Examines a variety of mistakes found in published materials and practiced by classroom teachers. Provides examples of mistakes in reading time, place value, price notation, geometry, and language. (YP)

Summarizes some student misconceptions concerning the concept of equality. Provides several ways to modify present instruction. Describes a way to model the relational view of equals using balances. (YP)

Discusses the use of drawings to nurture problem-solving attitudes and independent learning. Drawings help develop thinking skills, clarify misconceptions, develop representational preferences, supply a context for relationships in K-8 mathematics, and illustrate mathematical connections. (MDH)

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)

Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)

Uses of calculators to teach the concept of exponents are described. Topics covered on activity sheets include powers of two, number systems, and powers as repeated multiplication. Cooperative learning is emphasized. (KR)