Lists some ways that sequences were incorporated into mathematics lessons and explains a teacher's observations about the caliber of thinking and questioning that students develop as they learn appropriate ways to use numbers. Provides a number of questions that have been raised by students and the thinking prompted by a discussion of those…

Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

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)

Interviews with 72 mixed ability students, aged 7 to 12, about arithmetic problem-solving strategies, indicated that the preference between procedural and deductive strategies becomes a divergent reality across ability levels. Among the conclusions is that more able children tend to be doing a qualitatively different sort of mathematics than their…