In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being…

In reviewing the six articles within this "Instructional Science" special issue, we are reminded of Schoenfeld's ("Educ Res" 45(2):105-111, 2016) review of American Educational Research Association president-authored papers for the centennial celebration of AERA. There, he succinctly unveiled the content focus of AERA research…

Qualified learning materials is needed in the efforts to improve the quality of teaching-learning mathematics. Qualified learning materials can be obtained through development research. Learning materials in this study were learning materials that were developed based on guided discovery learning model. The learning materials was also developed by…

Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based…

In the monograph The Math Teacher (following the Third International Scientific Colloquium Mathematics and Children in 2011), the term "teacher" designates a person who teaches mathematics, and the context of each article reveals whether this implies the teacher at a pre-school institution, a school or a university instructor. In…

The importance of teaching mathematics as a body of strategies and methods of inquiry is stressed; examples of situations which emphasize skills in classification, generalization, using symbols, and proof are given. (DT)

This paper describes an approach for pre-service or in-service mathematics education that teaches sophisticated mathematics using only the tools of high school mathematics. The idea is to start with a standard problem from high school mathematics and let the solution to this problem serve as a platform for asking good mathematical questions and…

Instead of teaching his fifth-graders a formula, a teacher leads them to discover an important mathematical concept on their own. Learning through discovery is probably the very essence of meaningful understanding and retention. (Author/MLF)

The purpose of this study was to determine whether a greater increase in problem-solving ability of capable but poorly prepared college freshmen in a modern mathematics program occurs when students are taught to use discovery techniques. Two experimental and two control groups were formed from 70 college freshmen; two instructors were each…

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…

The idea of "complete permutations" of n distinct objects is explored in order to investigate an application of the concept that arises in Rex Stout's mystery novel, Too Many Cooks. (MN)