Core State Research Articles

Vulnerability to Achievement Stressors: More Evidence That Students With Learning Disabilities Require Intensive Intervention.

In this article, we introduce the term vulnerability to achievement stressors, which refers to differentially low achievement when shifts in the educational environment "stress" or threaten the capacity of an individual or a group of individuals to make academic progress. We also introduce a methodological framework for assessing vulnerability to achievement stressors. Vulnerability to achievement stressors in students with learning disabilities (LD), relative to students without disabilities, is illustrated with two achievement stressors: (a) the shift in learning standards codified in Common Core State Standards, specifically the increase in complexity of the fourth-grade fractions curriculum, and (b) the COVID-19 pandemic, which decreased instructional structure by disrupting in-person teaching. Because these illustrations were embedded within randomized controlled trials, each with an inclusive instruction condition and an intensive intervention condition, they also provide the basis for concluding that intensive intervention is more effective than inclusive instruction for addressing students with LD's vulnerability to achievement stressors and for narrowing their persistently severe achievement gaps.

Preparation, characterization and mechanism of SiO2@SiO2 core-shell microspheres through polymerization-induced colloid aggregation for fast separation using ultra performance liquid chromatography

The polymerization-induced colloid aggregation (PICA) method is commonly used to create SiO2@SiO2 core–shell silica microspheres (CSSMs), but it often encounters challenges such as incomplete shell coating and poor reproducibility. In this paper, the formation mechanism of the silica shell layer during the preparation of SiO2@SiO2 CSSMs using the PICA method was investigated. It was found that ureido modification can reduce the Zeta potential of the silica core surface, facilitating the deposition of coacervates formed by urea-formaldehyde resin (UF) and silica nanoparticles on the silica core surface to form the SiO2 shell layer when the Zeta potential of the surface is in the range of −20.1 mV to −4.8 mV. By controlling the interfacial state and surface potential of the SiO2 core, the issue of inconsistent reproducibility in preparing SiO2@SiO2 CSSMs can be overcome. Furthermore, optimization of experimental parameters such as pH, reaction temperature, water content, and reaction time can enhance the formation process. The thickness of the shell and pore size of CSSMs can be successfully adjusted by varying the reaction time and the particle size of colloidal silica sol, respectively. With optimal conditions, the semi-scale production yield of SiO2@SiO2 CSSMs can be increased to 50 g. The SiO2@SiO2 CSSMs were modified with octadecyltrichlorosilane (ODS) to be used as stationary phases in reversed phase liquid chromatography (RPLC) for fast separation of small solutes, peptides, and proteins. The superior separation efficiency indicates that the improved PICA method has the potential to be utilized as an alternative to the layer-by-layer method for large-scale production of SiO2@SiO2 CSSMs.

Cold Atmospheric Plasma in Cancer Therapy: Molecular Insights, Novel Concepts, and Future Opportunities

Over the past 2 decades, cold atmospheric plasma (CAP) has been playing increasingly pivotal roles in cutting edge biomedical applications and has developed into an innovative field of research of growing importance. One promising new medical application of CAP is cancer treatment. Being able to richly induce both reactive oxygen and nitrogen species, CAP has been shown to effectively control events critical to cancer initiation/progression; selectively inducing Deoxyribonucleic acid (DNA) damage and apoptotic cell deaths, reducing tumor volume and vasculature, halting metastasis and conferring anti-tumor effects by taking advantage of e.g., synergies among and between chemotherapeutic drugs and nanoparticles. This paper discusses molecular and immunological mechanisms of CAP treatment as a potential tool against cancers, with a focus on the novel mechanisms by which CAP interacts with chemotherapeutic drugs and nanotechnology. We then attempt to draw parallels between what is already known about the mechanisms of CAP activity, some novel concepts and attempts of CAP synergy, and the knowledge we would need to develop CAP as a potential therapeutic strategy in oncotherapy. HIGHLIGHTS This article focused on critical review of cold atmospheric plasma’s (CAP) application in cancer therapy. CAP technology in cancer treatment has been expected to cause a medical and therapeutic implications. CAP has strong anticancer efficacy and has been reported about the cell migration and apoptosis. The major role of reactive oxygen and nitrogen species of plasma discharge is to control the core state of cancer transition. GRAPHICAL ABSTRACT

EU Regulatory Polity 3.0 for Compliance with the Rule of Law: When Depoliticising Goals Lead to Uneven Politicisation

Abstract Since limiting judicial independence in Hungary and Poland, the politics of the rule of law crisis have been examined by various scholars discussing conflicts within and between EU and domestic institutions. The rule of law is no longer a purely national affair – it is of high political salience both for the Member States and the EU polity. The question addressed here is: how has the rule of law crisis reshaped the EU’s modes of governance? We argue that to safeguard this common value, the EU is evolving into a regulatory polity (3.0). This development marks a shift from Majone’s EU regulatory state’s focus on regulating markets (1.0) and regulation in core state powers in times of crises (2.0) to regulation on the core values of the polity (3.0). The article shows that in a context of growing dissensus over the rule of law, EU institutional actors have sought to strengthen “rulemaking,” “rule monitoring” and “rule enforcement” through a regulatory approach anchored in a market logic. It also shows that shifting from the traditional regulatory state 1.0 to regulation in core state powers 2.0, the regulatory polity 3.0 strengthens the EU’s institutional capacity to act when the rule of law is under strain through depoliticised “rule monitoring” and politicised “rulemaking“ and “rule enforcement“ as illustrated in the cases of Hungary and Poland discussed in this article.

“You forgot Poland?” Polish involvement in the Iraq war and its aftermath through a postcolonial lens

ABSTRACT This article examines Polish participation in the Iraq war (2003–2008) and its aftermath through a postcolonial lens within the context of Warsaw’s foreign policy choices in the post-Cold War era. After the fall of communism, Poland attempted to join “core” Western countries and institutions, while simultaneously distancing itself from the countries of the “periphery”. The article argues that Poland has operated in a liminal space during the Iraq war and its aftermath as it has been treated as an “internal other” of the West, and at the same time has “othered” the Iraqi periphery. The article does this by applying three key postcolonial theories to the case study: Said’s concept of orientalism, Coronil’s concept of occidentalism and Spivak’s ideas related to the subaltern. The article finds the following to be true: (a) Poland has been orientalised by core Western states while it has also orientalised the Iraqi and Middle Eastern periphery, (b) Poland has generally been a willing participant of occidentalist strategies concerning Iraq and the Middle East and (c) Western core states have attempted to speak for/silence Poland while Poland has spoken for/silenced the Iraqi/Middle Eastern periphery.

Full-Color Dynamic Afterglow in Carbon Dot-Based Materials Regulated by Dual-Phosphorescence Resonance Energy Transfer.

Developing afterglow materials with wide-range and time-dependent colors is highly desirable but challenging. Herein, by calcinating the mixture of Rhodamine B and NH4Al(OH)2CO3, carbon dots (CDs) are generated and in situ embedded in the porous Al2O3, forming the CDs@Al2O3 composite, which exhibits time-dependent phosphorescence colors (TDPCs) from blue to green after excited by a UV lamp. Photophysical studies reveal that the blue phosphorescence with a short lifetime of 214ms originates from the carbon core state, while the green phosphorescence with a long lifetime of 915ms is associated with the surface state of CDs. Simultaneous activation of the blue and green phosphorescence with different lifetimes induces the TDPC performance. Using CDs@Al2O3 as the donor, a series of long-wavelength fluorescent dyes including Rhodamine 123, Rhodamine 6G, and Rhodamine B as the acceptors, and epoxy resin (ER) as the matrix, a dual-phosphorescence resonance energy transfer system (CDs@Al2O3-dye-ER) is constructed to rationally regulate the afterglow emission, conferring the full-color dynamic afterglow from blue to red at different decay times with high afterglow quantum yields of up to 48.2%. The fascinating afterglow properties of the CDs@Al2O3-dye-ER composites enable their successful applications in multidimensional information encryption and polychrome 3D artworks.

Visualization of Unconventional Rashba Bands and Vortex Zero Mode in the Topological Superconductor Candidate AuSn4.

The noble metal alloy AuSn4 has recently been identified as an intrinsic surface topological superconductor, promisingly hosting the Majorana zero mode (MZM) for topological quantum computing. However, the atomic visualization of its nontrivial surface states and MZM remains elusive. Here, we report the direct observation of unconventional surface states and vortex zero mode in AuSn4 by scanning tunneling microscopy/spectroscopy. Unlike the trivial metallic bulk states of Sn-terminated surfaces, the Au-terminated surfaces exhibit pronounced surface states near the Fermi level, arising from unconventional Rashba bands characterized by shared helical spin textures. In the superconducting state, the Sn-terminated surfaces exhibit conventional Caroli-de Gennes-Matricon bound states, while the Au-terminated surfaces display sharp zero-energy core states resembling MZMs in a nonquantum-limit condition. This distinction may result from the dominant contribution of unconventional Rashba bands on the Au-terminated surface. Our results provide a new platform for studying termination-dependent topological surface states and MZM in noble-metal-based superconductors.

A hybrid approach combining UD and GA-CV-SVM to evaluate shear performance in high asphalt concrete core

The shear effect on high asphalt concrete core is significant. However, studies on the reliability of 100-meter-scale cores against shear damage remain limited. A key challenge in this research field is establishing the control criteria for the core and improving the computational efficiency of implicit limit state function (LSF). Additionally, the impact of material parameter uncertainty on the shear failure reliability of the core during the dam construction and impoundment stages remains unclear. To address this, a safety evaluation method based on time discretization was proposed, combining uniform design (UD), K-fold cross-validation (K-CV), and genetic algorithm (GA) to optimize the support vector machines (SVM). The core parameters of 52 asphalt concrete-core rockfill dams (ACCRDs) were analyzed, with the statistical values of the basic variables considered in determining the reliability index. The theoretical derivation of the critical shear failure safety index established a stability formula to assess the safety state of the dam core. The significance parameters were identified, and the sample points were generated at each stage using UD, and the Support Vector Regression (SVR) was applied to reconstruct the LSF, and reliability was calculated through the checking point method.

Model optimization and mechanism analysis of two-stage ejector considering nonequilibrium condensation

Two-stage ejectors are widely used in multi-effect distillation and refrigeration systems owing to their vacuum and pressurization capabilities. However, most studies on two-stage ejectors are based on the dry-gas hypothesis, which neglects the universal physical phenomenon of condensation. A wet-steam model of two-stage ejectors is established and compared to the dry-gas model in this paper. Simulation results indicate that the proposed wet-steam model more accurately describes the performance and complex flow field characteristics of the two-stage ejector. Moreover, the nonequilibrium condensation mechanism of the fluid within the two-stage ejector under variable conditions is revealed. The results show that as the two-stage main nozzle pressure increases from 300 kPa to 550 kPa, the liquid mass fraction increases, and the droplet nucleation rate of the two stages decreases by 14.17 % and 13.14 %. When the first-stage actuating pressure is increased, the first-stage fluid restricts the expansion state of the second-stage main jet core and weakens the vapor condensation in the region of the shock chain. Furthermore, the experimental results demonstrate that compared with the dry-gas model, the prediction error of entrainment ratio and the secondary flow obtained by the proposed model are reduced by 26.67 % and 43.04 %, respectively.

Conversion of Ultrasmall Glutathione-Coated Silver Nanoparticles during Dispersion in Water into Ultrasmall Silver Sulfide Nanoparticles.

Ultrasmall silver nanoparticles (2 nm) were prepared by reduction with sodium borohydride (NaBH4) and stabilized by the ligand glutathione (a tripeptide: glycine-cysteine-glutamic acid). NMR spectroscopy and optical spectroscopy (UV and fluorescence) revealed that these particles initially consist of silver nanoparticles and fluorescing silver nanoclusters, both stabilized by glutathione. Over time, the silver nanoclusters disappear and only the silver nanoparticles remain. Furthermore, the capping ligand glutathione eliminates hydrogen sulfide (H2S) from the central cysteine and is released from the nanoparticle surface as tripeptide glycine-dehydroalanine-glutamic acid. Hydrogen sulfide reacts with the silver core to form silver sulfide. After four weeks in dispersion at 4 °C, this process is completed. These processes cannot be detected by transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), or differential centrifugal sedimentation (DCS) as these methods cannot resolve the mixture of nanoparticles and nanoclusters or the nature of the nanoparticle core. X-ray photoelectron spectroscopy showed the mostly oxidized state of the silver nanoparticle core, Ag(+I), both in freshly prepared and in aged silver nanoparticles. These results demonstrate that ultrasmall nanoparticles can undergo unnoticed changes that considerably affect their chemical, physical, and biological properties. In particular, freshly prepared ultrasmall silver nanoparticles are much more toxic against cells and bacteria than aged particles because of the presence of the silver clusters.

Trust, trustworthiness and AI governance

An emerging issue in AI alignment is the use of artificial intelligence (AI) by public authorities, and specifically the integration of algorithmic decision-making (ADM) into core state functions. In this context, the alignment of AI with the values related to the notions of trust and trustworthiness constitutes a particularly sensitive problem from a theoretical, empirical, and normative perspective. In this paper, we offer an interdisciplinary overview of the scholarship on trust in sociology, political science, and computer science anchored in artificial intelligence. On this basis, we argue that only a coherent and comprehensive interdisciplinary approach making sense of the different properties attributed to trust and trustworthiness can convey a proper understanding of complex watchful trust dynamics in a socio-technical context. Ensuring the trustworthiness of AI-Governance ultimately requires an understanding of how to combine trust-related values while addressing machines, humans and institutions at the same time. We offer a road-map of the steps that could be taken to address the challenges identified.

Discursive and institutional standards of justice in the modern world-system

In the article the essence of standards of justice in the modern world-system is outlined in a general way. It is shown that these standards emerged in the European capitalist world-economy in consequence of the French Revolution. Standards of justice are interpreted as ideological semantic constructions that have been institutionalized simultaneously with establishment, first, of the ideology of liberalism as the geoculture of the modern world-system and, second, — of model of liberal state. Standards of justice are considered within theoretical theses and methodological guiding lines of I. Wallerstein's theory of the modern world-system. However, some theoretical theses of J. Alexander's civil society theory are also used to supplement and concretize considered in the article problems with some new arguments. For instance, Alexander's conceptual toolkit helped to distinguish discursive and institutional standards of justice. Reasons and peculiarities of establishment of standards of justice are considered and role these standards played in the providing of development of the modern world-system is shown. In particular, it is elucidated that owing to these standards elites of the core countries of the modern world-system managed to redirect the rebellion energy of the lower strata from antisystemic revolutions to struggle for inclusion to liberal state. This helped to calm the lower strata down and to guard structures of the modern world-system against essential damages. Standards of justice contributed to legitimation of social order of the modern world-system. Full integration of the lower strata to newly created national societies reinforced social solidarity, and this strengthened the core states even more. It is shown that for today in particular countries of periphery and semi-periphery trends of revision of current standards of justice and their replacement by alternative semantic constructions become visible.

Tunable multi-peak emission solid-state fluorescent carbon dots: Luminescence regulation mechanism and application in single-component-based LEDs

The design of solid-state fluorescent carbon dots (CDs) with multi-peak emission has become an urgent challenge to be solved with the in-depth research of CDs in LEDs. Here, one- and two-component solid-state white light CDs are synthesized by microwave-assisted hydrothermal method using the biological pollutant cyanobacteria, respectively. The solid-state fluorescence quantum yield of the one-component CDs was as high as 41.8 %, and the solid-state fluorescence mechanism of CDs is discussed to be mainly attributed to the self-quenching-resistant feature of “core-shell” structure and the reabsorption/RET-induced long-wavelength red light emission, and attenuation of the short emission wavelength. For two-component white light CDs, blue- and red-light CDs are obtained by simple dialysis separation, realizing the fluorescence tunability. The different origins of their multi-peak emission are discussed: core, edge and surface states. The synthesis yields of CDs are up to 62 %, enabling stable gram-scale production. The white- and red-light CDs are used as phosphors to fabricate fluorescent films and cold, pure, and warm white- and red-light LEDs with good resistance to photobleaching and temperature stability and CRI of 84.4, 85.7 and 61.5.

A novel joint estimation for core temperature and state of charge of lithium-ion battery based on classification approach and convolutional neural network

The core temperature (CT) of lithium-ion batteries (LIBs) is crucial for effective thermal management, and is significantly influenced by the state of charge (SOC) among other battery parameters. However, directly measuring CT and SOC poses challenges. This study introduces a novel joint estimation method for CT and SOC, in which classification approach is pioneeringly employed through a two-dimensional convolutional neural network (2D-CNN). SOC is initially estimated and subsequently utilized as an input to refine CT estimation. This process is facilitated by two 2D-CNNs that incorporate measured indices such as current, terminal voltage, surface temperature, and ambient temperature into their inputs. Techniques including data augmentation, sequential optimization, and Gaussian filtering are employed to enhance estimation effect. The methodology is validated using LIB charge/discharge data derived from experiments based on the urban dynamometer driving schedule (UDDS). Results demonstrate that the root-mean-square errors (RMSEs) for CT and SOC estimation are below 0.267 °C and 0.7 %, respectively, across a broad ambient temperature range of −15 °C–55 °C. Consequently, this study confirms the effectiveness of using classification for CT and SOC estimation, illustrating that the proposed method can precisely estimate CT and SOC of LIBs across a wide temperature spectrum. The effectiveness of the deep learning method based on classification in estimating CT and SOC has been validated. Furthermore, a comparative analysis reveals that incorporating SOC as an input for CT estimation notably reduces the training time required by the method.

Exploring the Photoluminescence Characteristics of Nitrogen-Doped Carbon Dots

Carbon dots, or C-Dots, are graphitic particles below 10 nm that exhibit room temperature photoluminescence (PL). The specific PL mechanism of C-Dots varies with synthesis paths and remains unresolved. This study utilizes direct current microplasmas for reliable and reproducible synthesis, exploring precursor outcomes and the discharge current's impact on surface chemistry and optical properties. The nitrogen-doped C-Dots (N-CQDs) synthesized display crystalline structures with a graphitic core, nitrogen doping, and a functionalized surface. Luminescence, originating from both core and surface states, can be finely controlled by adjusting synthesis conditions. N-CQDs, with a high photoluminescence quantum yield, hold promise for next-gen solar cell applications. The N-CQDs exhibit intriguing quantum-confined optical properties dependent on the level of nitrogen incorporation. Notably, the band energy structure of the N-CQDs is clarified, and they are integrated into a photovoltaic device as the photoactive layer, achieving an extraordinary open-circuit voltage of 1.8 V corroborating well with energy gat of CQDs and PL properties [1, 2]. We specifically highlight the use of nitrogen-doped C-Dots as an active absorbing layer in solar cells and discuss how doping can engineer their electrical, optical, and chemical properties. Nitrogen doping mainly occurs in the graphitic core as a substituted type of doping (63–67 atomic%), with enough to create emissive states without impacting the core structure. The optical and chemical properties remain stable even with re-dispersion, suggesting easy applicability for cellular imaging or optoelectronics [3]. Highly stable nitrogen-doped graphite quantum dots, prepared by atmospheric pressure microplasma, without post-synthesis treatments, yields stable, water-dispersible, and non-toxic quantum dots with a high PL quantum yield of approximately 70%.

Territorial autonomy and ethnic conflict: the Baloch ethnic question post-18th Amendment

ABSTRACT This article critically assesses the effectiveness of territorial autonomy under the 18th Constitutional Amendment in managing ethnic conflict in Pakistan's Balochistan province. It argues that limitations in the design and implementation of the federal provisions of the 18th Amendment have hindered the sustainable resolution of the ethnic conflict in Balochistan. Design-wise, the Amendment inadequately addresses key institutional factors that have historically contributed to Balochistan's marginalised status within the federation, notably the Senate's limited powers, non-ethnic-based provincial boundaries, and Baloch under-representation in core state institutions. Design inadequacies are exacerbated by poor implementation of the core federal provisions, especially related to natural resource ownership, local government, and the Council of Common Interests (CCI). Notable implementation hurdles include a persistent ‘centralist’ mind set, particularly pronounced within the military, actively seeking the overturn of the 18th Amendment. The persistence of the de-facto power of the military has undermined the efficacy of territorial autonomy as a conflict management tool.

Advance of Near-Infrared Emissive Carbon Dots in Diagnosis and Therapy: Synthesis, Luminescence, and Application.

Carbon dots (CDs) with good optical properties, biocompatibility, easy functionalization, and small size have attracted more and more attention and laid a good foundation for their applications in the biomedicine field. CDs emitted in near-infrared regions (NIR-CDs) can achieve high penetration depth imaging and produce high cytotoxic substance for disease treatment. Therefore, NIR-CDs are promising materials to realize high-quality imaging-guided diagnostic and therapeutic integration. This review first introduces the current mainstream synthesis methods of NIR-CDs by "top-down" and "bottom-up". Second, the luminescence modes of NIR-CDs are introduced, and the luminescence mechanisms based on carbon core state, surface state, molecular state, and crosslinking enhanced emission are summarized. Third, the applications and principles of NIR-CDs in imaging, drug delivery, and non-invasive therapeutics are introduced from a view of diagnosis and therapy. Finally, their prospects and challenges in biomedical and biotechnological applications are outlined.

Iron Loss and Temperature Rise Analysis of a Transformer Core Considering Vector Magnetic Hysteresis Characteristics under Direct Current Bias.

Direct current (DC) bias induced by the DC transmission and geomagnetically induced current is a critical factor in the abnormal operation of electrical equipment and is widely used in the field of power transmission and distribution system state evaluation. As the main affected component, the vector magnetization state of a transformer core under DC bias has rarely been studied, resulting in inaccurate transformer operation state estimations. In this paper, a dynamic vector hysteresis model that considers the impact of rotating and DC-biased fields is introduced into the numerical analysis to simulate the distribution of magnetic properties, iron loss and temperature of the transformer core model and a physical 110 kV single-phase autotransformer core. The maximum values of B, H and iron loss exist at the corners and T-joint of the core under rotating and DC-biased fields. The corresponding maximum value of the temperature increase is found in the main core limb area. The temperature rise of the 110 kV transformer core under various DC-biased conditions is measured and compared with the FEM (Finite Element Method) results of the proposed model and the model solely based on the magnetization curve B||H. The calculation error of the temperature rise obtained by the improved model is approximately 3.76-15.73% and is much less than the model solely based on magnetization curve B||H (approximately 50.71-66.92%).

Doppler sensitivity and resonant tuning of Rydberg atom-based antennas

Radio frequency antennas based on Rydberg atom vapor cells can in principle reach sensitivities beyond those of any conventional wire antenna, especially at lower frequencies where very long wires are needed to accommodate the increasing wavelength. They also have other desirable features such as consisting of nonmetallic, hence lower profile, elements. This paper presents a detailed theoretical investigation of Rydberg antenna sensitivity, elucidating parameter regimes that could cumulatively lead to a sensitivity increase 2–3 orders of magnitude beyond that of currently tested configurations. The key insight is to optimally combine the advantages of two well-studied approaches: (i) three laser ‘2D star configuration’ setups that, when enhanced with increased laser power, to some degree compensate for atom motion-induced Doppler broadening, and (ii) resonant coupling between a pair of near-degenerate Rydberg levels, tuned via a local oscillator to the incident signal of interest. The advantage of the star setup is subtle because it only restores the overall sensitivity to the expected Doppler-limited value, compensating for additional significant off-resonance reductions where differently moving atom sub-populations destructively interfere with each other in the net signal. An additional unique advantage of local oscillator tuning is that it leads to vastly narrower line widths, as low as ∼10 kHz set by the intrinsic Rydberg state lifetimes, rather than the typical ∼10 MHz scale set by the core state lifetimes. Intuitively, with this setup the two Rydberg states may be tuned to act as an independent high-q cavity, a point of view supported by a study of the frequency-dependence of the antenna resonant response. There are a number of practical experimental advances, especially larger ∼1 cm laser beam widths, required to suppress various extrinsic line broadening effects and to fully exploit this ‘Rydberg superheterodyne’ response.

Connections within the Multiplicative Field: A Case Study of Adán’s Mathematical Thinking

ABSTRACT Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to develop connections across concepts. This paper uses a case study of mathematical thinking from one 5th-grade student over a school year to demonstrate the connections in his thinking across whole numbers, fractions, and graphing work. Analyzing his solution strategies with three frameworks detailing multiplicative, proportional, and functional thinking, his strategies show a developing understanding of proportional reasoning, and functional thinking as he is building his multiplicative thinking and connections from whole numbers to fraction problem-solving strategies to graphing. Examining this student’s mathematical thinking points to the opportunity for connections across the multiplicative field through teaching mathematics in a manner more responsive to student sense-making.