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Timothy H. Lehmann – Educational Studies in Mathematics, 2024
Developing students' competence in algorithmic thinking is emerging as an objective of mathematics education, but despite its inclusion in mathematics curricula around the world, research into students' algorithmic thinking seems to be falling behind in this curriculum reform. The aim of this study was to investigate how the mathematical modelling…
Descriptors: Mathematical Models, Algorithms, Thinking Skills, Mathematics Instruction

Anghileri, Julia; Beishuizen, Meindert; Van Putten, Kees – Educational Studies in Mathematics, 2002
Explores written calculation methods for division used by pupils in England (n=276) and the Netherlands (n=259). Analyses informal strategies and identifies progression towards more structured procedures that result from different teaching approaches. Comparison of methods used shows greater success in the Dutch approach which is based on…
Descriptors: Algorithms, Arithmetic, Cognitive Processes, Division

Russell, Susan Jo – Teaching Children Mathematics, 2000
Examines the philosophy behind the issue of computational fluency in "Principles and Standards." (Author)
Descriptors: Algorithms, Arithmetic, Computation, Early Childhood Education

Schwank, Inge – Journal of Mathematical Behavior, 1993
Differences in students' (aged 12-14) construction and analysis of mathematical algorithms may be explained by the differences between predicative and functional cognitive structures. Analyzes the central role of internal and external representations and the characteristics of each. Discusses prototypical research design and development of a…
Descriptors: Algorithms, Cognitive Psychology, Cognitive Structures, Elementary Education

Kamii, Constance; And Others – Educational Horizons, 1991
Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)
Descriptors: Algorithms, Computation, Educational Change, Educational Strategies

Aspinwall, Leslie; Aspinwall, Julie S. – Mathematics Teaching in the Middle School, 2003
Describes how open-ended writing prompts provide a window into student understanding and mathematical thinking. (YDS)
Descriptors: Algorithms, Computation, Evaluation Methods, Mathematical Concepts

Mercer, Joseph – Mathematics Teacher, 1992
Raises and responds to questions about what and how to teach mathematics with the availability of calculators to all students. Discusses whether students need basic facts, mechanical skills, and knowledge of computational algorithms. Argues that students need to develop number sense and analytical skills using simple, symbolic, and graphing…
Descriptors: Algorithms, Basic Skills, Calculators, Elementary Secondary Education

Relf, Simon – Mathematics in School, 1990
Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)
Descriptors: Algorithms, Computation, Elementary School Mathematics, Elementary Secondary Education
Hennessy, Sara; And Others – 1988
This paper describes an educational program developed on the basis that the use of blocks and other manipulatives can be useful both for initial teaching of exchange operations in arithmetic and for remediation of the faulty strategies which very commonly arise during acquisition of written calculation algorithms. This computer program is a…
Descriptors: Algorithms, Arithmetic, Cognitive Development, Computer Assisted Instruction

Carroll, William M.; Porter, Denise – Teaching Children Mathematics, 1997
Describes teaching strategies in which children are encouraged to develop computational procedures that are meaningful to them. Authors state that classroom observation reveals most primary students to be capable of developing their own accurate solution procedures for multi-digit addition and subtraction as well as for simple multiplication and…
Descriptors: Algorithms, Associative Learning, Computation, Cooperative Learning

Otte, Michael – For the Learning of Mathematics, 1990
Compared and contrasted are the concepts intuition and logic. The ideas of conceptual thought and algorithmic thought are discussed in terms of the world as a labyrinth, intuition and time, and the structure of knowledge. (KR)
Descriptors: Abstract Reasoning, Algorithms, Cognitive Ability, Cognitive Processes

Olson, Alton T. – Journal of Computers in Mathematics and Science Teaching, 1993
Presents a series of solution methods to the Eight Queens Problem of placing eight queens on a chess board so that no one queen can capture another. Solution methods progress from empirical approaches to the use of computer algorithms. Geometric transformations are used to find other solutions. (MDH)
Descriptors: Algorithms, Computer Assisted Instruction, Enrichment Activities, Learning Activities

Guckin, Alice Mae; Morrison, Dwight – School Science and Mathematics, 1991
Described is a study that used LOGO to improve the proportional reasoning ability of students enrolled in mathematics classes for students poorly prepared for college-level mathematics. Included are the methodology, procedures for using logo, and a discussion of the results. (KR)
Descriptors: Algebra, Algorithms, Arithmetic, College Mathematics

Gardiner, Tony – Mathematics in School, 1990
Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)
Descriptors: Abstract Reasoning, Algorithms, Computation, Elementary School Mathematics

Mathematics in School, 1990
Described are four classroom activities that may be interspersed into a curriculum or offered as homework. Systematic procedures, alternative strategies, and trial and error are emphasized in these counting exercises. (KR)
Descriptors: Algorithms, Computation, Elementary School Mathematics, Elementary Secondary Education
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