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Promoting Algebraic Reasoning Using Students' Thinking.
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Bishop, Joyce W.; Otto, Albert D.; Lubinski, Cheryl A. – Mathematics Teaching in the Middle School, 2001
Describes how student thinking about geometric patterns can be used to develop algebraic reasoning and to make sense of mathematical notation and symbols. (Contains 11 references.) (YDS)
Descriptors: Algebra, Mathematics Instruction, Middle Schools, Patterns in Mathematics
Re-"Conceptualizing" Procedural Knowledge in Mathematics.
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Star, Jon R. – 2002
Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is…
Descriptors: Algebra, Cognitive Style, Concept Formation, Learning
What Is Algebra in Elementary School?
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Bay-Williams, Jennifer M. – Teaching Children Mathematics, 2001
Shares the results of some of the algebraic-thinking pattern problems presented in "Principles and Standards for School Mathematics." (KHR)
Descriptors: Algebra, Educational Principles, Elementary Education, Mathematics Instruction
Developing Algebraic Reasoning through Generalization.
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Lannin, John K. – Mathematics Teaching in the Middle School, 2003
Describes students' generalization strategies and justifications as they engage in patterning activities. (YDS)
Descriptors: Algebra, Concept Formation, Generalization, Mathematics Education
Building Explicit and Recursive Forms of Patterns with the Function Game.
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Rubenstein, Rheta N. – Mathematics Teaching in the Middle School, 2002
Describes how students can be guided to find an explicit rule for a pattern from a recursive rule. (YDS)
Descriptors: Algebra, Educational Strategies, Functions (Mathematics), Mathematics Instruction
New Approaches to Algebra: Have We Missed the Point?
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Thornton, Stephen J. – Mathematics Teaching in the Middle School, 2001
Helps students develop new insights into mathematical relationships through alternative representations. Examines patterns, symbolic, and functions approaches. (Contains 11 references.) (YDS)
Descriptors: Algebra, Graphs, Mathematics Instruction, Middle Schools
Do Numbers Have Shapes? Connecting Number Patterns and Shapes through the Vedic Matrix.
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Stemn, Blidi S.; Collins, Jill E. – Teaching Children Mathematics, 2001
Presents a lesson that teaches number patterns through the Vedic matrix found in Vedic mathematics from India. (KHR)
Descriptors: Algebra, Elementary Education, Foreign Countries, Mathematics Instruction
General Reasoning Processes and Elementary Algebraic Understanding: Implications for Initial Instruction.
English, Lyn D.; Warren, Elizabeth A. – Focus on Learning Problems in Mathematics, 1995
Assessment of general reasoning processes, elementary algebraic understanding, and novel problem solving of (n=147) seventh- and eighth-grade students found that abilities to generalize from patterns and tables of data and understanding variable constructs contributed significantly to application of algebraic concepts and processes. Questions…
Descriptors: Algebra, Foreign Countries, Generalization, Grade 7
Mathematical Investigations--Powerful Learning Situations.
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Chapin, Suzanne H. – Mathematics Teaching in the Middle School, 1998
Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…
Descriptors: Algebra, Area, Functions (Mathematics), Junior High Schools
Games in the Learning of Mathematics.
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Oldfield, Bernarde J. – Mathematics in School, 1991
The use of strategies is an important part of mathematical thinking. Presented are several games that help develop the reasoning strategies of hypothesis making and testing, proving and disproving, looking for patterns, and simplifying a difficult task. (MDH)
Descriptors: Abstract Reasoning, Algebra, Class Activities, Educational Games