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Schifter, Deborah; Bastable, Virginia; Russell, Susan Jo – National Council of Teachers of Mathematics, 2018
The "Reasoning Algebraically about Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the…
Descriptors: Mathematics Instruction, Elementary Schools, Middle Schools, Teaching Methods
Schifter, Deborah; Bastable, Virginia; Russell, Susan Jo – National Council of Teachers of Mathematics, 2016
The "Making Meaning for Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The twenty-nine cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific…
Descriptors: Mathematics Instruction, Mathematical Concepts, Classroom Environment, Teaching Methods
Bofferding, Laura, Ed.; Wessman-Enzinger, Nicole, Ed. – Research in Mathematics Education, 2018
Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…
Descriptors: Addition, Subtraction, Numeracy, Thinking Skills
Caldwell, Janet H.; Kobett, Beth; Karp, Karen – National Council of Teachers of Mathematics, 2014
Do your students have the incorrect idea that addition "makes numbers bigger" and subtraction "makes numbers smaller"? Do they believe that subtraction is always "taking away"? What tasks can you offer--what questions can you ask--to determine what your students know or don't know--and move them forward in their…
Descriptors: Arithmetic, Addition, Subtraction, Elementary School Mathematics
Karp, Karen; Caldwell, Janet; Zbiek, Rose Mary; Bay-Williams, Jennifer – National Council of Teachers of Mathematics, 2011
What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…
Descriptors: Subtraction, Mathematics Instruction, Addition, Mathematical Concepts
Harel, Guershon, Ed.; Confrey, Jere, Ed. – 1994
This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…
Descriptors: Addition, Arithmetic, Cognitive Development, Division