This article explores historical reasoning, an important activity in history learning. Based upon an extensive review of empirical literature on students' thinking and reasoning about history, a theoretical framework of historical reasoning is proposed. The framework consists of six components: asking historical questions, using sources,…

Students and instructors may be frustrated with students' lack of understanding of sociological concepts. We suggest that the difficulty of teaching and learning sociology is that sociological concepts and relationships require the use of abstract reasoning patterns. Many students are unaccustomed to using these abstract reasoning patterns. We use…

This paper takes the position that logical knowledge is distinct from conceptual and procedural knowledge and can make a unique contribution to the understanding of knowledge acquisition. This view of logical knowledge departs from the traditional Piagetian view of stages and the overriding view of logic as the sole means of constructing new…

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Students (N=49) enrolled in a physics course for elementary teachers were evaluated for their abilities to use: (1) combinatorial logic; (2) separation and control of variables; (3) proportional reasoning; and (4) reciprocal implications. Performance of four Piagetian tasks during interviews was treated as a measure of the degree to which students…

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)

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)

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…

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)