We investigated how pre-service teachers (PSTs) interpret their calculations in proportional tasks. A written questionnaire was administrated to 199 PSTs and an inductive content analysis approach used for data analysis. We found that one item that asked PSTs to interpret the meaning of their results had unusually low success; open coding on the…

Counting strategies initially used by young children to perform simple addition are often replaced by more efficient counting strategies, decomposition strategies and rule-based strategies until most answers are encoded in memory and can be directly retrieved. Practice is thought to be the key to developing fluent retrieval of addition facts. This…

The main objective of this article is to contribute to the limited research on teachers' knowledge of probability. In order to meet this objective, we presented prospective mathematics teachers with a variation of a well known task and asked them to determine which of five possible coin flip sequences was least likely to occur. To analyze…

There is much focus at the state and national levels in graduating students that are prepared for college and careers. In order for students to be prepared at the end of their K-12 education, indicators are also needed along the way about whether students are on track. Using historical state data, nine different methods were used to align…

This study focused on analyzing children's difficulties with two-step mathematical word problems. Seventy-one fifth-grade children in Puerto Rico were individually observed solving five problems. Two of these were two-step problems; the remaining three were one-step problems with the same mathematical structures as the components of the two-step…

This work studies the difficulties children have solving two-step word problems of a given structure (e.g., 7 lollypops/2 chocolate bars X 6 chocolate bars). Thirty-six children between the ages of 9 and 14 years were individually observed solving problems of the above type. Other tasks, repetition of the problem and model recognition, were used…

Recall of multiplication number facts is a major educational objective in elementary grades, yet some children never acquire total mastery. A microcomputer multiplication number facts training program was developed which incorporated programmed instructional features including feedback, positive reinforcement, vanishing, branching and pairing.…

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…

This research is aimed at diagnosing the problem-solving skill of elementary school children and subsequently improving their competence in early mathematics. To reach this goal, a computer assisted instruction (CAI) program on open sentences, incorporating knowledge about students' problem solving strategies and misconceptions, was constructed.…

Most studies of children's solution processes on simple addition and subtraction word problems have used individual interviews or the analysis of error patterns on paper-and-pencil tests as the primary data-gathering techniques. The present paper reports an investigation in which the contribution of eye-movement data was explored for studying…

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)

Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…