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Exploring the Origins, Uses, and Interactions of Student Intuitions: Comparing the Lengths of Paths.
Peer reviewed Peer reviewed
Chiu, Ming Ming – Journal for Research in Mathematics Education, 1996
Sixteen middle school students ranked the lengths of various paths in problem-solving interviews. Every student invoked at least one of four intuitions that originated from their everyday experiences: compression, detour, complexity, and straightness. Students continued to use their inadequate intuitions in the posttest before applying learned…
Descriptors: Algorithms, Interviews, Intuition, Junior High Schools
Effect of Different Instructional Methods on Error Types and the Underlying Dimensionality of the Test, Part I.
Birenbaum, Menucha; Tatsuoka, Kikumi K. – 1981
Error analysis performed on data sets revealed that seventh grade students used a variety of rules of operation for solving the signed-number arithmetic problems. The data sets were obtained from an experimental study in which students were randomly assigned to study either of two lessons written on a computer based education system. The two…
Descriptors: Algorithms, Arithmetic, Cognitive Processes, Computer Assisted Instruction
The Effect of a Scoring System Based on the Algorithm Underlying the Students' Response Patterns on the Dimensionality of Achievement Test Data of the Problem Solving Type.
Peer reviewed Peer reviewed
Birenbaum, Menucha; Fatsuoka, Kikumi K. – Journal of Educational Measurement, 1983
The outcomes of two scoring methods (one based on an error analysis and the second on a conventional method) on free-response tests, compared in terms of reliability and dimensionality, indicates the conventional method is inferior in both aspects. (Author/PN)
Descriptors: Achievement Tests, Algorithms, Data, Junior High Schools
Card Logic.
Peer reviewed Peer reviewed
Pagni, David L.; Shultz, Harris S. – Mathematics Teaching in the Middle School, 1999
Presents a problem that requires solving a card problem by exploring patterns that will lead to a logical solution. Involves students in developing and analyzing their own algorithms as well as discussing their reasoning with peers. (ASK)
Descriptors: Algorithms, Elementary Education, Junior High Schools, Mathematics Activities
On the Dimensionality of Achievement Test Data.
Peer reviewed Peer reviewed
Birenbaum, Menucha; Tatsuoka, Kikumi – Journal of Educational Measurement, 1982
Empirical results from two studies--a simulation study and an experimental one--indicated that, in achievement data of the problem-solving type where a specific subject matter area is being tested, the greater the variety of the algorithms used, the higher the dimensionality of the test data. (Author/PN)
Descriptors: Achievement Tests, Algorithms, Data Analysis, Factor Structure
The Use of Information from Wrong Responses in Measuring Students' Achievement.
Birenbaum, Menucha; Tatsuoka, Kikumi K. – 1980
Much valuable information can be gained by analyzing the students' wrong responses. When a student answers a free response item she/he gives the response which she/he considers to be the correct one. Therefore, diagnosing the algorithm that led the student to his/her answer provides an important source of information for assessing his/her…
Descriptors: Academic Achievement, Achievement Tests, Adaptive Testing, Algorithms
Discrete Mathematics and the Secondary Mathematics Curriculum.
Dossey, John – 1990
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Descriptors: Algebra, Algorithms, Computer Software, Curriculum Guides