Examining Prospective Middle Grade Teachers Proportional Reasoning

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ACKNOWLEDGEMENT

I would like to thank my supervisor for supporting me throughout my project and giving his valuable suggestions. Finally thanks to all my friends and family for their utmost support and inspiration.

DECLARATION

I, (Your name), would like to declare that all contents included in this dissertation stand for my individual work without any aid, & this dissertation has not been submitted for any examination at academic as well as professional level previously. It also represents my own views & not essentially the ones associated with university.

Signed __________________ Date _________________

TABLE OF CONTENTS

ACKNOWLEDGEMENTii

DECLARATIONiii

CHAPTER 1: INTRODUCTIONv

Background of the Research Studyv

Research Questionsvii

Purpose of the Research Studyvii

Outline of the Research Studyvii

CHAPTER 2: LITERATURE REVIEWix

What is Proportional reasoning?ix

Misconceptions about Proportional Reasoningx

Tourniaire and Pulos Errorsxi

Karplus and Peterson Errorsxii

Teachers' conceptions of studentsxiii

Current practicesxiv

Student comprehensionxv

REFERENCESxix

CHAPTER 1: INTRODUCTION

Background of the Research Study

The research study is based on examining the prospective middle grade teacher's proportional reasoning. The study mainly focuses on finding out the proportional reasoning of middle grades mathematics teachers before or after the completion of the algebra concepts. The topic is unique in its kind as it has not been researched in the past by the researchers. The study tends to analyze the abilities and capabilities of the middle grade mathematics teachers in giving proportional reasoning of the algebra concepts. The rate and proportional reasoning given by the teachers in mathematics is the central focus of the research study in order to find out the basis of their reasoning. The proportional reasoning is an important concept that is considered to be very important for the cognitive development of the students studying in the middle grades particularly. The importance of the proportional reasoning can be understood with the fact that whatever efforts and time is required to develop this concept within the students should be extended in order to assure its cautious development in the children. It is also known by the researchers and the teachers that the development of this concept takes long time by the students to understand it and applying it in their academic subjects. It takes them number of years to thoroughly understand the proportional reasoning. The concept of proportional reasoning is taken as the milestone for the later stages of understanding within the students. It helps the students in developing different new concepts that are related to the graphing, functions, measurement and algebraic equations. As the concept of the proportional reasoning is intricate, it is not easy for the teachers even to develop this concept within the students. The concept of proportional reasoning is associated with the development of the big ideas and needs the students to have good essential understanding of it. It is an important educational task that requires in depth understanding and analysis as a teacher while remaining sensitive to the kinds of reasoning that are considered to be most accessible point of entry for the students. It also helps the students and pushes them for developing refined types of ...