Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

Suggests having students write short summaries using the principles of the journalistic news "lead" to help them sharpen their abstraction skills. Includes samples of data blocks from which students would compose their summaries, kernel sentences from the samples, "kernel" kernel sentences, first draft summaries, and 30-word…

Four experiments are presented to support the theory that the rule system governing the law of large numbers is not tied to a content domain, and that it can be improved by formal teaching techniques. The experiments showed that statistical training enhanced everyday reasoning. Test problems and objective example problems are appended. (LMO)

This paper advocates an integrated study of English rather than the traditional approach of studying language, literature, and composition. Its focus is not on designing an integrated curriculum, but on using this approach to develop reasoning skills for secondary students. One integrated curriculum program for the development of reasoning skills…

Describes an instructional model for teaching abstract data types (ADTs) to high school students. Presents research results regarding students' conceptualizations of ADTs and their strategies of using them in computer science problem solving. To implement the ADTs, "black boxes" were used. (AEF)

Recent research literature has highlighted the interest of both teachers and researchers in using analogies to aid students' conceptual understanding. This appears to be especially relevant in secondary chemistry education due to the many abstract concepts that are included in the curricula. This paper reviews recent literature and considers…

This booklet contains proceedings of the Fourth Conference of the University/Urban Schools National Task Force. The conference was held to present information about four programs designed to help high school students to sharpen their reasoning skills. Criteria for program development state that: (1) the program can be taught to teachers in a…

This paper reported the results of a study designed to determine whether certain instructional strategies are superior to others in teaching problem solving to high school chemistry students. The effectiveness of four instructional strategies for teaching problem solving to students of various proportional reasoning ability, verbal and visual…

The authors describe one high school teacher's attempt to change her mathematics teaching in ways that are consistent with the National Council of Teachers of Mathematics'"Standards" documents. One of the coauthors is the teacher who teaches in a professional development school; the other, a researcher, conducted regular observations in…

This study investigated the grouping effect on student achievement in a chemistry laboratory when homogeneous and heterogeneous formal reasoning ability, high and low levels of formal reasoning ability, group sizes of two and four, and homogeneous and heterogeneous gender were used for grouping factors. The sample consisted of all eight intact…

The development of an instructional model for teaching formal mathematical concepts (probability concepts) to disadvantaged high school students through computer programming and some results from a field test are described in this document. The instructional model takes into account both learner characteristics (cognitive, affective, and…

Imagery use in high school mathematics classrooms was studied. A visual image was defined as a mental scheme depicting visual or spatial information, but this definition was not spelled out to teachers or students, in order to learn what they meant by the concept. Subjects were 13 high school teachers and 54 of their students interviewed over 3…

One of three related documents produced in response to a need for direct instruction in thinking skills at the secondary level, this program for high school students bases its approach on involvement of students in direct experiences. Designed to build on the thinking skills that the student already possesses and, ideally, on the experience gained…

One of three related documents produced in response to a need for direct instruction in thinking skills at the secondary level, this teaching guide for Book One and Book Two of "Thinking Through Language" is intended for junior or senior high school English teachers. The guide contains an introduction and summaries of Book One and Book Two,…