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In this article, the authors explain how they leveraged the popularity of the "Star Wars" franchise to introduce a task steeped in popular culture as a fun way to engage their students in investigating complex mathematics that have real-life connections to careers in toy design and engineering design in general. The authors share various aspects of the multiday lesson to highlight the students' deep mathematical reasoning. The article starts with the introduction of the task, in which the authors challenged students to sketch a 2D prototype droid using paper and pencil, followed by creation of their 3D prototype using technology. The lesson includes the students computing the "cost" of the action figure they created.

Machine learning (ML) has become increasingly prevalent in various domains. However, ML algorithms sometimes give unfair outcomes and discrimination against certain groups. Thereby, bias occurs when our results produce a decision that is systematically incorrect. At various phases of the ML pipeline, such as data collection, pre-processing, model selection, and evaluation, these biases appear. Bias reduction methods for ML have been suggested using a variety of techniques. By changing the data or the model itself, adding more fairness constraints, or both, these methods try to lessen bias. The best technique relies on the particular context and application because each technique has advantages and disadvantages. Therefore, in this paper, we present a comprehensive survey of bias mitigation techniques in machine learning (ML) with a focus on in-depth exploration of methods, including adversarial training. We examine the diverse types of bias that can afflict ML systems, elucidate current research trends, and address future challenges. Our discussion encompasses a detailed analysis of pre-processing, in-processing, and post-processing methods, including their respective pros and cons. Moreover, we go beyond qualitative assessments by quantifying the strategies for bias reduction and providing empirical evidence and performance metrics. This paper serves as an invaluable resource for researchers, practitioners, and policymakers seeking to navigate the intricate landscape of bias in ML, offering both a profound understanding of the issue and actionable insights for responsible and effective bias mitigation.

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations. Thoughtfully planned number talks allow for students to actively listen as they engage in rich mathematical discourse that interweaves a procedure with the conceptual understanding that undergirds it. This article discusses the authors' enactment of number talks to support students' development of their mathematical reasoning. They begin with purposeful planning that centers their learning objectives and share their practice of establishing norms in the class. They then examine how the series of number talks were enacted and include episodes highlighting student and teacher discourse. Last, they reflect on the series of number talks and convey their takeaways and final thoughts.

This study investigated the dose-dependent changes in the chemical composition of three dental ceramic materials—zirconia, lithium disilicate (LD), and VITA ENAMIC® hybrid composite (VITA En)—following irradiation with an ultra-short femtosecond (fs) laser (800 nm, 30 fs, 1 kHz) in an ambient air environment using average laser power (76 mW) and scanning speeds (50, 100, and 200 mm/s), simulating dental treatment processes. The chemical composition of the ablated regions was analyzed using energy dispersive spectroscopy. All irradiated samples showed increased carbon content (by up to 42%) and reduced oxygen (by up to 33%). The observed increase in C content is likely attributed to a combination of surface reactions, adsorption of carbon from the ambient environment, and carbon deposition from the laser-induced plasma, all facilitated by the high-energy conditions created by fs-laser pulses. Scanning electron microscopy revealed ablation with progressive controlled melting and recrystallization, with an absence of pile-up features typically associated with significant thermal damage. These findings demonstrate that ultra-short fs-laser irradiation induces highly controlled, dose-dependent changes in the chemical composition and surface morphology of dental ceramic materials.

Breast cancer presents a substantial health obstacle since it is the most widespread invasive cancer and the second most common cause of death in women. Prompt identification is essential for effective intervention, rendering breast cancer screening a critical component of healthcare. Although mammography is frequently employed for screening purposes, the manual diagnosis performed by pathologists can be laborious and susceptible to mistakes. Regrettably, the majority of research prioritizes mass classification over mass localization, resulting in an uneven distribution of attention. In response to this problem, we suggest a groundbreaking approach that seeks to identify and pinpoint cancers in breast mammography pictures. This will allow medical experts to identify tumors more quickly and with greater precision. This paper presents a complex deep convolutional neural network design that incorporates advanced deep learning techniques such as U-Net and YOLO. The objective is to enable automatic detection and localization of breast lesions in mammography pictures. To assess the effectiveness of our model, we carried out a thorough review that included a range of performance criteria. We specifically evaluated the accuracy, precision, recall, F1-score, ROC curve, and R-squared error using the publicly available MIAS dataset. Our model performed exceptionally well, with an accuracy rate of 93.0% and an AUC (area under the curve) of 98.6% for the detection job. Moreover, for the localization task, our model achieved a remarkably high R-squared value of 97%. These findings highlight that deep learning can boost the efficiency and accuracy of diagnosing breast cancer. The automation of breast lesion detection and classification offered by our proposed method bears substantial benefits. By alleviating the workload burden on pathologists, it facilitates expedited and accurate breast cancer screening processes. As a result, the proposed approach holds promise for improving healthcare outcomes and bolstering the overall effectiveness of breast cancer detection and diagnosis.

Objective: The retention of glass fiber post (GFP) is considered a key factor for the long-term success of restorations of endodontically treated teeth. This study aimed to compare the compressive strength of a ceramic crown supported by a GFP using different luting agents. Methods: Forty single-rooted premolars were randomly divided into four groups (n = 10 each): control group (teeth without a GFP), Ketac Cem group (glass ionomer), RelyX ARC group (conventional dual-curing resin), and RelyX U200 group (self-adhesive dual-curing resin). After luting of the posts and placement of all-ceramic crowns made using feldspathic porcelain (Noritake EX-3), they were exposed to thermocycling for 1000 cycles and compressive strength tests. Statistical analysis included Kruskal–Wallis test with Dunn’s multi-comparison test. Results: The Ketac Cem group and RelyX U200 group showed significantly greater fracture resistance to compressive loading than the control group. Conclusion: This study indicates a possible role of the luting agent used with the GFP in influencing the compressive strength of the restored teeth. In this study, the self-adhesive dual-curing resin and glass ionomer both offered resistance to fractures.

Most recommendation systems utilize personal data to device personalized recommendations for users. Even though it seems favorable, security risks like data breaches are inevitable. This research proposes a novel reinforcement learning ‘approach’ to recommend users without collecting identifiable data. With only user activity on a session, our proposed method can model and track user behavior and formulate a recommendation system. We conclude that our algorithms demonstrate positive results in capturing user behavior without collecting private data of any kind from the user. The research is two folds. On one hand, we experiment using traditional reinforcement learning techniques (MDP, Q-learning), and on the other hand, we use deep reinforcement learning algorithms (DQN, DDQN, and D3QN) on a movie recommendation scenario. Interestingly, we observe that MDP and D3QN works comparatively better on movie recommendations.

We utilized a mixed-methods design to examine the experiences of 15 school counselors and 26 teachers who participated in a professional development program focused on collaboration to enhance students' career development using project-based learning (PBL). PBL is a teaching method through which students engage in active learning by responding to a real-world challenge, problem, or question. We identified the following four themes: collaboration facilitators, collaboration challenges, classroom collaboration, and place-based collaboration. After participating in the program, teachers and school counselors reported being likely to engage with each other to incorporate career development in the classroom.

Abstract The big graph database provides strong modeling capabilities and efficient querying for complex applications. Subgraph isomorphism which finds exact matches of a query graph in the database efficiently, is a challenging problem. Current subgraph isomorphism approaches mostly are based on the pruning strategy proposed by Ullmann. These techniques have two significant drawbacks- first, they are unable to efficiently handle complex queries, and second, their implementations need the large indexes that require large memory resources. In this paper, we describe a new subgraph isomorphism approach, the HyGraph algorithm, that is efficient both in querying and with memory requirements for index creation. We compare the HyGraph algorithm with two popular existing approaches, GraphQL and Cypher using complexity measures and experimentally using three big graph data sets—(1) a country-level population database, (2) a simulated bank database, and (3) a publicly available World Cup big graph database. It is shown that the HyGraph solution performs significantly better (or equally) than competing algorithms for the query operations on these big databases, making it an excellent candidate for subgraph isomorphism queries in real scenarios.

As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

This study was situated in a semester-long classroom teaching experiment examining prospective teachers' understanding of number concepts and operations. The purpose of this paper is to describe the learning goals, tasks, and tools used to cultivate prospective teachers' understanding of addition and subtraction with whole numbers. Research regarding children's understanding of whole number concepts and operations was used in developing learning goals, pathways for learning, and instructional tasks for the prospective teachers. Furthermore, prior research regarding prospective teachers' whole number development supported the expectation that all of the instructional tasks were reasoned solely in base-eight. Classroom episodes indicate that base-eight allows prospective teachers to reason about addition and subtraction with whole numbers in similar ways that elementary aged students' reason in base-ten.

As students contribute to social and sociomathematical norms, they will often reorganize their own understandings. As such, the purpose of this article is to describe the ways in which prospective elementary teachers contributed to the norms that were established and "re"-established throughout an entire semester in an undergraduate mathematics content course. Findings illustrate that norms must be renegotiated between an instructor and prospective teachers when the mathematics content changes.

The use of bioactive materials has become a standard tool in the arsenal of tissue engineering and regenerative medicine applications. Bioactive materials have gained significant attention due to their ability to mimic tissues physically, chemically and mechanically. Although a plethora of both natural and synthetic polymers have been identified, wool-based keratin, which has a natural propensity to self-assemble, is biocompatible, cytocompatible, biodegradable, non-toxic and non-immunogenic, can also diminish the adhesion and growth of bacterial biofilm. Keratin based materials have subsequently been applied in various tissue engineering applications, from wound healing to drug and growth factor delivery to bone regeneration. This review focuses on the key properties of keratin, including porosity and pore size, swelling rate, degradation rate, wettability and mechanical properties responsible for its biofunctional activity, as well as recent advances in keratin-based biomaterials for biomedical applications.

By leveraging the strengths and commitments of each of the partners, a university, a private nonprofit, and a middle-sized urban school district, collaborated to impact student learning of key concepts in middle-grade mathematics and to change mathematics teaching. The project targeted middle grades mathematics because success in it is the greatest predictor of later school achievement. In well-researched learning modules, students visualize, interact with, and analyze mathematical representations connected to dynamic simulations of real-life phenomena in a curricular learning system comprising dynamic technologies, curriculum replacement units, and professional development. Through planned professional development, teachers have the technological skills, pedagogical skills and mathematical content knowledge required to engage their students in an interaction between the software, the curriculum materials, and the mathematics. Student learning gains and changes in teacher pedagogical, technological, and mathematical content knowledge provide evidence of the project's continued success after three years. Concomitant institutional changes in each of the partnering organizations attest to the project's sustainable impact.

The adoption of a new technology, the spreading of ideologies, the transmission of contagions, are examples of spreading phenomena that can be modelled at two distinct levels of resolution, a macroscopic and a microscopic level.In the present work, we consider the network at the microscopic level and represent its nodes as a system of interacting particles and propose a novel, physics-inspired approach. This approach assumes that nodes interact via `forces' that derive from the `potential' that each node creates at the location of the other nodes, leading to a potential gradient that indicates the `natural' direction of diffusion through the network. A set of influencers in the network, is determined from strategically selected nodes based on the value of their net potential. We use synthetic networks of various sizes and compare the influence spread resulting from a seed set determined from the potential-based model and alternate approaches, including the greedy algorithm of Kempe et al. Our findings indicate that this approach achieves comparable results to those of the greedy algorithm without the prohibitive computational cost, and consistently outperforms the other approaches by a large margin. We then apply our methodology to information spreading related to the Twitter Higgs Boson user dataset. The results are analyzed in the context of influence maximization, and we provide insights into the general application of this technique for information dissemination.

Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging mathematics in which they assumed the role of analysts creating mathematical models to understand historical events that influenced strategic planning during World War II. This interdisciplinary task provided students with the opportunity to see data as more than just numbers, but numbers with meaning that can have a substantial impact on the decisions affecting and influencing real-world outcomes.

Abstract The unveiling of communities within a network or graph, and the hierarchization of its members that results is of utmost importance in areas ranging from social to biochemical networks, from electronic circuits to cybersecurity. We present a statistical mechanics approach that uses a normalized Gaussian function which captures the impact of a node within its neighborhood and leads to a density-ranking of nodes by considering the distance between nodes as punishment. A hill-climbing procedure is applied to determine the density attractors and identify the unique parent (leader) of each member as well as the group leader. This organization of the nodes results in a tree-like network with multiple clusters, the community tree. The method is tested using synthetic networks generated by the LFR benchmarking algorithm for network sizes between 500 and 30,000 nodes and mixing parameter between 0.1 and 0.9. Our results show a reasonable agreement with the LFR results for low to medium values of the mixing parameter and indicate a very mild dependence on the size of the network.

Abstract Photo‐activated disinfection using photosensitizers has been proposed as an adjunct to conventional endodontic therapy for additional disinfection and improved treatment outcomes. This systematic review aims to investigate the effectiveness of photosensitizers used in laser endodontics disinfection. A comprehensive literature search is conducted to identify in vitro and in vivo studies involving photo‐activated disinfection in endodontic treatment. Publications are selected based on predetermined eligibility criteria. From 121 articles, 34 met the inclusion criteria, comprising eight polymicrobial and 26 bacteria‐specific studies. A total of 10 photosensitizers were investigated, including methylene blue, tolonium chloride, polyethylenimine and chlorin (e6), phenothia zinium, chitosan, rose bengal, malachite green, indocyanine green, chlorine p6 and curcumin. Photo‐activated disinfection using tolonium chloride or methylene blue can be an effective adjunct to conventional root canal therapy. More studies are needed to assess the performance of newer photosensitizers to optimize photo‐activated disinfection of the complex root canal space.

As teachers consider what it means for students to "do mathematics" successfully, they must explore their role as teachers in a way that strategically supports students as powerful agents for their own learning. As teachers foster a classroom environment based on agreed-on expectations, they must help students learn how to engage in whole-class discussions that create opportunities for learning among all students. This article shares an initial classroom episode in which classroom expectations were introduced to create an environment for all students in the first author's sixth grade class to engage in meaningful mathematics dialogue. This episode serves as a model for other middle school mathematics teachers as they embark on their own journey toward supporting their students as they move toward purposefully engaging in whole-class discussions.

Children's intuitive understandings of mathematical ideas--both correct, generalizable strategies alongside misconceptions--showcase the complexity of their thinking. However, recognizing children as complex thinkers is one thing but it is another thing altogether to leverage their ideas to plan for and carry out mathematics instruction. The purpose of this article is to describe our efforts to make students' thinking explicit in ways that lead to generalizable procedures for solving problems. Furthermore, we provide a set of principles and practices that we have found productive in our planning and implementation of mathematics tasks. As an example, the authors draw on their work in a classroom of fourth-grade students, where a classroom teacher, a university faculty member, and preservice teachers regularly focus and reflect on children's mathematical thinking.

The exploration of proportional relationships is foundational to the mathematics studied in the middle grades and beyond. Research has shown that an early emphasis on procedures often leaves students with a shallow understanding of the important underlying mathematical concepts of proportional relationships. One approach that addresses the needs of both teachers and students when it comes to mathematics that middle grades students find challenging (e.g., ratios and proportions) is a unified curricular activity system (i.e., a system of curricular materials, technology, and teacher professional development). The mixed-method study presented in this article outlines a curricular activity system that was designed to underpin middle grades mathematics teachers' implementation of a learning module addressing proportional relationships. The results of the study provide evidence that a curricular activity system in which teacher professional development is coherently aligned to technology-embedded curriculum impacts teachers' ability to teach as well as students' learning of proportional relationships.

Although educators agree that making connections with the real world, as advocated by "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), is important, making such connections while addressing important mathematics is elusive. The authors have found that math content coupled with the instructional strategy of "predict, check, explain" can bridge such real-world contexts. In so doing, this procedure supports the research-informed teaching practices of using evidence of student thinking and aiding meaningful mathematical discussion. In contrast to the common symbols-first approach, in which students manipulate symbols and memorize the mathematics, we have found that allowing students to investigate motion phenomena through the use of technology-based representations can foster students' deep understanding of mathematics. As an example, the authors describe a high-cognitive-demand task that connects a real-world context with mathematics while supporting seventh-grade students' understanding of rate and proportionality.

Who will make a better estimate concerning the number of jelly beans in a jar, a single person or a group of people? On one side of the debate is the notion that a person would make a better decision because he or she uses unique knowledge that the group may not possess. On the opposite side of the argument is the claim that because of their breadth of responses, the collective wisdom of a group will arrive at a better conclusion. This is the very dilemma that finance professor Jack Treynor posed to his students regarding "The Wisdom of the Crowds" (Surowiecki 2005). After reading this book, the authors wondered how middle school students would respond to the question. Moreover, they thought the question could be used as an entry point for them to leverage middle school students' mathematical intuitions regarding estimation and then link those estimates to data representation and analysis. In particular, they focused their effort on students' understanding of measures of center, as their experiences have suggested that although middle school students often use the word average, they do not necessarily specify which measure of central tendency they are referencing: mean, median, or mode or some completely different mathematics concept. In this article, the authors suggest that students' mathematical intuition about estimation can serve as an entry point for tasks exploring measures of center by answering the question "how many jelly beans are in the jar?"