Rivera Teaching to the Math Common Core State Standards

Focus on Kindergarten to Grade 5
2014
ISBN: 978-94-6209-503-8
Verlag: Sense Publishers
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 186 Seiten, eBook

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.

Zielgruppe

Research

Autoren/Hrsg.

Rivera, F. D.

Inhaltsverzeichnis

1. Dear Elementary Majors and Practicing and Beginning Elementary Teachers: An Introductio; 1.1 A Blended Multisourced Approach to Learning to Teach Mathematics; 1.2 Overview of the Remaining Chapters; 2. Getting to Know the Common Core State Standards for Mathematical Practice; 2.1 Content Activity 1: Generating Addition Facts; 2.2 The Eight Common Core State Standards for Mathematical Practice; 2.3 Content Activity 2: Building a Hexagon Flower Garden Design; 2.4 Problem Solving Contexts in Elementary School Mathematics; 2.4.1 Content Activity 3: Different Types of Problems in Elementary School Mathematics; 2.5 Representations in Elementary School Mathematics; 2.5.1 Content Activity 4: A Kindergarten Subtraction Task; 2.5.2 Content Activity 5: Representing Whole Numbers in Second Grade; 2.6 Connections in Elementary School Mathematics; 2.6.1 Content Activity 6: Repeating Patterns; 2.7 Reasoning and Proof in Elementary School Mathematics; 2.7.1 Content Activity 7: Division Problems in Third Grade; 2.7.2 Activity 8: Even and Odd Numbers in Second Grade; 2.8 Communication in Elementary School Mathematics; 2.8.1 Content Activity 9: Addition and Subtraction Strategies from First to Second Grade; 2.8.2 Content Activity 10: Generating Addition and Subtraction Facts in First Grade; 2.9 Doing Mathematics with an Eye on theContent-Practice Standards of the CCSSM; 3. Counting and Cardinality in Kindergarten; 3.1 Subitizing: Laying the Foundation for Early Multiplicative Thinking; 3.2 Counting and Writing Numbers and Number Words: Building on Rhythmic Structures; 3.3 Comparing Quantities; 3.4 Mapping the Content Standards with the Practice Standards; 3.5 Developing a Content Standard Progression Table for the Counting and Cardinality Domain; 4. Numbers and Operations (Part I); 4.1 Place Value in Base Ten: The Basic Mathematical Structure of Whole Numbers and Decimal Numbers in the CCSSM; 4.2 Representing Whole Numbers in Base Ten from K to Grade 4; 4.3 Representing Decimal Numbers in Grade 5; 4.4 Comparing and Ordering Whole Numbers and Decimal Numbers from Grades 1 to 5; 4.5 Rounding Whole Numbers from Grades 3 to 5; 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; 5. Operations and Algebraic Thinking; 5.1 Algebraic Thinking from Kindergarten to Grade 5; 5.2 The Four Fundamental Operations as General Methods for Combining and Generating More Numbers; 5.2.1 Addition; 5.2.2 Subtraction; 5.2.3 Multiplication; 5.2.4 Division; 5.3 Forming Equivalent Expressions and Understanding the General Meaning of the Equal Sign; 5.4 Instantiating Nonsymbolic Algebra Through Problem Solving in Arithmetical Activity; 5.5 Pattern Generalization as Instantiations of Nonsymbolic and Symbolic Algebra; 5.6 Mapping the Content Standards with the Practice Standards; 5.7 Developing a Content Standard Progression Table for the Operations and Algebraic Thinking Domai; 6. Numbers and Operations in Base Ten (Part II); 6.1 Analytical Subitizing in Kindergarten and Sticks and Circles or Labeled Circles in Grade 1; 6.2 Adding Whole Numbers in Base Ten from Grades 1 to 4; 6.3 Subtracting Whole Numbers in Base Ten from Grades 1 to 4; 6.4 Multiplying Whole Numbers in Base Ten from Grades 3 to 5; 6.5 Dividing Whole Numbers in Base Ten from Grades 3 to 4; 6.6 Adding, Subtracting, Multiplying, and Dividing Decimal Numbers in Grade 5; 6.7 Mapping the Content Standards with the Practice Standards; 6.8 Developing a Content Standard Progression Table for the Operations and Number Thinking Part II Domain; 7. Numbers and Operations – Fractions; 7.1 Equal Partitioning of Whole Shapes in Halves and Fourths in Grade 1; 7.2 Equal Partitioning of Whole Shapes in Thirds and Constructing Equivalent Shares in Grade 2; 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; 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; 7.5 Fraction Addition, Subtraction, Multiplication, and Simple Division in Grade 5; 7.6 Mapping the Content Standards with the Practice Standards; 7.7 Developing a Content Standard Progression Table for the Number and Operations – Fractions Domain; 8. Geometry; 8.1 Recognizing and Composing Shapes in Kindergarten and Grade 1; 8.2 Defi ning and Reasoning about Shapes in Grades 2, 3, and 5; 8.3 Lines and Angles in 2D Shapes in Grade 4; 8.4 The Coordinate Plane in Grade 5; 8.5 Mapping the Content Standards with the Practice Standards; 8.6 Developing a Content Standard Progression Table for Geometry Domain; 9. Measurement and Data; 9.1 Measuring from Kindergarten to Grade 5; 9.1.1 Qualitative Measurements in Kindergarten; 9.1.2 Measuring Lengths in Grades 1 and 2; 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; 9.1.4 Measuring Angles in Grade 4; 9.1.5 Measuring Volumes of Cubes and Other Right Rectangular Prisms in Grade 5; 9.1.6 Conversion Problems in Grades 4 and 5; 9.2 Telling and Writing Time in Grades 2 and 3; 9.3 Money in Grades 2 and 4; 9.4 Classifying, Representing, and Interpreting Data from Kindergarten to Grade 5; 9.4.1 Forming Categories Involving Discrete Objects in Kindergarten; 9.4.2 Structuring Data from Kindergarten to Grade 5; 9.5 Mapping the Content Standards with the Practice Standards; 9.6 Developing a Content Standard Progression Table for the Measurement and Data Domain; 10. Content-Practice Assessment; 10.1 General Conceptions Surrounding Assessment; 10.2 Norm- and Criterion-Referenced Tests; 10.3 Principles of Effective Classroom Assessments 135; 10.4 Formative Assessments; 10.5 Summative Assessments; 10.5.1 General Conceptions Surrounding Summative Assessments; 10.5.2 The Smarter Balanced Assessment (SBA); 10.6 Projects and Portfolios as Alternative Summative Assessments; 10.7 Math Journals and Lesson Investigations as Alternative Formative Assessments; 10.8 An Assessment Project; 11. Content-Practice Learning; 11.1 Defi ning Learning; 11.2 Changing Views of Learning and Their Effects in the Elementary Mathematics Curriculum; 11.3 Math Wars: Debating About What and How Students Should Learn Mathematics; 11.4 Understanding Piagetian and Vygotskian Views of Learning in Mathematics and Finding a Way Out of Extreme Views of Learning; 11.5 Learning Progressions in School Mathematics; 11.6 Learning from Neuroscience; 12. Content-Practice Teaching; 12.1 Describing (Good) Teaching; 12.2 Teaching Models in Elementary School Mathematics Settings; 12.2.1 E-I-S-Driven Teaching; 12.2.2 C-R-A Sequenced Teaching; 12.2.3 Van Hiele Sequenced Teaching; 12.2.3 Culturally-Relevant Teaching 155; 12.2.4 SDAIE-Driven Teaching; 12.2.5 Differentiated Instruction; 12.2.6 Flip Teaching; 12.3 Teaching with Concrete and Virtual Manipulatives, Computer-Based Learning Tools, and Video Games and Apps; 12.4 Teaching Mathematics with Guide Questions; 12.5 Content-Practice Unit Planning; 12.6 Content-Practice Lesson Planning; 12.7 A Planning Project; 13. Orchestrating a Content-Practice Driven Math Classroom; 13.1 Persistence and Struggles in Math Classrooms; 13.2 Fostering Persistent Content-Practice Learners; 13.3 Developing Effective Collaborative Content-Practice Learning Through Complex Instruction; 13.4 Other Collaborative Content-Practice Learning Techniques; 13.5 Developing an Optimal Content-Practice Learning Environment for All Elementary Students; 13.6 Dealing with Potential Behavior Problems; 13.7 Assigning Homework, Grading and Testing, and Seating; 13.8 A Classroom Management Plan Project.