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Monday, June 26, 2023

Photochemistry

From Wikipedia, the free encyclopedia
 
Photochemical immersion well reactor (50 mL) with a mercury-vapor lamp.

Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400 nm), visible light (400–750 nm) or infrared radiation (750–2500 nm).

In nature, photochemistry is of immense importance as it is the basis of photosynthesis, vision, and the formation of vitamin D with sunlight. It is also responsible for the appearance of DNA mutations leading to skin cancers.

Photochemical reactions proceed differently than temperature-driven reactions. Photochemical paths access high energy intermediates that cannot be generated thermally, thereby overcoming large activation barriers in a short period of time, and allowing reactions otherwise inaccessible by thermal processes. Photochemistry can also be destructive, as illustrated by the photodegradation of plastics.

Concept

Grotthuss–Draper law and Stark–Einstein law

Photoexcitation is the first step in a photochemical process where the reactant is elevated to a state of higher energy, an excited state. The first law of photochemistry, known as the Grotthuss–Draper law (for chemists Theodor Grotthuss and John W. Draper), states that light must be absorbed by a chemical substance in order for a photochemical reaction to take place. According to the second law of photochemistry, known as the Stark–Einstein law (for physicists Johannes Stark and Albert Einstein), for each photon of light absorbed by a chemical system, no more than one molecule is activated for a photochemical reaction, as defined by the quantum yield.

Fluorescence and phosphorescence

When a molecule or atom in the ground state (S0) absorbs light, one electron is excited to a higher orbital level. This electron maintains its spin according to the spin selection rule; other transitions would violate the law of conservation of angular momentum. The excitation to a higher singlet state can be from HOMO to LUMO or to a higher orbital, so that singlet excitation states S1, S2, S3... at different energies are possible.

Kasha's rule stipulates that higher singlet states would quickly relax by radiationless decay or internal conversion (IC) to S1. Thus, S1 is usually, but not always, the only relevant singlet excited state. This excited state S1 can further relax to S0 by IC, but also by an allowed radiative transition from S1 to S0 that emits a photon; this process is called fluorescence.

Jablonski diagram. Radiative paths are represented by straight arrows and non-radiative paths by curly lines.

Alternatively, it is possible for the excited state S1 to undergo spin inversion and to generate a triplet excited state T1 having two unpaired electrons with the same spin. This violation of the spin selection rule is possible by intersystem crossing (ISC) of the vibrational and electronic levels of S1 and T1. According to Hund's rule of maximum multiplicity, this T1 state would be somewhat more stable than S1.

This triplet state can relax to the ground state S0 by radiationless IC or by a radiation pathway called phosphorescence. This process implies a change of electronic spin, which is forbidden by spin selection rules, making phosphorescence (from T1 to S0) much slower than fluorescence (from S1 to S0). Thus, triplet states generally have longer lifetimes than singlet states. These transitions are usually summarized in a state energy diagram or Jablonski diagram, the paradigm of molecular photochemistry.

These excited species, either S1 or T1, have a half empty low-energy orbital, and are consequently more oxidizing than the ground state. But at the same time, they have an electron in a high energy orbital, and are thus more reducing. In general, excited species are prone to participate in electron transfer processes.

Experimental set-up

Photochemical immersion well reactor (750 mL) with a mercury-vapor lamp

Photochemical reactions require a light source that emits wavelengths corresponding to an electronic transition in the reactant. In the early experiments (and in everyday life), sunlight was the light source, although it is polychromatic. Mercury-vapor lamps are more common in the laboratory. Low pressure mercury vapor lamps mainly emit at 254 nm. For polychromatic sources, wavelength ranges can be selected using filters. Alternatively, laser beams are usually monochromatic (although two or more wavelengths can be obtained using nonlinear optics) and LEDs have a relatively narrowband that can be efficiently used, as well as Rayonet lamps, to get approximately monochromatic beams.

Schlenk tube containing slurry of orange crystals of Fe2(CO)9 in acetic acid after its photochemical synthesis from Fe(CO)5. The mercury lamp (connected to white power cords) can be seen on the left, set inside a water-jacketed quartz tube.

The emitted light must of course reach the targeted functional group without being blocked by the reactor, medium, or other functional groups present. For many applications, quartz is used for the reactors as well as to contain the lamp. Pyrex absorbs at wavelengths shorter than 275 nm. The solvent is an important experimental parameter. Solvents are potential reactants and for this reason, chlorinated solvents are avoided because the C–Cl bond can lead to chlorination of the substrate. Strongly absorbing solvents prevent photons from reaching the substrate. Hydrocarbon solvents absorb only at short wavelengths and are thus preferred for photochemical experiments requiring high energy photons. Solvents containing unsaturation absorb at longer wavelengths and can usefully filter out short wavelengths. For example, cyclohexane and acetone "cut off" (absorb strongly) at wavelengths shorter than 215 and 330 nm, respectively.

Photochemistry in combination with flow chemistry

Continuous flow photochemistry offers multiple advantages over batch photochemistry. Photochemical reactions are driven by the number of photons that are able to activate molecules causing the desired reaction. The large surface area to volume ratio of a microreactor maximizes the illumination, and at the same time allows for efficient cooling, which decreases the thermal side products.

Principles

In the case of photochemical reactions, light provides the activation energy. Simplistically, light is one mechanism for providing the activation energy required for many reactions. If laser light is employed, it is possible to selectively excite a molecule so as to produce a desired electronic and vibrational state. Equally, the emission from a particular state may be selectively monitored, providing a measure of the population of that state. If the chemical system is at low pressure, this enables scientists to observe the energy distribution of the products of a chemical reaction before the differences in energy have been smeared out and averaged by repeated collisions.

The absorption of a photon of light by a reactant molecule may also permit a reaction to occur not just by bringing the molecule to the necessary activation energy, but also by changing the symmetry of the molecule's electronic configuration, enabling an otherwise inaccessible reaction path, as described by the Woodward–Hoffmann selection rules. A 2+2 cycloaddition reaction is one example of a pericyclic reaction that can be analyzed using these rules or by the related frontier molecular orbital theory.

Some photochemical reactions are several orders of magnitude faster than thermal reactions; reactions as fast as 10−9 seconds and associated processes as fast as 10−15 seconds are often observed.

The photon can be absorbed directly by the reactant or by a photosensitizer, which absorbs the photon and transfers the energy to the reactant. The opposite process is called quenching when a photoexcited state is deactivated by a chemical reagent.

Most photochemical transformations occur through a series of simple steps known as primary photochemical processes. One common example of these processes is the excited state proton transfer.

Photochemical reactions

Examples of photochemical reactions

Organic photochemistry

Examples of photochemical organic reactions are electrocyclic reactions, radical reactions, photoisomerization and Norrish reactions.

Norrish type II reaction

Alkenes undergo many important reactions that proceed via a photon-induced π to π* transition. The first electronic excited state of an alkene lack the π-bond, so that rotation about the C–C bond is rapid and the molecule engages in reactions not observed thermally. These reactions include cis-trans isomerization, cycloaddition to other (ground state) alkene to give cyclobutane derivatives. The cis-trans isomerization of a (poly)alkene is involved in retinal, a component of the machinery of vision. The dimerization of alkenes is relevant to the photodamage of DNA, where thymine dimers are observed upon illuminating DNA to UV radiation. Such dimers interfere with transcription. The beneficial effects of sunlight are associated with the photochemically induced retro-cyclization (decyclization) reaction of ergosterol to give vitamin D. In the DeMayo reaction, an alkene reacts with a 1,3-diketone reacts via its enol to yield a 1,5-diketone. Still another common photochemical reaction is Howard Zimmerman's di-π-methane rearrangement.

In an industrial application, about 100,000 tonnes of benzyl chloride are prepared annually by the gas-phase photochemical reaction of toluene with chlorine. The light is absorbed by chlorine molecule, the low energy of this transition being indicated by the yellowish color of the gas. The photon induces homolysis of the Cl-Cl bond, and the resulting chlorine radical converts toluene to the benzyl radical:

Cl2 + hν → 2 Cl·
C6H5CH3 + Cl· → C6H5CH2· + HCl
C6H5CH2· + Cl· → C6H5CH2Cl

Mercaptans can be produced by photochemical addition of hydrogen sulfide (H2S) to alpha olefins.

Inorganic and organometallic photochemistry

Coordination complexes and organometallic compounds are also photoreactive. These reactions can entail cis-trans isomerization. More commonly photoreactions result in dissociation of ligands, since the photon excites an electron on the metal to an orbital that is antibonding with respect to the ligands. Thus, metal carbonyls that resist thermal substitution undergo decarbonylation upon irradiation with UV light. UV-irradiation of a THF solution of molybdenum hexacarbonyl gives the THF complex, which is synthetically useful:

Mo(CO)6 + THF → Mo(CO)5(THF) + CO

In a related reaction, photolysis of iron pentacarbonyl affords diiron nonacarbonyl (see figure):

2 Fe(CO)5 → Fe2(CO)9 + CO

Select photoreactive coordination complexes can undergo oxidation-reduction processes via single electron transfer. This electron transfer can occur within the inner or outer coordination sphere of the metal.

Types of photochemical reactions

Here are some different types of photochemical reactions-

  • Photo-dissociation: AB + hν → A* + B*
  • Photo induced rearrangements, isomerization: A + hν → B
  • Photo-Addition: A + B + hν → AB + C
  • Photo-substitution: A + BC + hν → AB + C
  • Photo-redox reaction: A + B + hν → A− + B+

Historical

Although bleaching has long been practiced, the first photochemical reaction was described by Trommsdorff in 1834. He observed that crystals of the compound α-santonin when exposed to sunlight turned yellow and burst. In a 2007 study the reaction was described as a succession of three steps taking place within a single crystal.

Santonin Photochemical reaction.

The first step is a rearrangement reaction to a cyclopentadienone intermediate 2, the second one a dimerization in a Diels–Alder reaction (3) and the third one an intramolecular [2+2]cycloaddition (4). The bursting effect is attributed to a large change in crystal volume on dimerization.

Specialized journals

Learned Societies

International conferences

The organization of these conferences is facilitated by the International Foundation for Photochemistry.

Kirchhoff's circuit laws

From Wikipedia, the free encyclopedia

Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis.

Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits.

Kirchhoff's current law

The current entering any junction is equal to the current leaving that junction. i2 + i3 = i1 + i4

This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:

The algebraic sum of currents in a network of conductors meeting at a point is zero.

Recalling that current is a signed (positive or negative) quantity reflecting direction towards or away from a node, this principle can be succinctly stated as:

where n is the total number of branches with currents flowing towards or away from the node.

Kirchhoff's circuit laws were originally obtained from experimental results. However, the current law can be viewed as an extension of the conservation of charge, since charge is the product of current and the time the current has been flowing. If the net charge in a region is constant, the current law will hold on the boundaries of the region. This means that the current law relies on the fact that the net charge in the wires and components is constant.

Uses

A matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE. The current law is used with Ohm's law to perform nodal analysis.

The current law is applicable to any lumped network irrespective of the nature of the network; whether unilateral or bilateral, active or passive, linear or non-linear.

Kirchhoff's voltage law

The sum of all the voltages around a loop is equal to zero: v1 + v2 + v3 + v4 = 0.

This law, also called Kirchhoff's second law, or Kirchhoff's loop rule, states the following:

The directed sum of the potential differences (voltages) around any closed loop is zero.

Similarly to Kirchhoff's current law, the voltage law can be stated as:

Here, n is the total number of voltages measured.

Derivation of Kirchhoff's voltage law

A similar derivation can be found in The Feynman Lectures on Physics, Volume II, Chapter 22: AC Circuits.

Consider some arbitrary circuit. Approximate the circuit with lumped elements, so that (time-varying) magnetic fields are contained to each component and the field in the region exterior to the circuit is negligible. Based on this assumption, the Maxwell–Faraday equation reveals that

in the exterior region. If each of the components has a finite volume, then the exterior region is simply connected, and thus the electric field is conservative in that region. Therefore, for any loop in the circuit, we find that
where are paths around the exterior of each of the components, from one terminal to another.

Note that this derivation uses the following definition for the voltage rise from to :

However, the electric potential (and thus voltage) can be defined in other ways, such as via the Helmholtz decomposition.

Generalization

In the low-frequency limit, the voltage drop around any loop is zero. This includes imaginary loops arranged arbitrarily in space – not limited to the loops delineated by the circuit elements and conductors. In the low-frequency limit, this is a corollary of Faraday's law of induction (which is one of Maxwell's equations).

This has practical application in situations involving "static electricity".

Limitations

Kirchhoff's circuit laws are the result of the lumped-element model and both depend on the model being applicable to the circuit in question. When the model is not applicable, the laws do not apply.

The current law is dependent on the assumption that the net charge in any wire, junction or lumped component is constant. Whenever the electric field between parts of the circuit is non-negligible, such as when two wires are capacitively coupled, this may not be the case. This occurs in high-frequency AC circuits, where the lumped element model is no longer applicable. For example, in a transmission line, the charge density in the conductor may be constantly changing.

In a transmission line, the net charge in different parts of the conductor changes with time. In the direct physical sense, this violates KCL.

On the other hand, the voltage law relies on the fact that the action of time-varying magnetic fields are confined to individual components, such as inductors. In reality, the induced electric field produced by an inductor is not confined, but the leaked fields are often negligible.

Modelling real circuits with lumped elements

The lumped element approximation for a circuit is accurate at low frequencies. At higher frequencies, leaked fluxes and varying charge densities in conductors become significant. To an extent, it is possible to still model such circuits using parasitic components. If frequencies are too high, it may be more appropriate to simulate the fields directly using finite element modelling or other techniques.

To model circuits so that both laws can still be used, it is important to understand the distinction between physical circuit elements and the ideal lumped elements. For example, a wire is not an ideal conductor. Unlike an ideal conductor, wires can inductively and capacitively couple to each other (and to themselves), and have a finite propagation delay. Real conductors can be modeled in terms of lumped elements by considering parasitic capacitances distributed between the conductors to model capacitive coupling, or parasitic (mutual) inductances to model inductive coupling. Wires also have some self-inductance.

Example

Kirshhoff-example.svg

Assume an electric network consisting of two voltage sources and three resistors.

According to the first law:

Applying the second law to the closed circuit s1, and substituting for voltage using Ohm's law gives:
The second law, again combined with Ohm's law, applied to the closed circuit s2 gives:

This yields a system of linear equations in i1, i2, i3:

which is equivalent to
Assuming
the solution is

The current i3 has a negative sign which means the assumed direction of i3 was incorrect and i3 is actually flowing in the direction opposite to the red arrow labeled i3. The current in R3 flows from left to right.

Experiential learning

From Wikipedia, the free encyclopedia
 
Shimer College students learning to cook by cooking, 1942.

Experiential learning (ExL) is the process of learning through experience, and is more narrowly defined as "learning through reflection on doing". Hands-on learning can be a form of experiential learning, but does not necessarily involve students reflecting on their product. Experiential learning is distinct from rote or didactic learning, in which the learner plays a comparatively passive role. It is related to, but not synonymous with, other forms of active learning such as action learning, adventure learning, free-choice learning, cooperative learning, service-learning, and situated learning.

Experiential learning is often used synonymously with the term "experiential education", but while experiential education is a broader philosophy of education, experiential learning considers the individual learning process. As such, compared to experiential education, experiential learning is concerned with more concrete issues related to the learner and the learning context.

The general concept of learning through experience is ancient. Around 350 BC, Aristotle wrote in the Nicomachean Ethics "for the things we have to learn before we can do them, we learn by doing them". But as an articulated educational approach, experiential learning is of much more recent vintage. Beginning in the 1970s, David A. Kolb helped develop the modern theory of experiential learning, drawing heavily on the work of John Dewey, Kurt Lewin, and Jean Piaget.

Experiential learning has significant teaching advantages. Peter Senge, author of The Fifth Discipline (1990), states that teaching is of utmost importance to motivate people. Learning only has good effects when learners have the desire to absorb the knowledge. Therefore, experiential learning requires the showing of directions for learners.

Experiential learning entails a hands-on approach to learning that moves away from just the teacher at the front of the room imparting and transferring their knowledge to students. It makes learning an experience that moves beyond the classroom and strives to bring a more involved way of learning.

Kolb's experiential learning model

Experiential learning focuses on the learning process for the individual. One example of experiential learning is going to the zoo and learning through observation and interaction with the zoo environment, as opposed to reading about animals from a book. Thus, one makes discoveries and experiments with knowledge firsthand, instead of hearing or reading about others' experiences. Likewise, in business school, internship, and job-shadowing, opportunities in a student's field of interest can provide valuable experiential learning which contributes significantly to the student's overall understanding of the real-world environment.

A third example of experiential learning involves learning how to ride a bike, a process which can illustrate the four-step experiential learning model (ELM) as set forth by Kolb and outlined in Figure 1 below. Following this example, in the "concrete experience" stage, the learner physically interacts with the bike in the "here and now". This experience forms "the basis for observation and reflection" and the learner has the opportunity to consider what is working or failing (reflective observation), formulate a generalized theory or idea about riding a bike in general (abstract conceptualization) and to think about ways to improve on the next attempt made at riding (active experimentation). Every new attempt to ride is informed by a cyclical pattern of previous experience, thought and reflection.

Figure 1 – David Kolb's Experiential Learning Model (ELM)


Concrete Experience
Active Experimentation


Reflective Observation

Abstract Conceptualization

Elements

Experiential learning can occur without a teacher and relates solely to the meaning-making process of the individual's direct experience. However, though the gaining of knowledge is an inherent process that occurs naturally, a genuine learning experience requires certain elements. According to Kolb, knowledge is continuously gained through both personal and environmental experiences. Kolb states that in order to gain genuine knowledge from an experience, the learner must have four abilities:

  • The learner must be willing to be actively involved in the experience;
  • The learner must be able to reflect on the experience;
  • The learner must possess and use analytical skills to conceptualize the experience; and
  • The learner must possess decision making and problem solving skills in order to use the new ideas gained from the experience.

Implementation

Experiential learning requires self-initiative, an "intention to learn" and an "active phase of learning". Kolb's cycle of experiential learning can be used as a framework for considering the different stages involved. Jennifer A. Moon has elaborated on this cycle to argue that experiential learning is most effective when it involves: 1) a "reflective learning phase" 2) a phase of learning resulting from the actions inherent to experiential learning, and 3) "a further phase of learning from feedback". This process of learning can result in "changes in judgment, feeling or skills" for the individual and can provide direction for the "making of judgments as a guide to choice and action".

Most educators understand the important role experience plays in the learning process. The role of emotion and feelings in learning from experience has been recognised as an important part of experiential learning. While those factors may improve the likelihood of experiential learning occurring, it can occur without them. Rather, what is vital in experiential learning is that the individual is encouraged to directly involve themselves in the experience, and then to reflect on their experiences using analytic skills, in order that they gain a better understanding of the new knowledge and retain the information for a longer time.

Reflection is a crucial part of the experiential learning process, and like experiential learning itself, it can be facilitated or independent. Dewey wrote that "successive portions of reflective thought grow out of one another and support one another", creating a scaffold for further learning, and allowing for further experiences and reflection. This reinforces the fact that experiential learning and reflective learning are iterative processes, and the learning builds and develops with further reflection and experience. Facilitation of experiential learning and reflection is challenging, but "a skilled facilitator, asking the right questions and guiding reflective conversation before, during, and after an experience, can help open a gateway to powerful new thinking and learning". Jacobson and Ruddy, building on Kolb's four-stage Experiential Learning Model and Pfeiffer and Jones's five stage Experiential Learning Cycle, took these theoretical frameworks and created a simple, practical questioning model for facilitators to use in promoting critical reflection in experiential learning. Their "5 Questions" model is as follows:

  • Did you notice?
  • Why did that happen?
  • Does that happen in life?
  • Why does that happen?
  • How can you use that?

These questions are posed by the facilitator after an experience, and gradually lead the group towards a critical reflection on their experience, and an understanding of how they can apply the learning to their own life. Although the questions are simple, they allow a relatively inexperienced facilitator to apply the theories of Kolb, Pfeiffer, and Jones, and deepen the learning of the group.

While it is the learner's experience that is most important to the learning process, it is also important not to forget the wealth of experience a good facilitator also brings to the situation. However, while a facilitator, or "teacher", may improve the likelihood of experiential learning occurring, a facilitator is not essential to experiential learning. Rather, the mechanism of experiential learning is the learner's reflection on experiences using analytic skills. This can occur without the presence of a facilitator, meaning that experiential learning is not defined by the presence of a facilitator. Yet, by considering experiential learning in developing course or program content, it provides an opportunity to develop a framework for adapting varying teaching/learning techniques into the classroom.

In schools

Experiential learning is supported in different school organizational models and learning environments.

  • Hyper Island is a global, constructivist school originally from Sweden, with a range of school and executive education programs grounded in experience-based learning, and with reflection taught as key skill to learn for life.
  • THINK Global School is a four-year traveling high school that holds classes in a new country each term. Students engage in experiential learning through activities such as workshops, cultural exchanges, museum tours, and nature expeditions.
  • The Dawson School in Boulder, Colorado, devotes two weeks of each school year to experiential learning, with students visiting surrounding states to engage in community service, visit museums and scientific institutions, and engage in activities such as mountain biking, backpacking, and canoeing.
  • In the ELENA-Project, the follow-up project of "animals live", experiential learning with living animals will be developed. Together with project partners from Romania, Hungary and Georgia, the Bavarian Academy of Nature Conservation and Landscape Management in Germany brings living animals in the lessons of European schools. The aim is to brief children for the context of the biological diversity and to support them to develop ecologically oriented values.
  • Loving High School in Loving, New Mexico, publishes career and technical education opportunities for students. These include internship for students who are interested in science, STEM majors, or architecture. The school is making good connections with local businesses, which helps students get used to working in such environments.
  • Chicago Public Schools operates eight early college STEM high schools through its Early College STEM School Initiative. The eight high schools offer four-years of computer science classes to every student. Additionally, students are able to earn college credits from local community colleges. Each school partners with a technology company which offers students internships and mentors from the company to expose students to jobs in STEM fields.
  • Robert H. Smith School of Business offers select undergraduate students a year-round advanced course whereby students conduct financial analyses and security trades to manage real investment dollars in the Lemma Senbet Fund.
  • Nonprofits such as Out Teach, Life Lab, Nature Explore, and the National Wildlife Federation, provide training for teachers on how to use outdoor spaces for experiential learning.
  • Many European schools take part in intercultural educational programs, such as the European Youth Parliament, which uses experience-based learning to promote intercultural understanding among young students, through indoor and outdoor activities, discussions and debates.
  • CertificationPoint connects work to learning by helping students gain real-world work experience and experiential knowledge within a mentored project-based learning environment.
  • Project-based learning gives a structure and process to teachers, through which they can teach students to solve real-life situations. In PBL teachers ensure that students collect information from various information sources.

In business education

As higher education continues to adapt to new expectations from students, experiential learning in business and accounting programs has become more important. For example, Clark & White (2010) point out that "a quality university business education program must include an experiential learning component". With reference to this study, employers note that graduating students need to build skills in "professionalism" – which can be taught via experiential learning. Students value this learning as much as industry.

Learning styles also impact business education in the classroom. Kolb positions four learning styles, Diverger, Assimilator, Accommodator and Converger, atop the Experiential Learning Model, using the four experiential learning stages to carve out "four quadrants", one for each learning style. An individual's dominant learning style can be identified by taking Kolb's Learning Style Inventory (LSI). Robert Loo (2002) undertook a meta-analysis of 8 studies which revealed that Kolb's learning styles were not equally distributed among business majors in the sample. More specifically, results indicated that there appears to be a high proportion of assimilators and a lower proportion of accommodators than expected for business majors. Not surprisingly, within the accounting sub-sample there was a higher proportion of convergers and a lower proportion of accommodators. Similarly, in the finance sub-sample, a higher proportion of assimilators and lower proportion of divergers was apparent. Within the marketing sub-sample there was an equal distribution of styles. This would provide some evidence to suggest that while it is useful for educators to be aware of common learning styles within business and accounting programs, they should be encouraging students to use all four learning styles appropriately and students should use a wide range of learning methods.

Professional education applications, also known as management training or organizational development, apply experiential learning techniques in training employees at all levels within the business and professional environment. Interactive, role-play based customer service training is often used in large retail chains. Training board games simulating business and professional situations such as the Beer Distribution Game used to teach supply chain management, and the Friday Night at the ER game used to teach systems thinking, are used in business training efforts.

In business

Experiential business learning is the process of learning and developing business skills through the medium of shared experience. The main point of difference between this and academic learning is more “real-life” experience for the recipient.

This may include for example, learning gained from a network of business leaders sharing best practice, or individuals being mentored or coached by a person who has faced similar challenges and issues, or simply listening to an expert or thought leader in current business thinking.

Providers of this type of experiential business learning often include membership organisations who offer product offerings such as peer group learning, professional business networking, expert/speaker sessions, mentoring and/or coaching.

Comparisons

Experiential learning is most easily compared with academic learning, the process of acquiring information through the study of a subject without the necessity for direct experience. While the dimensions of experiential learning are analysis, initiative, and immersion, the dimensions of academic learning are constructive learning and reproductive learning. Though both methods aim to instill new knowledge in the learner, academic learning does so through more abstract, classroom-based techniques, whereas experiential learning actively involves the learner in a concrete experience.

Benefits

  • Experience real world: For example, students who major in Chemistry may have chances to interact with the chemical environment. Learners who have a desire to become businesspeople will have the opportunity to experience the manager position.
  • Improved on-the-job performance: For example, municipal bus drivers trained via high-fidelity simulation training (instead of just classroom training) showed significant decreases in accidents and fuel consumption.
  • Opportunities for creativity: There is always more than one solution for a problem in the real world. Students will have a better chance to learn that lesson when they get to interact with real life experiences.

Representation of a Lie group

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Representation_of_a_Lie_group...