Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use the quadratic formula, which means that students know the appropriate strategy before they read each problem. In an alternative approach,…

We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils' understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or…

This study compared one lesson across four U.S. "traditional" textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of…

Assessments were made of the impact of various overt response modes on the problem-solving process. The Luchins Water Jar Problems were presented to undergraduate university students via interactive cathode ray tube computer terminals under four response mode conditions: Mnemonic Code, Multiple Choice (MC), Numerical List, and Constructed Response…

RESEARCH OBJECTIVES WERE (A) TO DEVELOP A BATTERY OF INSIGHT-PROBLEMS FOR USE IN PROBLEM-SOLVING RESEARCH, (B) TO REPLICATE A TRAINING EXPERIMENT IN ORDER TO DETERMINE WHAT A SUBJECT MIGHT HAVE LEARNED IN A SPECIFIC SITUATION WHICH COULD INFLUENCE NONSPECIFIC SITUATIONS, AND (C) TO ATTEMPT TO TEACH SUBJECTS STRATEGY WHICH WILL ALLOW THEM TO…

A comparative analysis is presented of adolescent participation in three-person family problem-solving groups, involving five families with an adolescent diabetic and three families with an adolescent with no diagnosed illness. Observation and interaction analysis of family problem-solving in a laboratory setting were used, as families were asked…

This paper describes the rationale behind and the development and utilization of a bibliographic instruction course which incorporates formal abstract reasoning skills. The limitations of the search strategy technique of bibliographic instruction are discussed as well as the fact that many college students have not developed sophisticated…