Development Of Mathematical Thinking Research Articles

MATHEMATICAL WRITING OF INTERMEDIATE SCHOOL’S LEVEL THREE FEMALE STUDENTS IN RIYADH CITY AND ITS RELATION WITH MATHEMATICAL THINKING

Purpose of the Study: The study sought to discover the level of mathematical thinking in mathematical writing among the female students of the intermediate third-level in Riyadh, and thus determine the relationship between the levels of mathematical writing and mathematical thinking among the female intermediate students of the third level.
 Methodology: In this research, the descriptive and analytical method is used. The analytical descriptive method was used to analyze 68 books of mathematics textbooks. The study tools consist of the mathematical writing analysis card for the records of the students and to measure their mathematical thinking.
 Main Findings: The development of mathematical thinking in mathematics education is the main domain of this research. Through the paper, the researcher explains the students’ mistakes in their mathematical writing.
 Applications of this study: The results of this study may serve to guide teachers to take care of student writing, the importance of providing a track record for students' writing and their training in the integrity of mathematical writing, showing them understanding and teaching them to provide appropriate learning.
 Novelty/Originality of this Study: In light of the results of the study, the researcher suggests conducting studies such as: determining the relationship between the level of mathematical writing among students and other variables such as achievement, mental ability and problem-solving. The study may also be conducted on the relationship between the teaching practices of the mathematics teachers in the mathematical communication between the students and the construction of a training program to develop the written communication among the students.

In-Game Actions to Promote Game-Based Math Learning Engagement

Game-based learning (GBL) has increasingly been used to promote students’ learning engagement. Although prior GBL studies have highlighted the significance of learning engagement as a mediator of students’ meaningful learning, the existing accounts failed to capture specific evidence of how exactly students’ in-game actions in GBL enhance learning engagement. Hence, this mixed-method study was designed to examine whether middle school students’ in-game actions are likely to promote certain types of learning engagement (i.e., content and cognitive engagement). This study used and examined the game E-Rebuild, a single-player three-dimensional architecture game that requires learners’ application of math knowledge. Using in-depth gameplay behavior analysis, this study sampled a total of 92 screen-recorded and video-captured gameplay sessions attended by 25 middle school students. We adopted two analytic approaches: sequential analysis and thematic analysis. Whereas sequential analysis explored which in-game actions by students were likely to promote each type of learning engagement, the thematic analysis depicted how certain gameplay contexts contributed to students’ enhanced learning engagement. The study found that refugee allocation and material trading actions promoted students’ content engagement, whereas using in-game building tools and learning support boosted their cognitive engagement. This study also found that students’ learning engagement was associated with their development of mathematical thinking in a GBL context.

Strategies on mathematical thinking. A superior experience

The present article is a systematization of experiences derived from a workshop developed with higher education graduates working as teachers in basic or upper secondary education. The aim of the workshop was to strengthen the participants’ competences in the design of didactic strategies focused on the development of mathematical thinking for their own students. The workshop addressed three specific teaching components: planning skills, learning environments and teaching strategies. It is important to highlight that an expected workshop outcome was a book chapter written with experiences drawn from the implementation of the designed didactic strategies. The ambition was to publish a book with financial support of the Research an Innovation Center and the Faculty of Exact Sciences. None of these two last objectives were fulfilled. The paper is divided in four parts: diagnostic evaluation, workshop design and implementation, participants´ satisfaction and conclusions.

CONTRIBUTIONS OF FIGURES NUMBERS IN THE DEVELOPMENT OF GEOMETRIC THOUGHT

This study was constituted with the purpose of promoting reflections on Mathematics of basic education, from a transdisciplinary view of teaching and learning processes. To do so, we aim to analyze the contributions of figures in the development of geometric thinking. We characterize this research in empirical-exploratory, because for Lakatos and Marconi (2017), this type of research distinguishes itself as a scientific process of investigation that allows the researcher to formulate questions, with three purposes: to raise hypotheses, to increase the familiarization of the researcher in order to research, modify or clarify concepts, based on a qualitative and quantitative approach, according to the depth of the discussion about the object in question. For this, we look for information in other researches, databases of universities and virtual libraries, periodicals. We hope that the results contribute to the critical and ethical awareness from views of the importance of the development of mathematical thinking, but specifically of geometric thinking, aiming at non-rupture with arithmetic thinking, in order to interweave with algebraic thinking . We consider this research relevant because mathematics teaching is based on abstract content that often makes no sense to the student, and here we show a part of mathematics that is formal but can be fun when well crafted in the classroom. Finally, we present pedagogical tools of innovation, aimed at contributing to the emancipation of the knowledge of this science, without ruptures.

The Use of Problem-Solving Heuristics Approach in Enhancing STEM Students Development of Mathematical Thinking

One of the major aims of STEM education is the development of mathematical thinking. The common misconception is that “doing mathematics” is the same as getting involved in “mathematical thinking”. Rallying to such argument, many would agree that mathematics should be taught as a thinking activity. Thus, this study endeavours to review the effects of a problem-solving heuristic application technique on learners’ mathematical thinking development. This two-phase study analysed the data utilising a descriptive design (N=660) and experimental design (N=54). In the first phase, 660 High School Leavers, with 93% obtaining an A grade in the Math National Examination, ages 18 – 19, registered with a college to undergo a two-year Diploma engineering program were administered a Mathematical Thinking Test. Then, fifty-four of these students participated in a seven-week Pre-Post experimental design to investigate the impact of heuristics application on their development of mathematical thinking. These student’s post-test score was also compared with a batch of one hundred and twenty third-year university students (N=120) majoring in STEM related courses where all these students have taken at least five university level related math courses. Firstly, the results indicate that the high school leavers grades obtained in the national Examination was not translated into their Mathematical Thinking prowess. Secondly, the results depicted a significant increase in the mathematical Thinking post-test score among the students who underwent a seven-week pre-post problem solving heuristic treatment. Thirdly, the students involved in the heuristic application treatment performed better than the third-year students in the Mathematical Thinking test. It is vital that the heuristic method of teaching mathematics be employed to enhance student’s development of mathematical thinking, especially for STEM students.

Rola języka w rozwoju myślenia matematycznego. Ujęcie kognitywne

Teza
 W pedagogice i psychologii badacze skupiają uwagę na społeczno-kulturowych aspektach uczenia się i nauczania. Wielu autorów porusza kwestie językowe w kształtowaniu myślenia matematycznego. Brak w literaturze sprecyzowanych definicji, istnieje wiele odrębnie funkcjonujących stanowisk co do roli języka w rozwoju myślenia matematycznego. Próbą integracji treści jest analiza tematu w ujęciu kognitywnym.
 Omówione koncepcje
 Podstawą interpretacji jest lingwistyka kognitywna. Przyjmuje, iż poznanie matematyczne jest osadzone w kulturze z dwojakich przyczyn. Po pierwsze, myślenie matematyczne rozwija się dzięki mechanizmowi metaforyzacji. Po drugie, matematyka jest rodzajem instruktażu przekazywanego dzięki imitacji oraz w wyniku interakcji społecznych.
 Wyniki i wnioski
 Język jest katalizatorem matematycznego myślenia. Matematyka to proces dziedziczenia kulturowego. Propozycja kognitywna może być traktowana w kategoriach wskazówek dydaktycznych. Sama istotność roli języka jest jednak niewystarczającą, istnieje potrzeba badań nad tym jak uczyć języka, aby stał się on efektywnym narzędziem w procesie kształtowania myślenia matematycznego.
 Oryginalność/wartość poznawcza podejścia
 Analiza teoretyczna ukazuje problem konstruowania odpowiedniego języka przyczyniającego się do efektywniejszego poznania matematycznego. Autorka dostrzega tendencję do redukcji pojęcia myślenia matematycznego do zdolności matematycznych oraz degradacji języka matematyki i utożsamianie go z językiem edukacji matematycznej.

Early numerical cognition and mathematical processes

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez (2000), I propose one particular conceptual metaphor, the Process → Object Metaphor (POM), as a key element in understanding the development of mathematical thinking.

Mogućnosti razvoja matematičkog mišljenja i učenja u samoorganiziranim aktivnostima djece u vrtiću

U radu se polazi od pretpostavke da djeca rane dobi mogu razvijati matematičko mišljenje i razvijati matematičke kompetencije i u aktivnostima koje ne organizira odrasla osoba, nego ih organiziraju oni sami. U takvim, samoorganiziranim istraživačkim aktivnostima, djeca aktivno istražuju fenomene koji ih zanimaju i rješavaju probleme u kojima je potrebno koristiti čak i vrlo složene matematičke operacije. Različite tehnike promatranja, proučavanja i razumijevanja ovakvih aktivnosti djece može voditi ostvarivanju jedne nove koncepcije učenja i poučavanja, tj. kurikula ranog odgoja usklađenog s prirodom učenja djece. U radu je prikazana jedna etnografska studija slučaja, u kojoj se istražuje obrazovni potencijal samoorganiziranih aktivnosti djece, tj. njihova povezanost s razvojem matematičkog mišljenja i učenja djece.

Use of board games in higher education literature review

There is a long standing history of mathematical games and puzzles being used to support mathematical thinking and concepts. The Maths Arcade is an initiative designed to provide a unique environment for students to play games in order to communicate with fellow students whilst developing a range of skills. The purpose of this study was to determine how these skills are developed and how they link to different games, we have found the evidence for this through reviewing a variety of sources focussing on game-play. We found that the playing of board games is fundamentally linked to the development of mathematical thinking and skills. These are developed in many ways including trial and improvement and discussion.

Realidades escolares en las clases de matemáticas

The article presents results of an investigation that had as objective to analyze realities of classes of mathematics teachers in an institution of basic and average education. In the theoretical reference are considered aspects like beliefs, conceptions, interactions in the classroom, pedagogical practices and didactic models. The research was developed under a qualitative approach, where it is interesting to establish the realities that are lived inside the classrooms in the mathematics classes, it tries to emphasize complex understandings and relationships that are given in the classrooms. There is still a traditional didactic approach, with constructivism, deriving from conceptions of mathematics. Teaching is synonymous of exposition of contents, with few actions that favor the development of mathematical thinking. The results were analyzed jointly with teachers, especially on possible reasons for these practices, and how they could be improved.

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

ABSTRACTIn this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students’ development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.

NEW TEACHING MATHEMATICS TEACHING EFFECTIVENESS OF THE USE OF INFORMATION AND COMMUNICATION TECHNOLOGIES

The possibilities of computer technologies in improving the quality of teaching mathematics and its application in the 7th grade students studied the impact on the development of mathematical thinking. Teachers and pupils kanşalıktı methodology to apply this technology meñgergendikteri tested and determined to improve the methods of teaching mathematics in the scientific literature of the main ideas, 7th grade, based on the best practices in the teaching of mathematics and taking into account the requirements set by the company's mastery of mathematical concepts and rules and reports identified the role of the computer in teaching and service, including through the effective use of the computer are determined based on the study of the material should be studied.

Implementing Constructivist Principles in Early Mathematics Education: Exploring Cognitively Guided Instruction

The aim of this paper is to review the literature on cognitively guided instruction (CGI) for early mathematics to determine how a CGI classroom embodies constructivist teaching-learning principles. A key philosophy of CGI is that teaching must be based on an understanding of each learner’s development of mathematical thinking. CGI also emphasizes contextualization in problem solving, promoting learners’ development of mathematical thinking by allowing them to share their thoughts with peers and teachers and solve problems in their own ways. These aspects of CGI correspond to constructivist teaching-learning principles. Therefore, we conclude that CGI may provide appropriate guidelines for developing constructivist teaching and learning practices for mathematics education among young children.

Decoding the Development of Mathematical Thinking

Decoding the Development of Mathematical Thinking

Pensamiento matemático y creatividad a través de la invención y resolución de problemas matemáticos

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas), novelty (unique idea) and elaboration (idea development). These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

ENSEÑANZA DEL CONCEPTO DE NÚMEROS DECIMALES Y SUS OPERACIONES DESDE LAS ETAPAS REAL O CONCRETA, GRÁFICA Y SIMBÓLICA

Este artículo es el resultado de una investigación1 realizada por docentes pertenecientes al Grupo de Investigación en Educación Matemática de la Universidad del Quindío (GEMAUQ), que se fundamentó en la comprensión del campo conceptual de las operaciones con números decimales, en el manejo de los instrumentos del conocimiento y en la ejecución de las operaciones intelectuales, con estudiantes de grado sexto. El trabajo de investigación propende por el desarrollo mental del estudiante en el aspecto matemático de las operaciones con números decimales, y el desarrollo de los procesos que involucran la construcción del conocimiento matemático. El objetivo de la investigación fue diseñar e implementar una estrategia didáctica desde las etapas real o concreta, gráfica y simbólica, que contribuya al Desarrollo del pensamiento matemático en el campo conceptual de las operaciones con números decimales en los estudiantes del grado sexto de las Instituciones educativas oficiales del departmento del Quindío. La estrategia didáctica se desarrolló a través de tres etapas: la real o concreta, la gráfica y la simbólica. La etapa real consiste en la manipulación de material concreto donde los estudiantes tienen la experiencia física conducente a adquirir habilidades; es decir se actúa sobre objetos para obtener un conocimiento por abstracción a partir de estos mismos objetos. En la etapa gráfica los estudiantes representan a través de figuras los temas trabajados en la etapa real o concreta. En la etapa simbólica se busca que los estudiantes representan simbólicamente los temas conceptualizados. Por último los estudiantes se enfrentan a situaciones problémicas donde después de haber conceptualizado dan solución matemática a la situación presentada. Con la estrategia planteada en la investigación desde las tres etapas se logró que los estudiantes alcanzaran un desarrollo de pensamiento y la apropiación del concepto de números decimales y sus operaciones.

فاعلیة برنامج قائم على استخدام قبعات التفکیر الست فی تنمیة التحصیل المعرفی والتفکیر الریاضی لدى طالبات الصف الثالث المتوسط بمدینة مکة المکرمة

يهدف البحث الحالي للکشف عن فاعلية برنامج قائم على استخدام قبعات التفکير الست في تنمية التحصيل المعرفي والتفکير الرياضي لدى طالبات الصف الثالث المتوسط بمدينة مکة المکرمة، وتحقيقا لهدف البحث استخدمت الباحثة المنهج التجريبي؛ حيث تکونـت عينة البحـث من (56) طالبة من طالبات الصف الثالث المتوسط ، حيث تم تقسيم عينة البحث إلى مجموعتين: تجريبية (28) طالبة، وضابطة (28) طالبة. وقد أخضعت عينة البحث لاختبار التفکير الرياضي ، واختبار التحصيل المعرفي وذلک بعد التحقق من خصائصهما السيکومترية کقياس قبلي على أفراد المجموعتين، وبعد الانتهاء من فترة التطبيق ، تم تطبيقهما کقياس بعدي. ولاختبار صحة فروض البحث عولجت بياناتها إحصائيا باستخـدام اختبـار (ت)، کما تم حساب حجم التأثير،ومن أهم النتائج التي تم التوصل لها: 1- يوجد فرق ذو دلالة إحصائية بين متوسطي درجات طالبات المجموعة التجريبية وطالبات المجموعة الضابطة في التطبيق البعدي لاختبار التحصيل المعرفي الکلي ومستوياته (الأدنى، الوسيط، الأعلى) لصالح طالبات المجموعة التجريبية . 2- يوجد فرق ذو دلالة إحصائية بين متوسطي درجات طالبات المجموعة التجريبية وطالبات المجموعة الضابطة في التطبيق البعدي لاختبار التفکير الرياضي ومحاوره (التفکير الاستقرائي – التفکير الاستنباطي – التفکير المنطقي – حل المشکلات) لصالح طالبات المجموعة التجريبية. The current research aims to reveal the effectiveness of a program based on the use of Six Thinking Hats in the collection of knowledge and the development of mathematical thinking with the average third-grade students in Mecca In order to achieve the goal of Find researcher used the experimental method; where the research sample consisted of 56 female students from the average of the third row, where the sample was divided into two groups: experimental (28 students), and a control (28) student. The research sample for testing mathematical thinking, and cognitive achievement test has been subjected, after verification of psychometric _khasaisma as a measure for the members of tribal groups, and after the completion of the application period, has been applied as a measure after me. To test the validity of hypotheses were treated statistically using test data (T), was also calculate the size of the effect, and the most important results that have been reached: 1. There is a statistically significant difference between mean scores of students in the experimental group and the control group students in the post application to test the total collection of knowledge and levels (minimum, median, high) for the benefit of students in the experimental group. 2. There is a statistically significant difference between mean scores of students in the experimental group and the control group students in the post application to test the mathematical thinking and themes (inductive thinking - thinking deductive - logical thinking - problem solving) for the benefit of students in the experimental group.

Butterflies and Moths in the Amazon: Developing Mathematical Thinking through the Rainforest

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011-12. The teachers were all participants in a newly developed Masters course that had been designed within a didactical design research framework with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. It reports on the research design, research questions and methods of data collection of the research study related to the project as a whole. Further it explores the impact on pupil learning arising from the teachers’ experiences of this course and, in particular, from the process of classroom inquiry through their action research projects. The analysis of classroom interaction utilises a theoretical framework based on the concept of joint action in didactics. This framework is applied to the analysis of data from one teacher-researcher’s action research project based on the development of a topic-based approach to teaching and learning mathematics on the theme of “The Rainforest”. The findings from this study highlight the ways in which the children actively engaged in the ‘milieu’, the ways in which the teacher developed the ‘didactic game’ by extending the ‘epistemic games’ through the use of the open-ended topic-based approach combined with effective teacher questioning. They also highlight the ways in which the discursive elements of ‘learning games‘ as part of these lessons proved to be very effective means through which to support the children to engage in the milieu and to develop mathematical thinking. It was evident in this study that children had very differing prior knowledge and experiences to bring to the problem solving elements of the tasks and that, due to their ability to visualise the problems, the mathematics became more accessible leading to an evolution in mathematical thinking for all.

Learning journals for university students’ reflection on advanced algebra

This work aims at demonstrating learning journals’ appraisal on the process of reflection and on the development of mathematical thinking (MT). A six-month study was carried out in an Advanced Algebra course. The analysis of the students’ journals was based on the view of content as a tool for ensuring different categories of reflection and of the dimensions of MT. The results showed how such tools promote the upgrading of students’ levels of reflection, including the variety of dimensions in the processing of MT that the students employed, which are indicators of improvement in this area of students’ learning development.

Aplicación de Actividades de modelización matemática en la educación secundaria costarricense

This paper describes the experience gained in implementing mathematical modeling activities as a methodological strategy in teaching issues such as proportions, with a group of eighth year of an academic-day-school, located in the province of San Jose, Costa Rica in 2012. Different techniques for gathering information were applied, such as participant observation and questionnaires. Among the relevant results are the cyclical development of mathematical thinking of students in the stages of mathematical modeling (description, manipulation, prediction and validation) for solving the problem; developing of teamwork skills; and appreciation of mathematics as a useful and effective discipline. To resolve the activities proposed in this study, social interactions such as sharing information, thoughts and ideas, were generated, stimulating the zone of proximal development of the participating students. Likewise, the mathematical modeling activities allowed students to have a positive role in mathematics classes, stimulating, in turn, a different attitude compared to regular classes.