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The aim of this study is to explore how structural and process aspects of secondary school students' mathematical reasoning support each other in a collaborative learning environment through the integration of "GeoGebra" software and the ACODESA method. The study involved four eighth-grade secondary school students, who participated in the research utilizing the classroom teaching experiment method. Data collection for the study included the utilization of three mathematical tasks focused on the triangle inequality and auxiliary elements of the triangle, alongside students' computer screenshots, written outputs, "GeoGebra" files, and audio-video recordings. Discourse analysis and Toulmin's model were adopted for data analysis. As a result of the data analysis, it was found that the process of comparing contributed to the construction of deductive reasoning, the processes of conjecturing and exemplifying contributed to the construction of abductive reasoning, and the processes of generalizing and identifying a pattern contributed to the construction of inductive reasoning. Additionally, the process of justifying was found to be linked to all structures of mathematical reasoning (deductive, abductive, and inductive). In conclusion, these connections between the structural and process aspects have improved our understanding of MR types and contributed to the elaboration of the conceptual model for mathematical reasoning available in the literature.

Critical nodes in transportation networks, such as major transit tunnels and interchange stations, are vital for maintaining system functionality following a disruptive event such as a large earthquake. This project focuses on evaluating the seismic resilience of BART’s Berkeley Hills Tunnel that intersects the Hayward Fault, one of California's most active seismic zones. The Hayward Fault poses a significant risk, with the potential for a magnitude 7+ earthquake that could severely impact the tunnel, potentially disrupting BART service and affecting the broader transit network. This study employs the latest fault displacement hazard data and models to estimate the probability of fault rupture displacements and assesses the resulting damage. It then evaluates the likelihood of service interruptions caused by potential Hayward Fault events. Theresults suggest that the tunnels may experience minor to significant damage depending on the amplitude of the faultdisplacement, which can lead to repair times ranging from a few weeks to over a year. The findings highlight the importance of improving tunnel resilience to minimize service disruptions and ensure efficient recovery following major earthquakes.

This study aims to develop a knowledge test to assess secondary school students' awareness of scientists. After determining the topics that the questions in the test would measure, 50 multiple-choice questions were prepared and presented to six experts in the field. Following the experts' feedback, the number of questions in the test was reduced to 44 due to issues related to question clarity, alignment with the curriculum, and cognitive appropriateness. The 44-question test underwent item analysis. The prepared test was subjected to a preliminary pilot application with 222 secondary school students. As a result of the preliminary pilot application, two questions with discrimination indices of 0.19 or lower were removed, and the final version of the test was arranged to consist of 42 questions for the pilot application. The pilot application was conducted with 211 secondary school students. In this application, secondary school students were administered the Knowledge Test of Scientists consisting of 42 questions, and item analysis was performed again. Two questions with discrimination indices of 0.19 or lower were removed from the pilot application. As a result of the pilot application, the Knowledge Test of Scientists had a KR-20 reliability coefficient of 0.94, and the Spearman Brown two-half test correlation coefficient was calculated as 0.92. The final version of the scale was arranged to consist of 40 items. These results demonstrate that the test is highly reliable, meaning that the test results accurately reflect the measured attribute and are replicable.

This study was carried out to develop a test to assess algorithmic thinking skills. To this end, the twelve steps suggested by Downing (2006) were adopted. Throughout the test development, 24 middle school sixth-grade students and eight experts in different areas took part as needed in the tasks on the project. The test was given to 252 students attending the sixth grade who were selected through purposeful sampling. The content validity of the test was ensured by means of obtaining expert opinion, whereas the construct validity was ensured by performing an independent sample t-test on the difference between the lower and upper groups. As a result, the algorithmic thinking skills assessment test was finalized with 22 main items and 2 sample items, totalling 24 items. The KR-20 reliability analysis proved a quite reliable test based on the reliability coefficient of 0.83. As mentioned earlier, the independent sample t-test was applied to the difference of lower and upper groups for construct validation of the test. It was seen that the test items are significant in discriminating the students in the lower and upper groups (p<0.01).

The purpose of this study is to examine the performances of university students' using dynamic mathematics software GeoGebra in argumentations and proving processes. A task related to the limit involving "sinx/x" was designed and 18 university students worked on the task during the collaborative learning, scientific debate, and self-reflection stages. Students' argumentations and proofs were analyzed based on Toulmin's model and Habermas' construct of rationality. The results revealed that the rationality components can be used to explain the implicit features of warrant in Toulmin's model. It was found that the semiotic mediation opportunities offered by GeoGebra and the teamwork and debate stages in the teaching method enabled the students to create geometrically the ranking relation between the value of an angle and the sine and tangent values of this angle. They also facilitated using the various kinds of representation and enhanced the transformations within and/or between the representations. GeoGebra tools as instruments of semiotic mediation helped the students to construct productive arguments, validate them, be productive by providing backing and rebuttal to the collective arguments put forward during the teamwork stage, and reach consensus thanks to scientific debate.

This study aims to reveal the mathematical reasoning process of 8th-grade students and the reasoning indicators they use in this process. The study was carried out in line with the data obtained from the Mathematical Reasoning Test (MRT) administered to 292 8th-grade students. The mathematical reasoning performances of the participants were generally at low and medium levels. Evidence was found that students used reasoning indicators such as "… for/because of…, /therefore/so/thus…", "if … then…", "because…", "should be/should be..." and "equal..." when reasoning. It is important that when evaluating the solutions to questions that require mathematical reasoning, students must be interviewed and confirmed how they reached those solutions. The limitations of the research are, firstly, that it is limited to 8th graders, and secondly, that students will get bored if the number of questions in the MRT is high. Students must be asked to justify their reasoning while solving problems that require mathematical reasoning.