## Teachers Engaged in Research: Inquiry Into Mathematics Classrooms, Grades 3-5The goal of this series is to use teachers' accounts of classroom inquiry to make public and explicit the processes of doing research in classrooms. Teaching is a complex, multi-faceted task, and this complexity often is not captured in research articles. Our goal is to illuminate this complexity. Research that is done in classrooms by and with teachers is necessarily messy, and our stance is that the ways in which this is so should be articulated, not hidden. Through the chapters in this volume we learn about the questions that capture the attention of teachers, the methodologies they use to gather data, and the ways in which they make sense of what they find. Some of the research findings could be considered preliminary, others confirmatory, and some may be groundbreaking. In all cases, they provide fodder for further thinking and discussion about critical aspects of mathematics education. |

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### Contents

1 | |

THE IMPACT OF CLASSROOM RESEARCH ON STUDENT AND TEACHER LEARNING Division of Fractions Barbara Adams and Janet Sharp | 13 |

REASONING AND SENSEMAKING What Can We Expect in Grades Three Through Five? Tammy CoviNadene RatcliffeCheryl ALufoirtskiJanet ... | 33 |

ARITHMETIC TO ALGEBRA A Teachers Journey June Soares | 49 |

EXPLORING MULTIPLICATIVE REASONING Judy Atcheson | 59 |

WRITING MATHEMATICAL WRITING Eileen Phillips | 83 |

APPLYING RESEARCH IN THE CLASSROOM Investigating ProblemSolving Instruction Christina Nugent | 113 |

TEACHER AS RESEARCHER Researcher As Learner Jennifer Segebart | 129 |

THE IMPORTANCE OF STUDENT SHARING SESSIONS Analyzing and Comparing Subtraction Strategies Meghan B Steinmeyer | 145 |

EXAMINING TEACHER QUESTIONING THROUGH A PROBABILITY UNIT Ken Valentine and Dorothy Y White | 155 |

GWEISTS STORY Researching Teaching With Others in a Lesson Study Transforms a Beginning Teachers Understanding Ann R TaylorLaurel D Pu... | 179 |

WHATS A LITERATURE PERSON LIKE YOU DOING TEACHING AND RESEARCHING IN ELEMENTARY LEVEL MATHEMATICS? Vicki Z... | 201 |

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Page xii - Teachers and student teachers who take an inquiry stance -work -within inquiry communities to generate local knowledge, envision and theorize their practice, and interpret and interrogate the theory and research of others. Fundamental to this notion is the idea that the work of inquiry communities is both social and political; that is, it involves making problematic the current arrangements of schooling; the -ways knowledge is constructed, evaluated, and used; and teachers' individual and collective...

Page xi - We use the metaphor of stance to suggest both orientational and positional ideas, to carry allusions to the physical placing of the body as well as to intellectual activities and perspectives over time. In this sense, the metaphor is intended to capture the ways we stand, the ways we see, and the lenses we see through as educators.

Page xviii - ... systematically document their own teaching and learning — their own thinking, planning, and evaluation processes as well as their questions, interpretive frameworks, changes in views over time, issues they see as dilemmas, and themes that recur. Often practitioner researchers capture these interpretive processes by collecting multiple versions of course syllabi and class handouts, plans and materials used for class activities, class assignments and problems posed, and the texts used in teaching...