This article discusses two mechanisms through which understanding static mathematical concepts (basic and more advanced mathematical concepts) in terms of fictive motions or motion events enhance our understanding of these concepts. It is suggested that at least two mechanisms are involved in this enhancing process. The first mechanism enables us…

This paper advocates reading philosophy and using its concepts in educational and social science research. The lengthy engagement with the various concepts and conceptual orders of poststructuralism required for post qualitative inquiry exceeds the scope of reading required for a conventional literature review at the beginning of a typical…

This Family and Practitioner Brief discusses how deaf children who have not had access to a complete language from birth often encounter unique challenges in developing academic language skills, particularly in the realm of inference-making.

There has been a long-standing debate on situational and symbolic mathematics, which is associated with how to design and execute mathematics education for all students. Brain studies can give some clues for how to deal with the debate. There are situational, verbalized, and visuospatial brain networks and the connectivity among the networks,…

Engineering design has been central to technology education. Currently, online collaborative platforms for designers are widely used as digital forms of an engineer's notebook. However, traditional forms are still valued as the medium of engineering design during the conceptual phase of design since a paper notebook and pen or pencil allow…

The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…

Since formal mathematics is discussed in terms of abstract symbols, many students face difficulties to acquire a clear understanding of mathematical concepts and ideas. Transforming abstract or dis-embodied representations of mathematical concepts and ideas into embodied representations is a strategy to make mathematics more tangible and…

For teachers to provide students with meaningful instruction in area measurement, teachers need robust understandings of area. Here, I describe two cycles of a "lesson experiment" used to investigate prospective teachers' understandings of area units in an undergraduate mathematics class. For each cycle, I collected and analyzed the…

The purpose of this article is to share how one teacher implemented exploratory writing within a mathematics lesson to support her third graders in making sense of fractions and communicating their mathematical ideas. The author defines exploratory writing, then describes the teacher's lesson while also presenting a general overview about how to…

In what follows, we revisit the most promising conceptions of "hope" while following Haraway's admonition to "stay with the trouble." Thirty-five years after Haraway's (1991) opening to the Manifesto for Cyborgs where she states that "irony is about contradictions that do not resolve into larger wholes" (p. 149), we…

The hammer-and-nail phenomenon highlights human tendency to approach a problem using a tool with which one is familiar instead of analyzing the problem. Pedagogical suggestions are offered to help students minimize their mathematical impulsivity, cultivate an analytic disposition, and develop conceptual understanding.

Cognitive conflict arises when students' expectation about a physical situation, such as the relative temperatures of metal and cloth, are not experimentally verified. The paper reviews this approach as a tool for promoting conceptual learning in undergraduate engineering courses, through three case studies. These cases demonstrate that cognitive…

Games have been used as instructional tools throughout history. Educational experiences are more effective when learners are active participants, and when teachers carefully choose fun games with appropriate game mechanics and clear curricular connections, students can engage in rigorous mental processes. At the same time, students may learn a…

Students often use incoherent strategies in their problem solving involving force and motion, as revealed, e.g. when they are asked to draw force diagrams for amusement rides involving circular motion, whether in horizontal or vertical planes. Depending on the questions asked, assignments involving circular motion can reveal different types of…

The authors designed a course--Origami and Geometry--and describe one of the activities in which origami was used to fold a regular dodecahedron. They find that origami can provide students with concrete material for observing geometrical structures and give them opportunities to examine their thoughts on geometry.