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This research was conducted in 2019 in collaboration with Japanese colleagues, with the research tasks translated from the original Japanese. In Finland, a total of 1112 students from grades 7–9 in primary school participated in the study. In our article, we examine Finnish students' mastery of the concept of percentages and how they express their mathematical thinking about percentages in a multimodal way. A multimodal expression of mathematical thinking can typically take the form of natural language, written mathematics, pictorial representations, mathematical symbolic language, or combinations of these, which can be used to manage information, such as through tables. Our focus is on Finnish primary-school students' mastery of the concept of percentages, and we then narrow our analysis to tasks where students have used a multimodal approach. We analyze the representations of the concept of percentages and the related thought processes. The concept of percentages was best mastered in grade 9 and weakest in grade 7. Students mostly used a combination of pictorial language, natural language, and mathematical symbolic language to describe their solution processes. However, describing their thinking in different ways did not necessarily highlight possible errors in their reasoning. [ABSTRACT FROM AUTHOR]

The objectives of this research were to study the efficacy of the mathematics instructional model (BRIGHT model) based on realistic mathematics education (RME) and model-eliciting activities (MEAs) approaches to enhance mathematical thinking (MT) for upper primary school students as follows: i) to compare the mathematics achievement of students before and after studying with the BRIGHT model, ii) to compare the MT of students before and after studying with the BRIGHT model, and iii) to evaluate the students' and mathematic teachers' satisfaction on learning activities by using the BRIGHT model. The results of this research were as follows: i) the mathematics achievement and MT of students after studying were significantly higher than before studying with the BRIGHT model; ii) the student satisfaction with learning activities using the BRIGHT model was satisfied all aspects of the assessment. The mean scores from highest to lowest were as follows: benefits that student received, learning atmosphere, and learning activities, respectively; and iii) the satisfaction teachers and educational superiors were very satisfied with the learning management process and applying the BRIGHT model. Therefore, learning through the BRIGHT mathematical modeling has shown all aspects of students' and mathematic teachers' expected development. [ABSTRACT FROM AUTHOR]

The research examines the logical and epistemological studies of Leonid Evgenievich Gabrilovich (1878-1953), a Russian philosopher, logic and engineer, and subsequently a Russian-American thinker. The works of L.E. Gabrilovich still remain practically unknown or little known in Russian philosophy. In the study of the philosophical concept of one of the main works of L.E. Gabrilovich “On Mathematical Thinking and the Concept of the Actual Form” (1914), the study of the theory of “actual forms”, which clarifies the foundations of human thinking, is central to the attention of readers. It is proved that the topics of mathematical formalism, the system of experience, the actual form and the problems of number touched upon by Gabrilovich were logical and epistemological aspects of his philosophy. The research covers the content of a review of this essay by Gabrilovich of the famous German mathematician and logic Leopold Löwenheim, published in 1915. The similarity of the theory of actual forms Gabrilovich’s and the meaning of the Löwenheim theorem is revealed. The analysis of Gabrilovich’s work conducted here covers little-known pages of Russian philosophical thought and should serve to enrich and fill existing lacunae in the study of Russian philosophy of the 20th century. In the process of studying the central work of Gabrilovich, results were obtained, on the basis of which they came to the conclusion that the Russian thinker sought to build a complete system of the science of philosophy. In his emigration, Gabrilovich turned to the legacy of such Russian philosophers as Vladimir Solovyov and Nikolai Berdyaev, which was surprisingly combined with mathematical thinking and the concept of actual forms. The study outlines the prospects for studying this and other works of Gabrilovich in the context of neo-Kantianism and the philosophy of mathematics. The original theory of “actual forms” proposed by Gabrilovich can be considered the result of a philosophical understanding of the foundations of mathematics, which was characteristic precisely for logical and epistemological philosophical searches.

We researched how the transition to remote learning during the COVID-19 pandemic affected the development of mathematical thinking and reading comprehension skills of high school students based on the analysis of the results of a standardized test for higher education admission. The total number of participants was N = 17,942, out of which N1 = 10,611 were pre-pandemic applicants and N2 = 7,331 were post-pandemic applicants. The pre-pandemic group took into consideration the exam results from September 2016 to June 2020. The post-pandemic group took into consideration the exam results from September 2020 up to May 2023. We conclude that emergency remote teaching decreased the average mathematical competence of incoming university students by 12.8%. Similarly, emergency remote teaching decreased the average reading achievement of students entering university by 8%. Therefore, the impact of emergency remote teaching was greater on mathematics skills than on reading achievements. [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Educational Psychological Studies (EPS) is the property of Refaad for Studies, Research & Development and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Our mathematical thinking sheds light on how we see our world and what knowledge we have about it. In spite of this, mathematical performance is still mostly measured in calculation skills, and this also predestines the success of learning. So at school, what is important is how correctly we solved the task and not the way we got there. An internationally unique Hungarian-developed test (DPV—Pedagogical Examination of Dyscalculia/Diszkalkulia Pedagógiai Vizsgálata) draws our attention to the opposite of this. The special feature of the test is its criterion orientation, which emphasizes the correctness of mathematical thinking while examining the abilities necessary for learning mathematics. The aim of our study was to investigate, as a function of background variables (gender and socioeconomic status (SES)), (1) whether the abilities and thought processes required for learning mathematics function at an adequate level, (2) what effect these may have on mathematical performance, and (3) to what extent all of this is influenced by mathematical anxiety. Our background variables were gender and socioeconomic status. A total of 999 Hungarian students aged 10–15 participated in our study, including 483 boys and 516 girls. In general, we can say that the development of the skills necessary for learning mathematics is closely related to the students' performance. Nevertheless, it happens that we encounter low performance despite good skills. In several cases, we can experience the presence of anxiety, especially math anxiety, which in most cases, regardless of the level of abilities, negatively affects the success of math learning processes. The findings confirm that socioeconomic status, gender, and performance are risk factors for mathematical anxiety. The following hypotheses have been formulated along the lines of the research objectives set out in the abstract: There are no differences in ability and mathematical performance between boys and girls. Girls are more anxious when they have to solve a mathematical problem. Socioeconomic status predicts ability level and the presence of math anxiety. Mathematical anxiety (MA) modifies the validity of mathematical ability (DPV). [ABSTRACT FROM AUTHOR]

The editorial in "Frontiers in Education" discusses mathematical thinking, practices, and processes in non-formal learning environments. The authors aim to highlight how non-formal mathematics learning can support formal learning and promote a love of mathematics in everyday life. The research topic emphasizes the importance of multidisciplinary collaboration, careful parameter setting, and recognizing the value of mathematics in unexpected places. The authors encourage further exploration of non-formal mathematical learning in post-secondary, adult, and marginalized groups to broaden understanding and appreciation of mathematics. [Extracted from the article]

Copyright of Revista Espacios is the property of Talleres de Impresos Oma and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Computational thinking (CT) has received much attention in mathematics education in recent years, and researchers have begun to experiment with the integration of CT into mathematics education to promote students' CT and mathematical thinking (MT) development. However, there is a lack of empirical evidence and new theoretical perspectives on the mechanisms of interaction between CT and MT. To address this research gap, this study analyses the participants' thinking processes in solving programming-based mathematical problems from a flexibility perspective, focusing on the interplay between computational and mathematical thinking, that is, how CT and MT work together to influence and determine the problem-solver's choice of solution strategy. Using data collected from a large design-based study, we summarise two types of flexibility and six subtypes of flexibility demonstrated by participants in the programming-based mathematical problem-solving process using thematic analysis. These different types of flexibility provide researchers and mathematics educators with new theoretical perspectives to examine the interplay of CT and MT. Findings will also contribute toward student learning characteristics in programming-based mathematical problem-solving to sketch the big picture of how CT and MT emerge in complementary or mismatching ways. [ABSTRACT FROM AUTHOR]

Students frequently struggled with the mathematizing process – forging connections between implicit and explicit mathematical thinking – when solving a context-rich applied problem. The current research investigated how students interact with and leverage purposively designed 'mathematizing' supports when solving applied math problems in a game-based, inquiry-oriented math learning environment. We conducted a naturalistic observation case study and a mixed-method study to investigate middle school students' usage of mathematizing supports in relation to their math problem-solving performance. The findings indicated a positive and predictive impact of using mathematizing supports on the logged and observed practice of mathematization as well as the performance of applied math problem solving by the students during and after gaming. However, not all students leverage in-game mathematizing supports or engage in problem mathematizing processes. The grounds of students' constructive interaction with a mathematizing support include their productive persistence in problem solving, their exercise of agency in gauging the utility of mathematizing, and their engagement with deductive reasoning from concrete to abstract. We also observed an interplay between internal and external mathematizing supports, which is moderated by the modality of learning settings. [ABSTRACT FROM AUTHOR]

The purpose of the study is to examine pre-service elementary teachers' noticing of students' mathematical thinking of division through animations and depictions. For this purpose, the data was collected from preservice teachers' written explanations of important moments identified when watching a video clip, as well as pre-service teachers' animations and depictions of classroom scenarios. Findings indicated that what the pre-service teachers noticed in the video clip was more general, as they attended to the whole class environment, students' behaviours and learning in total, and teacher pedagogy. The pre-service teachers, however, were more focused on particular students' mathematical thinking in their animations and depictions. Furthermore, between animations and depictions, the pre-service elementary teachers included the most details about students and teachers in the latter one. Therefore, this study concludes that while both preparing animations and depictions have a positive effect on the pre-service elementary teachers' noticing levels, preparing depictions better facilitates their attention to students' thinking about mathematics. [ABSTRACT FROM AUTHOR]

We researched how the transition to remote learning during the COVID-19 pandemic affected the development of mathematical thinking and reading comprehension skills of high school students based on the analysis of the results of a standardized test for higher education admission. The total number of participants was N = 17,942, out of which N1 = 10,611 were pre-pandemic applicants and N2 = 7,331 were post-pandemic applicants. The pre-pandemic group took into consideration the exam results from September 2016 to June 2020. The post-pandemic group took into consideration the exam results from September 2020 up to May 2023. We conclude that emergency remote teaching decreased the average mathematical competence of incoming university students by 12.8%. Similarly, emergency remote teaching decreased the average reading achievement of students entering university by 8%. Therefore, the impact of emergency remote teaching was greater on mathematics skills than on reading achievements.

The purpose of the study is to examine pre-service elementary teachers’ noticing of students’ mathematical thinking of division through animations and depictions. For this purpose, the data was collected from pre-service teachers’ written explanations of important moments identified when watching a video clip, as well as pre-service teachers’ animations and depictions of classroom scenarios. Findings indicated that what the pre-service teachers noticed in the video clip was more general, as they attended to the whole class environment, students’ behaviours and learning in total, and teacher pedagogy. The pre-service teachers, however, were more focused on particular students’ mathematical thinking in their animations and depictions. Furthermore, between animations and depictions, the pre-service elementary teachers included the most details about students and teachers in the latter one. Therefore, this study concludes that while both preparing animations and depictions have a positive effect on the pre-service elementary teachers’ noticing levels, preparing depictions better facilitates their attention to students’ thinking about mathematics.

This research aims to determine the relationship between computational thinking ability and mathematical critical thinking ability of seventh-grade students at SMPN 49 Jakarta. Computational thinking ability is skills or processes in solving problems effectively, while mathematical critical thinking ability is a process of analyzing problems to make an accurate decision. This research used correlation research with research subjects consisting of 14 female students and 16 male students. The instrument in this study is a test in the form of a description, which is measured using indicators. This study used decomposition, pattern recognition, abstraction, and algorithm thinking as indicators of computational thinking ability. This study uses elementary clarification, essential support, inference, advanced clarification, strategy, and tactics as indicators of mathematical critical thinking. The outcome of this research showed a positive correlation between computational thinking ability and students’ mathematical critical thinking ability. The relationship analysis shows a simultaneous and significant relationship between computational thinking and essential mathematical thinking abilities. The correlation test results using Pearson Product Moment obtained a result of 0.897 with a coefficient of determination of 80.5%. The magnitude of the correlation indicates that the two abilities have a solid relationship. If computational thinking ability is high, then mathematical critical thinking ability is also high, and if computational thinking ability is low, then mathematical critical thinking ability is also low.

This research was conducted in 2019 in collaboration with Japanese colleagues, with the research tasks translated from the original Japanese. In Finland, a total of 1112 students from grades 7–9 in primary school participated in the study. In our article, we examine Finnish students’ mastery of the concept of percentages and how they express their mathematical thinking about percentages in a multimodal way. A multimodal expression of mathematical thinking can typically take the form of natural language, written mathematics, pictorial representations, mathematical symbolic language, or combinations of these, which can be used to manage information, such as through tables. Our focus is on Finnish primary-school students’ mastery of the concept of percentages, and we then narrow our analysis to tasks where students have used a multimodal approach. We analyze the representations of the concept of percentages and the related thought processes. The concept of percentages was best mastered in grade 9 and weakest in grade 7. Students mostly used a combination of pictorial language, natural language, and mathematical symbolic language to describe their solution processes. However, describing their thinking in different ways did not necessarily highlight possible errors in their reasoning.

Copyright of GeSec: Revista de Gestao e Secretariado is the property of Sindicato das Secretarias e Secretarios do Estado de Sao Paulo (SINSESP) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The incorporation of Computer Science teaching in educational systems has increased in recent years. Given international interest, Chile has promoted projects to promote the development of students' digital skills. Focusing on this new educational context, this research reports the results regarding the identification of computational concepts and practices that can be articulated with the contents and skills of the curriculum. of Chilean mathematics. for first grade of primary school based on the use of the Bee-Bot robot. For this, the study followed a qualitative approach, developing a case study of the Chilean study program with the content analysis technique and using, as analysis categories, computational concepts and practices from the field of educational computing. In total, 30 learning objectives of the study program were analyzed. The results indicate that, although there is little articulation between computational concepts and first grade content proposed in the curriculum, there is greater articulation between computational practices and mathematical skills suggested in the Chilean curriculum. It is concluded that Computational Thinking can be developed from the earliest school levels using the Bee-Bot robot (or similar), and this is demonstrated by the structure of the Chilean primary mathematics curricular program. [ABSTRACT FROM AUTHOR]

Introduction: in classrooms it is common to find students with exceptional abilities, the lack of interest of schools and teachers to attend to this type of students generates that this type of students is truncated in their abilities, since their learning is approached at the same time. same rate of students with regular ability. In that order, some students develop logical-mathematical thinking skills in primary education, so the early introduction to algebra is a way to take advantage of the skills of this type of student and in turn enhance them in a way that is of interest. for them. Objective: Characterize didactic sequences for the development of early algebra in students with exceptional talent in Primary Education in mathematics. Materials and methods: It was carried out using a qualitative approach and design of multiple case studies. Techniques such as participant and nonparticipant observation, the interview with the teacher and students with exceptional talent and didactic analysis were used). Results: Significant advances were found in students with exceptional talent, by identifying a variable in a mathematical problem and presenting basic arguments in the solution, developing mathematical problem-solving and argumentation skills, by acquiring literal symbolic language and knowing how to justify conclusions. to math problems. Conclusions: It was concluded that the designed activities enhanced mathematical thinking in problem solving and argumentation skills in students due to the creativity, originality, discourse and mathematical language used in them. [ABSTRACT FROM AUTHOR]

The core components of mathematical activity are involved in mathematical investigation: problem formulation, processing of conditions for which there is no clear solution, formulation and justification of conjectures, and generalization. However, introducing mathematical investigation to students is a challenging activity. A crucial aspect of the student's learning and understanding of the process is the kind and degree of their engagement in the learning activity. This phenomenological study sought to describe how pre-service teachers engaged in an online problem-based learning (PBL) while doing a mathematical investigation (MI). The researcher explored the cognitive, behavioral, and affective components of the 35 pre-service mathematics education students who had their first-hand experience of MI through online PBL. The students were given two contextualized, ill-structured problems, worked in groups, and proposed solutions to the problem. Data from the teachers' observation notes, students' learning logs, and the transcripts of the focus group discussions were gathered. Qualitative data analysis suggests that students were involved in peer-to-peer learning that included task-related conflicts, pattern recognition, self-regulation, critical analysis, participation in the learning activity, attention to the tasks, and interaction with the learning community which led to their enjoyment and motivation in conducting MI. The extent of their engagement during the presentation and analysis of the problem, planning and developing a solution, presenting and assessing solution, and summary and debriefing were further analyzed. The findings revealed that while students were initially puzzled at the start of their investigation, they shared, welcomed new information, analyzed it, and valued different approaches to a challenging mathematical problem as they progress with their inquiry. The results also revealed respondents' perspectives on how to manage online PBL. These findings can help teachers design collaborative online activities. [ABSTRACT FROM AUTHOR]

In today's world, it is important for individuals to have critical thinking and mathematical thinking skills, which are high-level thinking skills. In advanced education systems, it is among the important priorities that students not only learn knowledge but also acquire high-level thinking skills. This study aims to examine the relationship between mathematical and critical thinking skills and academic achievements of secondary school students. In the study, relational screening model, one of the quantitative research models, was used. The research was carried out in a province located in the southern region of Turkey in the 2022-2023 academic year with students studying in secondary school (n=346) who were determined by maximum variation method selected from the types of purposeful sampling. Mathematical thinking scale and critical thinking scale was used as a data collection tool. In the process of analyzing the data, one-way analysis of variance and regression analysis techniques were used. According to the research findings, it was observed that there was a relationship between the critical thinking and mathematical thinking skills of the students, both the critical and mathematical thinking skills of the students did not differ significantly according to gender, and the mathematical thinking skills differed significantly according to the grade level. In addition, it was concluded that both mathematical and critical thinking skills of the students increased according to their grade levels. In addition, students' critical skills and academic achievement together explained 25.0% of the total variance of mathematical thinking skills. In other words, as students' critical thinking skills and academic achievement increase, their mathematical thinking skills also increase. [ABSTRACT FROM AUTHOR]

Copyright of Revista Transdisciplinaria de Estudios Sociales y Tecnológicos (RTEST) is the property of Editorial Exced and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Turkish Journal of Education is the property of Mehmet Tekerek and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Voces y Silencios is the property of Universidad de los Andes and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Background. The process of teaching mathematics represents a challenge for primary education, due to the different perspectives and disciplines involved. In addition, as an active and flexible process, it requires feedback on what the students actually achieved. An analysis of the different learning and development outcomes allows the teacher to understand the mathematical content and the method of teaching it in the classroom, with the objective of promoting the students’ conceptual development. Objective. The objective of our study was to analyze the general skills for problem solving which students developed, by applying dynamic evaluation. Design. A verification method was used to identify the students’ abilities and difficulties. A protocol for evaluating the process of solving mathematical problems was organized. The assessment included four simple problems and four complex ones. The participants were 15 students in the third grade of primary school attending a private school located in Mexico City. Results. The results showed that the students identified the types of mathematical operations (addition, subtraction, multiplication, and division) required to solve the problems as their objective. Therefore, their preparation of a solution plan, its execution, and its verification were based only on empirical thinking and quantitative information. Conclusions. We concluded that problem-solving is an intellectual activity that requires conceptual development to carry out a solution plan, execute it, and verify it, in addition to the main objective of answering the question posed by the problem. We propose that these characteristics be included in the organization of mathematics teaching in order to develop mathematical thinking.

Our mathematical thinking sheds light on how we see our world and what knowledge we have about it. In spite of this, mathematical performance is still mostly measured in calculation skills, and this also predestines the success of learning. So at school, what is important is how correctly we solved the task and not the way we got there. An internationally unique Hungarian-developed test (DPV—Pedagogical Examination of Dyscalculia/Diszkalkulia Pedagógiai Vizsgálata) draws our attention to the opposite of this. The special feature of the test is its criterion orientation, which emphasizes the correctness of mathematical thinking while examining the abilities necessary for learning mathematics. The aim of our study was to investigate, as a function of background variables (gender and socioeconomic status (SES)), (1) whether the abilities and thought processes required for learning mathematics function at an adequate level, (2) what effect these may have on mathematical performance, and (3) to what extent all of this is influenced by mathematical anxiety. Our background variables were gender and socioeconomic status. A total of 999 Hungarian students aged 10–15 participated in our study, including 483 boys and 516 girls. In general, we can say that the development of the skills necessary for learning mathematics is closely related to the students’ performance. Nevertheless, it happens that we encounter low performance despite good skills. In several cases, we can experience the presence of anxiety, especially math anxiety, which in most cases, regardless of the level of abilities, negatively affects the success of math learning processes. The findings confirm that socioeconomic status, gender, and performance are risk factors for mathematical anxiety. The following hypotheses have been formulated along the lines of the research objectives set out in the abstract: There are no differences in ability and mathematical performance between boys and girls. Girls are more anxious when they have to solve a mathematical problem. Socioeconomic status predicts ability level and the presence of math anxiety. Mathematical anxiety (MA) modifies the validity of mathematical ability (DPV).

As we move further into the digital age, the acquisition of digital literacy (DL) and computational thinking (CT) skills is emerging internationally as an essential goal for students in contemporary school curricula. As the world becomes more uncertain and volatile due to impacts of artificial intelligence (AI), international unrest, climate change, global economic instability and unforeseen catastrophes such as the Coronavirus (Covid-19) pandemic, it is necessary to review, revise and refine school education curricula and policies. The issue of what is essential for students to learn, and how they learn it, is of growing importance to international organisations such as the Organisation for Economic Co-operation and Development (OECD) and the United Nations Educational, Scientific and Cultural Organisation (UNESCO) and is emerging as a significant driver for educational reform across the globe. The growing prominence of CT and DL skills across many industry sectors has prompted recent changes to international assessment frameworks such as the Programme for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS). This paper will briefly discuss specific examples of alternative approaches to addressing CT in national curricula for the compulsory years of schooling and explain how CT has been adopted as a driver for mathematics curriculum change in Australia.

A critical part of supporting the development of students’ algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks—tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students’ algorithmic thinking skills. This paper presents three illustrative cases of emergent challenges evident as students grapple with the process of creating an algorithm. The first challenge highlights discrepancies between the method with which students solve a problem and the algorithm they create, and claim would, when implemented, solve the same problem. The second challenge pertains to the persistence of students’ normatively incorrect algorithms, despite going through multiple iterations of testing and revising. Finally, the third challenge concerns issues around the use of test problems for supporting students in their creation of generalized algorithms. These three challenges are discussed using student data (illustrative cases) from three different mathematical algorithmatizing tasks. Suggestions are put forth for addressing some of these challenges, with a particular emphasis on practical pedagogical suggestions for cultivating students’ mathematical thinking in the context of algorithmatizing tasks.

This study was undertaken given the need to develop mathematics modular instruction that integrates Sama students' culture with Science, Technology, Engineering, and Mathematics (STEM) amidst the COVID-19 pandemic. It sought to find whether students exposed to EthnoSTEM-Based Mathematics Instruction (EMI) have significantly better mathematical thinking than those taught with its conventional counterpart (CMI) during modular distance learning. EMI utilized mathematics learning modules that incorporate seaweed farming and mat weaving of the Sama. True Experiment between two groups employing Pre- and Post-tests was done to determine the effects of EMI on mathematical thinking. It was conducted among Grade 7 Sama students from a High School in Tawi-Tawi Province. A researcher-made Mathematical Thinking Test was validated by experts and pilot-tested for item and reliability analyses. Findings revealed that Sama students exposed to EMI have significantly better mathematical thinking than those taught with the CMI. Discussions, conclusions, and recommendations are provided. [ABSTRACT FROM AUTHOR]

In this study, the visual estimation skills of fourth grade elementary school students based on their mathematical thinking processes were investigated. The research questions focus on understanding how students' mathematical thinking processes influence their visual estimation skills. A total of 445 students participated in the study. The relational scanning model was used to determine the relationship between students' visual estimation skills and their mathematical thinking processes. The Mathematical Process Instrument and the Visual Estimation Skills test were used as data-gathering tools. The data obtained were analyzed using different statistical methods, including the chi-squared test, t-test, and single-factor analysis of variance. The findings contribute to our understanding of the complex relationship between mathematical thinking processes and visual estimation skills in students, addressing the research questions raised in the study. These results can inform educators and instructional designers when developing effective teaching materials and strategies that cater to students' diverse thinking processes. [ABSTRACT FROM AUTHOR]

Computational thinking, defined as a way of thinking that can be applied to various fields that require problem-solving skills, has become prevalent in education. Students, i.e., future specialists, have to be prepared for complex thinking competence, necessary for solving business and societal problems, for which a combination of mathematical thinking and computational thinking is essential. The preliminary premise is that there is a correlation between ability in specific mathematical and computational fields. Therefore, this paper aims to highlight the significance of investigating the relations between those fields from linguistic point of view. In order to better understand the relationship between abilities in specific mathematical and computational fields, this paper presents an analysis of a new approach, namely, developing hypotheses for exploring the relationship between metalanguages of different fields of Mathematics and Computer Science. Additionally, the paper describes the first stage of a study on a doctoral level in an attempt to suggest possible statistical analyses suitable for testing hypotheses based on meta-analysis of the current literature. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Turkish Educational Sciences is the property of Journal of Turkish Educational Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An abstract is a brief, comprehensive summary of the contents of the article; it allows readers to survey the This study aims to examine the development of the mathematical thinking skills of pre-service elementary mathematics teachers through error-based activity practices. The study was designed as a case study, which is one of the qualitative study designs. The study group of the research consisted of five pre-service mathematics teachers studying at a Turkish university. In selecting the study group, the criterion sampling method that is one of the purposive sampling methods was employed. Data were collected through face-toface interviews with pre-service teachers and diaries kept by them. Data were analyzed using the descriptive analysis method. Based on the findings obtained from the study, the error-based activities were observed to positively affect specifically the specialization and generalization processes of pre-service teachers. Following these two processes, the assumption and persuasion processes of the pre-service teachers were also revealed to have improved with the practice of error-based activity implementation. In conclusion, error-based activities were observed to have positively affected the mathematical thinking processes of pre-service teachers. [ABSTRACT FROM AUTHOR]

This study aims to describe students' mathematical thinking processes in terms of math anxiety. The method used in this research is descriptive qualitative. Data collection techniques were carried out through tests, documentation and interviews. The determination of the subject used a purposive sampling technique by taking 5 student level subjects who had very high, high, medium, low, and very low levels of math anxiety. The results showed that in the process of working on the test instrument in the form of HOTS questions, subjects with very low levels of anxiety were able to solve the first and second problems correctly. In the entry phase, the subject fulfills the I know, I want, and introduce rubik. And in the attack phase it fulfills the rubik's try, may be, and why. In the review phase it only fulfills the Rubik's check, and does not meet the rubik reflect and extend. This can be seen from the results of work that does not use a general formula.

Metacognitive awareness influences problem-solving thinking. Understanding metacognitive awareness is essential in the teaching and learning process. The purpose of this research is to determine the amount of metacognitive awareness and the characteristics of each level in problem solving. The extent of metacognitive awareness of 125 prospective mathematics teacher students from four different public and private universities was revealed in this exploratory qualitative study. To acquire research data, absolute value assignments, think-aloud transcripts, and semi-structured interviews were employed. Sources and methods are triangulated to assure data validity. The data was analyzed using fixed comparison analysis. The results of this study indicate that there are six levels of metacognitive awareness of prospective teacher students: tacit use, identity use, semi-aware use, aware use, strategic use, and reflective use. The six developed levels can identify all the characteristics of metacognitive awareness that arise in solving absolute value problems. Metacognitive awareness that has been developed can supporting the development of learning models, cognitive style characterization and tracing students' process of mathematical metacognitive awareness. [ABSTRACT FROM AUTHOR]

This exploratory and descriptive study aims to theoretically promote the schema of pseudo-thinking processes in mathematical problem-solving by students. The participants in this study were 36 eighth graders and one math teacher. The researchers collected the data using tests and interviews. The results showed that the structure of pseudo-thinking based on the processes of assimilation and accommodation is theoretically composed of five hierarchical components, namely (a) the structure of the problem, (b) the structure of the subject's thinking, (c) the analytic process, (d) the integration of structures or substructures, and (e) the complete integration of structures. When the subject integrates incomplete substructures into existing thinking schemes, assimilation or accommodation becomes imperfect, resulting in cognitive disequilibrium. The results of such a thought process are called pseudo-thinking. Pseudo-thinking processes can be refined and improved into actual thinking processes through reflection and scaffolding. Assimilation and accommodation occur through defragmentation or organization to rearrange the internal schema so that full structural integration occurs. In the end, the subject experiences cognitive equilibrium so that it becomes an actual student thought process. [ABSTRACT FROM AUTHOR]

The research aimed to identify the effect of using self-regulated learning in teaching mathematics to develop mathematical thinking and self-management for the sixth grade student . The research sample consisted of (66) sixth grade students distributed into two groups, One of them is experimental, consisting of (35) students, and self-regulated learning was used with them, The other was a control group of (31) students, and the usual method was used with her, The research tools were: a test of mathematical thinking skills (induction, logical thinking, problem solving). The research found: There is a statistically significant difference between the mean scores of the students of the experimental group and the scores of the students of the control group in the post application of each of the mathematical thinking skills test for the benefit of the students of the experimental group. The results also revealed that there is a statistically significant positive correlation between mathematical thinking among the experimental group. [ABSTRACT FROM AUTHOR]

The aim of this study is to understand how students' mathematical thinking is activated and nurtured in solving a modeling problem, where the problem situation involves the design of a system. From a STEM integrated perspective, 9th grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The theoretical framework proposes a conceptualization of the interplay between the mathematical modeling process, from a cognitive perspective, and the engineering design process. Central ideas refer to the cyclical nature of both processes and to the sub-processes involved in them. The empirical data were collected in two design-based research cycles with different 9th grade classes. The data from the groups' audio and video recording and the students' productions were analyzed under a directed qualitative content analysis informed by theory. The results showed a global pattern in the students' thinking in solving a design system problem. The overlapping and interplay between the mathematical modeling and the design process was a prominent characteristic of students' thinking. The modeling cycle was mirrored by a design cycle, with both running in parallel. System thinking pushed and drove students' mathematical thinking, from the system requirements to the prototype validation. [ABSTRACT FROM AUTHOR]

In the research reported in this article, we seek to explore aspects of differential thinking and thinking-with-GeoGebra that emerge when high school students investigate activities on the calculation of areas and volumes. Initially, we discuss issues about mathematical thinking and differential thinking, proposing a perspective on differential thinking formed by four aspects: Notion of limit and continuity; Notion of infinitesimal; Defined integral concept; Visualgeometric design. From the methodological point of view, based on qualitative research, we developed teaching experiments with 6 pairs of students from the 10, 11 and 12 grades of High School, considering the elaboration of a task composed of 5 activities. In the article, based on the notion of sampling in qualitative research, we discuss the investigation developed by one pair of 12th grades about the activity entitled "The Problem of Volume". In the data analysis, we highlighted the role of visualization and experimentation-with-technologies in the development of students' thinking. In particular, we emphasize how the resources or potentialities of the software offered ways for students to articulate the four aspects that make up differential thinking in the proposed perspective. This study contributes to the production of knowledge about the use of digital technologies in Mathematics Education, in particular to the relation to the teaching of Calculus in High School. [ABSTRACT FROM AUTHOR]

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