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Seeley, Cathy L. – ASCD, 2016
In "Making Sense of Math," Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: (1) Making sense of math by fostering habits of mind that…
Descriptors: Mathematics, Problem Solving, Thinking Skills, Mathematics Instruction
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Holden, Becky – Teaching Children Mathematics, 2007
Seeking more effective mathematics instruction, this author decided to incorporate Cognitively Guided Instruction (CGI) into first-grade classroom lessons. Students in CGI mathematics classrooms are prompted to use their prior knowledge to solve new problems, establish cognitive structures to which new learning can be connected, and be driven by…
Descriptors: Mathematics Instruction, Thinking Skills, Problem Solving, Teaching Methods
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Singer, Florence Mihaela – Mind, Brain, and Education, 2007
Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…
Descriptors: Teacher Effectiveness, Cognitive Structures, Concept Formation, Cognitive Development
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Kamii, Constance; Ewing, Janice K. – Childhood Education, 1996
Argues that teaching should be based on Piaget's constructivism because it explains the nature of human knowledge; explains children's knowledge construction from birth to adolescence; and informs educators how Piaget's distinction among physical, social, and logicomathematical knowledge changes the way many subjects should be taught. Elementary…
Descriptors: Cognitive Structures, Constructivism (Learning), Early Childhood Education, Elementary Secondary Education
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Peterson, Penelope L.; And Others – Educational Leadership, 1989
Recent research suggests that knowledge is stored in the learner's head as a network of concepts or constructs. Children's mathematical problem-solving strategies become increasingly abstract as they are able to engage in more abstract thinking. An experimental study using an alternative Cognitively Guided Instruction approach is described.…
Descriptors: Cognitive Structures, Elementary Education, Learning Processes, Mathematics Instruction
Arcavi, Abraham – 1999
As biological and socio-cultural beings, humans are encouraged and aspire to "see" not only what comes "within sight," but also what is not possible to see. Visualization is described as offering a method of seeing the unseen. These ideas are organized into sections that focus on seeing the unseen in data, seeing the unseen in…
Descriptors: Cognitive Structures, Elementary Secondary Education, Foreign Countries, Higher Education
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Treffers, A. – Educational Studies in Mathematics, 1987
Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)
Descriptors: Arithmetic, Cognitive Development, Cognitive Structures, Division
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Zeman, Marvin – Journal of Mathematical Behavior, 1991
Describes how an eight year old devised a part-whole schema during a school mathematics process involving the development of a geometric model to conceptualize fractions. Provides examples that utilize this schema in dealing with the relative size of fractions, as well as addition and subtraction, multiplication, and division of fractions.…
Descriptors: Cognitive Structures, Concept Formation, Elementary Education, Elementary School Mathematics
Ashlock, Robert B. – Focus on Learning Problems in Mathematics, 1987
Focuses on the language used by elementary mathematics teachers and its relationship to students' understanding of mathematical concepts, as well as their misconceptions. Describes eight situations in which the use of precise, formal mathematical terms could be replaced by informal language, particularly when introducing new concepts. (TW)
Descriptors: Classroom Communication, Cognitive Structures, Discourse Analysis, Elementary Education
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Lee, Lesley; Wheeler, David – Educational Studies in Mathematics, 1989
Used are test and interview data to extract evidence as to what level tenth graders have coordinated the worlds of arithmetic and algebra and can move freely between them. More dissociation is shown than was expected. (Author/MVL)
Descriptors: Algebra, Arithmetic, Cognitive Structures, Concept Formation
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Bouvier, Alain – For the Learning of Mathematics, 1987
Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)
Descriptors: Cognitive Development, Cognitive Structures, Concept Formation, Elementary School Mathematics
Narode, Ronald B. – 1987
Beneath educational pedagogies lie philosophical assumptions about the nature of learning, knowledge, truth and morality. These different philosophies form the foundations of a variety of instructional programs in all academic disciplines. This paper addresses constructivism, a recent attempt to provide a philosophical pedagogy which affects…
Descriptors: Cognitive Development, Cognitive Structures, Concept Formation, Elementary School Mathematics