is the vehicle for action research and professional learning which supports

    teachers to develop and refine their PCK to teach place value with improved mathematics

    outcomes for students. Lesson Study was selected due to its ability to provide an ongoing

    learning cycle to instil long term change in teachers practice (Goos, Dole, & Makar, 2007).

  • 2

    Action research such as Lesson Study, can develop teachers PCK by deprivatising

    classrooms (City et al., 2009). It provides opportunities for participants to become reflective

    practitioners and align teacher and school goals to promote a professional culture (Sagor,

    1991).

    1.2.1 Problem of Practice

    In this research Lesson Study enables teachers to identify a problem of practice and engage in

    systematic enquiry (Sagor, 1991; Thomas, 2011). The focus for the teacher problem of

    practice is to use questioning, through systematic enquiry, to scaffold student learning and

    improve assessment outcomes.

    Evidence is collected to monitor the progress of mathematics outcomes (Askew, Brown,

    Rhodes, Wiliam, & Johnson, 1997) to support the development of accountability in

    educational practitioners (City et al., 2009).

    1.2.2 Research Questions

    Through the research we aim to discover whether the provision of opportunities for teachers

    to be involved in the Lesson Study increases mathematical understanding for both teachers

    and students (Sagor, 1991) by answering these key research questions:

    Can Lesson Study improve teachers conceptions of students understanding of place value?

    What changes in teachers classroom practice occur as a result of their engagement in the Lesson Study process?

    As a result of planning, implementing and reviewing