Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary SchoolIn Children's Mathematics: Cognitively Guided Instruction, Thomas Carpenter, Megan Franke, and Linda Levi helped tens of thousands of teachers understand children's intuitive problem-solving and computational processes. More important, the authors helped teachers figure out how to use that knowledge to enhance students' understanding of arithmetic. In this book the same author team takes teaching and learning mathematics to the next level, revealing how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic and provide a solid foundation for learning algebra. This book also shows how teachers can increase their own knowledge of mathematics in the process of interacting with their children and reflecting about their practice. Thinking Mathematically provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what problems and questions help to elicit them. Special features of the book help teachers develop their own understanding of mathematics along with their students':
|
Contents
Equality | 9 |
Developing and Using Relational Thinking | 27 |
Making Conjectures About Mathematics | 48 |
Copyright | |
8 other sections not shown
Common terms and phrases
addition and subtraction algebraic notation algorithms answer arithmetic and algebra associative property basic properties bers big cage big ideas blocks calculations challenge change the order chapter chil Children's Mathematics commutative property conceptions conjec dents different numbers discussion distributive property Emma engage students equal sign represents equation example explicit express mathematical expressions figure fundamental properties grades groups help students important mathematical ideas involving kids larger numbers learning algebra linking cubes list of conjectures math metic mice minus multiplicative inverse notation number facts number operations number sentence true number you started odd numbers Okay open number sentences order of operations procedures proof properties of number property of addition property of multiplication questions real number recognize relational thinking Sarah second-grade solutions solve specific strategy Susie symbols TEACHER COMMENTARY tences THINKING MATHEMATICALLY tion true number sentence true/false and open true/false number sentences tures understanding whole number