High

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Implementation of reform curricula requires teachers to adopt new approaches to teaching. Research has provided promising results about the influence of educative curriculum on teachers’ learning and instruction. However, this approach generally focuses on teachers as isolated learners. Using a design-based research approach, the authors developed a web-based tool, iPlan, which provides access to educative curriculum materials in an online interactive learning platform.

Online math videos for student learning are abundant; yet they are surprisingly uniform in their monologic, expository mode of presentation and their emphasis on procedural skill. In response, we created an alternative model of online math videos that feature the unscripted dialogue of secondary school students, who convey sources of confusion and resolve the dilemmas that arise during problem solving.

Experimentation is one of the important strategies used in engineering design to understand the relationship between relevant variables so that they can be manipulated to generate optimized solution for a particular problem or design. The understanding of students’ experimentation strategies allows educators to help students improve their design experiments by providing scaffolds or guidance. The purpose of this study is to investigate students’ experimentation strategies while they work on a design challenge.

In science and engineering education, the use of heuristics has been introduced as a way of understanding the world, and as a way to approach problem-solving and design. However, important consequences for the use of heuristics are that they do not always guarantee a correct solution. Learning by Design has been identified as a pedagogical strategy that can guide individuals to properly connect science learning via design challenges.

Ambitious efforts are taking place to implement a new vision for science education in the United States, in both Next Generation Science Standards (NGSS)-adopted states and those states creating their own, often related, standards. Inservice and pre-service teacher educators are involved in supporting teacher shifts in practice toward the new standards. With these efforts, it will be important to document shifts in science instruction toward the goals of NGSS and broader science education reform.

Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.