Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students' failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors' components such as the…

In this article we describe secondary school practising teachers' professional noticing expertise, which includes (a) attending to the details of students' written or verbal responses, (b) interpreting students' mathematical understandings, and (c) deciding how to respond to students based on their understandings, with a focus on algebraic-pattern…

This paper presents protests from academically successful students who privately conveyed to the researchers their feelings of personal discontent with schools. The criterion to select this "sample" was that these students, dissatisfied with school but having good marks, would reveal what others, academically less successful, could not…

A comparison of 28 mildly mentally retarded children with 28 children of average intelligence (mean mental age six years) in learning conservation skills found both groups benefited from Direct Instruction methods, but retarded children acquired only pseudoconservation from Observational Learning methods. Their learning was not tenacious and did…

Students often fail to apply knowledge and skills learned in one context to other situations. Although the implicit assumption in educational practice has been that transfer takes care of itself, a knowledge of the mechanisms of transfer can enable educators to help their students integrate general and local knowledge. (TE)

This is a qualitative study of 22 9th graders performing generalizations on a task involving linear patterns. Our research questions were: What enables/hinders students' abilities to generalize a linear pattern? What strategies do successful students use to develop an explicit generalization? How do students make use of visual and numerical cues…

Argues that more attention should be given to teaching students how to learn the rudiments of specific metabolic pathways. This approach describes a unique way of learning the glycolytic pathway in stepwise fashion. The pedagogy involves clear rote components that are connected to a set of generalizations that develop and enhance important…

Models and modeling are frequently used as instructional tools in science education to convey important information concerning both the explanatory and structural features of topic areas in science. The efficacy of models as such rests almost entirely upon students' ability to conceptualize them as abstracted "representations" of…

Discusses issues and problems concerning concept development among students in elementary social studies programs. Suggests good teaching uses analogies and metaphors to facilitate learning. Recommends illustrating key concepts through myths, fables, and parables. Argues that using stories that show how things work allows students to apply the…

Argues that social studies teachers need to involve their students in building their own pyramids of knowledge from basic facts into broad general principles. Discusses a class at Moorhead State University (Minnesota) that uses the inquiry method to help student teachers learn to construct lessons that follow the…

Asserts that teaching concept formation and generalization development are central to any social studies program. Presents a classroom activity designed to teach geographic concepts to middle school students. Includes four figures and instructional procedures to be used in the activity. (CFR)

Presents a method for improving reading comprehension through direct instruction of inductive reasoning. Students gather clues to personality of characters as play progresses and from these arrive at an overall generalization concerning the complexities of the character. (SRT)

This study examined the effect of using an outdoor nature investigation program on the ability of third-grade students to transfer knowledge. Specifically, the study determined whether the program enhanced students' ability to transfer declarative (facts and concepts), procedural (process skills), and schematic (experience) knowledge to a set of…

Defines a generalization as "a descriptive statement of broad application indicating a relationship between two or more concepts." Argues that successful teaching about generalizations can only occur when students understand the relationship between concepts and facts. Discusses four issues and four approaches related to teaching…