In the last four columns the authors introduced the concept of critical thinking competency standards and elaborated a number of such standards, targeting the analysis of thought, the assessment of thought, and the cultivation of intellectual virtues. In this column they focus on three subject-specific critical thinking competency standards. It is…

In the last three columns the authors introduced the concept and provided several examples of critical thinking competency standards that target the cultivation of intellectual traits. In this column the authors continue the discussion of these competency standards that are essential to teaching and learning because they go beyond the development…

In this article the author has used 19th-century arithmetic and algebra textbooks as a way to reflect on current practices in developmental mathematics education. Five areas of special interest were found: motivation, relevance, depth, pedagogy, and textbooks. Philosophic and practical statements from vintage textbook authors remind educators of a…

In the last three columns, the authors introduced the idea of ethical reasoning, discussed its importance to education, and briefly dealt with a number of understandings essential to skilled ethical reasoning. In this column, the authors continue this discussion. They distinguish between simple and complex ethical questions and reason through an…

This manuscript proposes a theoretical model that provides an alternative for assessing, advising, and placing underprepared students in colleges and universities. It advocates combining cognitive and affective assessment data along with information about students' personal circumstances to make more precise placement decisions via advising that…

This paper discusses a pilot study of the effects of a curriculum focus intervention on students' prealgebra achievement. Elements of the intervention include identification of high-priority learning objective; structured repeatable testing; and a coherent, rubric-based feedback component. This research differs from traditional mastery learning…

The development of ethical reasoning abilities is vitally important--both for living an ethical life and creating an ethical world. In this article, the authors set out some of the foundations of ethical reasoning. Their aim is to introduce some important intellectual tools and understandings for insightfully reasoning through ethical issues and…

In the last two articles, the authors introduced the concept of Socratic questioning and its relationship to critical thinking. They illuminated how understanding the concepts embedded in critical thinking naturally generates questions. For example, a thinker who understands the elements of thought asks questions which probe the parts of thinking.…

The "Critical Thinking and the Art of Close Reading" series (which includes this column and three others) focuses on some of the most basic understandings necessary for close reading (Paul & Elder, 2003). To read well, in addition to having these understandings, students must be able to identify the big picture within a text, to determine the key…

The typical college student is unable to deeply comprehend what he or she reads. Most students have few, if any, intellectual tools that would enable them to read deeply, and then apply what they have read. The "Critical Thinking and the Art of Close Reading" series (which includes this column and the past three columns) focuses on some of the…

Outlines the differences between inferences and assumptions in critical thinking processes. Explains that as students develop critical intuitions, they increasingly notice how their point of view shapes their experiences. (AUTH/NB)

Urges education to help students learn through conceptual thinking. States that the first step must be to teach the subtleties of words--without a command of the language, important discriminations can be confused. Asserts that if students are to think well conceptually, surface language must dissolve, and alternative ways to communicate must be…

Argues that students should continuously question the purpose of their daily classroom activities and assignments. Explains that when students are required to consider purpose, they begin to develop important intellectual skills, and to bring relevance to their critical thinking and daily life. (NB)

Suggests that there are three ways of taking in information: internalizing inert information, forming activated ignorance, or achieving activated knowledge. Explains that only activated knowledge leads the learner, by implication, to more knowledge, and that seeking the logic of things can lead to discovery of activated knowledge. (NB)

States that average and below average students' learning styles tend to be more concretely dimensional. Providing developmental students with physical models (e.g. adding and subtracting of integers using two color chips on a number line) helps them to abstract the more complex meanings and ideas of higher mathematical thought. (PGS)