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The level of difficulty of mathematical test items is a critical aspect for evaluating test quality and educational outcomes. Accurately predicting item difficulty during test creation is thus significantly important for producing effective test papers. This study used more than ten years of content and score data from China's Henan Provincial College Entrance Examination in Mathematics as an evaluation criterion for test difficulty, and all data were obtained from the Henan Provincial Department of Education. Based on the framework established by the National Center for Education Statistics (NCES) for test item assessment methodology, this paper proposes a new framework containing eight features considering the uniqueness of mathematics. Next, this paper proposes an XGBoost-based SHAP model for analyzing the difficulty of mathematics tests. By coupling the XGBoost method with the SHAP method, the model not only evaluates the difficulty of mathematics tests but also analyzes the contribution of specific features to item difficulty, thereby increasing transparency and mitigating the "black box" nature of machine learning models. The model has a high prediction accuracy of 0.99 for the training set and 0.806 for the test set. With the model, we found that parameter-level features and reasoning-level features are significant factors influencing the difficulty of subjective items in the exam. In addition, we divided senior secondary mathematics knowledge into nine units based on Chinese curriculum standards and found significant differences in the distribution of the eight features across these different knowledge units, which can help teachers place different emphasis on different units during the teaching process. In summary, our proposed approach significantly improves the accuracy of item difficulty prediction, which is crucial for intelligent educational applications such as knowledge tracking, automatic test item generation, and intelligent paper generation. These results provide tools that are better aligned with and responsive to students' learning needs, thus effectively informing educational practice. [ABSTRACT FROM AUTHOR]

In this paper, we describe an educational experience in the context of the Master's degree that is compulsory in Spain to become a secondary education mathematics teacher. Master's students from two universities in Madrid (Spain) attended lectures that addressed—emphasizing the concourse of a dynamic geometry software package—some historical, didactic and mathematical issues related to linkage mechanisms, such as those arising in the 18th and 19th centuries during the development of the steam engine. Afterwards, participants were asked to provide three different kinds of feedback: (i) working on an assigned group task, (ii) individually answering a questionnaire, and (iii) proposing some classroom activity, imagining it would be addressed to their prospective pupils. All three issues focused on the specific topic of the attended lectures. In the framework of Mason's reflective discourse analysis, the information supplied by the participants has been analyzed. The objective was to explore what they have learned from the experience and what their perception is of the potential interest in linkages as a methodological instrument for their future professional activity as teachers. This analysis is then the basis upon which to reflect on the opportunities (and problems) that this particular bar-joint linkages methodological approach could bring towards providing future mathematics teachers with attractive tools that would contribute to enhancing a STEAM-oriented education. Finally, the students' answers allow us to conclude that the experience was beneficial for these pre-service teachers, both in improving their knowledge on linkages history, mathematics, industrial, technological and artistic applications, and in enhancing the use in the classroom of this very suitable STEAM context. [ABSTRACT FROM AUTHOR]

In recent years, using micro-lectures (a short video of less than ten minutes) as a digital learning medium has become popular for integrating technology into mathematics lessons, providing new experiences to students and helping them to master mathematical concepts. It is important to note that the effectiveness of a micro-lecture depends on how teachers use it and on students' perceptions of learning support media. Therefore, this research aims to determine Junior High School students' achievements and satisfaction using micro-lectures on the topic of Direct and Inverse Proportions. Teachers' micro-lectures in this research were designed based on their teaching styles, learning objectives, and considering the needs of their students. A quasi-experiment with 3, 2, and 1 pretest-posttest design with experimental and control groups was also used. In the first and second experimental groups, teachers used the same version of the micro-lectures in their classrooms as the main learning medium and at home to preview and review Direct and Inverse Proportions materials. At the same time, the control group used conventional expository learning activities. Finally, a learning satisfaction questionnaire was used to determine students' perceptions of using micro-lectures in their mathematics lessons. Findings indicate that the use of micro-lectures in the experimental classes I and II is better than in the control class and led to improved learning achievements and student satisfaction. Meanwhile, there is no significant difference between using micro-lectures inside and outside classrooms. Students' report cards also showed that their learning satisfaction using this technique was higher than the control class. Practical implications and suggestions for further investigation are to be also discussed at the end of the paper. [ABSTRACT FROM AUTHOR]

In the context of the science, technology, engineering, arts and mathematics disciplines in education, subjects tend to use contextualized activities or projects. Educational robotics and computational thinking both have the potential to become subjects in their own right, though not all educational programs yet offer these. Despite the use of technology and programming platforms being widespread, it is not common practice to integrate computational thinking and educational robotics into the official curriculum in secondary education. That is why this paper continues an initial project of integrating computational thinking and educational robotics into a secondary school in Barcelona, Spain. This study presents a project-based learning approach where the main focus is the development of skills related to science, technology, engineering, arts and mathematics and the acquisition of computational thinking knowledge in the second year of pupils' studies using a block-based programming environment. The study develops several sessions in the context of project-based learning, with students using the block-programming platform ScratchTM. During these sessions and in small-group workshops, students will expand their knowledge of computational thinking and develop 21st-century skills. We demonstrate the superior improvement of these concepts and skills compared to other educational methodologies. [ABSTRACT FROM AUTHOR]

This paper provides a historical account of the development of algorithmic complexity in a form that is suitable to instructors of mathematics at the high school or undergraduate level. The study of algorithmic complexity, despite being deeply rooted in mathematics, is usually restricted to the computer science curriculum. By providing a historical account of algorithmic complexity through a mathematical lens, this paper aims to equip mathematics educators with the necessary background and framework for incorporating the analysis of algorithmic complexity into mathematics courses as early on as algebra or pre-calculus. [ABSTRACT FROM AUTHOR]

The paper estimates the effect of students’ position in the classroom register on their academic performance. We use a unique dataset from Poland which contains information on the academic outcomes of students in the humanities, science and mathematics lower secondary school exams as well as the position students occupy in their classroom register. We find that students whose names are recorded near the end of the class list have lower performance than those students whose names are recorded near the beginning of the list. The effect appears to be larger for performance in the humanities exam, and for low-achieving boys who attend large classes. [ABSTRACT FROM AUTHOR]

Using the classification methods for mathematical problems in textbooks (Fan & Zhu, 2000) and strategies used to solve problems (Fan & Zhu, 2007), this paper reports the results of an analysis and classification of the type of mathematical problems and problem-solving strategies in a sample made up of the five most widely-used mathematics textbooks for the first year of junior high school in the 2013- 2014 school year in Mexico. It is concluded that the textbooks focus on providing a comprehensive range of problems that, for the most part, do not allow multiple problem-solving strategies, whereas others can be solved using an algorithm or direct procedure. [ABSTRACT FROM AUTHOR]

This paper offers the results of an analysis of the level of mathematical anxiety, understood to mean a feeling of discomfort experienced when someone is required to take mathematics classes, as displayed in students of secondary education in Costa Rica. The study was performed with a sample of 3,725 students in public secondary education in Costa Rica in 2013. The results show statistically significant differences between the sexes in the level of mathematical anxiety, with female students experiencing moderately higher anxiety levels. Differences in anxiety levels are also determined by the student's educational level, with significant differences found between third-cycle students (7th, 8th and 9th grades) and diversified education students (10th and 11th grades); the latter displayed moderately higher anxiety levels. Nonetheless, the study concludes that despite the differences observed, only 22.4% of students show high or very high levels of mathematical anxiety. [ABSTRACT FROM AUTHOR]

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through a symbiosis of induction and abduction from experience and deduction from the relationships generated in exemplification. In other words, experience can be organised in such a way that shifts of understanding take place as a result of learners’ own actions. Actions, in this context, include mental acts of organisational reflection. [ABSTRACT FROM AUTHOR]

In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept, and consequently are more often mistakenly identified as examples. We describe and discuss these notions and present a study regarding kindergarten children’s grasp of nonexamples of triangles. [ABSTRACT FROM AUTHOR]

The process of examination marking is complex, requiring examiners to engage in a variety of cognitive operations. While consideration has been given to marking practices in a few specific contexts, those of General Certificate of Secondary Education (GCSE) examiners have yet to receive serious attention. This study's aims, therefore, were: first, to investigate the cognitive strategies used when marking GCSEs; and second, to interpret them within the context of psychological theories of human judgement. Two contrasting GCSE examination papers were considered: Mathematics used a 'points-based' marking scheme, while Business Studies relied on a 'levels-based' scheme. Small groups of experienced examiners marked script samples, and using a concurrent 'think aloud' method, verbal protocols were obtained. Using a semi-structured interview schedule, the examiners were then questioned retrospectively. Qualitative data analysis supported a model of five distinct cognitive marking strategies, which can be interpreted within dual-processing theories of judgement. The implications for GCSE marking are discussed. [ABSTRACT FROM AUTHOR]

The CAME1 project was inaugurated in 1993 as an intervention delivered in the context of mathematics with the intention of accelerating the cognitive development of students in the first two years of secondary education. This paper reports substantial post-test and long-term National examination effects of the intervention, yet, by discussing the methodology used, questions the assumptions implicit in the original intention. It is now suggested that a better view is to regard CAME as a constructive criticism of normal instructional teaching, with implications for the role of mathematics teachers and university staff in future professional development. [ABSTRACT FROM AUTHOR]

My purpose in this paper is to present a didactic tool – a set of specially designed problems and questions for discussion – that can help making students better aware of the various aspects of the formal notion of limit of a sequence. The didactic tool will be justified using results from my own and other authors' research on students' naïve or erroneous conceptions of limit of a sequence. [ABSTRACT FROM AUTHOR]