The digital age 4.0 governs the progress of society and individuals require the acquisition of skills to face this reality. Education is the only way that will allow human beings to adapt to the new global challenges. Therefore, the achievement of productive experiences must be the priority of the current educational system to train competent…

In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

As problems become increasingly complex, science educators need to better understand how new knowledge is constructed and applied in heterogeneous team collaborations, and how to teach students to productively engage in these processes. We discuss the emergence of insights in collaborative sensemaking and suggest a model that articulates the…

This study investigated what 12 prospective mathematics teachers (PTs) in a middle school mathematics method course reported during a video-stimulated recall interview about their experiences when they were engaged in a doing math task that yielded an Opportunity for Productive Struggle (OPS). We investigated their reported feelings during the…

This paper attempts to show that the significant difference between the enthymeme and the dialectic syllogism rests on the similarity of purpose of both dialectic and rhetoric, and on the differences in the respondents to which they address themselves. To support this thesis, the author reviews several contemporary approaches which have dealt with…

This paper outlines the increasing prospects for improving the problem solving component of future mathematics programs. Of particular interest is the development of a viable growth schema for general problem solving strategies and skills. The plan presented here provides for five levels of problem solving sophistication. The main body of the…

This paper discusses Program Management (PM), a decision-making process which uses a diachronic, idea-generating communication mode. Decision making according to a PM model entails obtaining a mandate or authorization, identifying the problem, exploring for knowledge and generating solutions, reviewing proposals and developing resources,…

The development and use of intuitive thinking, at all levels of education, have been of concern to scholars in recent years. This paper discusses the findings and theories of various scholars about intuitive thinking and learning, including the work of Jean Piaget, Jerome Bruner, Richard Jones, and Robert Ornstein. The paper also explores the use…

This paper describes global changes in education to be expected as a result of the expansion of information technology. Technology expands access to alternate sources of information and changes the approach to teaching and learning. A case is made for a lifelong approach to learning and cites certain specific factors that should be included. The…

By engaging in philosophical discussion in their writing, freshman composition students can discover that writing is a mediating tool between the self and the objective world, a means to examine the nature of reality and their thinking processes. Introducing philosophical issues opens the door for the investigation of difficult and abstract topics…

Action Research begins by identifying goals as perceived in the community; input is sought in neighborhood hearings or by running a series in the local newspaper and inviting response. Once a research group is organized, Action Research continues as a five-stage flexible study plan for practitioner improvement involving turning goals into…

Too often college composition students see language as an end in itself, rather than as a means to realization of self and world, and teachers need to establish a classroom environment that stimulates and demands that students use their language to find out about themselves. Techniques helpful in shaping composition classes toward this end…

A technique to teach cognitive skills to directly facilitate abstract and rational thinking is described. Based on George Kelly's theory of personal constructs, his Role Construct Repertory Test has students construe similarities and differences among important course concepts rather than provide individual definitions or examples of those…

The purpose of this study was to investigate in children from ages 4 to 10 the development of logical propositions and to determine whether or not there is a developmental sequence in children's ability to supply missing elements of syllogisms. A specially designed instrument, consisting of an equal number of items with missing major premises,…

Tagmemic invention offers a student several ways of decreasing the unfamiliarity of the early stages of writing. The process of inquiry and the heuristic devices provide the orientation and tools for dealing with new writing tasks with increased confidence and likelihood of success. In the theory of tagmemic rhetoric, language behavior and…