Search results for: S. Kartal
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 14

Search results for: S. Kartal

14 Analysis of Process for Solution of Fiber-Ends after Biopolishing on the Surface of Cotton Knit Fabric

Authors: P. Altay, G. Kartal, B. Kizilkaya, S. Kahraman, N. C. Gursoy

Abstract:

Biopolishing is applied to remove the fuzz or pills on the fiber or fabric surface which will reduce its tendency to pill or fuzz after repetitive launderings. After biopolishing process, the fuzzes ripped by cellulase enzymes cannot be thoroughly removed from fabric surface, they remain on the fabric or fiber surface; accordingly disturb the user and lead to decrease in productivity of drying process. The main objective of this study is to develop a method for removing weakened fuzz fibers and surface pills from biofinished fabric surface before drying process. Fuzzes in the lattice structure of fabric were completely removed from the internal structure of the fabric by air blowing. The presence of fuzzes leads to problems with formation of pilling and faded appearance; the removal of fuzzes from the fabric results in reduced tendency to pill formation, cleaner, smoother and softer surface, improved handling properties of fabric with maintaining original color.

Keywords: biopolishing, fuzz fiber, weakened fiber, biofinished cotton fabric

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13 Search for Flavour Changing Neutral Current Couplings of Higgs-up Sector Quarks at Future Circular Collider (FCC-eh)

Authors: I. Turk Cakir, B. Hacisahinoglu, S. Kartal, A. Yilmaz, A. Yilmaz, Z. Uysal, O. Cakir

Abstract:

In the search for new physics beyond the Standard Model, Flavour Changing Neutral Current (FCNC) is a good research field in terms of the observability at future colliders. Increased Higgs production with higher energy and luminosity in colliders is essential for verification or falsification of our knowledge of physics and predictions, and the search for new physics. Prospective electron-proton collider constituent of the Future Circular Collider project is FCC-eh. It offers great sensitivity due to its high luminosity and low interference. In this work, thq FCNC interaction vertex with off-shell top quark decay at electron-proton colliders is studied. By using MadGraph5_aMC@NLO multi-purpose event generator, observability of tuh and tch couplings are obtained with equal coupling scenario. Upper limit on branching ratio of tree level top quark FCNC decay is determined as 0.012% at FCC-eh with 1 ab ^−1 luminosity.

Keywords: FCC, FCNC, Higgs Boson, Top Quark

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12 Torsional Rigidities of Reinforced Concrete Beams Subjected to Elastic Lateral Torsional Buckling

Authors: Ilker Kalkan, Saruhan Kartal

Abstract:

Reinforced concrete (RC) beams rarely undergo lateral-torsional buckling (LTB), since these beams possess large lateral bending and torsional rigidities owing to their stocky cross-sections, unlike steel beams. However, the problem of LTB is becoming more and more pronounced in the last decades as the span lengths of concrete beams increase and the cross-sections become more slender with the use of pre-stressed concrete. The buckling moment of a beam mainly depends on its lateral bending rigidity and torsional rigidity. The nonhomogeneous and elastic-inelastic nature of RC complicates estimation of the buckling moments of concrete beams. Furthermore, the lateral bending and torsional rigidities of RC beams and the buckling moments are affected from different forms of concrete cracking, including flexural, torsional and restrained shrinkage cracking. The present study pertains to the effects of concrete cracking on the torsional rigidities of RC beams prone to elastic LTB. A series of tests on rather slender RC beams indicated that torsional cracking does not initiate until buckling in elastic LTB, while flexural cracking associated with lateral bending takes place even at the initial stages of loading. Hence, the present study clearly indicated that the un-cracked torsional rigidity needs to be used for estimating the buckling moments of RC beams liable to elastic LTB.

Keywords: lateral stability, post-cracking torsional rigidity, uncracked torsional rigidity, critical moment

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11 Effect of Tool Geometry and Welding Parameters on Macrostructure and Weld Strength in Friction Stir Welded of High Density Polyethylene Sheets

Authors: Mustafa Kemal Bilici, Memduh Kurtulmuş, İlyas Kartal, Ahmet İrfan Yükler

Abstract:

Friction stir welding is a solid-state joining process that has gained acceptable progress in recent years. This method which was first used for welding of aluminum and its alloys is now employed for welding of other materials such as polymers and composites. The aim of the present work is to investigate the mechanical properties of butt joints produced by friction stir welding (FSW) in high density polyethylene sheets of 4 mm thickness. The effects of critical welding parameters and tool design have affected on mechanical properties, weld surface and macrostructure of friction stir welded polyethylene. Experiments were performed at tool rotational speeds of 600, 900, 1200 and 1500 r/min and traverse speeds of 30, 45 and 60 mm/min, tool diameters (d) of 4, 5, 6 mm and tool shoulder diameters (D) 20, 25, 30 mm. A strength value of 80 % of the base material was achieved at the isolated optimum welding condition. According to the tool design, the welding parameters and the mechanical properties changed to a great extent. The highest tensile strength was achieved at low feed rates, high tool rotation speeds and shoulder diameters/pin diameters ratio.

Keywords: friction stir welding, mechanical properties, polyethylene, high density polyethylene, tool design

Procedia PDF Downloads 357
10 Facilitation of Digital Culture and Creativity through an Ideation Strategy: A Case Study with an Incumbent Automotive Manufacturer

Authors: K. Ö. Kartal, L. Maul, M. Hägele

Abstract:

With the development of new technologies come additional opportunities for the founding of companies and new markets to be created. The barriers to entry are lowered and technology makes old business models obsolete. Incumbent companies have to be adaptable to this quickly changing environment. They have to start the process of digital maturation and they have to be able to adapt quickly to new and drastic changes that might arise. One of the biggest barriers for organizations in order to do so is their culture. This paper shows the core elements of a corporate culture that supports the process of digital maturation in incumbent organizations. Furthermore, it is explored how ideation and innovation can be used in a strategy in order to facilitate these core elements of culture that promote digital maturity. Focus areas are identified for the design of ideation strategies, with the aim to make the facilitation and incitation process more effective, short to long term. Therefore, one in-depth case study is conducted with data collection from interviews, observation, document review and surveys. The findings indicate that digital maturity is connected to cultural shift and 11 relevant elements of digital culture are identified which have to be considered. Based on these 11 core elements, five focus areas that need to be regarded in the design of a strategy that uses ideation and innovation to facilitate the cultural shift are identified. These are: Focus topics, rewards and communication, structure and frequency, regions and new online formats.

Keywords: digital transformation, innovation management, ideation strategy, creativity culture, change

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9 Changes in the Quality of Life of Turkish Patients with Trauma-Related Phthisis Bulbi

Authors: Titap Yazicioglu

Abstract:

Purpose: Losing an eye due to trauma is a challenging situation that reduces the quality of life by causing physical, cosmetic, and serious psychological problems. This study aimed to evaluate the effect of aesthetic rehabilitation on the change in psychological status and quality of life of patients with eye loss resulting in phthisis bulbi. Materials and Methods: The files of 25 males and 15 females with an average age of 27.5 years who had trauma-related phthisic eye and had applied to the Department of Ophthalmology at the Dr. Lütfi Kırdar Kartal Education and Research Hospital, Istanbul, Turkey, for aesthetic rehabilitation during the years 2015-19 were retrospectively analyzed. The Beck Depression Inventory (BDI), Beck Anxiety Scale(BAS), and Short Form 36 quality-of-life survey (SF-36) were used to collect data on admission and one-year follow-up. Results: Of the patients reviewed, 65% stated that eye loss had caused their avoidance of family and social environments; 30% had moderate anxiety and depression. The post-operative sub-dimension scores of general health, emotional role function, and physical and social functions were statistically significant (p = 0.001; p<0.01), but the variations in the sub-dimension scores of vitality, mental health, and total physical health were not (p>0.05). Conclusion: Lossing an eye is a traumatic event that can affect all aspects of a person’s social and professional life. A patient who has suffered from the psychological damage of physical loss of eye needs a prosthesis that can give the desired function and appearance in different aspects of life.

Keywords: eye loss, phthisis bulbi, quality of life, psychological trauma

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8 The Effects of Extracorporeal Shock Wave Therapy on Plantar Pressure in Patients with Calcaneal Spur

Authors: Zehra Betül Karakoç

Abstract:

Aim: The aim of our study is to determine the changement pf plantar pressure after extracorporeal shock wave therapy (ESWT) in a patient with calcaneal spur (CS). Method: Thirty patients with CS who received ESWT treatment at Kartal Yavuz Selim State Hospital between May 2020 and November 2022 participated in this study. Demographic information of the cases was obtained. Pain levels and plantar pressure were measured with Visuel Analog Scale (VAS) and pedobarography, respectively. Pedobarography measured the maximal strength, peak pressure level, and contact area values of the hind, middle, forefoot, and toes. The cases were re-evaluated 4 weeks after the application of 15 Hz, 2-3 bar, 2,000 beats ESWT for 3 sessions. 22 cases participated in the second evaluation. The data of all patients were evaluated bilaterally. Results: Pain intensity levels after treatment were statistically significantly decreased compared to before treatment (p=0.012). Maximum force and contact area values of total foot and forefoot increased significantly (p < 0.05). Conclusion: We consider that the increased max force value of total foot and forefoot area after ESWT is due to the normal walking rate gained related to decreased pain. ESWT treatment may have positive effects on foot pressure distribution and body biomechanics. In order to interpret the results of our study more clearly, randomized controlled studies with a larger number of cases were planned in the future.

Keywords: calcaneal spur, ESWT, plantar pressure, pain

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7 Investigation of Electrospun Composites Nanofiber of Poly (Lactic Acid)/Hazelnut Shell Powder/Zinc Oxide

Authors: Ibrahim Sengor, Sumeyye Cesur, Ilyas Kartal, Faik Nuzhet Oktar, Nazmi Ekren, Ahmet Talat Inan, Oguzhan Gunduz

Abstract:

In recent years, many researchers focused on nano-size fiber production. Nanofibers have been studied due to their different and superior physical, chemical and mechanical properties. Poly (lactic acid) (PLA), is a type of biodegradable thermoplastic polyester derived from renewable sources used in biomedical owing to its biocompatibility and biodegradability. In addition, zinc oxide is an antibacterial material and hazelnut shell powder is a filling material. In this study, nanofibers were obtained by adding of different ratio Zinc oxide, (ZnO) and hazelnut shell powder at different concentration into Poly (lactic acid) (PLA) by using electrospinning method which is the most common method to obtain nanofibers. After dissolving the granulated polylactic acids in % 1,% 2,% 3 and% 4 with chloroform solvent, they are homogenized by adding tween and hazelnut shell powder at different ratios and then by electrospinning, nanofibers are obtained. Scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), Differential scanning calorimeter (DSC) and physical analysis such as density, electrical conductivity, surface tension, viscosity measurement and antimicrobial test were carried out after production process. The resulting structures of the nanofiber possess antimicrobial and antiseptic properties, which are attractive for biomedical applications. The resulting structures of the nanofiber possess antimicrobial, non toxic, self-cleaning and rigid properties, which are attractive for biomedical applications.

Keywords: electrospinning, hazelnut shell powder, nanofibers, poly (lactic acid), zinc oxide

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6 Paradigmatic Approach University Management from the Perspective of Strategic Management: A Research in the Marmara Region in Turkey

Authors: Recep Yücel, Cihat Kartal, Mustafa Kara

Abstract:

On the basis of strategic management, it is believed in the necessity of a number of innovations in the postmodern management approach in the management of universities in our country. In this sense, some of these requirements are the integration of public and private universities, international integration, R & D status and increasing young population will create a dynamic structure. According to the postmodern management approach, universities, in our country despite being governed by the classical approach autonomous universities; academically are thought solid, to be non-hierarchical and creative. In fact, studies that require a multidisciplinary academic environment, universities and there is a close cooperation between formal and non-formal sub-units. Moreover, terms of postmodern management approaches, the requirements specified in the direction of solving the problem of an increasing number of universities in our country is considered to be more difficult. Therefore, considering the psychological impact on the academic personnel the university organizational structure, the study are trying to aim to propose an appropriate model of university organization. In this context, the study sought to answer the question how to have an impact innovation and international integration on the academic achievement of the classical organizational structure. Finally, in the study, due to the adoption of the classical organizational structure of the university, integration is considered to be difficult, academic cooperation between universities at the international level and maintaining it. In addition, it was understood that block the efforts of this organization structure, academic motivation, development and innovation. In this study under these purposes; on the basis of the existing organization and management structure of the universities in the Marmara Region in Turkey, a study was conducted with qualitative research methods. The data have been analyzed using content analysis and assessment was based on the results obtained.

Keywords: university, strategic management, postmodern management approaches, multidisciplinary studies

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5 First Cracking Moments of Hybrid Fiber Reinforced Polymer-Steel Reinforced Concrete Beams

Authors: Saruhan Kartal, Ilker Kalkan

Abstract:

The present paper reports the cracking moment estimates of a set of steel-reinforced, Fiber Reinforced Polymer (FRP)-reinforced and hybrid steel-FRP reinforced concrete beams, calculated from different analytical formulations in the codes, together with the experimental cracking load values. A total of three steel-reinforced, four FRP-reinforced, 12 hybrid FRP-steel over-reinforced and five hybrid FRP-steel under-reinforced concrete beam tests were analyzed within the scope of the study. Glass FRP (GFRP) and Basalt FRP (BFRP) bars were used in the beams as FRP bars. In under-reinforced hybrid beams, rupture of the FRP bars preceded crushing of concrete, while concrete crushing preceded FRP rupture in over-reinforced beams. In both types, steel yielding took place long before the FRP rupture and concrete crushing. The cracking moment mainly depends on two quantities, namely the moment of inertia of the section at the initiation of cracking and the flexural tensile strength of concrete, i.e. the modulus of rupture. In the present study, two different definitions of uncracked moment of inertia, i.e. the gross and the uncracked transformed moments of inertia, were adopted. Two analytical equations for the modulus of rupture (ACI 318M and Eurocode 2) were utilized in the calculations as well as the experimental tensile strength of concrete from prismatic specimen tests. The ACI 318M modulus of rupture expression produced cracking moment estimates closer to the experimental cracking moments of FRP-reinforced and hybrid FRP-steel reinforced concrete beams when used in combination with the uncracked transformed moment of inertia, yet the Eurocode 2 modulus of rupture expression gave more accurate cracking moment estimates in steel-reinforced concrete beams. All of the analytical definitions produced analytical values considerably different from the experimental cracking load values of the solely FRP-reinforced concrete beam specimens.

Keywords: polymer reinforcement, four-point bending, hybrid use of reinforcement, cracking moment

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4 Examining Reading Comprehension Skills Based on Different Reading Comprehension Frameworks and Taxonomies

Authors: Seval Kula-Kartal

Abstract:

Developing students’ reading comprehension skills is an aim that is difficult to accomplish and requires to follow long-term and systematic teaching and assessment processes. In these processes, teachers need tools to provide guidance to them on what reading comprehension is and which comprehension skills they should develop. Due to a lack of clear and evidence-based frameworks defining reading comprehension skills, especially in Turkiye, teachers and students mostly follow various processes in the classrooms without having an idea about what their comprehension goals are and what those goals mean. Since teachers and students do not have a clear view of comprehension targets, strengths, and weaknesses in students’ comprehension skills, the formative feedback processes cannot be managed in an effective way. It is believed that detecting and defining influential comprehension skills may provide guidance both to teachers and students during the feedback process. Therefore, in the current study, some of the reading comprehension frameworks that define comprehension skills operationally were examined. The aim of the study is to develop a simple and clear framework that can be used by teachers and students during their teaching, learning, assessment, and feedback processes. The current study is qualitative research in which documents related to reading comprehension skills were analyzed. Therefore, the study group consisted of recourses and frameworks which made big contributions to theoretical and operational definitions of reading comprehension. A content analysis was conducted on the resources included in the study group. To determine the validity of the themes and sub-categories revealed as the result of content analysis, three educational assessment experts were asked to examine the content analysis results. The Fleiss’ Cappa coefficient revealed that there is consistency among themes and categories defined by three different experts. The content analysis of the reading comprehension frameworks revealed that comprehension skills could be examined under four different themes. The first and second themes focus on understanding information given explicitly or implicitly within a text. The third theme includes skills used by the readers to make connections between their personal knowledge and the information given in the text. Lastly, the fourth theme focus on skills used by readers to examine the text with a critical view. The results suggested that fundamental reading comprehension skills can be examined under four themes. Teachers are recommended to use these themes in their reading comprehension teaching and assessment processes. Acknowledgment: This research is supported by Pamukkale University Scientific Research Unit within the project, whose title is Developing A Reading Comprehension Rubric.

Keywords: reading comprehension, assessing reading comprehension, comprehension taxonomies, educational assessment

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3 Body, Experience, Sense, and Place: Past and Present Sensory Mappings of Istiklal Street in Istanbul

Authors: Asiye Nisa Kartal

Abstract:

An attempt to recognize the undiscovered bounds of Istiklal Street in Istanbul between its sensory experiences (intangible qualities) and physical setting (tangible qualities) could be taken as the first inspiration point for this study. ‘The dramatic physical changes’ and ‘their current impacts on sensory attributions’ of Istiklal Street have directed this study to consider the role of changing the physical layout on sensory dimensions which have a subtle but important role in the examination of urban places. The public places have always been subject to transformation, so in the last years, the changing socio-cultural structure, economic and political movements, law and city regulations, innovative transportation and communication activities have resulted in a controversial modification of Istanbul. And, as the culture, entertainment, tourism, and shopping focus of Istanbul, Istiklal Street has witnessed different changing stages within the last years. In this process, because of the projects being implemented, many buildings such as cinemas, theatres, and bookstores have restored, moved, converted, closed and demolished which have been significant elements in terms of the qualitative value of this area. And, the multi-layered socio-cultural, and architectural structure of Istiklal Street has been changing in a dramatical and controversial way. But importantly, while the physical setting of Istiklal Street has changed, the transformation has not been spatial, socio-cultural, economic; avoidably the sensory dimensions of Istiklal Street which have great importance in terms of intangible qualities of this area have begun to lose their distinctive features. This has created the challenge of this research. As the main hypothesis, this study claims that the physical transformations have led to change in the sensory characteristic of Istiklal Street, therefore the Sensescape of Istiklal Street deserve to be recorded, decoded and promoted as expeditiously as possible to observe the sensory reflections of physical transformations in this area. With the help of the method of ‘Sensewalking’ which is an efficient research tool to generate knowledge on sensory dimensions of an urban settlement, this study suggests way of ‘mapping’ to understand how do ‘changes of physical setting’ play role on ‘sensory qualities’ of Istiklal Street which have been changed or lost over time. Basically, this research focuses on the sensory mapping of Istiklal Street from the 1990s until today to picture, interpret, criticize the ‘sensory mapping of Istiklal Street in present’ and the ‘sensory mapping of Istiklal Street in past’. Through the sensory mapping of Istiklal Street, this study intends to increase the awareness about the distinctive sensory qualities of places. It is worthwhile for further studies that consider the sensory dimensions of places especially in the field of architecture.

Keywords: Istiklal street, sense, sensewalking, sensory mapping

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2 Unveiling the Dynamics of Preservice Teachers’ Engagement with Mathematical Modeling through Model Eliciting Activities: A Comprehensive Exploration of Acceptance and Resistance Towards Modeling and Its Pedagogy

Authors: Ozgul Kartal, Wade Tillett, Lyn D. English

Abstract:

Despite its global significance in curricula, mathematical modeling encounters persistent disparities in recognition and emphasis within regular mathematics classrooms and teacher education across countries with diverse educational and cultural traditions, including variations in the perceived role of mathematical modeling. Over the past two decades, increased attention has been given to the integration of mathematical modeling into national curriculum standards in the U.S. and other countries. Therefore, the mathematics education research community has dedicated significant efforts to investigate various aspects associated with the teaching and learning of mathematical modeling, primarily focusing on exploring the applicability of modeling in schools and assessing students', teachers', and preservice teachers' (PTs) competencies and engagement in modeling cycles and processes. However, limited attention has been directed toward examining potential resistance hindering teachers and PTs from effectively implementing mathematical modeling. This study focuses on how PTs, without prior modeling experience, resist and/or embrace mathematical modeling and its pedagogy as they learn about models and modeling perspectives, navigate the modeling process, design and implement their modeling activities and lesson plans, and experience the pedagogy enabling modeling. Model eliciting activities (MEAs) were employed due to their high potential to support the development of mathematical modeling pedagogy. The mathematical modeling module was integrated into a mathematics methods course to explore how PTs embraced or resisted mathematical modeling and its pedagogy. The module design included reading, reflecting, engaging in modeling, assessing models, creating a modeling task (MEA), and designing a modeling lesson employing an MEA. Twelve senior undergraduate students participated, and data collection involved video recordings, written prompts, lesson plans, and reflections. An open coding analysis revealed acceptance and resistance toward teaching mathematical modeling. The study identified four overarching themes, including both acceptance and resistance: pedagogy, affordance of modeling (tasks), modeling actions, and adjusting modeling. In the category of pedagogy, PTs displayed acceptance based on potential pedagogical benefits and resistance due to various concerns. The affordance of modeling (tasks) category emerged from instances when PTs showed acceptance or resistance while discussing the nature and quality of modeling tasks, often debating whether modeling is considered mathematics. PTs demonstrated both acceptance and resistance in their modeling actions, engaging in modeling cycles as students and designing/implementing MEAs as teachers. The adjusting modeling category captured instances where PTs accepted or resisted maintaining the qualities and nature of the modeling experience or converted modeling into a typical structured mathematics experience for students. While PTs displayed a mix of acceptance and resistance in their modeling actions, limitations were observed in embracing complexity and adhering to model principles. The study provides valuable insights into the challenges and opportunities of integrating mathematical modeling into teacher education, emphasizing the importance of addressing pedagogical concerns and providing support for effective implementation. In conclusion, this research offers a comprehensive understanding of PTs' engagement with modeling, advocating for a more focused discussion on the distinct nature and significance of mathematical modeling in the broader curriculum to establish a foundation for effective teacher education programs.

Keywords: mathematical modeling, model eliciting activities, modeling pedagogy, secondary teacher education

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1 The Impact of Supporting Productive Struggle in Learning Mathematics: A Quasi-Experimental Study in High School Algebra Classes

Authors: Sumeyra Karatas, Veysel Karatas, Reyhan Safak, Gamze Bulut-Ozturk, Ozgul Kartal

Abstract:

Productive struggle entails a student's cognitive exertion to comprehend mathematical concepts and uncover solutions not immediately apparent. The significance of productive struggle in learning mathematics is accentuated by influential educational theorists, emphasizing its necessity for learning mathematics with understanding. Consequently, supporting productive struggle in learning mathematics is recognized as a high-leverage and effective mathematics teaching practice. In this study, the investigation into the role of productive struggle in learning mathematics led to the development of a comprehensive rubric for productive struggle pedagogy through an exhaustive literature review. The rubric consists of eight primary criteria and 37 sub-criteria, providing a detailed description of teacher actions and pedagogical choices that foster students' productive struggles. These criteria encompass various pedagogical aspects, including task design, tool implementation, allowing time for struggle, posing questions, scaffolding, handling mistakes, acknowledging efforts, and facilitating discussion/feedback. Utilizing this rubric, a team of researchers and teachers designed eight 90-minute lesson plans, employing a productive struggle pedagogy, for a two-week unit on solving systems of linear equations. Simultaneously, another set of eight lesson plans on the same topic, featuring identical content and problems but employing a traditional lecture-and-practice model, was designed by the same team. The objective was to assess the impact of supporting productive struggle on students' mathematics learning, defined by the strands of mathematical proficiency. This quasi-experimental study compares the control group, which received traditional lecture- and practice instruction, with the treatment group, which experienced a productive struggle in pedagogy. Sixty-six 10th and 11th-grade students from two algebra classes, taught by the same teacher at a high school, underwent either the productive struggle pedagogy or lecture-and-practice approach over two-week eight 90-minute class sessions. To measure students' learning, an assessment was created and validated by a team of researchers and teachers. It comprised seven open-response problems assessing the strands of mathematical proficiency: procedural and conceptual understanding, strategic competence, and adaptive reasoning on the topic. The test was administered at the beginning and end of the two weeks as pre-and post-test. Students' solutions underwent scoring using an established rubric, subjected to expert validation and an inter-rater reliability process involving multiple criteria for each problem based on their steps and procedures. An analysis of covariance (ANCOVA) was conducted to examine the differences between the control group, which received traditional pedagogy, and the treatment group, exposed to the productive struggle pedagogy, on the post-test scores while controlling for the pre-test. The results indicated a significant effect of treatment on post-test scores for procedural understanding (F(2, 63) = 10.47, p < .001), strategic competence (F(2, 63) = 9.92, p < .001), adaptive reasoning (F(2, 63) = 10.69, p < .001), and conceptual understanding (F(2, 63) = 10.06, p < .001), controlling for pre-test scores. This demonstrates the positive impact of supporting productive struggle in learning mathematics. In conclusion, the results revealed the significance of the role of productive struggle in learning mathematics. The study further explored the practical application of productive struggle through the development of a comprehensive rubric describing the pedagogy of supporting productive struggle.

Keywords: effective mathematics teaching practice, high school algebra, learning mathematics, productive struggle

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