No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Principles and Standards for School Mathematics: A Guide for Mathematicians
... The teachers need to be selective in choosing or making mathematical problems that will be given to students. Good problems will provide an opportunity for students to strengthen, expand, and stimulate their understanding of a concept [7], [8]. ...
... Training and habituation are needed to produce polished problems with minimum errors either in the mathematical concepts, language, or appropriacy. Pre-service teachers have to be served with an opportunity to develop the ability to present such problems to support student mathematical learning [8], [13], [14]. ...
... Related to mathematical connections, [8] noted that mathematical connections could be in the form of interrelationships among mathematical ideas as well as the relationship of mathematical ideas with other subjects or everyday life. Based on this, mathematical problems can be divided into mathematical problems that accommodate the context of everyday life, mathematical problems that include knowledge from subjects other than mathematics, and mathematical problems that do not contain both of them. ...
This study aimed to expose pre-service elementary school teachers' awareness of selecting and using real-life context in the problems they posed. The participants of this study were asked to create mathematical problems. The findings showed that some of the participants were more focused on the mathematical concepts and procedures, but tended to ignore the contexts of the problems proposed. As a result, they created problems using numbers and stories that are not relevant to everyday life or are termed pseudo-problems. Some of the real-problems submitted by the participants were not based on an awareness of problem-context relevance.
... Kurikulum matematika saat ini pada dasarnya (dibanyak negara) selaras dengan dengan harapan yang diuraikan dalam kurikulum Amerika Serikat (United States of America National Council of Teachers of Mathematics Standards), yaitu suatu organisasi profesi pendidikan matematika di Amerika Serikat yang sangat berpengaruh, yang sejak tahun 1980an telah menyerukan diadakannya perombakan secara menyeluruh terhadap praktek pembelajaran matematika di banyak negara, termasuk di Amerika Serikat sendiri, yang antara lain mendorong agar praktek pembelajaran matematika beralih dari pembelajaran yang bersifat teacher-centered ke pembelajaran yang bersifat student-centered, dan mengubah para siswa yang sebelumnya merupakan pembelajar yang pasif (passive learners) menjadi siswa merupakan pembelajar yang aktif (active learners) NCTM (Council, 1989), (Ferrini-Mundy & Martin, 2000). Dalam pembelajaran matematika, seperti dikemukakan dalam NCTM (Council, 1989), (Ferrini-Mundy & Martin, 2000) diharapkan para siswa akan meningkat kemampuannya dalam hal penalaran (reasoning), pemecahan masalah (problem solving), komunikasi matematis (mathematical communication), koneksi-koneksi matematis (mathematical connections), dan dalam hal menggunakan representasi matematis(mathematical representation). ...
... Kurikulum matematika saat ini pada dasarnya (dibanyak negara) selaras dengan dengan harapan yang diuraikan dalam kurikulum Amerika Serikat (United States of America National Council of Teachers of Mathematics Standards), yaitu suatu organisasi profesi pendidikan matematika di Amerika Serikat yang sangat berpengaruh, yang sejak tahun 1980an telah menyerukan diadakannya perombakan secara menyeluruh terhadap praktek pembelajaran matematika di banyak negara, termasuk di Amerika Serikat sendiri, yang antara lain mendorong agar praktek pembelajaran matematika beralih dari pembelajaran yang bersifat teacher-centered ke pembelajaran yang bersifat student-centered, dan mengubah para siswa yang sebelumnya merupakan pembelajar yang pasif (passive learners) menjadi siswa merupakan pembelajar yang aktif (active learners) NCTM (Council, 1989), (Ferrini-Mundy & Martin, 2000). Dalam pembelajaran matematika, seperti dikemukakan dalam NCTM (Council, 1989), (Ferrini-Mundy & Martin, 2000) diharapkan para siswa akan meningkat kemampuannya dalam hal penalaran (reasoning), pemecahan masalah (problem solving), komunikasi matematis (mathematical communication), koneksi-koneksi matematis (mathematical connections), dan dalam hal menggunakan representasi matematis(mathematical representation). Untuk terbentuknya kemampuan koneksi matematik tersebut, dalam NCTM Standards (Ferrini-Mundy & Martin, 2000) dijelaskan bahwa pembelajaran matematika harus diarahkan pada pengembangan kemampuan berikut: (1) memperhatikan serta menggunakan koneksi matematik antar berbagai ide matematik, (2) memahami bagaimana ide-ide matematik saling terkait satu dengan lainnya sehingga terbangun pemahaman menyeluruh, dan (3) memperhatikan serta menggunakan matematika dalam konteks di luar matematika (Suryadi, 2011). ...
... Dalam pembelajaran matematika, seperti dikemukakan dalam NCTM (Council, 1989), (Ferrini-Mundy & Martin, 2000) diharapkan para siswa akan meningkat kemampuannya dalam hal penalaran (reasoning), pemecahan masalah (problem solving), komunikasi matematis (mathematical communication), koneksi-koneksi matematis (mathematical connections), dan dalam hal menggunakan representasi matematis(mathematical representation). Untuk terbentuknya kemampuan koneksi matematik tersebut, dalam NCTM Standards (Ferrini-Mundy & Martin, 2000) dijelaskan bahwa pembelajaran matematika harus diarahkan pada pengembangan kemampuan berikut: (1) memperhatikan serta menggunakan koneksi matematik antar berbagai ide matematik, (2) memahami bagaimana ide-ide matematik saling terkait satu dengan lainnya sehingga terbangun pemahaman menyeluruh, dan (3) memperhatikan serta menggunakan matematika dalam konteks di luar matematika (Suryadi, 2011). ...
The Trending topic in International Mathematics and Science Study (TIMSS) and the Program for International Student Assessment (PISA) have become a new standard for mathematics learning. One of the objectives of the study from TIMSS and PISA is to know the students' abilities in reasoning, identifying, and understanding, and using the basic mathematics needed in daily life. Or in other words, students must have mathematical literacy. The concept of mathematical literacy is intended the ability of individuals to formulate, use, and interpret mathematics in various contexts. This includes mathematical reasoning and using mathematical concepts, procedures, facts, and equipment to describe, explain, and predict phenomena or events (OECD, 2013). Indonesia has participated in TIMSS and PISA studies several times, from the TIMSS and PISA study results, it shows that students have not been able to develop optimally about their thinking abilities in mathematics schools and are still low in ability (1) to understand complex information, (2) theory , analysis and problem solving, (3) using tools, procedures and problem solving and (4) conducting investigations. In 2014, the National Council of Teachers of Mathematics (NCTM) stated that learning mathematics today is still too formal, lacks connection with the meaning, understanding, and application of mathematical concepts, and fails to give sufficient attention to the ability of reasoning and solving problem. These results indicate that there needs to be a change in curriculum orientation, which is not to burden students with content but prioritize the aspects of essential abilities needed by all citizens to participate in developing their country in the 21st century. Therefore it is necessary to develop a mathematics curriculum that enhances students' abilities in reasoning and problem solving in order to improve the quality of mathematics for students knowledge and skill in this global era.
... With mathematics, students are encouraged to think and reason, both in solving problems related to everyday life and mathematical problems themselves. Content standards contained in mathematics learning include numbers and operations, algebra, geometry, measurement, data analysis and probability (Ferrini, 2000). Furthermore, algebra can be defined as a branch of mathematics that studies quantities, relationships and certain structures. ...
... Another thing was also revealed that algebra is an important aspect that is mastered by students because algebra determines the success of students' achievements in more advanced classes. Ferrini (2000) states that all students must study algebra, because algebra competency is very important for use in life, either in work or as preparation for higher education. In line with this, Kriegler (2008) stated that algebra is the main gateway in efforts to understand more complex mathematics. ...
Background: Algebra is one of the most important topics in school mathematics. However, the facts in the field found that there were still many errors made by students in solving problems on linear equations in one variable.Aim: This research aims to describe and analyze students' learning obstacles in one-variable linear equation material.Method: This research used a qualitative research approach with a phenomenological design. This research used a purposive sampling technique, the research subjects were 28 class VIII students of Junior High School in Palu City. Data collection was carried out by triangulating data through description tests, in-depth interviews, and documentation studies.Result: Learning obstacles found in the one-variable linear equation material are categorized into 3 types, namely ontogenic obstacles, epistemological obstacles, and didactical obstacles. ontogenic obstacles are found because there is a leap in students' thinking from an arithmetic mindset to an algebraic mindset. Epistemological obstacles are found due to limited context for students which causes errors in working on questions. Some epistemological obstacles are the concept of linear equations, algebraic operations, and applications to equations. The didactical obstacle was found because the teacher's teaching was procedural so the formation of the concept of one-variable linear equations and inequalities in students did not go well.Conclusion: The importance of initial strengthening is related to students' understanding of coefficients, variables, and constants, providing strengthening of the arithmetic thinking process to algebraic thinking, as well as techniques and methods in delivering material and the teaching materials used.
... The contextual feature is very important for developing students' memory as the material embed deeply in students' memory. The representation form refers to students' expressions of mathematical ideas in their efforts to solve mathematics problems (Ferrini-Mundy, 2000). ...
... This result implied that students who learn from these books might be engaged more in combinedform problems. According to the National Council for Mathematics Teachers (Ferrini-Mundy, 2000), using combined forms in mathematics problems was highly recommended because it encouraged students to get used to various forms of representation. Figure 3. Sample of problems in Indonesian and Singaporean textbooks regarding the aspect of representation form Figure 3 illustrates the sample problems in Indonesian and Singaporean textbooks. ...
Several studies revealed that mathematics problems in textbooks, which were expected to encourage students' reasoning and problem-solving skills, were still lacking. This study aimed to compare Pythagorean problems in Indonesian and Singaporean mathematics textbooks based on the cognitive level of Bloom's taxonomy, representation form, contextual feature, and response type. The data were collected through documentation and observation. The research results indicated that on the cognitive level, the C3-C4 level dominated the Pythagorean problems in Indonesian and Singaporean textbooks. Regarding representation form, Pythagorean problems in Indonesian textbooks used visual and combined forms, while Singaporean textbooks applied mostly combined forms. In contextual feature and response type, Pythagorean problems in Indonesian and Singaporean textbooks used non-application and closed-ended problems. Therefore, the result of this study is expected to contribute to the improvement of high-quality mathematics textbooks, which can compete internationally to support students' learning. Abstract: Beberapa penelitian menunjukkan soal-soal matematika dalam buku ajar Indonesia yang diharapkan dapat mendorong kemampuan penalaran dan pemecahan masalah siswa masih kurang. Penelitian ini bertujuan untuk membandingkan soal-soal Teorema Pythagoras dalam buku matematika Indonesia dan Singapura berdasarkan tingkat kognitif Bloom, bentuk representasi, fitur kontekstual, dan tipe respon. Pengumpulan data dilakukan melalui dokumentasi dan observasi. Hasil penelitian menunjukkan bahwa pada tingkat kognitif, soal Pythagoras dalam buku teks Indonesia dan Singapura sebagian besar berada pada kategori C3-C4. Terkait bentuk representasi, soal-soal Pythagoras dalam buku Indonesia lebih banyak menggunakan bentuk visual dan gabungan, sedangkan buku Singapura lebih banyak menggunakan bentuk gabungan. Pada aspek fitur kontekstual dan tipe respon, soal-soal Pythagoras baik dalam buku Indonesia dan buku Singapura menggunakan soal non-aplikasi dan soal tertutup. Oleh kare itu, hasil penelitian ini diharapkan dapat berkontribusi pada peningkatan kualitas buku teks matematika yang dapat bersaing secara internasional, untuk mendukung pembelajaran siswa.
... The NGSS highlights the importance of creating access for traditionally underserved groups in science (NGSS Lead States, 2013). Additionally, equity is the first of the six NCTM mathematics principles (Ferrini-Mundy, 2000;National Council of Teachers of Mathematics, 2000). Furthermore, societal impact, AI4K12's fifth big idea in AI, is closely related to equity and access in terms of recognizing bias and reaching various underrepresented populations (e.g., geographic, socioeconomic, race, ethnicity, disability, Educ. ...
Artificial intelligence (AI) holds tremendous potential for promoting equity and access to science, technology, engineering, and mathematics (STEM) education, particularly for students with disabilities. This conceptual review explores how AI can address the barriers faced by this underrepresented group by enhancing accessibility and supporting STEM practices like critical thinking, inquiry, and problem solving, as evidenced by tools like adaptive learning platforms and intelligent tutors. Results show that AI can positively influence student engagement, achievement, and motivation in STEM subjects. By aligning AI tools with Universal Design for Learning (UDL) principles, this paper highlights how AI can personalize learning, improve accessibility, and close achievement gaps in STEM content areas. Furthermore, the natural intersection of STEM principles and standards with the AI4K12 guidelines justifies the logical need for AI–STEM integration. Ethical concerns, such as algorithmic bias (e.g., unequal representation in training datasets leading to unfair assessments) and data privacy risks (e.g., potential breaches of sensitive student data), require critical attention to ensure AI systems promote equity rather than exacerbate disparities. The findings suggest that while AI presents a promising avenue for creating inclusive STEM environments, further research conducted with intentionality is needed to refine AI tools and ensure they meet the diverse needs of students with disabilities to access STEM.
... The National Council of Teachers of Mathematics (NCTM) emphasizes that problem-solving constitutes the primary objective of mathematics education within school settings (Mundy, 2000;Haji, 2019). This emphasis underscores its pivotal role not only as an educational goal but also as a fundamental method for teaching and learning mathematics (Posamentier & Krulik, 2008;Posamentier et al., 2006;Schoenfeld, 1985). ...
Mathematics education in Indonesia faces challenges primarily due to the limited problem-solving skills of students, prompting a need for effective teaching materials to enhance classroom learning. Despite this, many educators still rely on conventional methods that are less effective in fostering mathematical understanding. Consequently, there is a demand for alternative resources that can better support mathematics education. This study aims to develop a valid and practical e-module based on Ethno-Realistic Mathematics Education (Ethno-RME) to improve problem-solving abilities among eighth-grade students. Employing a design research approach within the development studies framework, the study includes preliminary and formative evaluation stages. Evaluation tools encompass expert assessments of content and media quality, walkthroughs, documentation, and problem-solving assessments. The outcome is an Ethno-RME-based e-module focused on number patterns, validated through expert reviews and positively evaluated for practicality by students. This research highlights the e-module's potential to significantly enhance students' mathematical problem-solving skills, offering educators an innovative tool to support effective mathematics teaching.
... In the NCTM (2000) report (Ferrini-Mundy, 2000), problem-solving is regarded as one of the five process standards, in which modelling with mathematics is at its core. Moreover (as stated by Artigue (2012)), posing and solving mathematical problems and modelling mathematically are two of the eight transverse cognitive competencies. ...
... In the NCTM (2000) report (Ferrini-Mundy, 2000), problem-solving is regarded as one of the five process standards, in which modelling with mathematics is at its core. Moreover (as stated by Artigue (2012)), posing and solving mathematical problems and modelling mathematically are two of the eight transverse cognitive competencies. ...
... International research bodies such as the Trends in International Mathematics and Science Study (TIMSS) and the National Center for Educational Statistics ((NCES), 2016) have found that students continue to trail in mathematics-related subjects. Again, as evidenced by the National Council for Teachers of Mathematics (NCTM), the Principles and Standards for School Mathematics by Ferrini-Mundy (2000), and the National Mathematics Advisory Panel (2008) publications, effective mathematics instruction worldwide has been the focal point in mathematics curriculum and educational reforms over the past two decades. ...
This book chapter is an expanded study of a previously published article on factors affecting K-12 students' mathematics achievement in the 21st century, using only peer-reviewed articles published from 2012 to 2022. The Boolean search approach was employed to gather articles from electronic research databases. Preferred Reporting Items for Systematic Review and Meta-Analysis Protocols (PRISMA-P) were used to select 65 articles for the study. A total of 33 axial codes were identified as specific factors in the systematic review conducted. A detailed capture of all articles and their focus is presented in this expanded study.
... International research bodies such as the Trends in International Mathematics and Science Study (TIMSS) and the National Center for Educational Statistics ((NCES), 2016) have found that students continue to trail in mathematics-related subjects. Again, as evidenced by the National Council for Teachers of Mathematics (NCTM), the Principles and Standards for School Mathematics by Ferrini-Mundy (2000), and the National Mathematics Advisory Panel (2008) publications, effective mathematics instruction worldwide has been the focal point in mathematics curriculum and educational reforms over the past two decades. ...
Purpose: This study aimed to use a systematic review of factors affecting K-12 mathematics achievement in the 21st century using only peer-reviewed articles published from 2012 to 2022. Methodology: A systematic literature review of factors affecting K-12 mathematics achievement in the 21st century using only peer-reviewed articles published from 2012 to 2022. The Boolean search approach was employed to gather articles from electronic research databases. Preferred Reporting Items for Systematic Review and Meta-Analysis Protocols (PRISMA-P) were used to select a final of 65 articles for the study. A total of 33 axial codes were identified as specific factors from the systematic review conducted. Findings: Analysis of the research questions showed a high percentage of the articles conducted in Europe, North America, and Asia, with fewer publications on other continents. The findings showed low published research articles in the era of the COVID-19 pandemic. A final review of the 65 articles uncovered a total of 32 axial codes as the specific variables affecting K-12 students' mathematics achievements. These axial codes include gender, socioeconomic status, teacher qualification, and class size. Unique Contribution to Theory, Practice, and Policy: While many of these studies have found students, teachers, and schools-related variables as predicting or affecting students' mathematics achievement, comprehensive research into the specific factors within the identified variables is less researched. This study will bridge this gap and contribute to the research and academic resources pool. Governments and other education stakeholders worldwide can use the findings from this study as a guide in making decisions and improving learners' academic standards.
... For this, students were aware of different threat which appears in the downloading the different application and programme (Potgieter, 2015). Similarly, NCTM (2000) as cited in Ferrini-Mundy (2000) has been focused in the use of mobile technology is an open learning system in ISSN: 977-2565-5000-04 learning mathematics. It emphasizes the important of ICT in mathematics education. ...
This study is mainly focused on the students' mobile using habit and its impact on teaching and learning mathematics. The study method was survey with 119 students of public and institutional schools in the Chandragiri Municipality of Kathmandu. Questionnaire is use for identifying the access and use of mobile for learning and achievement test for measuring the students' achievement as tools for the study. The study found that 89.9% students had access of smartphones at their home including personal as well as their own. The utilization of mobile smart phone is the genuine concern for the proper utilization for learning. The results indicated that, the use of mobile in planned learning for a specified time enhanced the mathematics performance of students. Adversely, those students who engaged on mobile/smart phones higher in hours and not using mobile for learning purpose decreased their achievement in mathematics. Gender difference observed in using mobile that boys used mobile more hours than the girls. Further, entertainment type of application/programme such as music videos, song were the favorite program for girls whereas games related programme was the favorite programme for boys in the use of mobile/smart phones. Two hours/day was found the standard time to use mobile/smart phones for better performance in mathematics.
... The field of mathematics education has witnessed substantial advances in teaching and learning processes on a global scale. Efforts are being made to enhance the capacity of mathematics teachers by improving their content knowledge and pedagogical skills, as underlined by Pepin et al. (2017) and Ferrini-Mundy (2000). The learning outcomes achieved by students often reflect the quality of teachers' pedagogical and content knowledge. ...
Proficiency in spatial visualization plays a significant role in learning 3D geometry. Spatial visualization ability can be enhanced through the use of relevant teaching and learning techniques. The study aimed to investigate the impact of computer-aided instructional techniques on improving students' spatial visualization skills in learning 3D geometry, addressing the issue of low spatial visualization ability among students. The study followed a mixed research approach with a quasi-experimental design. Twenty mathematics teachers were purposively selected, and 267 Level-4 students from six ordinary-level secondary schools were purposively chosen for the study. Data were gathered using interviews, and pre- and post-tests of control and treatment groups through the use of computer simulation and animation of 3D figures in the treatment group, while the control group was taught using traditional methods. The Statistical Package for Social Sciences (SPSS) was used to compute descriptive and inferential statistics from quantitative data, while thematic analysis was applied to analyze qualitative data. The results from mathematics teachers’ interviews indicate that teachers put less emphasis on enhancing students’ spatial visualization abilities. Students from the treatment group outperformed the control groups on spatial visualization ability in terms of test scores. Additionally, an independent sample t-test revealed a statistically significant difference between the control and treatment groups in terms of spatial visualization ability. The computer-aided instructional approach is relevant in enhancing students’ spatial visualization abilities. To improve students' spatial visualization skills, the researchers propose in-service training for teachers to incorporate computer simulations and animations into the teaching and learning of 3D geometry.
... It is commonly accepted that in the early ages, the emphasis in mathematics teaching is placed on the areas of Numbers and Operations, Geometry, and Measurement, together with the transversal development of mathematical processes such as, for example, reasoning and problem-solving. Of these areas, numbers and their operations are undoubtedly the focus in early education and of which there is greater knowledge of its development during the first years of life [19,20,21]. In Chile, four learning objectives explicitly address content in the numerical area (comparison, ordering, counting, and adding and subtracting) which were taken as the main assessment objectives during this report. ...
... Learning mathematics intends that students have mathematics abilities, there is problem solving, communication, connection, reasoning, and representation (Mundy, 2000;Wu, 1996). The same thing was also stated by Widana (2018) that learning mathematics can train students' critical thinking and reasoning to make a conclusion, make good evaluations and decisions on problem solving, and develop the ability to communicate ideas through various ways and forms. ...
This study was intended to identify learning obstacles faced by students on the distance between two points and the distance between point-to-line materials. The data in this study was obtained through a test, interview, and documentation of students who have learned the materials. The research method used was the qualitative method with a case study approach. This study involved 33 students of class XII and a teacher as a participant. Learning obstacles found in this study were ontogenical, didactical, and epistemological obstacles. The ontogenical obstacles were the students' lack of basic geometry ability and counting operations of the square root which caused the students to make mistakes in applying the Pythagoras formula, determining the position of perpendicular lines, as well as completing arithmetic operations of the square root. The didactical obstacle was the fact that students were only emphasized on using a quick formula to solve three-dimensional problems. This fact resulted in the uncompleted concept received by students. Consequently, the students forget the proper procedure for solving the problems easily, and they tend to make mistakes in applying the quick formula. The epistemological obstacle was the lack of students' comprehension of a concept to determine the distance between a point to a line if the triangle which is formed is not a right triangle. This lack of comprehension caused the students can’t solve a mathematics problem. The implication of this study is learning materials used by students should be arranged based on students' needs which consider the analysis of learning obstacles so that the learning objectives can be achieved
... This was the fundamental reason why problem-solving skills had been stressed in elementary education from the very beginning stage. The National Council of Teachers of Mathematics (NCTM) found in 2000 that problem-solving is not just an objective of mathematical learning but also a strategy and a pattern of thinking (Mundy, 2000). Besides that, students must sharpen their minds and expand their capacity to emphasize their problem-solving ability. ...
This research’s objective is to investigates the reliability and validity of the needs analysis instrument for mathematics problem-solving based on the computational thinking module among primary school mathematics teachers. For the needs analysis phase, the researchers applied a quantitative method involving a questionnaire. The instrument calibration method is test of language validity, content validity, empirical validity and reliability. The instrument’s reliability was tested in a pilot study involving 50 primary school mathematics teachers. The pilot study was analyzed using SPSS version 26. The pilot test results show that Cronbach’s alpha value for Construct A: computational thinking skills is 0.786, Construct B: problem-solving skills is 0.772, and the need for the problem-solving module is 0.775. Finally, the researcher expects that this instrument will assist other researchers in the needs analysis phase of developing a mathematical module based on computational thinking in problem-solving. Keywords: Validity, reliability, mathematics, module, computational
... The impact of theories on a broad range of applications, and their utility in various sciences, could gain the interest of the global research and educational community in mathematics teaching. In fact, the National Council of Teachers of Mathematics in America, known as NCTM (Ferrini-Mundy, 2000;NCTM, 2014), endorses the vitality of introducing probability, and therefore statistics, into mathematics curricula is of utmost relevance. This fact is confirmed today by their crucial role at every education level (Langrall, 2018). ...
Data analysis is one of the most popular fields of mathematics and includes statistics and probability. These two mathematical domains are some of the most well-known, influencing everyday life and the various sciences. Their teaching lays the foundation for primary education and culminates in secondary education. Probability and statistics are necessary for today and the future of several professions. This research attempts to highlight the multidisciplinary character of these two disciplines through the textbooks of primary education in Greece and Singapore. It aims to highlight the dependence of mathematics teaching on interdisciplinarity through textbooks. The textbook analysis was chosen because books offer varied learning opportunities. The researchers selected the books, partaking in the comparative analysis. After defining the basic principles dividing lines for the differentiation of the exercises, the analysis was conducted. It included two stages. In the first stage, the activities of the books were examined in their framework application. Then, their interdisciplinary character was accentuated in the scientific field. The results reveal a substantial dependence of data analysis on interdisciplinarity. More interesting is that the distribution of interdisciplinary exercises is prevalent in the scientific milieus.
... Las reflexiones sobre la complejidad de los objetos matemáticos, y la articulación de los componentes de esta complejidad, son frecuentes en muchos de los enfoques teóricos utilizados en el área de la Educación Matemática (Rondero y Font, 2015). Uno de los documentos que han tenido gran influencia sobre la enseñanza de las matemáticas, es el de los Principios y Estándares del National Council of Teachers of Mathematics (Ferrini-Mundy, 2000), pero en éstos sólo se considera el proceso de conexión, que es entendido como aquél que permite conectar diferentes contenidos matemáticos entre sí y que también permite conectar las matemáticas con contextos extra matemáticos. Sin embargo, aparte del proceso de conexión es importante también contemplar la doble mirada del proceso complejidad-articulación al aplicar estos procesos a los objetos matemáticos, permitiendo una mayor profundización en los mismos. ...
Este trabajo tiene por objetivo analizar algunas de las posibles causas que originan las dificultades del aprendizaje de las matemáticas por parte de los estudiantes. Partimos de considerar acerca de la complejidad de los objetos matemáticos, en la cual están involucrados, entre otros, aspectos epistemológicos, históricos y cognitivos. Tal complejidad se agudiza cuando los estudiantes ingresan al nivel medio superior, y no saben articular adecuadamente los saberes matemáticos, lo que les podría permitir realizar en forma más apropiada la transición entre el pensamiento concreto y el pensamiento abstracto. Se discute brevemente la vinculación entre Neuroeducación y Educación Matemática, lo que arroja elementos conceptuales adicionales sobre la problemática antes descrita, en donde se incluye la generalización de los saberes matemáticos. El estudio de lo anteriormente mencionado puede permitir reducir en parte los índices de reprobación y deserción escolar, relacionados con el desinterés de los estudiantes en el estudio de las matemáticas, y en general de las Ciencias Exactas.
... The new mathematics curriculum was designed to incorporate key features of the US-based National Council of Teachers of Mathematics (NCTM) standards (Ferrini-Mundy, 2000), which emphasise a constructivist view of teaching and learning mathematics. This new mathematics curriculum aimed to address the Chapter 1: Introduction 3 limitations of the past mathematics curriculum, as discussed in Dolma's (2016) study. ...
This research explored the beliefs, knowledge and skills of Bhutanese pre-service mathematics teachers and their preparedness to teach a reformed mathematics curriculum. Data were collected when the participants joined a series of inquiry-oriented, technology-enabled calculus workshops. These data analyses revealed many inconsistencies between the participants’ espoused and enacted beliefs and is alignments between their mathematical knowledge and skills when compared to the intentions of the newly reformed curriculum. From this, implications have been drawn about the preparedness of the soon-to-graduate pre-service mathematics teachers, and recommendations are made regarding ways future pre-service teachers mathematical beliefs, knowledge and skills may be enhanced.
... As the literature shows, the statistical measures of mean, median, and mode comprise a fundamental portion of the content knowledge elementary teachers need to possess. Curriculum documents around the world recommend that students develop some understanding of mean, median, and mode before entering secondary school (Council Australian Education, 1994;Ferrini-Mundy, 2000). So, these contents should be considered in data analysis knowledge. ...
Data analysis knowledge is an indispensable aspect of teachers’ data literacy, which not only has a profound impact on the cultivation of students’ data analysis ability, but also is related to reasonable decision-makings in education. Based on the analyses of teachers’ data literacy and data analysis ability, this study constructed a cognitive model of teachers’ data analysis knowledge and developed an instrument for measuring teachers’ data analysis knowledge. Meanwhile, from a data-driven approach, G-DINA package in software R was used to select a well-fitted GDM Model from a series of cognitive diagnostic models such as DINA, DINO, RRUM, ACDM, LLM, G-DINA and Mixed Model for parameter assessment of cognitive diagnosis, and the reliability and model fit of the instrument were analyzed afterwards. By analyzing the pre-service dataset of 531 Chinese teachers, it made the conclusion that teachers with the same attributes have differences in attribute mastery and knowledge status, and teachers show a main learning path of A8 → A4 → A1 → A3 → A7 → A5 → A2 → A6 in terms of data analysis knowledge. It provided a systematic case study for the assessment of pre-service teachers’ knowledge of data analysis, and also provides a new perspective in assessing other knowledges and abilities.
... Pembelajaran matematika menurut NCTM memaparkan lima standar kemampuan matematika yang harus dimiliki siswa, meliputi kemampuan pemecahan masalah (problem solving), kemampuan komunikasi (communication), kemampuan koneksi (connection), kemampuan penalaran (reasoning), dan kemampuan representasi (representation). Kemampuan representation merupakan salah satu kemampuan yang harus dimiliki siswa dalam pembelajaran matematika karena kemampuan representasi memiliki peran penting dalam permasalahan matematika (Ferrini-Mundy, 2000). ...
Tujuan penelitian ini adalah untuk mengetahui efektivitas model pembelajaran Think Talk Write (TTW) dengan pendekatan saintifik dan open-ended terhadap kemampuan representasi matematis siswa. Populasi penelitian ini adalah siswa kelas VII SMP Negeri 2 Randublatung Tahun Ajaran 2020/2021. Dengan menggunakan cluster random sampling terpilih sampel yaitu kelas VII A sebagai kelas eksperimen 1, kelas VII B sebagai kelas eksperimen 2, dan kelas VII C sebagai kelas kontrol. Hasil penelitian menunjukkan: (1) terdapat perbedaan kemampuan representasi matematis siswa kelas eksperimen TTW dengan pendekatan saintifik, TTW dengan pendekatan Open-ended, dan kontrol (2) kemampuan representasi matematis siswa kelas eksperimen TTW dengan pendekatan saintifik lebih baik daripada kelas konvensional (3) kemampuan representasi matematis siswa kelas eksperimen TTW dengan pendekatan Open-ended lebih baik daripada kelas konvensional (4) tidak ada perbedaan kemampuan representasi matematis siswa dengan TTW dengan pendekatan saintifik dan TTW dengan pendekatan Open-ended (5) ada pengaruh keaktifan terhadap kemampuan representasi matematis siswa kelas eksperimen TTW dengan pendekatan saintifik (6) ada pengaruh keaktifan terhadap kemampuan representasi matematis siswa kelas eksperimen TTW dengan pendekatan Open-ended (7) kemampuan representasi siswa kelas eksperimen TTW dengan pendekatan saintifik dan eksperimen TTW dengan pendekatan Open-ended mencapai KKM. Dari hasil penelitian disimpulkan bahwa penerapan model pembelajaran Think Talk Wrtite (TTW) dengan pendekatan Saintifik dan Open-ended lebih baik daripada pembelajaran konvensional.
... According to Mundy (2000), the NCTM's target is "to provide the vision and leadership necessary to ensure a mathematics education of the highest quality for all students" (p. 868). ...
The purpose of this critical review is to explore international perspectives on the
analysis of the content of developed mathematics textbooks. This led us to explore
the contributions to our knowledge of the compatibility of the content of the
developed mathematics textbooks in the Kingdom of Saudi Arabia (KSA) with the
standards of the National Council of Teachers of Mathematics (NCTM) in the
United States of America (USA) between 2013 and 2019. This study sought to
extract and synthesise the recommendations subsequent to comparing them
according to the methodology, samples, grades, the number of NCTM standards
that were covered, and the results of the analyses. Moreover, this review sought to
identify the areas of the mathematics curriculum which covered a low percentage
of NCTM standards according to such studies, and to help the stakeholders to
develop these curricula. It was recommended that a study should be conducted in
order to evaluate the content of developed mathematics for grades not covered in
their studies, such as primary grades 1 to 2 and secondary grades 2 to 3. We found
that the mathematics curriculum for the first secondary grade achieved a low
percentage of NCTM standards.
... (2) mathematical reasoning, (3) mathematical problem-solving, (4) mathematical connection,dan (5) mathematical representation (Ferrini-Mundy & Martin, 2000). Oleh karena itu, kamampuan matematis seseorang akan berdampak kuat terhadap kemampuan berpikirnya, apabila kemampuan berpikir tersebut selalu diasah dan dikembangkan secara kontinu. ...
Penelitian ini bertujua untuk memberi gambaran dalam mengembangkan instrument sebagai bentuk pengukur Creativity And Innovation Skills siswa pada mata pelajaran matematika. Langkah-langkah dalam mengembangkan instrumen adalah menyusun spesifikasi, menulis, menelaah, uijicoba, menganalisis, memperbaiki, dan merancang instrument. Spesifikasi intrumen menunjukkan keseluruhan karakteristik yang dimiliki instrument. Penulisan soal merupakan penjabaran dari berbagai indicator yang menjadi acuan pedoman pertanyaan-pertanyan yang sesuai dengan karakteristik pada kisi-kisi yang telah disusun. Kegiatan analisis dilakukan terhadap masing-masing butir soal yang telah diberi bobot skor. Memperbaiki tes merupakan upaya perbaikan-perbaikan terhadap butir soal yang kurang sesuai dengan yang diharapkan. Setelah semua buitr soal disusun, danalisis dan diperbaiki, selanjutnya adalah merancang butir-butir soal tersebut menjadi instrument
... Dentro de los estándares de educación matemática de la American Mathematical Society, la resolución de problemas es fundamental (Ferrini-Mundy, 2000), por ello propone un empleo abundante y diverso de experiencias, como método de indagación y aplicación, así como el uso de enfoques de resolución de problemas para investigar y entender los contenidos matemáticos, formular problemas en situaciones intra y extra matemáticas, resolver problemas no rutinarios, verificar e interpretar los resultados con respecto al problema original, generalizar soluciones y estrategias y adquirir confianza en el uso significativo de la Matemática. ...
La relación del sujeto con el conocimiento es una cuestión esencial en el marco del desarrollo acelerado de la ciencia y la tecnología, razón que ha instituido el aprender a aprender como uno de los pilares de la educación. Las formas de adquisición del conocimiento, son diversas, pero una de las más cotidianas y connaturales es la resolución de problemas. Un contexto tan complejo, en el que de forma acelerada se genera un enorme volumen de información, hace pensar en la necesidad de comprender y valorar el papel de la resolución de problemas como acto epistemológico, que favorece la incorporación de nuevos saberes al sistema de conocimientos del sujeto. Pero, ¿mediante qué procederes se propicia desde la docencia la resolución de problemas para que el estudiante alcance nuevos saberes? Se consultan diversas fuentes de información pertinentes al tema a la par que se muestran varias de las tendencias o perspectivas más sobresalientes en el tratamiento de la resolución de problemas como situación de aprendizaje y sus regularidades. Con este trabajo se expone una visión sintética de los recursos existentes para el tratamiento de la resolución de problemas desde un enfoque epistemológico, lo que propicia un mejor aprovechamiento de esta situación de aprendizaje orientado al aprender a aprender.
... Dengan memperhatikan Peraturan Menteri Pendidikan nasional No. 22 tahun 2016 tentang standar proses dan pentingnya pembelajaran matematika, maka kemampuan pemecahan masalah matematis merupakan faktor yang penting dalam mengimplementasikannya. Pemecahan masalah merupakan landasan dalam pembelajaran matematika, tanpa kemampuan pemecahan masalah pada diri peserta didik maka kegunaan dan kekuatan ide-ide matematika, pengetauan, dan keterampilannya sangat terbatas (Ferrini-Mundy, 2000;Septian, 2017;Suwarman, 2017). Berarti pemecahan masalah adalah prinsip dasar peserta didik dalam mempelajari matematika di sekolah merupakan salah satu bentuk kemampuan matematis yang paling dasar dan utama. ...
... First Group Competence: The ability to ask and answer both in mathematics and using mathematics; mathematical thinking ( This is also in line with the goals expected by the National Council of Teachers of Mathematics (NCTM) in mathematics learning. NCTM (2000) sets five standard mathematical abilities that must be possessed by students, namely problem-solving ability, communication skills, connection capabilities, reasoning abilities, and the ability of representation [5]. In the 2013 curriculum mathematical competencies are expected after students learn mathematics: 1) Understand concepts and apply mathematical procedures in everyday life (mathematical understanding); 2) Perform mathematical operations for simplification, and analysis of existing components (mathematical connection); 3) Perform mathematical reasoning which includes making generalizations based on patterns, facts, phenomena or existing data, making guesses and verifying them (mathematical reasoning); 4) Solve problems and communicate ideas through symbols, tables, diagrams, or other media to clarify the situation or problem (mathematical problem solving and communication); 5) Grow a positive attitude such as a logical attitude, critical, careful, thorough, and not easily give up in solving problems. ...
Education for Sustainable Development (ESD) has long been socialized by the government to be developed and implemented in education, but currently, its implementation has not been carried out optimally. ESD is education that makes students aware of their environmental life in creating a sustainable future by not sacrificing future generations. One effort to achieve the ESD goal is to introduce it to the community. ESD has three main objectives namely economic goals, ecological / environmental objectives, and social goals. Awareness in each individual needs to be built from elementary and middle school age so that it is embedded and embedded in the mind to realize the goals of ESD. This is where the concept of sustainable development (sustainable development) needs to be studied and applied to schools. The purpose of this paper is to investigate the ability to solve geometrical problems based on ESD and Sustainability Consciousness, then develop mathematical competencies that are relevant to the components of ESD geometry. The type of research used is qualitative research. The results of his study showed that 46.25% of students were able to solve geometric problems based on ESD, while 53.75% of students were still categorized as unable to solve them, and 31.25% of students had Sustainability Consciousness in the economic dimension, but for the environmental and social dimensions they did not have.
... Educators [AMTE], 2019; Ma, 1999;Ferrini-Mundy, 2000). The SMPs embody these ideas and "describe varieties of expertise that mathematics educators at all levels should seek to develop in their students" (NGA & CCSSO, 2010; p. 6, emphasis added). ...
Over the last forty years, standards and recommendations for teachers and learners of K-12 mathematics in the US have evolved to highlight mathematical practices (e.g., Common Core State Standards of Mathematics, Standards for Mathematical Practice [SMPs]). Practice standards (i.e., SMPs) describe mathematical competencies that should be developed in learners of mathematics at all levels. National organizations (e.g., Conference Board of Mathematical
Sciences) have specifically called for attention to be given to SMPs in collegiate mathematics content courses for prospective elementary (ages 5-12) teachers (PTs). The goal of this paper is to help instructors of such courses, especially those new to the field of mathematics education, gain familiarity with the organizations and documents that support the development of these practices and conceptualize ways in which they might engage PTs in their content courses in
SMPs. First, we synthesize the evolution of mathematics standards for K-12 learners and teachers in the US. Second, we report results from an investigation into the ways in which mathematics teacher educators (MTEs) are addressing SMPs in their content courses for PTs. In this study, SMP3: Construct viable arguments and critique the reasoning of others was reported by MTEs as being addressed in their courses more than any other SMP. This finding precipitated a qualitative analysis of the ways in which PTs were being provided opportunities to engage in SMP 3 within the descriptions and samples of tasks provided by the MTEs. We will share and discuss example tasks that provided opportunities for PTs to analyze others’ thinking. Lastly, we consider the potential benefits of leveraging children’s thinking in SMP 3-related tasks for PTs and provide resources for MTEs who are interested in utilizing samples of children’s thinking in their classes.
... (2) mathematical reasoning, (3) mathematical problem-solving, (4) mathematical connection,dan (5) mathematical representation (Ferrini-Mundy & Martin, 2000). Oleh karena itu, kamampuan matematis seseorang akan berdampak kuat terhadap kemampuan berpikirnya, apabila kemampuan berpikir tersebut selalu diasah dan dikembangkan secara kontinu. ...
Penelitian ini bertujuan untuk memberi gambaran dalam mengembangkan instrument sebagai bentuk pengukur Creativity And Innovation Skills siswa pada mata pelajaran matematika. Langkah-langkah dalam mengembangkan instrumen adalah menyusun spesifikasi, menulis, menelaah, uijicoba, menganalisis, memperbaiki, dan merancang instrument. Spesifikasi intrumen menunjukkan keseluruhan karakteristik yang dimiliki instrument. Penulisan soal merupakan penjabaran dari berbagai indicator yang menjadi acuan pedoman pertanyaan-pertanyan yang sesuai dengan karakteristik pada kisi-kisi yang telah disusun. Kegiatan analisis dilakukan terhadap masing-masing butir soal yang telah diberi bobot skor. Memperbaiki tes merupakan upaya perbaikan-perbaikan terhadap butir soal yang kurang sesuai dengan yang diharapkan. Setelah semua buitr soal disusun, danalisis dan diperbaiki, selanjutnya adalah merancang butir-butir soal tersebut menjadi instrument.
... The principles and standards for NCTM (School Mathematics comprehensive reference on developing mathematical knowledge [12]. The NCTM's Principles and Standards Principles can streamline the processes and products of mathematics learning in developing differences in students' abilities in their processes and products [13]. ...
The purpose of this study is to develop understanding of concepts in mathematics through the application of the NCTM's Principles and Standards. This research method is descriptive. The results obtained are understanding concepts in mathematics can be developed through the application of NCTM Principles and Standards consisting of 6 principles, namely: 1. Equity, 2. Curriculum, 3. Teaching, 4. Learning, 5. Assessment, and Technology. Understanding concepts in mathematics that can be developed are: a. defining concepts verbally and in writing, b. Make examples and not examples, c. Using various symbols to present a concept, d. Change the form of representation to various forms, e. Identifying the characteristics of a concept, f. compare various concepts, and g. interpret concepts.
... It has been recognized that one of primary aims of education is to foster student's reasoning which isthe main activity in mathematical activities [1]. Therefore, it becomes crucial task for mathematics teachers to involve reasoning activities in mathematical learning and make mathematics meaningful. ...
Covariational reasoning plays a significant role for solving problems. This study examines the covariational reasoning of master program students when solving mathematical problems such as fraction, velocity and acceleration, proportion, and integral. 26 students of mathematics education master program, Universitas Negeri Surabaya, are involved in this study. Generally, mental action of students is more prominent on fraction and proportion than on the other issues. On fraction and proportion problems, most students are able to fulfill all mental actions such as coordinating the value, the direction, and the amount of change of one variable, and also coordinating the average and the instantaneous rate of change of the function. However, on velocity, acceleration, and integral problems most students cannot show their mental actions well. They only fulfill 3 of 5 mental actions of covariational reasoning. Generally, the shape of their graph related to those problems are irrespective with initial point. These findings suggest that learning in mathematics should place increased emphasis on problem involving graph to promote covariational reasoning of the students.
... Its focus on a particular type of polytomous attribute -the expert-defined polytomous attributes. Examples of using polytomous attributes could be found in National Assessment of Educational Progress for science achievement where students are classified based on grade levels and content areas (National Assessment Governing Board, 2009), and creating the principles and standards for different grade students in school mathematics (Mundy, 2000). Chen and de la Torre (2013) proposed a model (polytomous generalized DIN A; pG-DINA) for expert-defined polytomous attributes based on the generalized cognitive diagnosis framework described by De La Torre (2011). ...
Polytomous attributes, which indicates multilevel of cognitive complexity (e.g., the multiple occurrences of the attributes), can provide additional diagnostic information educational measurements. In this study, we propose a higher-order deterministic inputs, noisy "and" gate (HG-DINA) model for specifying the joint distribution of polytomous attributes in cognitive diagnosis. This framework provides a new generalized approach to capturing several commonly used cognitive diagnosis models (CDMs) with polytomous attributes. It stems from a reparameterization of polytomous Q-matrix and attributes profile. We extend the polytomous Q-matrix to a higher dimensional and restricted dichotomous one and model the attribute mastery degree which arises from the latent attribute traits resembling the θ of item response models. In addition, HG-DINA can capture the cognitive load effects in the multilevel complexity attributes. Markov chain Monte Carlo estimation is given for separable response distributions. The simulation study is presented to examine the viability of the model and the performance of the algorithm. In addition, the implication study shows an example of how to illustrate the application of the model in practice. A proportional reasoning data example is presented, and the results coincide with the finding from conventional pG-DINA and 2PL models.
... According to Draper (2002); Ferrini-Mundy (2000); Stylianides & Stylianides (2007) understanding can be categorized, parted, and elaborated into a number of components to form a deeper view about student"s thinking process. Furthermore, Suherman (2003) stated that understanding is an adequate definition about something, more than memorizing, enables the students to catch the meaning or main idea and explains it by using their previous knowledge. ...
The purpose of this study is to describe students’ relational understanding in solving problems for FI students. The subjects of this research are Senior High School students having field independent cognitive style in Malang and chosen randomly. The subjects consist of two students. Sheet of GEFT test, sheet of Combinatorial questions, and interview sheet were used in this study. The finding of the study showed that medium-academic achievement student had an ability on relational understanding as the same as the high-academic achievement student. Meanwhile, the process in solving problem made by the high-academic achievement student was likely similar to the accurate process in solving problems.
As a new generation of assessment instrument, cognitive diagnosis integrates the measurement objectives into the cognitive model to diagnose the fine-grained knowledge of students. Taking the PISA 2012 dataset in mathematics from Shanghai, Hong Kong, Macau and Taiwan as the research subject, this study constructed a cognitive model with the attributes of Mathematical Abstraction, Logical Reasoning, Mathematical Modeling, Intuitive Imagination, Mathematical Operation and Data Analysis, and made an analysis of the mastery of students’ mathematical competencies of different attributes in four regions, and the learning paths of the students’ mathematical competencies were constructed. The results showed that Shanghai had the obvious advantages in each attribute; the mastery mode of Hong Kong, Macau and Taiwan showed a common trend, and they all indicated a relatively low percentages of competencies in Logical Reasoning and Intuitive Imagination. In terms of the learning paths, the learning paths in the four regions reflected diversities, but obvious main learning paths existed. Majority of the knowledge states’ abilities were below 0. While in Hong Kong, Taiwan, and Macau, more knowledge states’ abilities were above 0. This research provided a reference for the systematic analysis of students’ knowledge status and learning path.
Resumo: O presente estudo analisa o impacto da Realidade Aumentada (RA) no ensino de sólidos geométricos na Educação de Jovens e Adultos (EJA), buscando compreender não apenas sua previsão técnica, mas também sua contribuição para uma aprendizagem significativa e contextualizada. Uma pesquisa, de abordagem qualitativa, foi realizada com alunos do 8º e 9º anos do Ensino Fundamental na modalidade EJA, com idades entre 18 e 50 anos , utilizando atividades práticas e o aplicativo Sólidos RA para a exploração de conceitos geométricos. Os resultados indicam que a RA, além de fornecer uma abordagem inovadora e atraente, possibilita a ressignificação dos conceitos matemáticos ao aproximá-los da realidade dos estudantes. A tecnologia favoreceu a compreensão de sólidos geométricos ao oferecer visualização interativa tridimensional, permitindo que os alunos estabelecessem relações entre os conceitos matemáticos e sua aplicação cotidiana. No entanto, observou-se que a eficácia da RA no ensino da EJA não pode ser reduzida à memorização de nomenclaturas e classificações, sendo necessário considerar sua capacidade de estimular o pensamento crítico e a autonomia dos estudantes. Dessa forma, a integração da RA ao ensino de sólidos geométricos na EJA se apresenta como uma ferramenta potencialmente transformadora, indo além do aspecto tecnológico para promover uma experiência educacional mais contextualizada, engajadora e significativa.
Este artigo é derivado de uma pesquisa de grupo de Grupo de Estudos Tecendo Redes Cognitivas de Aprendizagem da Universidade Federal do Ceará - Campus Fortaleza, com apoio da Secretaria Estadual do Ceará. O propósito deste estudo é direcionar alternativas para a prática de ensino em Geometria Plana e Sequência, com foco na formação profissional de futuros professores de Matemática, utilizando abordagens visuais e interativas através do software GeoGebra. A metodologia adotada será a Engenharia Didática, em conjunto com a Teoria das Situações Didáticas, para conduzir a investigação. Dessa forma, o objetivo é contribuir para a formação inicial e continuada de professores de Matemática por meio da criação de situações didáticas que envolvam a Geometria Plana com questões olímpicas, promovendo a visualização e a compreensão do conteúdo com o apoio do GeoGebra.
Deductive reasoning is essential to most of our scientific and technological achievements and is a crucial component to scientific education. In Western culture, deductive reasoning first emerged as a dedicated mode of thinking in the field of geometry, but the cognitive mechanisms behind this major intellectual achievement remain largely understudied. Here, we report an unexpected cognitive bias in geometric reasoning that challenges existing theories of human deductive reasoning. Over two experiments involving almost 250 participants, we show that educated adults systematically mistook as valid a set of elementary invalid inferences with points and circles in the Euclidean plane. Our results suggest that people got “locked” on unwarranted conclusions because they tended to represent geometric premisses in specific ways and they mainly relied on translating, but not scaling, the circles when searching for possible conclusions. We conducted two further experiments to test these hypotheses and found confirmation for them. Although mathematical reasoning is considered as the hallmark of rational thinking, our findings indicate that it is not exempt from cognitive biases and is subject to fundamental counter-intuitions. Our empirical investigations into the source of this bias provide some insights into the cognitive mechanisms underlying geometric deduction, and thus shed light on the cognitive roots of intuitive mathematical reasoning.
Geometry can be challenging for students due to its abstract nature; The difficulty is often associated with low spatial abilities; to overcome these challenges, educators can employ dynamic and visual learning approaches to help students learn and understand geometric concepts more effectively. This study aimed to develop a Geo Math application by integrating the GeoGebra applets on geometry that fulfill valid, practical, and effective aspects that are expected to improve spatial abilities. This research utilized development research using the ADDIE model, which consists of 5 stages: analysis, design, development, and trial implementation. It went through several trial stages consisting of validation experts, one-to-one trials, and small group trials, and the evaluation stage was carried out through a pre-post-test quasi-experimental study. Based on the results, it can be concluded that the Geo Math application was very feasible to support the implementation of learning mathematics, especially in learning geometric transformations, which could assist students in constructing concepts from various transformations effectively. The interactive and dynamic nature of GeoGebra applets within the application allowed students to visualize and manipulate geometric objects and could make abstract mathematical concepts more concrete and accessible, which could improve students’ spatial abilities.
Background: Mathematics is not just a science for its own sake; it is a science that proves to be useful for most other sciences. Mathematical connections play a crucial role in helping students develop a deeper understanding and enhance their thinking about mathematics. These connections represent relationships between different mathematical ideas, between mathematics and other subjects, and between mathematics and everyday life.Aim: This study aims to classify students' mathematical connection abilities when solving non-routine mathematical problems.Method: This research employs a qualitative approach using descriptive and exploratory methods. The study involved 23 students who exhibited mathematical connection skills in problem-solving. Data collection methods included tests, observations, and interviews. The data analysis process consisted of two main stages: data reduction and data presentation. To ensure data validation, the triangulation method was used by comparing the results from the subject tests (answer sheets), observations, and interviews.Results: The findings of this study revealed three distinct classifications of students’ mathematical connections when solving non-routine problems: 1) Patterns; 2) Variables; and 3) ArgumentsConclusion: The implications of these findings suggest that teachers need to be aware of the different classifications of students' mathematical connections. This awareness will enable them to implement mathematics learning strategies that cater to the diverse mathematical connection classifications found in their classrooms. For instance, teachers can utilize different mathematics learning media tailored to students’ learning styles, such as mind, incubation, and visual learning. By doing so, students can better optimize their mathematical connections and achieve improved outcomes in their mathematics learning.
While much STEM education research has focused on mathematics as a tool for STEM, this chapter will identify ways that STEM was used to deepen the knowledge, use, and enjoyment of mathematics via the use of the freely available, widely-adopted middle school curriculum from Illustrative Mathematics (IM). IM purposely designed its research-based K-12 mathematics curriculum to invite all students into mathematics by leveraging contexts through a culturally relevant, problem-based approach. Researchers analyzed interview data in a multiple-case study from four diverse school districts across the United States. The findings suggest that aspects of the curriculum's instructional model, such as collaborative real-world and mathematical problem-solving and explicit mathematical discourse structures, impacted shifts in educator classroom practice, perceived student engagement and achievement in mathematics, and long-term valuing of problem-based instruction. The outcomes have practical implications for supporting teachers to understand how mathematical understanding can be enriched through STEM problems.
The ability to think geometrically is hierarchical so students need to master the initial level of thinking before they are going to the next level. Geometry learning strategies need to consider the level of students' thinking abilities. Assessment with paper-based tests has weaknesses in terms of practicality and does not develop students' technological literacy in the digitalization era. This study aims to analyze the need for the development of a website-based instrument to assess the geometric thinking skills of elementary school students referring to Van Hiele's theory. This research is a literature review with a qualitative approach. The articles reviewed in this research are articles that discuss thinking skills based on Van Hiele's theory with research subjects of elementary school students and published from 2021 to 2023. Data were analyzed by Miles and Huberman's interactive model. The results showed that a web-based instrument for assessing the geometric thinking abilities of elementary school students based on Van Hiele's theory was needed to systematically assess students' geometric thinking abilities then could be followed up with learning activities according to students' abilities. The level of thinking of elementary school students assessed is from visualization to abstraction which is adapted to the material and curriculum of the elementary school.
Melalui pembelajaran matematika, siswa dapat menggunakan banyak strategi dalam menelesaikan masalah yang dihadapi. Oleh karena itu, penelitian ini bertujuan untuk mengetahui kemampuasn kompetensi strategis siswa yang dipengaruhi oleh motivasi belajar dan penggunaan media pembelajaran wordwall. Penelitian ini telah dilaksanakan pada kelas V SDN 31 Tumampua V Kabupaten pangkajene dengan kemampuan matematika yang setara. Pengumpulan data dilakukan mengunakan instrumen kompetensi strategis yaitu soal matematika yang berbentuk essay test sebanyak 5 nomor, instrumen efektivitas penggunaan media wordwal berupa angket tertutup dengan skala likert serta instrument motivasi belajar juga berupa angket dengan skala likert. Hasil penelitian menunjukan bahwa terdapat pengaruh secara bersama-sama antara penggunaan media wordwall dan motivasi belajar secara positif dan signifikan terhadap kompetensi strategis siswa.
This study aims to understand the impact of problem-based learning (PBL) on mathematical representation in students using Geogebra and model discovery learning in X SMAS Tamansiswa Singosari. It uses quasi-experimental research with purposive sampling and control group design. The results show that all data is normal and homogeneous, with a value of 4.71>2.03. The study also reveals that the overall learning process for experimental students is better than that of control students.
Bu çalışmada ortaöğretim (lise) matematik öğretmenlerinin istatistiksel akıl yürütme becerilerinin, alan bilgileri kapsamında değerlendirilmesi ve istatistiksel akıl yürütmeye dair alan bilgilerini ortaya koyma yaklaşımlarının incelenmesi amaçlanmıştır. Çalışma kapsamında öğretmenlerin istatistiksel akıl yürütmeye dair alan bilgisi ve istatistiksel akıl yürütme alan bilgisini ortaya koyma yaklaşımları; değişebilirliğe ilişkin akıl yürütme, dağılıma ilişkin akıl yürütme, informel çıkarımsal akıl yürütme ve dağılımın kapsadığı merkez ile ilgili akıl yürütme çeşitlerine göre incelenmiştir. Çalışmada nitel araştırmalar içerisinde yer alan özel durum çalışması yöntemi kullanılmıştır. Çalışmanın katılımcılarını 17 ortaöğretim matematik öğretmeni (10 erkek, 7 kadın) oluşturmaktadır. Söz konusu öğretmenler amaçlı örnekleme yöntemleri arasında yer alan tipik durum örnekleme yöntemi kullanılarak belirlenmiştir. Veri toplama aracı olarak istatistiksel akıl yürütme becerilerini alan bilgileri doğrultusunda ortaya koyan istatistiksel akıl yürütmeye dair alan bilgisi formu (İAY-AB) kullanılmıştır. Söz konusu form Gökçe (2019) tarafından hazırlanmış olup; beş adet açık uçlu sorudan oluşmaktadır. Verilerin analizi Gökçe (2019, s. 97) tarafından hazırlanan derecelendirme ölçeği kullanılarak ve alt problemlere göre ayrı ayrı ele alınarak yapılmıştır. Derecelendirme ölçeğindeki göstergeler baz alınarak veriler içerik analizine tabii tutulmuştur. Elde edilen bulgular doğrultusunda ortaöğretim matematik öğretmenlerinin istatistiksel akıl yürütmeye dair alan bilgilerinin beklenen düzeyde olmadığı, geliştirilmesi gerektiği tespit edilmiştir. Çalışma sonucunda katılımcıların önemli bir bölümünün istatistiksel akıl yürütmeye dair alan bilgilerini ortaya koyma yaklaşımlarında kullandıkları dört akıl yürütme becerisini bir arada içeren sorularda düşük ve orta düzeyde akıl yürütme becerisine sahip oldukları görülmüştür. Bu çalışmanın sonuçlarından hareketle istatistiksel akıl yürütme becerilerinin gelişimine yönelik etkinlikler planlanarak, bu etkinliklerin öğretmenler üzerindeki etkileri gözlemlenebilir.
International curriculum and policy directions have called to embed critical thinking across discipline areas including mathematics; however, conceptually, this is under-theorised and under-researched in the field of mathematics education. This paper presents the conceptualisation of critical mathematical thinking (CMT) and the application of a literature informed conceptual framework; in particular, it examines what CMT capabilities young students exhibit as they enter formal schooling. We present the findings from one-on-one task-based interviews, undertaken with 16 young students (aged 5–6) as a means to investigate their CMT capabilities and refine the CMT framework. The interview data were analysed using the new critical mathematical thinking conceptual framework. The data confirms the definition and understanding of CMT in young students, indicating a need for curriculum refinement, improved teaching practices, and further research in this area.
Kemampuan berpikir lateral merupakan kemampuan untuk berpikir kreatif dengan menggunakan inspirasi untuk memecahkan suatu masalah dengan sudut pandang yang tidak terduga. Pemberian masalah matematika open ended merupakan cara yang tepat dalam mengetahui kemampuan berpikir lateral siswa karena dapat memunculkan beberapa cara penyelesaian yang berbeda. Salah satu faktor yang mempengaruhi perbedaan kemampuan berpikir siswa adalah gaya belajar, yaitu gaya belajar sensing dan intuition. Penelitian ini merupakan penelitian kualitatif yang bertujuan untuk mendeskripsikan kemampuan berpikir lateral siswa dalam memecahkan masalah matematika open ended ditinjau dari gaya belajar sensing dan intuition dengan subjek penelitian yaitu dua siswa kelas IX di salah satu SMP negeri Surabaya. Pengambilan data dilakukan dengan pemberian angket gaya belajar, tes kemampuan matematika, tes pemecahan masalah, dan pedoman wawancara. Analisis data melalui tahap reduksi data, penyajian data, dan penarikan kesimpulan. Hasil dari penelitian ini menunjukkan bahwa dalam memecahkan masalah matematika open-ended, siswa dengan gaya belajar sensing dan intuition keduanya dapat menyebutkan informasi yang diketahui dan informasi yang ditanyakan pada soal serta dapat membuat beberapa rencana penyelesaian masalah berdasarkan informasi yang diberikan. Namun siswa dengan gaya belajar sensing tidak dapat menyelesaian masalah sesuai yang direncanakan sebelumnya dan hanya mengecek perhitungannya saja, sehingga tidak melakukan pengecekan kebenaran jawaban. Sedangkan subjek dengan gaya belajar Intuition dapat melaksanakaan penyelesaian masalah sesuai dengan rencana yang disusun dan mengecek kebenaran jawaban. Subjek dengan gaya belajar intuition juga dapat memikirkan metode lain yang tidak umum, yaitu dengan metode grafik
The purpose of this study is 1) to develop DOMI KALI media, 2) to describe the feasibility of the DOMI KALI media, 3) to describe the practicality of the DOMI KALI media. The method used is adapted from the ADDIE model with four stages, namely: analysis, design, development and implementation. The subjects of the trial were the third grade students of Sumbersari Elementary School 2. The instruments of data collection used validation sheets, questionnaires, unstructured interviews. The results showed that the DOMI KALI media is feasible to use. It obtained a percentage of 90.69% of the experts so that it was included in the feasible category. DOMI KALI is right to understand multiplication and more pleasant learning atmosphere. It is suggested to the teacher to use the DOMI KALI Media as a tool in learning activities so that the multiplication counting operation material is more fun.
This study describes the students’ thinking processes in solving two variables linear equation system problems based on students’ systematic and intuitive cognitive styles. This research is a descriptive qualitative research. This study uses a questionnaire given to 19 students at one junior high school in Pamekasan Regency to see the students’ cognitive style. Based on the results of the study among 19 students in class 8.6 there were 12 students (63.16%) with split cognitive style, 1 student (5.26%) with undifferentiated cognitive style, 3 students (15.79%) with systematic cognitive style, 1 student (5.26%) with integrated cognitive style, and 2 students (10.52%) with an intuitive cognitive style. From the 19 students, 2 students were taken as research subject in which 1 student had systematic cognitive style and 1 student had intuitive cognitive style. Both subjects were given 2 problems about the two variable linear equation systems to see students’ thought processes based on APOS theory. The results of the study stated that students’ thinking processes in solving problems are different. Students with systematic cognitive styles tend to be more accurate and coherent in solving problems than students with intuitive cognitive styles. The students’ thinking process with systematic cognitive styles in solving two variables linear equation system problems involves the stages of action, process, objects and schemas. On the other hand, the students’ thinking process with an intuitive cognitive style in solving problems is not optimally conducted at the stages of action and process. This result can help teachers in understanding students’ thinking processes in solving problems so that it can be used to determine the right strategies in the learning process to improve their thinking processes.
This study aims to develop remedial mathematics learning tools based on Lesson Study for Learning Community. This research uses a mixed method that combines two previous forms of research, namely research and development and experimental research. The subjects of the research were grade VII students. This type of research is a step of research by combining two forms of research that have been there before, namely the development of research and experimental research. The learning tools developed in this study were on the material for the addition and subtraction of integer in grade VII SMP including Learning Implementation Plan, Student Worksheet, and Learning Outcomes Test. After obtaining a valid, practical, and effective device, the device is then tested in the experimental class to find out whether there is an effect on students problem solving abilities. homogeneity test shows the value of sigh. 0.671 on the pre test and 0.450 in the post test so that it can be concluded that the assumption of homogeneity of variance is fulfilled. Based on the results of the validity, effectiveness, and practicality test, the researcher concluded that the learning platform through bridge games and Lesson Study for Learning Community (LSLC) is a valid, effective, and practical device. At the time of the field trial research was also carried out. From the results of the test differences in problem solving in the two classes using the Mann Whitney Test shows the value of sighing. 0,000 (p<0.05), so it can be concluded that there are differences in problem solving between the control class using conventional instruction and the experimental class using Lesson Study for Learning Community (LSLC) based remedial learning with significant results so that when compared with conventional methods this device gets higher results than in students who use conventional methods.
This paper presents findings from a two-year qualitative study examining integration of computer science (CS) and computational thinking (CT) into elementary mathematics instruction. Integrated units were developed by elementary teachers and CS/CT coaches with support from university faculty with expertise in CS/CT and elementary mathematics. CS/CT instruction primarily relied on the Scratch environment, although some lessons made use of Code.org materials. This research primarily relied on two theories of integration (i.e. Kiray, 2012. A new model for the integration of science and mathematics: The balance model. Energy Education Science and Technology Part B: Social and Educational Studies, 4(3), 1181–1196) that provided insight into the level of interconnection between the disciplines and the relative amount of instructional time spent within each discipline. Findings revealed that cross-grade CS/CT concepts included sequencing, looping, and conditional logic. Within each category: (a) concepts were taught with increasing complexity across the grades, (b) the mathematics was dominant and CS/CT was important but secondary, and (c) three types of lessons emerged: No integration, partial integration, and full integration. Lastly, lessons generally included a transition from less integrated to more integrated activities with an initial focus on discipline-specific conceptual understanding prior to integrated activities.
Howe serves as the chair of the AMS committee advising the NCTM on the revision of its standards for K-12 mathematics education. This article describes the revision and the issues the committee has considered. The two committee reports appear on pages 270-276.