Navigating through Data Analysis and Probability in Prekindergarten-Grade 2

Linda Jensen Sheffield, Mary Cavanagh, Linda Dacey, Carol R. Findell, Carole Greenes, and Marian Small

National Council of Teachers of Mathematics |  2002  | 100 páginas | PDF | 2,9 Mb

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This book demonstrates how some fundamental ideas about data analysis and probability can be introduced to build a strong foundation in young students. Activities designed to introduce and promote familiarity with essential concepts develop and extend students' ideas about data analysis and simple probability through the use of bar graphs, tallies, frequency tables, and Venn diagrams. Helpful margin notes provide teaching tips, anticipated student responses to questions, samples of students' work, and ways to modify the activities for students experiencing difficulty or needing enrichment. The supplemental CD-ROM 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 - Data Collection, Organization, and Display . 11

Build a Graph . 15

What’s Your Favorite?  . 18

Junk Sort  . 22

All about Shoes  . 25

Chain It . 27

Families. 30

Row Your Boat  . 33

Morley Most and Lutie Least  . 36

Chapter 2 - Question Posing and Data Analysis .  41 (falta)

Back and Forth . 44 (falta)

Mystery Graphs . 50

Conducting a Survey . 53 (falta)

What a Difference a Day Makes . 55

Whom Do You Believe? . 58

Travel Agent . 61 (falta)

Chapter 3 - Probability . 63 (falta)

Possible or Impossible . 65

Spin It . 67

Which Bag Is Which?  . 70

Some Sums . 73 (falta)

Looking Back and Looking Ahead . 77 (falta)

Appendix - Blackline Masters and Solutions  . 79 (falta)

Vertical Graph Mat . 80

Horizontal Graph Mat . 81

Mary Had a Little Lamb . 82

Mystery Graphs . 83

Which Is Which? . 84

More than One Story. 85

Our Survey . 86

About Students . 87

More about Students  . 88

Favorite Colors  . 89

Children in a Class . 90

Class Trip . 91 (falta)

Spin It  . 93

Color Predictions  . 95

Color Splits  . 96

Solutions  . 97 (falta)

References  . 98 (falta)

Introduction
Table of Standards and Expectations, Data Analysis and Probability, Pre-K–12 (faltam)
Applet Activities
Get Organized
Shape Sorter
Guess the Rule
Make the Rule
Probability Games
Preset Spinner
Make Your Own Spinner
Dice Sums
Blackline Masters and Templates (faltam)
Blackline Masters
Ages of Students
Number of Students’ Pets
Number of Students’ Siblings
Students’ Favorite Sport
One-Half-Inch Grid Paper
One-Inch Grid Paper
Two-Centimeter Grid Paper

Readings from Publications of the National Council of Teachers of Mathematics

Collecting Data Outdoors: Making Connections to the Real World
Carole Basile
Teaching Children Mathematics

Describes a process of data collection with young children using the outdoors as a mathematical context. The process of data collection and processing introduces children to more abstract mathematics as they sort and classify data, create graphs, compare datasets, examine patterns, and interpret graphical representations.

 

Exploring Data: Kindergarten Children Do It Their Way
Frances R. Curcio e Susan Folkson
Teaching Children Mathematics

Describes situations in which children developed mathematical concepts through processes of sorting and classifying, comparing, measuring, matching with one-to-one correspondence, and enumerating. Data were gathered while observing informal discourse, during sharing sessions, and in a reading session.

Young Students Investigate Number Cubes
Alex Friedlander
Teaching Children Mathematics

Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system.

Making Sense of Graphs: Critical Factors Influencing Comprehension and Instructional Implications
Susan N. Friel, Frances R. Curcio, e George W. Bright
Journal for Research in Mathematics Education

This article outlines critical factors that appear to influence graph comprehension and identifies instructional implications. The factors identified are purpose, task characteristics, discipline characteristics and reader characteristics. A sequence for ordering the introduction of graphs is proposed and ways instruction may be modified to promote graph sense making.

Pictures, Tables, Graphs, and Questions: Statistical Processes
Andrew C. Isaacs e Catherine Randall Kelso
Teaching Children Mathematics

Outlines an approach to the problem of over- or underquantification for students by teaching science as a process of collecting, organizing, and analyzing data that naturally integrates with mathematics. 

Students’ Probabilistic Thinking in Instruction 
Graham A. Jones, Cynthia W. Langrall, Carol A. Thornton, e A. Timothy Mogill
Journal for Research in Mathematics Education

Evaluates the thinking of third grade students in relation to an instructional program in probability which was informed by a research-based framework that included a description of students' probabilistic thinking. Reveals that overcoming misconceptions in sample space, applying both part-part and part-whole reasoning, and using invented language to describe probabilities were key patterns in producing growth in probabilistic thinking.

Hamster Math: Authentic Experiences in Data Collection

Beth Jorgensen

Teaching Children Mathematics

Describes the data collection and interpretation project of primary grade students involving predicting, graphing, estimating, measuring, number problem construction, problem solving, and probability.

Classification and Logical Reasoning 

Melfried Olson e Judith Olson

Teaching Children Mathematics

These activities explore classification and logical reasoning by providing students with opportunities to generate multiple answers and engage in multiple classifications of the same item. No solutions are suggested so that students will look to themselves as the mathematical authorities. Sample items for classification include birthday months, toys, holidays, and geometric figures. Numbers are classified by skip counting and factoring.

The Shape of Fairness 

Elizabeth Penner e Richard Lehrer

Teaching Children Mathematics

Describes how young children used geometric shapes to model a fair playing space for "Mother, may I?"

Take Two: Fair or Unfair? 

Lynae Sakshaug

Teaching Children Mathematics

Problem Solvers poses a problem for classroom use and gives a solution to a previously published problem.

Responses to the Take Two: Fair or Unfair? Problem

Lynae Sakshaug

Teaching Children Mathematics

Presents answers to the problem appearing in the January, 1999 Problem Solvers section of this journal, which was a strategy game called "Take Two" in which two players played by placing seven chips in a row and removing one or two chips each turn.

Which Graph Is Which?

Lynae Sakshaug

Teaching Children Mathematics

Introduces a problem that can be used to help children develop graph sense. Involves two graphs of which students must determine which one applies to which situation.

Young Children Deal with Data 

Judith V. Taylor

Teaching Children Mathematics

Presents activities having to do with data generation, organization, interpretation, representation, drawing conclusions, and making predictions on the basis of data which students have collected.