**1. Introduction**

There is no lack of pedagogical theories aimed at the K-12 education sector, many of which can be utilized together in order to provide an excellent education for children. Some of these theories are being employed in lower classmen with higher education to improve the educational outcomes of young adult learners [1–5]. Malcolm Knowles [6] popularized the term

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"andragogy," which refers to adult learning theories. These ideas became widespread in the 1960s, and typically referred to informal education for later year adults, who could draw on their life experiences as part of their learning. Formal education such as that experienced at university, community college or trade school, did not adopt such principles. These young adult learners can benefit from teaching and learning methods used in the high schools, but with extensions or adaptations to meet their undergraduate needs. Many have typically not gained sufficient "life experience" to benefit from andragogical teaching methodology as defined, and hence fall into an "in-between" educational group, where teaching methods need to be developed more formally.

however, while they can evaluate and make sense of information, typically only one single

Utilizing a Differentiation Framework, Piagetian Theories and Bloom's Taxonomy to Foster…

http://dx.doi.org/10.5772/intechopen.75646

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More recently, Piagetian theory has been extended to include further thought patterns, commonly known as post-Piagetian (pP) or post-formal ideas. In a study by Wu and Chiou [10], post-formal thinking was linked to creativity, and also the need for creativity in science (and likely STEM) fields to pursue and generate original thought. Although formal operational thinking is required for performing systematic tasks—a necessity in STEM fields—it does not allow for creativity, as formal thinkers believe there is only one correct answer [10]. Therefore, successful STEM researchers need to display both formal and creative thinking. Post-formal or pP levels of development are said to include two further stages: (e) relativistic thinking; and (f) dialectical thinking. In relativistic thinking, the learner begins to observe contradictions with potential solutions, and ultimately accepts that more than one solution is plausible given different ways of viewing a particular situation. This acceptance of other perspectives enables more novel solutions to ultimately be found. In dialectical thinking, the learner is open to new knowledge, and in fact *expects* to change their current thought pattern as new knowledge is found or presented. This is known as an "evolution of knowledge" thought pattern, and essentially can only evolve *from* contradictions of thought. Dialectical thinking enables the learner to synthesize new thought, and is essential for the creative process. Researchers operating at this level are typically more creative [10]. A final stage in thinking skill suggested here is (g) creative or independent thinking, where post-formal thinking has become an independent process, and the learner no longer relies upon guidance to come up with individual thought. This helps distinguish the educator demonstrating and encouraging development of thinking patterns (e) and (f) to research students versus those who have since mastered the "art" of thinking. The ultimate goal of a successful PhD student is one who is equipped with sufficient thinking intellect to be independent, and hence thinking stage (g) is included in the current discussion. These last three stages can equally be applied to professionals in their respective fields who have gained expert-level competence and independence

Given seven progressive stages of thinking skill development and acquirement, influenced by many outside factors influencing the rate of development, a typical class will consist of students operating at varying thinking levels. As such, it is important to run all classes, even in higher education settings, in a differentiated fashion to meet the needs of all students.

Carol Tomlinson has made the differentiated teaching and learning pedagogy famous, particularly in the K-12 educational sector [11–13], also more recently known as personalized learning. The ultimate goals of differentiated teaching is to promote growth in learning of *all* students from their starting point, ultimately promoting independence of learning within their particular stage of intellectual thinking development. With the explosion of the computer age, many automated tools are being developed to provide drill practice for students at their level of competency, gradually increasing or decreasing the level of difficulty as required. This is one of many tools at an educator's disposal to utilize in the classroom. Others include providing

**2.2. Differentiated or personalized learning theories**

answer will be considered "correct" [8, 10].

of thought.

This chapter outlines some key adaptations of pedagogical methods suitable in post-secondary education, followed by applications of these methods in chemical engineering undergraduate laboratory classes. It is anticipated that these methods would be useful for all Science, Technology, Engineering, and Mathematics (STEM) undergraduate and graduate education.
