Variational Theory Research Articles

Variation theory as a teaching theory in the theatre classroom

PurposeThe paper presents and discusses an example of findings from a research project. Filmed material from teaching situations in theatre has been the starting point for analysing and planning similar teaching situations in research lessons, where variation theory was used. The aim of using variation theory is to develop teaching practices in the school subject of theatre at upper secondary school level in Sweden.Design/methodology/approachIn the article, one example from the last part of a three-step research project design is discussed. In the third part of the design five research lessons, based on variation theory, were conducted. The starting point for planning the research lessons was teaching situations called didactic interventions, when the teacher interrupts the theatre rehearsals of a stage production and gives response on the student´s acting. The specific situations are used when planning five research lessons based on variation theory. In this paper, one example from one of the research lessons is presented, exemplifying how variation theory has been applied.FindingsThe example shows how variation theory was used in analysing and facilitating teaching in the classroom. The findings suggest that teachers can use variation theory as a way to strengthen the student’s experience of specified objects of learning, in this case, interplay in acting. Another conclusion is that variation theory is helpful when planning whole class teaching situations in the school subject of theatre.Originality/valueThis paper fulfils an identified need to study how to develop teaching practices in the school subject of theatre.

A translation-matched, experimental comparison of three types of wh-island effects in Spanish and English

According to the historical empirical consensus in the field, wh-argument extraction from embedded wh-questions gives rise to island effects in English, but not in Spanish. This observation – which was important for the development of a parameters-based theory of cross-linguistic variation in islands – has recently been challenged by experimental studies showing wh-island effects in both languages. However, these studies typically employ different materials and experimental conditions between languages, limiting direct comparison. Our study addresses this limitation by testing wh-islands in both English and Spanish with translation-matched materials. We present twelve acceptability judgment experiments with approximately 100 participants per experiment. In each language, we examine wh-argument extraction from three wh-clause types (introduced by whether, why and when) under two matrix verb types (know and ask), amounting to six wh-islands that are relevant to assess the reported contrasts. We test (i) for the presence or absence of wh-island effects in the two languages, (ii) for a gradient contrast in effect size, and (iii) for evidence of increased individual variation in Spanish as compared to English. We find (i) that wh-island effects are present in both English and Spanish, (ii) that they are rather large in both languages and larger in Spanish for most wh-island types, and (iii) that Spanish does not show more individual variation in wh-island effects than English. Our results speak against the cross-linguistic contrast as originally proposed, suggesting that its use as evidence for theories that encode cross-linguistic variation in wh-island effects might need to be reconsidered.

Quantum Chemistry Study on Cl-Initiated Reactions of 2-Chloropropane and 2-Methylpropanoyl Halogen (Cl, Br, F): Mechanism, Kinetics, and Atmospheric Implications.

Halogenated volatile organic compounds (HVOCs) pose significant bioaccumulative and toxicological risks, necessitating effective strategies for their removal. Here, we show, through a computational study employing density functional theory and coupled cluster methods, the detailed mechanism and kinetic properties of Cl-initiated degradation reactions of 2-chloropropane (2-CP, (CH3)2CHCl) and 2-methylpropanoyl halide ((CH3)2CHCOX, X = Cl, Br, F). The reaction rate constants of all the channels were calculated by the canonical variational transition state theory (CVT) with the correction of the small curvature tunneling effect (SCT) at 200-1000 K. The subsequent transformation pathways of the major radical products of (CH3)2CHCl and (CH3)2CHCOCl in the presence of O2, NO, and HO2 radical were investigated. The results elucidate the reaction pathways and rate constants, which are in excellent agreement with the experimental data at 296 K. We further explore the atmospheric implications of these reactions by assessing the atmospheric lifetime (τ) and ozone depletion potential (ODP). Additionally, we delve into the aquatic toxicity and bioaccumulation potential of the reactants and their transformation products. This study not only advances our knowledge of the atmospheric fate of halogenated hydrocarbons but also underscores the importance of considering the environmental and toxicological impacts in the development of HVOC mitigation strategies.

Enhancing Eyringpy: Accurate Rate Constants with Canonical Variational Transition State Theory and the Hindered Rotor Model.

The recrossing effect and hindered rotations can lead to significant inaccuracies in rate constant calculations using transition state theory and the harmonic oscillator approximation. To address these issues, we enhanced Eyringpy, a Python-based computational tool, by integrating the canonical variational transition state theory (CVT) and the hindered rotor model, effectively mitigating the limitations of traditional methods. CVT rate constants are calculated using electronic structure data from nonstationary points along the minimum-energy path. Additionally, we developed an algorithm based on reaction force analysis to autonomously select relevant nonstationary points. Torsions are modeled using one-dimensional hindered rotor approaches proposed by Pitzer-Gwinn and Ayala-Schlegel.

Kinetic Study on the H-Abstraction Reactions from 1-Nitropropane by H and OH Radicals.

To improve the comprehension of the combustion kinetics of 1-nitropropane (1-NP), the H-abstraction reactions from 1-NP by H and OH radicals are theoretically explored using the canonical variational transition-state theory combined with the multistructural torsional anharmonicity and small-curvature tunneling corrections (MS-CVT/SCT). The M08-HX/cc-pVTZ method is adopted for geometry optimizations and frequency calculations due to its effective performance in describing the current reaction systems with an average mean unsigned deviation of 0.95 kcal mol-1 against the benchmark by the high-level DLPNO-CCSD(T)/CBS(T-Q) method. The rate constants for the investigated reactions are calculated using the MS-CVT/SCT method at 200-2000 K, and a good agreement is achieved by comparing our calculations with the available literature data. The rate constant calculations show that the multistructural torsional anharmonicity, variational effect, and tunneling effect have different influences on the H-abstraction reactions 1-NP + H/OH, and the reaction channel at the Cβ position is the most important above the room temperature. With our calculations, a literature combustion kinetic model of 1-NP is revised, and the new model demonstrates improved performance across most conditions. Sensitivity analysis demonstrates that the H-abstraction reaction channel, 1-NP + OH = CH3CHCH2NO2 + H2O, alters the combustion kinetics of 1-NP and plays an important role in controlling its ignition process.

What matters in teaching for students’ learning opportunities of subtraction in the 1–20 number range?

ABSTRACT Not all students in early grades develop efficient strategies for solving subtraction tasks. In this paper, we examine subtraction teaching in the 1–20 number range. We analyzed two first-grade lessons addressing similar subtraction tasks, using variation theory to identify what aspects of the content were foregrounded in the teaching. The analysis showed that both lessons supported the discernment of aspects of subtraction. However, the learning opportunities differed depending on what aspects the students were enabled to discern, the recurrence and variation of the elicited aspects, and how the teachers made the aspects visible by means of representations. The findings highlight how teaching can make it more likely for students to experience aspects of learning necessary to solve subtraction tasks such as 13–5 = _ . Additionally, the findings show how subtraction can be taught to enhance strategies using number relations that are also useful in higher number ranges.

Preschool class pupils’ enhanced subitizing abilities by learning study interventions

PurposeThis study explores variation theory-based interventions’ contribution to enhancing preschoolers’ subitizing abilities during iterative lessons. Results are presented according to low, middle and high achievers, focused on those with prominent challenges.Design/methodology/approachIn total 68 Swedish preschoolers participated. They were randomly assigned to one of the intervention/control groups: 23 mixed design, 24 variation theory design and 21 controls. Data from 59 pupils were analyzed. A learning study with three lesson designs for each intervention group was used in autumn 2022 and spring 2023, respectively. The mixed design met ordinary textbook material and variation theory (VT) group instructions designed by VT during autumn, whereas all met instructions designed by VT in spring. Each group was divided into two subgroups. The controls followed business-as-usual math teaching. Two tests assessed pupils’ results before and after the interventions.FindingsAll groups showed significant improvements between pre- and post-tests. Pupils in the mixed and VT groups developed more knowledge than the controls. The low-achieving group developed the most. The VT group exhibited a more complex pattern of variation and a greater increase than the mixed group. The intervention groups showed a greater improvement in both tests’ results than the controls.Originality/valueThere is agreement on the importance of subitizing abilities as a predictor of future mathematical development; however, lesson design and research on pupils’ development regarding lessons offered are limited.

Mini-review on periodic properties of MEMS oscillators

This paper features a survey of the periodic property of micro-electro-mechanical systems by the homotopy perturbation method, the variational iteration method, the variational theory, He’s frequency formulation, and Taylor series method. Fractal MEMS systems are also introduced, and future prospective is elucidated. The emphasis of this min-review article is put mainly on the developments in last decade, so the references, therefore, are not exhaustive.

Source-Based Writing: Students’ Approaches and Critical Aspects of Learning

This study explores upper-secondary school students’ source-based writing skills and what teachers can focus on to improve these skills. The students who participated were enrolled in university preparatory programmes at a Swedish municipal upper-secondary school. The results are based on 73 texts written by students in the subject Swedish (first-language education) and 11 interviews based on the students’ texts. Before the interviews, I went through the students’ texts and prepared questions about their use of sources. I use phenomenography to describe four different ways of using sources and variation theory to identify four critical aspects of learning this skill. To use sources in the most developed way, students need to be able to discern that: (1) acknowledging sources varies with literacy practice; (2) ideas from sources support arguments in own writing; (3) own ideas are separate from those of others; and (4) sources are compared and evaluated throughout the writing process. These critical aspects can be used to plan the teaching of source-based writing for upper-secondary school students.

Kritiska aspekter för lärande i ekologi – en studie av biologiundervisning inom lärarutbildningen

Based on variation theory, we analyze how a teacher educator in biology enacts the objects of learning (a) how the need for energy and matter is met in different organisms and (b) flows of energy and cycles of matter in ecosystems. The teacher's enactment is then compared with the students' lived objects of learning, as expressed in their written interactions in relation to the teacher's reflection questions. The study concludes that the enacted and lived objects of learning do not always correspond and critical aspects for knowledge development in ecology for the current group of teacher students are identified. Based on the analysis, the study suggests some areas that require special focus in teacher education in ecology. Carbohydrate as a carrier of energy between trophic levels, as well as the conversion of carbohydrate to water and carbon dioxide during cellular respiration, are examples of areas that the study highlights.

Atmospheric Chemistry of Chloroprene Initiated by OH Radicals: Combined Ab Initio/DFT Calculations and Kinetics Analysis.

Chloroprene (CP; CH2═C(Cl)-CH═CH2) is a significant toxic airborne pollutant, often originating from anthropogenic activities. However, the environmental fate of CP is incompletely understood. High level CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ calculations combined with kinetic modeling were employed here to glean new insight into the reaction mechanism, energies, and kinetics of the reaction of CP with OH radical (•OH). We report the energies of four different addition pathways and six different abstraction pathways. The •OH attack on the terminal C1 atom of the =CH2 group (which is directly attached to the =CCl moiety), leading to the formation of HOCH2-•C(Cl)-CH═CH2, was found to be a major path. The barrier height for the formation of the corresponding transition state was found to be -1.9 kcal mol-1 below that of the starting CP + •OH reactants. Rate coefficients were calculated for addition and abstraction pathways involving the CP + •OH reaction under pre-equilibrium approximation conditions, employing a combination of canonical variational transition state theory and small curvature tunneling. The overall rate coefficient for the reaction of CP + •OH at 298 K was found to be 1.4 × 10-10 cm3 molecule-1 s-1. The thermochemistry of the possible channels and atmospheric implications are provided. In addition, the fate of HOCH2-•C(Cl)-CH═CH2 in the presence of 3O2 was investigated. We found the reaction of the CP-derived peroxy radical adduct with HO2 and NO to make contributions to the formation of products such as formaldehyde, HO2 radical, Cl atom, HOCH2C(OOH)(Cl)CH═CH2, HOCH2C(O)Cl, ClC(O)CH═CH2, HOCH2C(O)CH═CH2, and HC(O) radical.

Research on entropy weight variation evaluation method for wind power clusters based on dynamic layered sorting

This paper presents an evaluation method for the entropy-weighting of wind power clusters that comprehensively evaluates the allocation problems of wind power clusters by considering the correlation between indicators and the dynamic performance of weight changes. A dynamic layered sorting allocation method is also proposed. The proposed evaluation method considers the power-limiting degree of the last cycle, the adjustment margin, and volatility. It uses the theory of weight variation to update the entropy weight coefficients of each indicator in real time, and then performs a fuzzy evaluation based on the membership function to obtain intuitive comprehensive evaluation results. A case study of a large-scale wind power base in Northwest China was conducted. The proposed evaluation method is compared with fixed-weight entropy and principal component analysis methods. The results show that the three scoring trends are the same, and that the proposed evaluation method is closer to the average level of the latter two, demonstrating higher accuracy. The proposed allocation method can reduce the number of adjustments made to wind farms, which is significant for the allocation and evaluation of wind power clusters.

Formation of acetonitrile (CH3CN) under cold interstellar, tropospheric and combustion mediums

The knowledge of the formation of gas-phase carcinogenic acetonitrile (CH3CN) is limited in interstellar, troposphere, and combustion mediums; thus, its formation and fate are of great importance for all these gas-phase environments when accessing its toxicity and its wide range of applications. In this work, we propose a mechanism for the formation of CH3CN from the reaction of OH/O2 on ethanimine (CH3CH=NH) using ab initio/Density Functional Theory (DFT) potential energy surface in combination with microcanonical variational transition state theory (µVTST) and Ramsperger–Kassel–Marcus (RRKM)/master equation (ME) simulation to predict the rate constants and branching fraction in the temperature range of 100 K to 1000 K and pressure range of 0.0001 bar to 100 bar. The reaction starts with cis (Z) and trans (E) CH3CH=NH isomer with OH radical followed by spontaneous formation via pre-reactive complex, forming the carbon and nitrogen-centered radicals. The O2 radical then attacks the carbon and nitrogen-centered radicals to form acetonitrile (CH3CN) and HO2 radicals. The results show that N–H and C–H dominate the H-atoms abstraction by OH radicals is similar to its isoelectronic analogous reaction system, i.e., CH3CHO + OH/O2 and CH3CHCH2 + OH/O2 and similar to methanimine (CH2NH) systems. The calculated rate constants for OH-initiated oxidation of CH3CH=NH are in the range of ~ 10–11 cm3 molecule−1 s−1 (at 300 K) and are in very good agreement with previous experimental values of its isoelectronic reaction system. The atmospheric lifetime due to the loss of CH3CHNH by OH radical (10 to 11 h) is in very good agreement with the similar pollutants in the troposphere temperature range between 200 and 320 K. The results indicate that its contribution to global warming is negligible. However, the formation of products such as CH3CN may interact with other atmospheric species, which could lead to the production of potentially hazardous compounds such as cyanogen (N2C2) and hydrogen cyanide (HCN).

Theoretical Kinetics of Radical-Radical Reaction NH2ṄH + ṄH2 and Its Implications for Monomethylhydrazine Pyrolysis Mechanism.

Significant discrepancies were observed between the experiments and the simulations for ṄH2 time-histories in monomethylhydrazine pyrolysis with the robust mechanism proposed by Pascal and Catoire. The rate of formation analyses for ṄH2 indicated the significance of the reaction NH2ṄH + ṄH2 = H2NN + NH3, which has not been well-defined. In this study, ab initio calculations were performed for the theoretical description of the NH2ṄH + ṄH2 chemistry. Most stationary points on the potential energy surface were quantified at the CCSD(T)/CBS//M06-2X/aug-cc-pVTZ level, and the multireference methods were employed for barrier-less reaction and some transition states. The temperature- and pressure-dependent rate coefficients were determined using classical and microcanonical variational transition state theories. Four primary reaction channels were identified as competitive: 1) The H atom abstraction reaction yielding N2H2(T) + NH3, dominating at 1350-3000 K across the 0.001-100 atm pressure range. 2) The H atom abstraction reaction forming N2H2(S) + NH3, dominating at 800-1350 K and competing with the processes of chemical activation and collisional stabilization below 800 K. 3) The chemical-activated reaction resulting in H2NN(S) + NH3, dominating below 800 K at 0.001 atm. 4) The collisional-stabilized recombination reaction leading to N3H5, becoming significant as pressure increases and dominating below 600 and 650 K at 1 and 100 atm, respectively. The implications of newly calculated NH2ṄH + ṄH2 kinetics for the monomethylhydrazine pyrolysis mechanism were evaluated, and updates were implemented. Sensitivity analyses indicated the necessity of additional research efforts to comprehend the dynamics of CH3NH2 unimolecular and N2H2 + ṄH2 reaction systems. The rate coefficients presented in this study can be employed to develop the chemical kinetic model of nitryl-containing systems.

Effects of Variation Theory Integrated Guided Inquiry-Based Instruction on Grade Ten Students Self-Belief in Learning Solid Geometry

In mathematics education, students’ beliefs that could take many different forms like students' beliefs about mathematics learning mathematics teaching; and about themselves play a significant role in their learning and achievement. In particular, self-belief (SB) that is students’ evaluation and judgment about themselves in learning solid geometry, which encompassing control belief (CB), goal orientation (GO), self-concept (SC), self-efficacy (SE), and task value (TV), is critical to their success in learning solid geometry. Addressing these SB dimensions can substantially improve students' learning outcomes in solid geometry. Innovative, student-centered instructional approaches like GIBI, especially when combined with variation theory, offer a potential solution for overcoming Ethiopian secondary schools’ educational challenges by promoting active learning and providing varied examples to enhance engagement and achievement. However, there is a lack of research on the effectiveness of this combined approach in Ethiopia context. This study aims to fill this gap by investigating the effects of variation theory integrated GIBI on grade ten students' SB in learning solid geometry in Ethiopia. Employing a quasi-experimental with non-equivalent control group pretest-posttest design, 102 students from three public secondary schools in Debre Tabor city, Amhara region were randomly assigned into three groups: Experimental Group 1 (EG1) received GIBI with variation theory, Experimental Group 2 (EG2) received GIBI without variation theory, and the Control Group (CG) received traditional teaching methods. A SB questionnaire was used to measure students' CB, GO, SC, SE, and TV before and after the intervention. The results revealed significant improvements in the SB dimensions among students in EG1 compared to those in EG2 and CG. Specifically, EG1 students showed higher post-test scores in CB (F (2,99)=40.29, p=0.000, η²=0.449); GO (F (2,99)=3.43, p=0.036, η²=0.065); SC (F (2,99)=32.09, p=0.000, η²=0.393); SE (F (2,99)=24.02, p=0.000, η²=0.327); and TV (F (2,99)=5.35, p=0.000, η²=0.097). Tukey post hoc tests indicated that EG1 students' scores were significantly higher than those of the CG in CB and GO, and higher than EG2 and CG in SC, SE, and TV. These findings suggest that the integration of variation theory with GIBI effectively enhances students' SB in learning solid geometry, thereby addressing the educational challenges faced by Ethiopian students. The study recommends adopting this instructional approach more widely to improve student outcomes in mathematics.

Using students’ critical aspects to deepen understanding of nuclear physics concepts

Identifying students’ understanding provides a pathway to develop focused teaching to facilitate conceptual understanding. This study aims to gain more insight into undergraduate students’ conceptual understanding of two nuclear physics concepts: nuclear binding energy (NBE) and nuclear force; as the literature has shown that students face difficulties in learning and understanding such concepts. Phenomenography was used to provide a special qualitative research approach to exploring students’ in-depth understanding which was not addressed in previous studies. Data was collected from purposively selected students (N = 30) through semi-structured interviews. Phenomenography was used to reveal the different ways in which students understand these concepts and serves as indicators of potential conceptual difficulties. Based on these, the relevant and irrelevant critical aspects discerned by students are identified using the variation theory of learning. These critical aspects illustrate how the students understand each concept. For instance, NBE is the energy that must be added to a nucleus to separate it into its constituents and relates to a relevant critical aspect. However, NBE is also the energy that binds nucleons and this relates to an irrelevant critical aspect. These critical aspects can provide crucial information that can assist physics instructors in developing focused teaching and learning strategies. Thus, the responses to the interview can be used as a basis for teaching and learning nuclear physics concepts.

Variation Theory and Montessori Education

In this article we examine the relation between variation theory and Maria Montessori’s didactic theory. Montessori believed that training and sharpening of the child’s senses are crucial for their continued learning; she therefore developed specific sensorial materials to be used in Montessori preschools for such a purpose. As noted by interpreters of Montessori education, a key principle in this material, as well as in variation theory, is the use of variation and invariance. However, in this article, lessons in two different areas than the training of the senses are analysed from a variation-theoretical perspective on learning; these lessons originate from Montessori’s own writings and from extracts from Montessori training courses. The result shows that a systematic use of variation and invariance can be seen as a more fundamental part of Montessori’s didactic theory and is not only applied in the sensorial training. The article will offer theoretical concepts useful when explaining why lessons in various areas should be presented in the way they are described.

Reconciling Accuracy and Feasibility for Barrierless Reaction Steps by the PCS/DDCI/MC-PDFT Protocol: Methane and Ethylene Dissociations as Case Studies.

Several enhancements have been introduced into state-of-the-art computational protocols for the treatment of barrierless reaction steps in the framework of variable reaction coordinate variational transition state theory. The first step is the synergistic integration of the Iterative Difference Dedicated Configuration Interaction (I-DDCI) and Pisa Composite Scheme, which defines a reduced cost, yet very accurate, computational workflow. This approach provides a near black box tool for obtaining 1D reference potentials. Then, a general strategy has been devised for tuning the level of theory used in Monte Carlo (MC) sampling, employing Multiconfiguration Pair Density Functional Theory (MC-PDFT) with dynamically adjusted Hartree-Fock exchange. Concurrently, partial geometry optimizations during the MC simulations account for the coupling between the reaction coordinates and conserved modes. The protocol closely approaches full size consistency and yields highly accurate results, with several test computations suggesting rapid convergence of the I-DDCI correction with the basis set dimensions. The capabilities of the new platform are illustrated by two case studies (the hydrogen dissociation from CH4 and C2H4), which highlight its flexibility in handling different carbon hybridizations (sp3 and sp2). The remarkable accuracy of the computed rate constants confirms the robustness of the proposed method. Together with their intrinsic interest, these results pave the way for systematic investigations of complex gas-phase reactions through a reliable, user-friendly tool accessible to specialists and nonspecialists alike.

Blind non-linear spectral unmixing with spatial coherence for hyper and multispectral images

Multi and hyperspectral images have become invaluable sources of information, revolutionizing various fields such as remote sensing, environmental monitoring, agriculture and medicine. In this expansive domain, the multi-linear mixing model (MMM) is a versatile tool to analyze spatial and spectral domains by effectively bridging the gap between linear and non-linear interactions of light and matter. This paper introduces an upgraded methodology that integrates the versatility of MMM in non-linear spectral unmixing, while leveraging spatial coherence (SC) enhancement through total variation theory to mitigate noise effects in the abundance maps. Referred to as non-linear extended blind end-member and abundance extraction with SC (NEBEAE-SC), the proposed methodology relies on constrained quadratic optimization, cyclic coordinate descent algorithm, and the split Bregman formulation. The validation of NEBEAE-SC involved rigorous testing on various hyperspectral datasets, including a synthetic image, remote sensing scenarios, and two biomedical applications. Specifically, our biomedical applications are focused on classification tasks, the first addressing hyperspectral images of in-vivo brain tissue, and the second involving multispectral images of ex-vivo human placenta. Our results demonstrate an improvement in the abundance estimation by NEBEAE-SC compared to similar algorithms in the state-of-the-art by offering a robust tool for non-linear spectral unmixing in diverse application domains.

How do pedagogic causal mechanisms in vocational education work?

ABSTRACT This study introduces Pedagogic Causal Mechanisms (PCMs) in vocational education as a way to analyse and improve teaching and learning. PCMs are specific processes that directly connect educational inputs to learning outcomes. This paper uses an automotive mechanics lesson in Eswatini to show how PCMs work, focusing on Variation Theory as an example that creates an ‘Ah ha moment’ for students. Variation Theory demonstrates PCMs by highlighting key features through simple contrasts while keeping other elements constant. The research first describes the lesson in detail, then uses broader theories of vocational pedagogy to analyse it. It then introduces causal mechanisms as a concept, before defining PCMs more specifically. After explaining PCMs, the study shows how they provide particularly useful educational explanations, enhance professional judgement, and work with other PCMs to build situation-specific causality plans.