**2. Development of an educational framework for STEM education**

#### **2.1. Piagetian and post-Piagetian (pP) learning theories**

Piaget's theory, or Piagetian theory, has had a huge impact on the educational beliefs of educators around the world, and has largely dictated the "expected" intellectual development of children as they progress from birth to adulthood [7]. While this theory is still well accepted in many educational domains, the connections with biological progression of childhood development have come under scrutiny. It is well documented that students acquire new knowledge in a series of progressive stages (matching Piagetian stages), except that this development occurs at vastly different rates between students, with factors such as level of maturity, experience, culture, and individual ability strongly influencing these rates [8]. Due to these different rates of progression, it has been well observed that as many as 50% of freshmen students in higher education have yet to complete the final stage of Piagetian acquirement of knowledge [7].

Briefly, the four stages outlined by Piaget are (a) the sensorimotor stage for infants (0–2 years); (b) the pre-operational stage (2–7 years); (c) the concrete operational stage (7–11 years); and (d) the formal operational stage (12–15 years) [7–9]. The sensorimotor stage sees infants acquiring knowledge using their sensory skills such as touch, sight, or feelings, and is present with the infant right up until the time speech begins. The pre-operational stage occurs when young children use the additional skill of language to bring further meaning to their knowledge development. While language is used to describe various situations, there is often an over-exaggeration and little logic to the verbal explanations, and others opinions have little impact on the learner, although they may be copied. At the concrete operational stage, children are able to expand their thought processes and overall intellect by incorporating logic, comparing objects, and understanding concrete ideas [8]. In the final stage of Piaget's theory, the learner can deal with more abstract ideas, construct their own thought patterns, and evaluate information provided; however, while they can evaluate and make sense of information, typically only one single answer will be considered "correct" [8, 10].

"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

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

Piaget's theory, or Piagetian theory, has had a huge impact on the educational beliefs of educators around the world, and has largely dictated the "expected" intellectual development of children as they progress from birth to adulthood [7]. While this theory is still well accepted in many educational domains, the connections with biological progression of childhood development have come under scrutiny. It is well documented that students acquire new knowledge in a series of progressive stages (matching Piagetian stages), except that this development occurs at vastly different rates between students, with factors such as level of maturity, experience, culture, and individual ability strongly influencing these rates [8]. Due to these different rates of progression, it has been well observed that as many as 50% of freshmen students in higher education have yet to complete the final stage of Piagetian acquire-

Briefly, the four stages outlined by Piaget are (a) the sensorimotor stage for infants (0–2 years); (b) the pre-operational stage (2–7 years); (c) the concrete operational stage (7–11 years); and (d) the formal operational stage (12–15 years) [7–9]. The sensorimotor stage sees infants acquiring knowledge using their sensory skills such as touch, sight, or feelings, and is present with the infant right up until the time speech begins. The pre-operational stage occurs when young children use the additional skill of language to bring further meaning to their knowledge development. While language is used to describe various situations, there is often an over-exaggeration and little logic to the verbal explanations, and others opinions have little impact on the learner, although they may be copied. At the concrete operational stage, children are able to expand their thought processes and overall intellect by incorporating logic, comparing objects, and understanding concrete ideas [8]. In the final stage of Piaget's theory, the learner can deal with more abstract ideas, construct their own thought patterns, and evaluate information provided;

**2. Development of an educational framework for STEM education**

**2.1. Piagetian and post-Piagetian (pP) learning theories**

4 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

need to be developed more formally.

education.

ment of knowledge [7].

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 of thought.

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.

#### **2.2. Differentiated or personalized learning theories**

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 differentiated homework sheets; group work to conduct more open-ended problems; inquirybased learning tasks; experiential learning tasks; active learning; and many more. Each of these tasks, if carefully constructed, provides opportunities for learners to actively engage with the material, promoting depth of learning within their zone of proximal development (ZPD) [14], all the while challenging them to the next level of thinking.

there would be less dependence on the instructional approach, providing more freedom for students to explore abstract problems (DP2). Challenging tasks would rely on students' prior mastery of problem-solving skills, concentrating more on developing adaptations of these skills to non-routine problems (DP3). Collaborative tasks with other students would see the students now begin to rely on each other to add to existing knowledge, having now mastered the key functioning of a team (DP4). Independence would be demonstrated when learners rely on their own problem-solving skills, and those of their peers, to independently work

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A detailed study by Valiandes [22] was conducted in 13 Cypriot primary schools, covering 479 fourth-grade students (average age 9 years) and 24 teachers. The students were functional at the pre-operational and concrete operational thinking stages of Piaget. An important aspect of this study was the in-depth support given to the teachers to adequately train them in differentiated teaching strategies. Students were tested on literacy skills, and post-test results were significantly better for students participating in differentiated learning than the control group, which had largely instructional-based learning. Typical observations of differentiated instruction included noting the time spent by the teacher (a) commenting on student general behavior; (b) providing additional examples; (c) direct teaching/asking questions; and (d) providing student guidelines for work. Other observations included identifying the degree of activity variation; providing personalized support to students; providing learning opportunities to students of all readiness levels; time for students to reflect on basic knowledge and skills, or prerequisite knowledge; prioritizing order of activities; accomplishing lesson objectives; and providing differentiated homework. Many of these observations fit well into the DP in the concrete operational level. As a result of this in-depth study, differentiated practices

*"instruction planning based on constructivism learning theory, the hierarchical order of learning activities (DP1), the maximization of students' active participation in the learning process, the reduction of teachers' talking time during teaching (DP2), the variation of activities, the opportunity for students to work at their own pace, the personalized support that students receive (DP3), the differentiation of activities according to students' interests and learning profile (DP4), and the continuous evaluation of students' achievement with a simultaneous and ongoing evaluation of the effectiveness of the learning* 

The above quote has been interlaced with the identification of the five DPs as explained earlier, to demonstrate that these principles broadly cover many descriptions of differentiated practices. This example shows both the effectiveness of differentiated instruction at (mostly) the concrete operational level, as well as the importance of fully equipping teachers with the

Educators of lower classmen in the higher education sector may encounter significant numbers of students operating in the concrete or formal operational levels, and hence differentiating the instruction would follow a similar pattern to those outlined above in Section 2.2.1. This is adequately demonstrated by a few reported studies of freshmen level mathematics

problems and make sense of more abstract ones as well (DP5).

were described as [22]:

*process (DP5)."*

appropriate skills in delivering such instruction.

*2.2.2. Differentiated learning in higher education*

This method of teaching (and learning) is quite popular at the K-12 level, despite some inevitable critics [15]. However, it is yet to gain popularity and commonality in higher and graduate level education. Much of this is to do with the fact that the original Piagetian theory concluded formal operational thinking by age 15, and hence there was no need for differentiated learning in higher education settings, since *all* students would be performing at the same intellectual level of thinking. More recent post-formal thinking levels, and an acceptance of different rates of thinking development in all learners, strongly dictate the necessity to continue differentiated learning into the higher education sector.

#### *2.2.1. Differentiated learning in K-12 education*

Differentiated learning is described by a number of key characteristics by several researchers in the field [16–23], and these have been further summarized into five key differentiation principles, DP1–DP5 below [24]:


For concrete operational thinkers, the educator would likely recap prior core knowledge before beginning a new topic, and identify the types of activities that students prefer to assist their learning (DP1). When teaching the key concepts of the topic, the educator would incorporate variety in the activities, but would provide strong guidance and instructional teaching regardless of activity being undertaken (DP2). Problem-solving and critical thinking would be explicitly demonstrated to the students to enable them to follow similar patterns when solving problems on their own (DP3). Group activities would feature strongly in the learning, however in the early stages, students would learn "how to work in groups" more so than relying specifically on group tasks to promote further learning (DP4). Finally, the educator would provide tasks that competent learners within this thinking category could successfully complete unaided, but the vast majority of tasks would be those following pre-specified steps.

By contrast, for formal operational thinkers, the educator would create opportunities for learners to be more responsible for their own learning. For example, while he/she would still identify the existing knowledge of the learners, review of the core knowledge would be up to the student (DP1) and, although the key concepts would still be taught in multiple ways, there would be less dependence on the instructional approach, providing more freedom for students to explore abstract problems (DP2). Challenging tasks would rely on students' prior mastery of problem-solving skills, concentrating more on developing adaptations of these skills to non-routine problems (DP3). Collaborative tasks with other students would see the students now begin to rely on each other to add to existing knowledge, having now mastered the key functioning of a team (DP4). Independence would be demonstrated when learners rely on their own problem-solving skills, and those of their peers, to independently work problems and make sense of more abstract ones as well (DP5).

A detailed study by Valiandes [22] was conducted in 13 Cypriot primary schools, covering 479 fourth-grade students (average age 9 years) and 24 teachers. The students were functional at the pre-operational and concrete operational thinking stages of Piaget. An important aspect of this study was the in-depth support given to the teachers to adequately train them in differentiated teaching strategies. Students were tested on literacy skills, and post-test results were significantly better for students participating in differentiated learning than the control group, which had largely instructional-based learning. Typical observations of differentiated instruction included noting the time spent by the teacher (a) commenting on student general behavior; (b) providing additional examples; (c) direct teaching/asking questions; and (d) providing student guidelines for work. Other observations included identifying the degree of activity variation; providing personalized support to students; providing learning opportunities to students of all readiness levels; time for students to reflect on basic knowledge and skills, or prerequisite knowledge; prioritizing order of activities; accomplishing lesson objectives; and providing differentiated homework. Many of these observations fit well into the DP in the concrete operational level. As a result of this in-depth study, differentiated practices were described as [22]:

*"instruction planning based on constructivism learning theory, the hierarchical order of learning activities (DP1), the maximization of students' active participation in the learning process, the reduction of teachers' talking time during teaching (DP2), the variation of activities, the opportunity for students to work at their own pace, the personalized support that students receive (DP3), the differentiation of activities according to students' interests and learning profile (DP4), and the continuous evaluation of students' achievement with a simultaneous and ongoing evaluation of the effectiveness of the learning process (DP5)."*

The above quote has been interlaced with the identification of the five DPs as explained earlier, to demonstrate that these principles broadly cover many descriptions of differentiated practices. This example shows both the effectiveness of differentiated instruction at (mostly) the concrete operational level, as well as the importance of fully equipping teachers with the appropriate skills in delivering such instruction.

#### *2.2.2. Differentiated learning in higher education*

differentiated homework sheets; group work to conduct more open-ended problems; inquirybased learning tasks; experiential learning tasks; active learning; and many more. Each of these tasks, if carefully constructed, provides opportunities for learners to actively engage with the material, promoting depth of learning within their zone of proximal development (ZPD) [14],

This method of teaching (and learning) is quite popular at the K-12 level, despite some inevitable critics [15]. However, it is yet to gain popularity and commonality in higher and graduate level education. Much of this is to do with the fact that the original Piagetian theory concluded formal operational thinking by age 15, and hence there was no need for differentiated learning in higher education settings, since *all* students would be performing at the same intellectual level of thinking. More recent post-formal thinking levels, and an acceptance of different rates of thinking development in all learners, strongly dictate the necessity to con-

Differentiated learning is described by a number of key characteristics by several researchers in the field [16–23], and these have been further summarized into five key differentiation

For concrete operational thinkers, the educator would likely recap prior core knowledge before beginning a new topic, and identify the types of activities that students prefer to assist their learning (DP1). When teaching the key concepts of the topic, the educator would incorporate variety in the activities, but would provide strong guidance and instructional teaching regardless of activity being undertaken (DP2). Problem-solving and critical thinking would be explicitly demonstrated to the students to enable them to follow similar patterns when solving problems on their own (DP3). Group activities would feature strongly in the learning, however in the early stages, students would learn "how to work in groups" more so than relying specifically on group tasks to promote further learning (DP4). Finally, the educator would provide tasks that competent learners within this thinking category could successfully complete unaided, but the vast majority of tasks would be those following pre-specified steps. By contrast, for formal operational thinkers, the educator would create opportunities for learners to be more responsible for their own learning. For example, while he/she would still identify the existing knowledge of the learners, review of the core knowledge would be up to the student (DP1) and, although the key concepts would still be taught in multiple ways,

all the while challenging them to the next level of thinking.

6 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

tinue differentiated learning into the higher education sector.

**1.** Understand student need and preferred learning modes.

**4.** Foster collaboration between students and their faculty. **5.** Create independent learners and ownership of learning.

**2.** Focus on key concepts and provide multiple approaches to learning. **3.** Provide challenging learning experiences within each student's ZPD.

*2.2.1. Differentiated learning in K-12 education*

principles, DP1–DP5 below [24]:

Educators of lower classmen in the higher education sector may encounter significant numbers of students operating in the concrete or formal operational levels, and hence differentiating the instruction would follow a similar pattern to those outlined above in Section 2.2.1. This is adequately demonstrated by a few reported studies of freshmen level mathematics classes [25, 26]. In the study by Chamberlin and Powers [25], freshmen mathematics students taking "number and operations" were studied. Data were initially gathered on the students to judge their interests and preferred learning modes (DP1). Graduated activities were then implemented, each aimed at differing levels of intellectual readiness based on an analysis of the students' pre-requisite core knowledge. These activities included class extension activities, student work groups, student choice in activities, direct instructional modification as required, differentiated homework sheets, and formative/summative testing (DP2–DP4). Analysis of the pre- and post-testing indicated that students receiving differentiated instruction improved by 1.7 points out of 8, while the control group improved by only 0.3 points. It was concluded that the differentiated learning was successful, and mastery of required skills and independence in performance was observed (DP5) at the thinking operational levels of the students. The range of activities particularly identifies students working in the concrete and formal operation stages.

framework as it commonly stands in K-12 education (concrete and formal operations only), and then extended for later-year learners (post-formal thinking). Note that sensorimotor and pre-operational levels have been left blank, given that the focus is on higher educational training. Next to DP5 for each thinking level is a description of characteristics a learner will display once they have achieved independence with learning *at that thinking level*. This figure is to be interpreted as a continuum for both thinking and learning skills, and the characteristics described will alert the educator that the learner is ready to progress to the next level of intellectual thinking. The ages and approximate school year levels next to Piagetian and pP thinking stages are intended as a guide only, and are *very fluid*, with a particular reminder of the many outside influences that affect the rate of progression through these stages. This is true also for progressing through the various learning stages within each thinking level. Finally, the vertical axis to the right of the figure *loosely* assigns the different levels of Bloom's taxonomy, which also covers different thinking stages from lower to

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To the best of the author's knowledge, Appendix A is believed to be the first attempt by linking intellectual thinking skills at the higher and graduate education levels with a differentiation framework. Extensions to this level have not typically been considered to this depth. Several school systems provide differentiated curricula in all mainstream classes to grade 10, and then assume a more "one-size-fits-all" approach beyond this level (e.g., [27]). This is despite the general acceptance that Piagetian rates of progression are fluid, and competence in formal operational thinking by age 16 is no longer expected in *all* students. Hence, Appendix A is an

Bloom's taxonomy was originally published in 1956, and later developed and modified in 2002 by Krathwohl [28]. This most common form of Bloom's taxonomy is the cognitive domain, represented by lower order thinking (LOT) and higher order thinking (HOT) activities. However, two other domains have also been developed, which include the affective

The cognitive domain can be used in a number of ways by the educator, and indeed learners, to fully master a topic of interest. In Appendix A, it can be seen that the six main cognitive stages of Bloom's taxonomy (LOT: remember, understand, and apply; and HOT: analyze, evaluate, and create) are loosely matched with the Piagetian and pP developmental thinking skills. In this way, the broad matching of categories indicates that it takes many years to move through the LOT and HOT cognitive domains suggested by Bloom, showing that progressive intellectual development is required to access higher levels of Bloom's taxonomy. This taxonomy is progressive in a similar manner as Piagetian thinking skills, and demonstrates that

On a much smaller scale, an educator may commonly use this taxonomy for a particular topic or even a single class being presented to learners. Tasks will be organized such that early activities require students to remember and understand new terminology and concepts, and later ones will provide opportunity in applying these concepts to progressively more difficult

domain (interests, attitudes, and values) and the psychomotor domain (motor skills).

attempt to provide additional differentiation assistance from grade 10.

one must be comfortable with LOT before accessing HOT.

higher order thinking.

**2.3. Bloom's taxonomy**

What might a differentiated classroom look like for upper classmen, or learners intellectually ready to undertake relativistic and/or dialectical thinking? In these two stages, the learner would gradually take on a more active role in their learning skill development through the five DPs. While these principles remain similar, the learner would become more active in participating and directing the learning, with the educator playing a guidance role. In relativistic thinking stages, the educator may still outline the required pre-requisite knowledge but would expect the student to revise accordingly. The educator would still deliver key concepts in multiple ways, but the learner would also be expected to experiment with different modes of learning, in order to maximize knowledge retention. In DP3–DP4, the activities presented to the students would begin at lower level (concrete thinking) to confirm knowledge of new concepts, but would progress to include abstract and ill-defined problems that present different solution paths.

In the dialectical thinking stage, the learner would take an even more active role in understanding his/her needs at the beginning of a new topic, and deciphering the key concepts of that topic. This level of learning/instruction within a formal institution would be seen in graduate level classes, advanced students in lower level classes, or research studies. As such, the activities in DP3 and DP4 would be learner-initiated (possibly at the initial direction of the educator), where learners would delve in depth into the chosen topic and make sense of the apparent contradictions presented. Students may eventually come to the realization of new knowledge as a result of these apparent anomalies.

In the final creative thinking stage, the learner has essentially mastered all previous stages of intellectual thinking development and can pursue a new field of interest at depth, and with the ability to creatively synthesize new knowledge. This would typically be seen with an advanced PhD student and/or experienced researchers, as well as expert industry professionals.

The extension of differentiated teaching and learning to the later stages of post-formal thinking is graphically displayed in Appendix A. The horizontal axis describes a progression in *differentiated learning skills* (DP1–DP5), while the vertical axis describes a progression in *thinking skills* (Piagetian and pP thinking stages). This arrangement shows the differentiation framework as it commonly stands in K-12 education (concrete and formal operations only), and then extended for later-year learners (post-formal thinking). Note that sensorimotor and pre-operational levels have been left blank, given that the focus is on higher educational training. Next to DP5 for each thinking level is a description of characteristics a learner will display once they have achieved independence with learning *at that thinking level*. This figure is to be interpreted as a continuum for both thinking and learning skills, and the characteristics described will alert the educator that the learner is ready to progress to the next level of intellectual thinking. The ages and approximate school year levels next to Piagetian and pP thinking stages are intended as a guide only, and are *very fluid*, with a particular reminder of the many outside influences that affect the rate of progression through these stages. This is true also for progressing through the various learning stages within each thinking level. Finally, the vertical axis to the right of the figure *loosely* assigns the different levels of Bloom's taxonomy, which also covers different thinking stages from lower to higher order thinking.

To the best of the author's knowledge, Appendix A is believed to be the first attempt by linking intellectual thinking skills at the higher and graduate education levels with a differentiation framework. Extensions to this level have not typically been considered to this depth. Several school systems provide differentiated curricula in all mainstream classes to grade 10, and then assume a more "one-size-fits-all" approach beyond this level (e.g., [27]). This is despite the general acceptance that Piagetian rates of progression are fluid, and competence in formal operational thinking by age 16 is no longer expected in *all* students. Hence, Appendix A is an attempt to provide additional differentiation assistance from grade 10.

#### **2.3. Bloom's taxonomy**

classes [25, 26]. In the study by Chamberlin and Powers [25], freshmen mathematics students taking "number and operations" were studied. Data were initially gathered on the students to judge their interests and preferred learning modes (DP1). Graduated activities were then implemented, each aimed at differing levels of intellectual readiness based on an analysis of the students' pre-requisite core knowledge. These activities included class extension activities, student work groups, student choice in activities, direct instructional modification as required, differentiated homework sheets, and formative/summative testing (DP2–DP4). Analysis of the pre- and post-testing indicated that students receiving differentiated instruction improved by 1.7 points out of 8, while the control group improved by only 0.3 points. It was concluded that the differentiated learning was successful, and mastery of required skills and independence in performance was observed (DP5) at the thinking operational levels of the students. The range of activities particularly identifies students working in the concrete

8 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

What might a differentiated classroom look like for upper classmen, or learners intellectually ready to undertake relativistic and/or dialectical thinking? In these two stages, the learner would gradually take on a more active role in their learning skill development through the five DPs. While these principles remain similar, the learner would become more active in participating and directing the learning, with the educator playing a guidance role. In relativistic thinking stages, the educator may still outline the required pre-requisite knowledge but would expect the student to revise accordingly. The educator would still deliver key concepts in multiple ways, but the learner would also be expected to experiment with different modes of learning, in order to maximize knowledge retention. In DP3–DP4, the activities presented to the students would begin at lower level (concrete thinking) to confirm knowledge of new concepts, but would progress to include abstract and ill-defined problems that present differ-

In the dialectical thinking stage, the learner would take an even more active role in understanding his/her needs at the beginning of a new topic, and deciphering the key concepts of that topic. This level of learning/instruction within a formal institution would be seen in graduate level classes, advanced students in lower level classes, or research studies. As such, the activities in DP3 and DP4 would be learner-initiated (possibly at the initial direction of the educator), where learners would delve in depth into the chosen topic and make sense of the apparent contradictions presented. Students may eventually come to the realization of new

In the final creative thinking stage, the learner has essentially mastered all previous stages of intellectual thinking development and can pursue a new field of interest at depth, and with the ability to creatively synthesize new knowledge. This would typically be seen with an advanced PhD student and/or experienced researchers, as well as expert industry

The extension of differentiated teaching and learning to the later stages of post-formal thinking is graphically displayed in Appendix A. The horizontal axis describes a progression in *differentiated learning skills* (DP1–DP5), while the vertical axis describes a progression in *thinking skills* (Piagetian and pP thinking stages). This arrangement shows the differentiation

and formal operation stages.

ent solution paths.

professionals.

knowledge as a result of these apparent anomalies.

Bloom's taxonomy was originally published in 1956, and later developed and modified in 2002 by Krathwohl [28]. This most common form of Bloom's taxonomy is the cognitive domain, represented by lower order thinking (LOT) and higher order thinking (HOT) activities. However, two other domains have also been developed, which include the affective domain (interests, attitudes, and values) and the psychomotor domain (motor skills).

The cognitive domain can be used in a number of ways by the educator, and indeed learners, to fully master a topic of interest. In Appendix A, it can be seen that the six main cognitive stages of Bloom's taxonomy (LOT: remember, understand, and apply; and HOT: analyze, evaluate, and create) are loosely matched with the Piagetian and pP developmental thinking skills. In this way, the broad matching of categories indicates that it takes many years to move through the LOT and HOT cognitive domains suggested by Bloom, showing that progressive intellectual development is required to access higher levels of Bloom's taxonomy. This taxonomy is progressive in a similar manner as Piagetian thinking skills, and demonstrates that one must be comfortable with LOT before accessing HOT.

On a much smaller scale, an educator may commonly use this taxonomy for a particular topic or even a single class being presented to learners. Tasks will be organized such that early activities require students to remember and understand new terminology and concepts, and later ones will provide opportunity in applying these concepts to progressively more difficult tasks. The depth of LOT and HOT will vary depending on the intellectual thinking level of the learner (Piagetian and pP), and hence the ability to "create" new knowledge for any given topic will be limited by the depth of thinking capability of the learner.

and act. This curiosity-driven learning increases engagement and interest of students, helping them to achieve learning independence. Similarities can be observed with the Piagetian and pP thinking stages, where the earlier ones are concerned with experience (touch, visual, smell, etc.); the intermediate stages develop reflection and thinking about observations; and the final

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As an activity in an educator's toolkit, this theory can be shown as a small in-class thinking task to explain an observation; as a longer-term real-life assignment or design project; or as a formal experimental class. Such activities could form the instruction over DP2–DP4, depending on depth and time constraints. To avoid confusion, an *experimental class* is a subset of

Following the differentiation framework and interactions with Piagetian and pP theories, as well as Bloom's taxonomy, the educator must start at DP1 by "knowing the student needs." Knowing these needs will determine which Piagetian thinking skills primarily make up the laboratory class. For lower classmen, the students would typically be operating over a range of concrete, formal, and relativistic, while for upper classmen, the latter two would be more common, perhaps with some operating at dialectical thinking stage. However, each class is unique, and this must be determined by the educators running the theory classes, and dis-

Having decided on two or three thinking skill levels that best represent the class, the educator will then develop the practical class on a particular unit operation with key learning objectives in mind, mostly within the DP2–DP4 range. Within this range, the level of difficulty of the tasks increases, from providing conceptual knowledge of the experiment through to applying this knowledge, and then analyzing and evaluating the resulting data. This is akin to the middle part of a Bloom's taxonomy cycle. DP5, where students practice independence, may be incorporated by a final task that requires the students to come up with a part or all of an extended investigation from their experimental task. This will build on their knowledge gained within the previous DPs, and will equip them with independent skills *within* their thinking skill range. When developing the experimental class, the educator should also keep in mind the experiential learning cycle just described, allowing adequate opportunity for reflection and cognitive thinking after an observation, followed by tasks that allow the

A common method to incorporate different levels of thinking operational ability is to include choice between the required tasks. Those operating at higher thinking levels will typically choose the tasks that satisfy their need and hunger for learning, while those at lower levels will choose tasks more suitable for them. Rarely do students choose "the easy way out," as discovered by Hutton-Prager and O'Haver [30], and the vast majority of students genuinely

A planning template is shown in **Table 1**, demonstrating how the educational framework and pedagogies can be used to develop a meaningful laboratory class. The final format to the

stages promote action of a learner to discover new information for her/himself.

*experiential learning*, and not all experiential activities need to include experiments.

cussed with the educators running the practical classes (as is most usually the case).

**3.2. Developing an experimental activity in chemical engineering**

students to actively use their newly gained knowledge.

engage with material by challenging themselves.

Fully independent learners operating in the creative domain of post-formal thinking will have developed their own methods of learning a new topic to expert level, based on a culmination of all previous learning they have experienced to that point. Even at this fully independent thinking stage, a learner to a new topic of interest will still need to progress through LOT and HOT in order to become sufficiently competent in a new field. These learners will have the skills to generate *actual* new knowledge, as opposed to learners operating at lower thinking skill levels, who will create new knowledge *for them* in their overall development. This is a key difference between a researcher or industry expert generating new knowledge and a learner becoming competent in their field.

The five broad DP also to some degree have links with Bloom's LOT and HOT. For example, in DP1 and DP2, the teaching and learning focus is on understanding existing knowledge and learning concepts of a new topic. In DP3 and DP4, the focus shifts to applying this newly gained knowledge to progressively more difficult tasks, which require some degree of the analysis and evaluation of the assigned problem. Finally, in DP5, independence of the learner within their current thinking skill category is reached when they are able to become fully competent with the range of tasks required, creating new knowledge *for them*.

To recap, Bloom's taxonomy can be used as a tool to (a) demonstrate life-long learning; (b) frame the teaching of a given topic; and (c) frame the learning of a given topic for more independent learners.
