Navigating through Geometry in Grades 3–5

M. Katherine Gavin, Louise P. Belkin, Ann Marie Spinelli, e Judy St. Marie

NCTM | 2001 | 135 páginas | PDF | 6,8 Mb

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The "big ideas" of geometry–shape, location, transformations, and spatial visualization–are the focus of this book. Sequential activities will enrich the curriculum and help students develop a strong sense of geometric concepts and relationships, leading them to experience the joy and wonder of geometry and other mathematics. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.

Table of Contents
About This Book . vii
Introduction . 1 (falta)
Chapter 1- Shapes  . 9 (falta)
Build What I’ve Created . 11
Thinking about Triangles  . 15
Roping In Quadrilaterals . 22 (PDF)
Building Solids . 26
Searching for the Perfect Solids  . 31
Chapter 2 - Location . 35 (falta)
Find the Hidden Figure . 37
Xs and Os . 40
Can They Be the Same? . 44
Chapter 3 - Transformations . 47 (falta)
Patchwork Symmetry  . 49
Symmetry Detectives—Learn the Secret Code! . 52
Going Logo for Symmetry! . 55
Tetrominoes Cover-Up . 59
Motion Commotion . 64
Zany Tessellations . 68
Chapter 4 - Spatial Visualization  . 75 (falta)
Puzzles with Pizzazz . 77
Exploring Packages  . 80
It’s All in the Packaging . 83
It’s the View That Counts! . 86
Fraction Fantasy . 88 (falta)
Geo City  . 90
Looking Back and Looking Ahead . 95 (falta)
Appendix - Blackline Masters and Solutions . 99 (falta)
Geodot Paper for Geoboards . 100
Quadrilateral Pieces . 101
Ring Labels . 102
Mystery Rings . 103
Two- and Three-Dimensional Shapes . 104
Counting Parts of Solids . 105
Patterns for the Perfect Solids . 106
Patterns for Other Solids . 108
Coordinate Grid A . 109
Coordinate Grid B . 110
Coordinate Grid C . 111
Coordinate Grid D  . 112
Similar and Nonsimilar Shapes . 113
Quarter-Inch Grid Paper  . 114
Half-Inch Grid Paper  . 115
Alphabet Symmetry . 116
Alphabet-Symmetry Chart . 117
Turn It Around . 118
Tetrominoes Cover-Up Game Board . 120
Tetrominoes Spinner . 121
Motion Commotion . 122
Tangrams . 123
Puzzles  . 124
Isodot Paper . 125 (falta)
Geodot Paper  . 126
One-Inch Grid Paper . 127  (falta)
Building Permit Application . 128
Sample Geo City Map  . 129
Solutions  . 130
References  . 133  (falta)

Contents of CD-ROM

Applets  (falta)
Exploring Geometric Solids and Their Properties
Geoboard
Isometric Drawing Tool
Pattern Patch
Shape Sorter
Tangram Challenges

Templates
Pattern Blocks  (falta)
Quilt-Patch Work Space
Puzzle Set  (falta)
Students’ Tessellation Art  (falta)
Blackline Masters  (falta - parcialmente)

Publications of the National Council of Teachers of Mathematics

Geometry Results from the Third International Mathematics and Science Study 
Michael T. Battista
Teaching Children Mathematics

Presents an overview of the geometry findings of the Third International Mathematics and Science Study (TIMSS) and ways to use problems from the study to assess students' understanding of geometry.
Characterizing the van Hiele Levels of Development in Geometry 
William F. Burger e J. Michael Shaughnessy
Journal for Research in Mathematics Education
math.byu.edu (link direto)

Describes the van Hiele levels of reasoning in geometry according to responses to clinical interview tasks concerning triangles and quadrilaterals. Subjects were 13 students from grades 1 through 12 plus a university mathematics major. Students' behavior on tasks was consistent with the van Hiele original general description of the levels
The Art of Tessellation (PDF - 2,8 Mb)
Paul Giganti Jr. e Mary Jo Cittadino
Arithmetic Teacher

Discusses an experience in presenting tessellations in both classrooms and teacher inservice workshops. Describes preliminary activities, nibble techniques, and tessellation art. Provides 2 worksheets and a glossary of tessellation terms. Lists materials and 27 references
Math Is Art
Tim Granger
Teaching Children Mathematics
soe.ucdavis.edu (link direto)

Describes a unit of study focusing on tessellations to show students another view of mathematics.

From Paper to Pop-Up Books  
Vanessa Evans Huse, Nancy Larson Bluemel, e Rhonda Harris Taylor
Teaching Children Mathematics

Describes geometry-related activities that explore tessellation patterns and use origami and paper to create three-dimensional figures and pop-up cards

Why Are Some Solids Perfect? Conjectures and Experiences by Third Graders 
Richard Lehrer e Carmen L. Curtis
Teaching Children Mathematics

ncisla.wceruw.org (link direto) 

Describes how classification came alive in a third grade classroom as children searched for rules or properties defining the five Platonic solids, then constructed a precise definition to classify these solids.

Shape Up! 
Christine D. Oberdorf e Jennifer Taylor-Cox
Teaching Children Mathematics

Identifies common misconceptions about polygons. Discusses current practices used to teach geometry to search for the source of misconceptions, and describes ways to help students avoid these misconceptions

Symmetry the Trademark Way   (falta)
Barbara S. Renshaw
Arithmetic Teacher

Trademark designs provide a familiar yet innovative way for students to look at a number of mathematical concepts. How line and rotational symmetry can be presented using trademarks is the focus of this article. The emphasis is on the design of bulletin boards

Learning Geometry: Some Insights Drawn from Teacher Writing
Deborah Schifter
Teaching Children Mathematics

Contributes to the emerging picture of children's development of understanding in geometry and the kinds of teaching that can support it. Describes how teachers can use episode writing to capture student thinking and make instructional decisions.

Developing Geometric Thinking through Activities That Begin with Play
Pierre M. van Hiele
Teaching Children Mathematics

print.nycenet.edu (link direto)

Rich and stimulating instruction in geometry can be provided through playful activities with mosaics such as pattern blocks or design tiles. Presents an intriguing mosaic puzzle to describe activities at various developmental levels and how the activities can help develop children's geometric thinking.

Navigating through Data Analysis and Probability in Grades 3–5

Suzanne Chapin, Alice Koziol, Jennifer MacPherson, e Carol Rezba
National Council of Teachers of Mathematics | | 120 páginas | PDF | 3,89 Mb

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Investigations involving data give students opportunities to depict the shape of data sets and use statistical characteristics of the data to describe similarities and differences among related sets. An assortment of discussions, activities, and investigations emphasize the collection and analysis of data and develop the idea of probability as a measure of the likelihood of events that are meaningful and real to students. The accompanying CD-ROM features applets for students to manipulate and resources for teachers' professional development. It also features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.

Índice

Table of Contents

About This Book . vii

Introduction . 1 (falta)

Chapter 1 - From Questions to Method: Beginning the Process . 11 (falta)

Questions, Please?  . 13

What’s My Method? . 17

Chapter 2 - Using Data Analysis Methods . 21 (falta)

Long Jump  . 23

How Many Stars Can You Draw in One Minute? . 29

Do You Get Enough Sleep?. 34

Exploring the Mean  .39

Chapter 3 - Inferences and Predictions . 45 (falta)

The Foot, the Whole Foot, and Nothing but the Foot! . 47

Can You Catch Up? . .. 51

Chores—How Many Hours a Week Are Typical? . 56

Chapter 4 - What Are the Chances? . 61 (falta)

How Likely Is It to Land in the Trash Can? . 62

Is There Such a Thing as a Lucky Coin? . 68

Spin City . 73

Is It Fair? . 79

Looking Back and Looking Ahead .83

Appendix - Blackline Masters and Solutions  . 87 (falta)

Determining a Purpose for a Data Investigation . 88 (falta)

Getting Ready . 92

A Question to Investigate  . 94

Data Sets . 96

What’s My Method?—Descriptions  .98

What’s My Method?—Explorations .100

Summer Olympics 2000 . 101

How Long Is One Minute?  . 102

How Many Stars?—Another Class . 103

How Much Sleep Do You Get? . 104

How Much Sleep Do Children Typically Get? . 105

Women’s Soccer Results  . 106

The Foot, the Whole Foot, and Nothing but the Foot—Group Data  . 108

The Foot, the Whole Foot, and Nothing but the Foot—Class Data . 109

Can You Catch Up?. 110

Chores—How Many Hours a Week Are Typical? . 111

Stem-and-Leaf Plot of the Group’s Sample Data  . 112

Sample versus Population—How Do They Compare? . 113

Paper Toss Recording Sheet . 114

Spin It . 115

Matching Line Plots with Spinners . 116

Number Cards . 117

Rule Cards  . 118

Answer Key for Women’s Soccer Results . 119 (falta)

References . 120 (falta)

Contents of CD-ROM

Introduction

Table of Standards and Expectations, Data Analysis and Probability,

Pre-K–12

Applet Activities (falta)

  Probability Games

  Preset Spinner (on-line: illuminations.nctm)

  Make Your Own Spinner (on-line: illuminations.nctm)

  Dice Sums

  Coin Toss 

Blackline Masters and Templates

Readings from Publications of the National Council of Teachers of Mathematics

Problem Solving: Dealing with Data in the Elementary School

Harry Bohan, Beverly Irby, and Dolly Vogel

Teaching Children Mathematics

Describes the Elementary Mathematics Research Model, which furnishes a vehicle for problem solving through real data collection and analysis.

Using Probability Experiments to Foster Discourse

Thomas G. Edwards and Sarah M. Hensien

Teaching Children Mathematics

Describes how three experiments suitable for upper-elementary students can be used to foster classroom discourse in which students begin to explore probability.

Making Charts: Do Your Students Really Understand the Data?

Louis Feicht

Mathematics Teaching in the Middle School

Presents an activity in which students learn how to label graphs in order to make them meaningful.

Teaching Statistics: What’s Average?

Susan N. Friel

The Teaching and Learning of Algorithms in School Mathematics

Daily Activities for Data Analysis

Chris Hitch and Georganna Armstrong

Arithmetic Teacher

Presents four sets of activities to develop the concepts of data analysis and graphing. Students estimate sample populations using beans, examine graphs from newspapers and magazines, predict the most popular color of cars, and simulate quality control in a manufacturing process.

Understanding Students’ Probabilistic Reasoning  (falta)

Graham A. Jones, Carol A. Thornton, Cynthia W. Langrall, and James E. Tarr

Developing Mathematical Reasoning in Grades K–12

The Lunch-Wheel Spin

Julia A. Mason and Graham A. Jones

Arithmetic Teacher

Describes a problem formulated by fourth-grade students about having more pizza for lunch, and the clarifying, predicting, modeling, simulating, comparing, and extending activities that occurred in addressing the problem from a probabilistic perspective.

Children’s Concepts of Average and Representativeness

Jan Mokros and Susan J. Russell

Journal for Research in Mathematics Education

Interviews with (n=21) fourth, sixth, and eighth graders, who were asked to construct their own notion of average and representativeness in open-ended problems, identified five basic constructions of average as mode, an algorithmic procedure, what is reasonable, midpoint, and a mathematical point of balance. 

Teaching Mathematics with Technology: Statistics and Graphing

Janet Parker and Connie C. Widner

Arithmetic Teacher

Presents a series of four steps used in data analysis processes that help students investigate and interpret real world situations. Gives activities that employ computer software to create representative graphs of the data in the analysis process.

What Do Children Understand about Average?

Susan J. Russell and Jan Mokros

Teaching Children Mathematics

Interviews with fourth, fifth, and sixth graders found that they thought about the concept of average as mode, median, and/or a procedure. Presents approaches to develop the concept of average

Exploring Probability through an Evens-Odds Dice Game

Lynda R. Wiest and Robert J. Quinn

Mathematics Teaching in the Middle School

Presents a dice game that students can use as a basis for exploring mathematical probabilities and making decisions while they also exercise skills in multiplication, pattern identification, proportional thinking, and communication. 

Mean and Median: Are They Really So Easy?

Judith S. Zawojewski and J. Michael Shaughnessy

Teaching Mathematics in the Middle School

Analyzes National Assessment of Education Progress (NAEP) items to assess student understanding of spread as well as center, such as mean and median. Discusses implications for teaching statistics in 5th and 6th grade mathematics.

Obstacles épistémologiques relatifs à la notion de limite

Anka Sierpinska

Recherches en Didactique des Mathematiques, Vol. 6, n°1, pp. 5-67, 1985

PDF - 2,4 Mb


Nenhum link disponível

Résumé

La recherche dont il est question dans le présent article se place dans la voie des recherches indiquée par Guy Brousseau dans son article (1983). Découvrir les obstacles épistémologiques lié aux mathématiques à enseigner à l’école et trouver les moyens didactiques pour aider les élèves à les surmonter - voilà, brièvement, deux principaux problèmes de ce programme de recherche. Ici, il s’agit du cas particulier de la notion de limite et l’article ne touche qu’au premier de ces problèmes : on propose une liste d’obstacles épistémologiques relatifs à la notion de limite présents encore chez des élèves d’aujourd’hui ; on ne propose pas les situations didactiques qui permettraient aux élèves de franchir ces obstacles.

Abstract

The present paper is concerned with a research the direction of which was indicated by Guy Brousseau in his 1983. To discover the epistemological obstacles connected with mathematics to be taught at school and to.elaborate didactical means to help the students to overcome them- these are, briefly, two main problems of this research programme. In this paper, the particular case of the notion of limit is considered and only the first of the two above mentionned problems is dealt with : a list of epistemological obstacles relative to the notion of limit is proposed ; there are no proposals of didactical situations enabling the students to overcome these.

Resumen

La investigación que trata este artículo se situa dentro de la línea de investigaciones indicadas por Guy Brousseau (1983). Descubrir los obstáculos epistemológicos ligados a las matemáticas que se enseñan en la escuela y encontrar los medios didácticos para ayudar los alumnos a superarlos. Brevemente presentamos aqui dos problemas principales de ese programa de investigación. Se trata del caso particular de la noción de limite y el artículo toca solamente el primero de esos problemas : se propone una lista de obstáculos epistemológicos relativos a la noción de límite presentes todavía en los alumnos de hoy en dia ; no se proponen situaciones didácticas que permitirian a los alumnos de superar esos obstáculos.

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