A common feature of many assessment plans is the use of multiple-choice questions. Although there are criticisms of multiple-choice questions, this assessment format is here to stay--multiple-choice questions are effective means of evaluation in large classes, central to many licensing and entry exams, used in most adaptive learning platforms, and…

To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. "Concreteness fading" is a theory of instruction that offers a solution for making these connections. As originally…

Introductory programming courses (CS1) are difficult for novices. Inspired by "Problem solving followed by instruction" and "Productive Failure" approaches, we define an original "necessity-driven" learning design. Students are put in an apparently well-known situation, but this time they miss an essential ingredient…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

This concluding commentary takes the perspective of research on practicing scientists and engineers to consider what open areas and future directions on relational thinking and learning should be considered beyond the impressive research presented in the special issue. Areas for more work include (a) a need to examine educational applications of…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

In our work in environmental education (EE) as part of formal schooling we partnered with local schools to explore the practice of embedding, or integrating EE within formal school curriculum using inquiry-based pedagogies. In this paper we report on and discuss our growing understanding of the practice of pedagogical documentation and the…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

This paper discusses how modifying the true-or-false (T/F) test, by requiring written explanations, reveals major weaknesses and hazards of the simple (unexplained) T/F tests popular among teachers. But, more important, the modification transforms the test into a very efficient formative assessment tool. It opens a window that allows a teacher to…

An intelligence model of processes and content of thought is proposed. Processes include remembering, evaluating, generating, and transforming, while content is self, forms, ideas, and persons, determining levels of complexity for learning. The TETRA model is compared with J.P. Guilford's aptitude structure of intellect. Theory implications for…

A framework for using and changing concepts in the study of science is described. (JD)

This paper describes the methods and techniques called Conceptual Analysis (CA), a rigorous procedure to generate (without involuntary omissions and repetitions) knowledge bases for the development of knowledge-based systems. An introduction is given of CA and how it can be used to produce knowledge bases. A discussion is presented on what is…

Presents young children's concepts related to probability grouped by definite, possible, and definitely not. Discusses the teaching methods of the probability concepts. (YP)

Examines classic fairy tales, noting the lack of attention given the role of imagination in children's learning. Discusses features of fairy stories such as structure, oppositional concepts, and emotional component, then infers four principles about young children's learning. Gives two examples of how these principles can influence teaching to be…

A cognitive or internal representation refers to an organized system of information which reflects certain, but not all, of the information about reality being represented. This paper considers various opinions, controversies, and debates about what representation is, how it comes about, and what forms of representation can be distinguished. The…