The purpose of this study is to explore how primary school students reexamine their conjectures and proofs when they confront counter-examples to the conjectures they have proved. In the case study, a pair of Japanese fifth graders thought that they had proved their primitive conjecture with manipulative objects (that is, they constructed an…

Through a case study of four elementary education undergraduates, we seek new analytic constructs that could help make clearer how arguments discovered or tested in quite special cases might come to support assertions that are understood to hold in general. We began analysis from a particular standpoint: to focus fundamentally on learners'…

This classroom scholarship report presents a group of elementary students' experiences learning the traditional long division algorithm. The traditional long division algorithm is often taught mechanically, resulting in the student's performance of step-by-step procedures with no or weak understanding of the concept. While noting some initial…

Addresses the early stages of children's introduction to the use of variables in formal algebraic notation. Describes a teaching approach that aims to situate the use of formal notation in meaningful contexts. Presents a study of a teaching sequence based on children working with this approach using graphical feedback in problem solutions. (AIM)

Examines problem-solving results among second-grade students in three schools that were all using a reformed mathematics curriculum. Except for one problem, more students used a mental procedure than the standard written algorithms, and both methods were used with approximately the same degree of accuracy. (AIM)

Investigates procedural and conceptual aspects in preservice elementary school teachers' understanding of the Fundamental Theorem of Arithmetic. Participants' responses indicated that a possibility of alternative prime decompositions was often not overruled, and this influenced students' ability to make inferences regarding factors and divisors of…

Analysis of episodes from a mathematics course for prospective elementary teachers run as a whole-class constructivist teaching experiment provides a detailed look at how classroom norms for mathematical justification were established given the prospective teachers' traditional expectations of school mathematics and the teacher's reform-oriented…

Attempts to reconstruct the productive ideas that evolved from already existing sources for the teaching and understanding of negative numbers. Discusses examples from developmental research. (Author/MKR)

Presents case study data of low- and high-achieving nine-year olds focusing on construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in strategies for dealing with isomorphic combinatorial problems presented in hands-on and written form. Results showed that achievement level does not predict…

Describes a study in which Australian children aged 5-8 years old (N=70) were presented with a range of measurement tasks to determine the strategies and devices that they would choose to use to measure length. Results are in conflict with the normal curriculum sequence. Contains 30 references. (DDR)

Investigated were the effects of programing instruction with BASIC on mathematical thinking skills and concept development in grade six. Posttests assessed programing ability, generalization, and understanding of variables. Observations and interviews were also used. The groups having programing instruction scored significantly higher than the…

The status of mathematics instruction, especially in the elementary school, is discussed. A meaningful, holistic approach is advocated, rather than an emphasis on rules and procedures. (MNS)

How multiplication is usually taught in school and how it could be taught are discussed. Development of understanding is illustrated through children's words and work. (MNS)

What are often missing for children in classroom instruction are experiences with numbers that stretch beyond computation skills and word problems. This lesson models such an experience for third graders. Students use small boxes of raisins in several problem-solving activities. Children apply whole number operations, estimate, consider…

Mathematics is considered a performing art. Examples illustrating this view are presented. Activities discussed are from the Madison Project materials and the mathematics program at University High School in Urbana, Illinois. Activities stress inventing strategies for attacking problems for elementary and secondary school mathematics. (RH)