F. D. Rivera

Teaching to the Math Common Core State Standards (eBook, PDF)

Focus on Grade 5 to Grade 8 and Algebra 1

• Format: PDF

Produktbeschreibung

This is a methods book for preservice middle level majors and beginning middle school teachers. It takes a very practical approach to learning to teach middle 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 Grade 5 through Grade 8 and (traditional pathway) Algebra I 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 Common Core state 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 middle school 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 prepares preservice middle level majorsand beginning middle school teachers to work within the realities of accountable pedagogy and to develop a proactive disposition that is capable of supporting all middle school students in order for them to experience growth in mathematical understanding that is necessary for high school and beyond, including future careers.

Produktdetails

• Verlag: Sense Publishers
• Erscheinungstermin: 17. Juni 2015
• Englisch
• ISBN-13: 9789462099623
• Artikelnr.: 44610415

Inhaltsangabe

Dear Preservice Middle Level Majors and Beginning Middle School Teachers: An Introduction; A Blended Multisourced Approach to Learning to Teach Middle School Mathematics; Overview of the Remaining Chapters; Getting to Know the Common Core State Standards for Mathematical Practice; Content Activity 1: Exploring and Proving Parity; The Eight Common Core State Standards for Mathematical Practice; Content Activity 2: Building a Hexagon Flower Garden Design; Problem Solving Contexts in Middle School Mathematics; Content Activity 3: Different Types of Problems in Middle School Mathematics; Representations in Middle School Mathematics; Content Activity 4: From Multiplication of Whole Numbers to Direct Proportions to Simple Linear Relationships; Connections in Middle School Mathematics; Content Activity 5: The Pythagorean Theorem and Irrational Numbers; Reasoning and Proof in Middle School Mathematics; Communication in Middle School Mathematics; Content Activity 6: Solving Multiplication Problems with Tape Diagrams; Doing Mathematics with an Eye on the Content-Practice Standards of the CCSSM; The Real Number System (Part I) from Grade 5 to Grade 6: Whole Numbers, Decimal Numbers, and Fractions; Place Value Structure of Whole Numbers and Decimal Numbers in Grade 5; Standard Algorithms for Whole Number Operations in Grades 5 and 6; A Brief Overview of the Addition and Subtraction Standard Algorithms in the Elementary Grades up to Grade 4; Multiplication Standard Algorithm in Grade 5; Division Standard Algorithm in Grade 6; Operations with Fractions; Fractions in the Elementary Grades up to Grade 4; All Cases of Adding and Subtracting Fractions in Grade 5; Multiplying Fractions in Grade 5; Dividing Fractions in Grades 5 and 6; Operations with Decimal Numbers in Grades 5 and 6; Multiplying with Decimal Numbers in Grades 5 and 6; Dividing Decimal Numbers in Grades 5 and 6; Adding and Subtracting Decimal Numbers in Grades 5 and 6; Mapping the Content Standards with thePractice Standards; Developing a Content Standard Progression Table for the Real Number System Part I Domain; The Real Number System (Part II) from Grade 6 to Grade 8 and Algebra 1: Integers, Rational Numbers, and Irrational Numbers; Integers and Integer Operations in Grades 6 and 7; Concepts of Positive and Negative Integers in Grade 6; Addition of Integers in Grade 7; Subtraction of Integers in Grade 7; Multiplication of Integers in Grade 7; Divisions of Integers in Grade 7; Absolute Value in Grades 6 and 7; Concept of Absolute Value in Grade 6; Absolute Value and Distance in Grade 7; Rational Numbers and Operations in Grade 6 and 7; Rational Numbers in Grade 6; Rational Number Operations in Grade 7; Decimals that Transform into Rational Numbers in Grade 7; Irrational Numbers and Operations in Grade 8 and Algebra 1; Mapping the Content Standards with the Practice Standards; Developing a Content Standard Progression Table for the Real Number System Part II Domain; Ratio and Proportional Relationships and Quantities; Ratio and Rate Relationships in Grade 6; Proportional Relationships in Grade 7; Graphs of Proportional Relationships from Grades 6 through 8; Quantitative Relationships in Algebra 1; Mapping the Content Standards with the Practice Standards; Developing a Content Standard Progression Table for the Quantities and Ratio and Proportion Domains; Technology-Mediated Tools for Teaching and Learning Middle School Mathematics; Getting to Know the TI-84+ Graphing Calculator; Getting to Know the GeoGebra Dynamic Software Tool; Getting to Know a Calculator-Based Ranger; Getting to Know Apps and Other Virtual-Based Manipulatives for Classroom Use; Understanding Technology Use in the Mathematics Classroom; Expressions and Operations; Numerical and Algebraic Expressions in School Mathematics; Writing and Simplifying Numerical Expressions in Grade 5; Greatest Common Factors, Least Common Multiples, and Simple Factoring Involving Numerical Expressions in Grade 6; Simplifying and Operating with Numerical Expressions that Involve Integer and Fractional Exponents and Numbers in Scientific Notation in Grades 6 and 8; Algebraic Expressions in Grades 6 and 7 and Algebra 1; Constructing, Simplifying, and Factoring Algebraic Expressions in Grades 6 and 7 and Algebra 1; Adding, Subtracting, Multiplying, and Factoring Polynomials in Algebra 1; Understanding Simple Nonalgebraic (Transcendental) Exponential Expressions in Algebra 1; Deepening Variable Understanding in Algebra 1; Mapping the Content Standards with the Practice Standards; Developing a Content Standard Progression Table for the Expressions Domain; Equations and Inequalities; Algebraic Thinking from Grades 6 to 8 and Algebra 1; Different Contexts for Using Variables from Grades 6 to 8 and Algebra 1; Solving Equations from Grades 6 to 8 and Algebra 1; Solving Inequalities from Grades 6 to 8 and Algebra 1; Word Problem Solving Applications Involving Equations and Inequalities from Grades 6 to 8 and Algebra 1; Mapping the Content Standards with the Practice Standards; Developing a Content Standard Progression Table for the Equations and Inequalities Domain; Functions and Models; Rules, Patterns, and Relationships in Grade 5; Dependent Variables, Independent Variables, and Quantitative Relationships in Grade 6; Unit Rates and Proportional Relationships in Grade 7; Nonsymbolic Algebra and Functions in Grade 8; Symbolic Algebra and Functions in Algebra 1; Mapping the Content Standards with the Practice Standards; Developing a Content Standard Progression Table for the Domains of Functions and Models; Measurement and Geometry; Quadrilaterals, Volumes of Right Rectangular Prisms with Whole-Number Edge Lengths, and the First Quadrant Coordinate Plane in Grade 5; The Four-Quadrant Coordinate Plane, Areas of Polygons, Nets and Surface Areas, and Volumes of Right Rectangular Prisms with Fractional Edge Lengths in Grade 6; Scale Drawings, Slicing, Drawing Shapes with Given Conditions, Circumference and Area of a Circle, Finding Unknown Angles in a Figure, and More Problems Involving Area, Surface Area, and Volume of 2D and 3D Objects in Grade 7; Volumes of Cylinders, Cones, and Spheres and Transformation Geometry, Congruence, Similarity, Informal Proofs, and the Pythagorean Theorem in Grade 8; Mapping the Content Standards with the Practice Standards; Developing a Content Standard Progression Table for the Measurement and Geometry Domains; Data, Statistics, Probability, and Models; Representing Data in Grades 5, 6, and 8; Analyzing Data in Grades 5, 6, 7, and 8; Statistical Modeling in Algebra 1; Probability Models and Probabilities of Simple and Compound Events in Grade 7; Mapping the Content Standards with the Practice Standard; Developing a Content Standard Progression Table for the Data, Statistics, and Probability Domains; Content-Practice Assessment; General Conceptions on Assessment; Norm- and Criterion-Referenced Tests; Principles of Effective Classroom Assessments; Formative Assessments; Summative Assessments; What are Summative Assessments?; Smarter Balanced Assessment (SBA); Projects and Portfolios as Alternative Summative Assessments; Math Journals and Lesson Investigations as Alternative Formative Assessments; Exploring Assessment Systems; An Assessment Project; Content-Practice Learning; Defining Learning; Changing Views of Learning and Their Effects in the Middle School Mathematics Curriculum; Math Wars: Debating About What and How Middle School Students Should Learn Mathematics; Understanding Piagetian and Vygotskian Views of Learning in Mathematics and Finding a Way Out of Extreme Views of Learning; Learning Progressions in School Mathematics; Learning from Neuroscience; Content-Practice Teaching; Describing (Good) Teaching; Teaching Models in Middle School Mathematical Settings; E-I-S-Driven Teaching; C-R-A Sequenced Teaching; Van Hiele Sequenced Teaching; Culturally-Relevant Teaching; SDAIE-Driven Teaching; Differentiated Instruction; Flip Teaching; Teaching with Manipulatives and Computer and Video Games and Apps; Teaching Mathematics with Guide Questions; Content-Practice Unit Planning; Content-Practice Lesson Planning; A Planning Project; Orchestrating a Content-Practice Driven Math Class; Persistence and Struggle in Math Classrooms; Fostering Persistent Content-Practice Learners; Developing Effective Collaborative Content-Practice Learning Through Complex Instruction; Other Collaborative Content-Practice Learning Techniques; Developing an Optimal Content-Practice Learning Environment for all Middle School Students; Dealing with Potential Behavior Problems; Assigning Homework, Grading and Testing, and seating Arrangement Issues; A Classroom Management Plan Project.