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Ulrich, Catherine; Norton, Anderson – Research in Mathematics Education, 2019
Psychological studies of early numerical development fill a void in mathematics education research. However, conflations between magnitude awareness and number, and over-attributions of researcher conceptions to children, have led to psychological models that are at odds with findings from mathematics educators on later numerical development. In…
Descriptors: Mathematics Education, Number Systems, Mathematical Concepts, Perceptual Motor Learning
Kurz, Terri L.; Yanik, H. Bahadir; Lee, Mi Yeon – Clearing House: A Journal of Educational Strategies, Issues and Ideas, 2016
Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.
Descriptors: Animals, Number Concepts, Mathematics, Mathematics Education
Fazio, Lisa K.; Bailey, Drew H.; Thompson, Clarissa A.; Siegler, Robert S. – Grantee Submission, 2014
We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both…
Descriptors: Mathematics Instruction, Mathematical Concepts, Numbers, Mathematics Achievement
Fazio, Lisa; Siegler, Robert – UNESCO International Bureau of Education, 2011
Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…
Descriptors: Class Activities, Learning Activities, Teaching Methods, Numbers
Latham, Dorothy – Mathematics Teaching Incorporating Micromath, 2007
In the renewed "Primary Framework for Mathematics" for England, great emphasis is given to calculation and its prerequisites (DfES, 2006). Expectations are increased for calculations and the recall of number facts, with mental calculation owning a higher profile, while progression in written calculation is clarified. The greater focus on…
Descriptors: Foreign Countries, Computation, Number Systems, Manipulative Materials

Thwaites, G. N. – Mathematics in School, 1989
Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)
Descriptors: Arithmetic, Computation, Elementary School Mathematics, Mathematical Concepts

Trafton, Paul R.; Zawojewski, Judith S. – Arithmetic Teacher, 1990
The concepts of number sense and numeration, operations, and whole-number computations and their importance are discussed. Activities cover developing concepts of operations, exploring patterns and relationships, and building an understanding of mathematical structure. (KR)
Descriptors: Computation, Elementary Education, Elementary School Mathematics, Learning Activities

Thompson, Charles S. – Arithmetic Teacher, 1989
The content of the standards focusing on numbers and numeration for grades K-8 are discussed. Several activities for developing number concepts and skills are described. (YP)
Descriptors: Computation, Elementary Education, Elementary School Mathematics, Mathematical Concepts
Sowder, Judith T., Ed.; Schappelle, Bonnie P., Ed. – 1989
Research on computational estimation and mental computation has received a considerable amount of attention from mathematics educators during the past decade. These proceedings resulted from a meeting to explore dimensions of number sense and its related fields. The participants came from three groups: mathematics educators actively pursuing…
Descriptors: Cognitive Processes, Cognitive Psychology, Computation, Estimation (Mathematics)

Strand, Susan – Arithmetic Teacher, 1990
Discusses activities using base-10-block skits to teach number system concepts in first grade classrooms. Describes the students' responses to the activities. (YP)
Descriptors: Arithmetic, Computation, Elementary Education, Elementary School Mathematics

Stanford Univ., CA. School Mathematics Study Group. – 1968
This is unit three of a fifteen-unit secondary mathematics textbook. This unit contains two chapters. The first chapter discusses integers and the second chapter discusses rational numbers. Operations with both types of numbers as well as the structure of the systems are discussed. (MK)
Descriptors: Computation, Integers, Mathematical Concepts, Mathematics Curriculum

McAuley, Joe – Mathematics in School, 1990
Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)
Descriptors: Addition, Arithmetic, Computation, Integers
Ebby, Caroline Brayer – Journal of Mathematical Behavior, 2005
This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular…
Descriptors: Sociocultural Patterns, Number Systems, Problem Solving, Mathematical Concepts

Lappan, Glenda, Ed. – Arithmetic Teacher, 1988
Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)
Descriptors: Computation, Concept Formation, Early Childhood Education, Elementary Education

Hennemann, A. Louise; Hennemann, Willard – School Science and Mathematics, 1983
Use of the hand-dialed, transparent, nonelectronic SEE-Calculator is proposed. Pupils can dial numbers into appropriate columns, watching the gears work; place-value concepts are enhanced. Both activities and flowcharting are suggested. (MNS)
Descriptors: Algorithms, Audiovisual Aids, Calculators, Computation
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