F. D. Rivera
Sense Publishers | 2014 | páginas | rar - pdf | 981 kb
link (password : matav)
This is a methods book for elementary majors and preservice/beginning elementary teachers. It takes a very practical approach to learning to teach elementary school mathematics in an emerging Age of the Common Core State Standards. The Common Core State Standards in Mathematics (CCSSM) is not meant to be “the” official mathematics curriculum; it was purposefully developed primarily to provide clear learning expectations of mathematics content that are appropriate at every grade level and to help prepare all students to be ready for college and the workplace. A quick glance at the Table of Contents in this book indicates a serious engagement with the recommended mathematics underlying the kindergarten through grade 5 portions of the CCSSM first, with issues in content-practice assessment, learning, teaching, and classroom management pursued next and in that order.
In this book we explore what it means to teach to the CCSSM within an alignment mindset involving content-practice learning, teaching, and assessment. The CCSSM content standards, which pertain to mathematical knowledge, skills, and applications, have been carefully crafted so that they are teachable, learnable, coherent, fewer, clearer, and higher. The practice standards, which refer to institutionally valued mathematical actions, processes, and habits, have been conceptualized in ways that will hopefully encourage all elementary students to engage with the content standards more deeply than merely acquiring mathematical knowledge by rote and imitation. Thus, in the CCSSM, proficiency in content alone is not sufficient, and so does practice without content, which is limited. Content and practice are both equally important and, thus, must come together in teaching, learning, and assessment in order to support authentic mathematical understanding.
This blended, multisourced text is a “getting smart” book. It helps elementary majors and preservice/beginning elementary teachers work within the realities of accountable pedagogy and develop a proactive disposition that is capable of supporting all elementary students in order for them to experience growth in mathematical understanding necessary for middle school and beyond, including future careers.
CONTENTS
1. Dear Elementary Majors and Practicing and Beginning Elementary Teachers: An Introduction 1
1.1 A Blended Multisourced Approach to Learning to Teach Mathematics 4
1.2 Overview of the Remaining Chapters 5
2. Getting to Know the Common Core State Standards for Mathematical Practice 7
2.1 Content Activity 1: Generating Addition Facts 7
2.2 The Eight Common Core State Standards for Mathematical Practice 11
2.3 Content Activity 2: Building a Hexagon Flower Garden Design 11
2.4 Problem Solving Contexts in Elementary School Mathematics 16
2.4.1 Content Activity 3: Different Types of Problems in Elementary School Mathematics 16
2.5 Representations in Elementary School Mathematics 17
2.5.1 Content Activity 4: A Kindergarten Subtraction Task 17
2.5.2 Content Activity 5: Representing Whole Numbers in Second Grade 20
2.6 Connections in Elementary School Mathematics 20
2.6.1 Content Activity 6: Repeating Patterns 21
2.7 Reasoning and Proof in Elementary School Mathematics 22
2.7.1 Content Activity 7: Division Problems in Third Grade 22
2.7.2 Activity 8: Even and Odd Numbers in Second Grade 23
2.8 Communication in Elementary School Mathematics 24
2.8.1 Content Activity 9: Addition and Subtraction Strategies from First to Second Grade 25
2.8.2 Content Activity 10: Generating Addition and Subtraction Facts in First Grade 27
2.9 Doing Mathematics with an Eye on theContent-Practice Standards of the CCSSM 28
3. Counting and Cardinality in Kindergarten 31
3.1 Subitizing: Laying the Foundation for Early Multiplicative Thinking 31
3.2 Counting and Writing Numbers and Number Words: Building on Rhythmic Structures 33
3.3 Comparing Quantities 35
3.4 Mapping the Content Standards with the Practice Standards 37
3.5 Developing a Content Standard Progression Table for the Counting and Cardinality Domain 37
4. Numbers and Operations (Part I) 41
4.1 Place Value in Base Ten: The Basic Mathematical Structure of Whole Numbers and Decimal Numbers in the CCSSM 42
4.2 Representing Whole Numbers in Base Ten from K to Grade 4 43
4.3 Representing Decimal Numbers in Grade 5 43
4.4 Comparing and Ordering Whole Numbers and Decimal Numbers from Grades 1 to 5 44
4.5 Rounding Whole Numbers from Grades 3 to 5 45
4.6 Mapping the Content Standards with the Practice Standards 45
4.7 Developing a Content Standard Progression Table for Part I of the Numbers and Operations in Base Ten Domain 46
5. Operations and Algebraic Thinking 47
5.1 Algebraic Thinking from Kindergarten to Grade 5 47
5.2 The Four Fundamental Operations as General Methods for Combining and Generating More Numbers 52
5.2.1 Addition 52
5.2.2 Subtraction 54
5.2.3 Multiplication 54
5.2.4 Division 56
5.3 Forming Equivalent Expressions and Understanding the General Meaning of the Equal Sign 57
5.4 Instantiating Nonsymbolic Algebra Through Problem Solving in Arithmetical Activity 59
5.5 Pattern Generalization as Instantiations of Nonsymbolic and Symbolic Algebra 61
5.6 Mapping the Content Standards with the Practice Standards 66
5.7 Developing a Content Standard Progression Table for the Operations and Algebraic Thinking Domain 66
6. Numbers and Operations in Base Ten (Part II) 67
6.1 Analytical Subitizing in Kindergarten and Sticks and Circles or Labeled Circles in Grade 1 67
6.2 Adding Whole Numbers in Base Ten from Grades 1 to 4 68
6.3 Subtracting Whole Numbers in Base Ten from Grades 1 to 4 72
6.4 Multiplying Whole Numbers in Base Ten from Grades 3 to 5 76
6.5 Dividing Whole Numbers in Base Ten from Grades 3 to 4 79
6.6 Adding, Subtracting, Multiplying, and Dividing Decimal Numbers in Grade 5 83
6.7 Mapping the Content Standards with the Practice Standards 87
6.8 Developing a Content Standard Progression Table for the Operations and Number Thinking Part II Domain 87
7. Numbers and Operations – Fractions 89
7.1 Equal Partitioning of Whole Shapes in Halves and Fourths in Grade 1 90
7.2 Equal Partitioning of Whole Shapes in Thirds and Constructing Equivalent Shares in Grade 2 92
7.3 Unit Fractions and Equivalent Fractions with Denominators 2, 3, 4, 6, and 8 as Equal Shares and Numbers on a Number Line and Whole Numbers as Improper Fractions in Grade 3 95
7.4 Numerical Equivalence of Fractions Involving Denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100, All Improper Fractions, Fraction Addition and Subtraction with Like Denominators, Simple Fraction Multiplication, and Decimal Fraction Addition and Comparison in Grade 4 99
7.5 Fraction Addition, Subtraction, Multiplication, and Simple Division in Grade 5 104
7.6 Mapping the Content Standards with the Practice Standards 109
7.7 Developing a Content Standard Progression Table for the Number and Operations – Fractions Domain 109
8. Geometry 111
8.1 Recognizing and Composing Shapes in Kindergarten and Grade 1 111
8.2 Defi ning and Reasoning about Shapes in Grades 2, 3, and 5 114
8.3 Lines and Angles in 2D Shapes in Grade 4 114
8.4 The Coordinate Plane in Grade 5 116
8.5 Mapping the Content Standards with the Practice Standards 117
8.6 Developing a Content Standard Progression Table for Geometry Domain 117
9. Measurement and Data 119
9.1 Measuring from Kindergarten to Grade 5 119
9.1.1 Qualitative Measurements in Kindergarten 119
9.1.2 Measuring Lengths in Grades 1 and 2 120
9.1.3 Finding Perimeters and Measuring Lengths with Halves and Fourths of an Inch, Areas, and Estimated Liquid Volumes and Masses of Objects in Standard Units in Grade 3 121
9.1.4 Measuring Angles in Grade 4 123
9.1.5 Measuring Volumes of Cubes and Other Right Rectangular Prisms in Grade 5 124
9.1.6 Conversion Problems in Grades 4 and 5 125
9.2 Telling and Writing Time in Grades 2 and 3 125
9.3 Money in Grades 2 and 4 126
9.4 Classifying, Representing, and Interpreting Data from Kindergarten to Grade 5 127
9.4.1 Forming Categories Involving Discrete Objects in Kindergarten 127
9.4.2 Structuring Data from Kindergarten to Grade 5 127
9.5 Mapping the Content Standards with the Practice Standards 127
9.6 Developing a Content Standard Progression Table for the Measurement and Data Domain 128
10. Content-Practice Assessment 129
10.1 General Conceptions Surrounding Assessment 131
10.2 Norm- and Criterion-Referenced Tests 135
10.3 Principles of Effective Classroom Assessments 135
10.4 Formative Assessments 136
10.5 Summative Assessments 136
10.5.1 General Conceptions Surrounding Summative Assessments 136
10.5.2 The Smarter Balanced Assessment (SBA) 137
10.6 Projects and Portfolios as Alternative Summative Assessments 140
10.7 Math Journals and Lesson Investigations as Alternative Formative Assessments 141
10.8 An Assessment Project 142
11. Content-Practice Learning 145
11.1 Defi ning Learning 145
11.2 Changing Views of Learning and Their Effects in the Elementary Mathematics Curriculum 146
11.3 Math Wars: Debating About What and How Students Should Learn Mathematics 147
11.4 Understanding Piagetian and Vygotskian Views of Learning in Mathematics and Finding a Way Out of Extreme Views of Learning 147
11.5 Learning Progressions in School Mathematics 148
11.6 Learning from Neuroscience 149
12. Content-Practice Teaching 151
12.1 Describing (Good) Teaching 151
12.2 Teaching Models in Elementary School Mathematics Settings 154
12.2.1 E-I-S-Driven Teaching 154
12.2.2 C-R-A Sequenced Teaching 154
12.2.3 Van Hiele Sequenced Teaching 155
12.2.3 Culturally-Relevant Teaching 155
12.2.4 SDAIE-Driven Teaching 156
12.2.5 Differentiated Instruction 156
12.2.6 Flip Teaching 157
12.3 Teaching with Concrete and Virtual Manipulatives, Computer-Based Learning Tools, and Video Games and Apps 157
12.4 Teaching Mathematics with Guide Questions 158
12.5 Content-Practice Unit Planning 159
12.6 Content-Practice Lesson Planning 165
12.7 A Planning Project 167
13. Orchestrating a Content-Practice Driven Math Classroom 175
13.1 Persistence and Struggles in Math Classrooms 175
13.2 Fostering Persistent Content-Practice Learners 176
13.3 Developing Effective Collaborative Content-Practice Learning Through Complex Instruction 177
13.4 Other Collaborative Content-Practice Learning Techniques 180
13.5 Developing an Optimal Content-Practice Learning Environment for All Elementary Students 180
13.6 Dealing with Potential Behavior Problems 181
13.7 Assigning Homework, Grading and Testing, and Seating 183
13.8 A Classroom Management Plan Project 185
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