Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

Discussion boards have the unique capacity to support higher-order constructivist learning and the development of a learning community, This chapter provides ten conditions that support the effective use of an online discussion.

A study investigated the effectiveness of using a small-group discussion as the main vehicle for the construction of an initial representation of a problem that activates previously acquired knowledge. College students (N=39) were randomly assigned to either an experimental condition or a control condition and asked to brainstorm about a presented…

Examines and identifies students' mental models of an abstract mathematical concept regarding intuition. Observes how students think reflectively on their mental models in a whole-class discussion in terms of logical thinking. (DDR)

Describes a study of first-year medical students that tested the effects of problem-based tutorial group discussion on learning new information from a text. Highlights include effects of small-group instruction on cognition; randomized experimental and control groups; recall; and results that showed the positive effects of problem-based group…

The purpose of this exploratory experimental study was to examine how online cognitive facilitation that promotes cognitive presence, while keeping facilitator's social presence constant, affects student learning and satisfaction in an online community of inquiry. In this context, we explored the following questions: (1) Does online high cognitive…

Using the children's book "Tops and Bottoms" by Janet Stevens--an adaptation of the classic fable of the Tortoise and the Hare--students are given opportunities to build connections between a problem-solving situation and mathematics and to communicate solutions through writing, symbols, and diagrams. A key concept is to demonstrate to students…

Sentences are understood by outlining associative relations between the concepts representing the meanings of the words. When the words are received the activation spreads from their conceptual counterparts to the other concepts in memory, so that some implicit thoughts are often added to the mental representation of a sentence. As sentences are…