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Mathematics Teacher, 2019
Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…
Descriptors: Algebra, Error Patterns, Misconceptions, Mathematics Skills
Roscoe, Matt B. – Mathematics Teacher, 2012
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Descriptors: Teaching Methods, Mathematical Logic, Mathematics Instruction, Learning Processes
Quinn, Anne Larson – Mathematics Teacher, 2009
Many students find proofs frustrating, and teachers struggle with how to help students write proofs. In fact, it is well documented that most students who have studied proofs in high school geometry courses do not master them and do not understand their function. And yet, according to NCTM's "Principles and Standards for School Mathematics"…
Descriptors: Mathematical Logic, Validity, Number Concepts, Teaching Methods

Gadanidis, George – Mathematics Teacher, 1994
Presents a historical overview of learning theories in mathematics education applied to the teaching of integers. Theories discussed are meaning vs. rote learning; direct vs. incidental; discovery vs. exposition; concrete vs. abstract; and construction vs. transmission. Includes a reproducible activity sheet and 19 references. (MKR)
Descriptors: Cognitive Processes, Constructivism (Learning), Elementary Secondary Education, Higher Education

O'Shea, Thomas – Mathematics Teacher, 1991
During a six-week methods course for preservice elementary school teachers, student pairs were asked to solve a problem and record their experiences in a dairy. Presented are the dairy entries of two students as they worked on determining the number of squares that can be formed on a five-peg geoboard. (MDH)
Descriptors: Cooperative Learning, Diaries, Experiential Learning, Geometry

Ward, Cherry D. – Mathematics Teacher, 2001
Describes constructivism as an educational theory promoted by the National Council of Teachers of Education (NCTM), the ideals of NCTM's standards, the validity of NCTM's approach, and the research behind NCTM's recommendations. Includes examples of what teachers can do to promote student construction of knowledge in the classroom and resources…
Descriptors: Constructivism (Learning), Curriculum Development, Elementary Secondary Education, Learning Processes

Glidden, Peter L. – Mathematics Teacher, 2001
Describes computation of a continued radical to approximate the golden ratio and presents two well-known geometric interpretations of it. Uses guided-discovery to investigate different repeated radicals to see what values they approximate, the golden-rectangle interpretation of these continued radicals, and the golden-section interpretation. (KHR)
Descriptors: Computation, Discovery Learning, Geometric Concepts, Learning Processes
Clausen, Mary C. – Mathematics Teacher, 2005
The problem of solving mathematical equations can be quite tough for some students hence they face a great difficulty when applying ideas to the actual process. Students in algebra classes are taught coding in which they write down what they will need to do to solve the equation and this coding makes the students more adept at solving equations…
Descriptors: Children, Cognitive Development, Equations (Mathematics), Algebra

Bonsangue, Martin V.; Gannon, Gerald E,; Pheifer, Laura J. – Mathematics Teacher, 2002
Reports findings from the team teaching of a course in mathematical problem solving designed for secondary and community college teachers to clarify the concept of ."ecessary and sufficient" conditions. Discusses assigned problems and students' incorrect interpretations. Student interpretations showed how simple mistakes can often lead to rich…
Descriptors: Algebra, Elementary Secondary Education, Learning Problems, Learning Processes

Blais, Donald M. – Mathematics Teacher, 1988
The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…
Descriptors: Algebra, Cognitive Development, Cognitive Processes, Cognitive Structures

Kysh, Judith – Mathematics Teacher, 1991
Described is an alternative first year algebra program developed to bridge the gap between the NCTM's Curriculum and Evaluation Standards and institutional demands of schools. Increased attention is given to graphing as a context for algebra, calculator use, solving "memorable problems," and incorporating geometry concepts, while…
Descriptors: Algebra, Area, Calculators, Course Content

Hutcheson, James W. – Mathematics Teacher, 1975
Techniques are suggested for preparing practice exercises in algebra and trigonometry. (JP)
Descriptors: Algebra, Games, Instructional Materials, Learning Processes

Winter, Mary Jean; Carlson, Ronald J. – Mathematics Teacher, 2000
Describes a laboratory-type activity, liquid assets, used to illustrate, develop, or reinforce central concepts in first-year algebra. These include linear function, slope, intercept, and dependent and independent variables. Presents a group activity for collecting data, transition from group to individual activity in plotting data points, and…
Descriptors: Algebra, Concept Formation, Group Activities, Learning Processes

Hope, Jack A.; Kelly, Ivan W. – Mathematics Teacher, 1983
Several common errors reflecting difficulties in probabilistic reasoning are identified, relating to ambiguity, previous outcomes, sampling, unusual events, and estimating. Knowledge of these mistakes and interpretations may help mathematics teachers understand the thought processes of their students. (MNS)
Descriptors: Cognitive Processes, Error Patterns, Learning Processes, Logical Thinking

Moyer, Patricia S.; Hsia, Wei Shen – Mathematics Teacher, 2001
Describes an investigation of polygons and their properties in which students apply very basic understandings of geometric properties. (KHR)
Descriptors: Concept Formation, Geometry, Interdisciplinary Approach, Learning Processes
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