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Greeno, James G. – Journal for Research in Mathematics Education, 1991
This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…
Descriptors: Cognitive Development, Cognitive Structures, Concept Formation, Elementary Secondary Education
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Fischbein, Efraim; Schnarch, Ditza – Journal for Research in Mathematics Education, 1997
Describes a study that investigated probabilistic intuitions held by students (N=98) from grade 7 through college through the use of a questionnaire. Of the misconceptions that were investigated, availability was the only one that was stable across age groups. Contains 20 references. (DDR)
Descriptors: Age Differences, Cognitive Structures, Concept Formation, Elementary Secondary Education
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Gutierrez, Angel; And Others – Journal for Research in Mathematics Education, 1991
Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)
Descriptors: Cognitive Development, Cognitive Structures, Concept Formation, Developmental Stages
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McDonald, Janet L. – Journal for Research in Mathematics Education, 1989
Students at concrete or formal operational reasoning levels made similarity judgments on geometric concepts and mathematical expressions on ratio, proportion, and similarity. Clear prototypical maps could be derived for both groups. Formal operational students structured subject matter content significantly more like subject matter experts than…
Descriptors: Cognitive Structures, Concept Formation, Educational Research, Geometric Concepts
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Graeber, Anna O.; And Others – Journal for Research in Mathematics Education, 1989
Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)
Descriptors: Cognitive Structures, College Students, Computation, Concept Formation
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Williams, Steven R. – Journal for Research in Mathematics Education, 1991
A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)
Descriptors: Calculus, Cognitive Development, Cognitive Structures, College Mathematics
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Resnick, Lauren B.; And Others – Journal for Research in Mathematics Education, 1989
Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…
Descriptors: Cognitive Structures, Concept Formation, Decimal Fractions, Diagnostic Teaching
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Cramer, Kathleen A.; And Others – Journal for Research in Mathematics Education, 1989
This aptitude-treatment interaction study explored the relationship between cognitive restructuring ability and treatments varying in the amounts of teacher guidance on tasks with fractions. An interaction was found between cognitive restructuring ability and levels of teacher guidance for items having continuous perceptual distracters. (MNS)
Descriptors: Aptitude Treatment Interaction, Cognitive Structures, Concept Formation, Elementary Education