Inhelder and Piaget found that somewhere between 12 and 15 years of age, children's thinking shifted from concrete to formal operations. To determine if this shift occurs at approximately the same age for learning disabled children (N=27) compared to normal learning children (N=27) was the task of the study reported. (JN)

Assessed was the level of thinking of 140 students who had been placed in developmental algebra as entering college freshmen. Scores on the Group Assessment of Logical Thinking, Scholastic Aptitude Tests, college placement tests; high school grade point average, and developmental algebra final grade were analyzed. Group characteristics are…

How computers have affected diagnosis in mathematics is discussed. A distinction is made between errors and mistakes, followed by consideration of computers as a diagnostic tool. The development of algorithms to diagnose errors and of models of student performance is described. (MNS)

Ties together the educational threads of teaching thinking skills and improving the intellectual performance in deaf learners. Identifies six criteria for curriculum or research decisions related to teaching for higher-level problem solving. Applications of these ideas to mathematics are left to the reader. (MDH)

Describes the theory and known influences on learned helplessness, particularly in the mathematics field, and discusses prevention and remediation with respect to this phenomenon. (PK)

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

Recent contributions from theory, research, and practice in second-language instruction are discussed in relation to mathematics education. Three methods of teaching and learning second languages are described--"Delayed Oral Production," the "Silent Way," and the "Counseling Learning/Community Language Learning." (KR)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

Discussed are some situations students face that result in cognitive conflict, possible sources of these conflicts, and strategies which students use to resolve, remove, or circumvent them. A global account for observed systematic errors is offered based on a general problem-solving rule called the "Matching Rule." (KR)

Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…

This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…

Discussed are inconsistencies and cognitive conflict with respect to current mathematical knowledge of students and how that knowledge might be modified is discussed. The inconsistencies that students generate for themselves and those produced by the teacher are described. (KR)

Discussed are possible reasons behind the inconsistencies in the learning of calculus. Implicated are students' beliefs, mathematical paradigms including concept image and concept definition, language use, and curriculum sequencing. (KR)

Discussed are the issues of inconsistencies and compartmentalization and the use of inconsistencies in the classroom. Included are discussions on paradoxes, the naive student, logical reasoning ability, and the development of the students' cognitive structures. (KR)

Discusses a system of classification for students' inconsistent ideas in mathematics, the sources of students' mathematical inconsistency, and instructional strategies for helping students to resolve apparent learning inconsistencies. Language, curriculum, and instruction are included in the discussion. (KR)