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

The current research aimed to understand the effect of mathematical beliefs of middle school students on their metacognitive skills in solving mathematical problems. In examining the matter, the study utilized a mixed method. In the first step, a linear regression test was utilized to determine the effect of belief on students' metacognitive skills in solving geometry problems. Furthermore, a qualitative approach was used to compare the metacognitive skills of high and low-belief students. This study involved 72 middle school students sitting in the 8th grade at Tarakan 1 State Junior High School. Based on the linear regression results, it is known that students' beliefs positively influenced their metacognitive skills in solving geometric problems. Furthermore, it was found that when both selected subjects with high and low beliefs started solving the problems, they started by planning. Then, they monitored what they had done, but there were differences in evaluating the solutions. Additionally, students who believe strongly in problem solving will be more aware of what they are thinking and thus have an impact on improving their learning outcomes. [ABSTRACT FROM AUTHOR]

Mathematical beliefs and metacognitive knowledge play significant roles in solving mathematical problems; thus, this study aims to investigate the influence of middle school students' beliefs on their metacognitive knowledge when solving geometry problems. This study utilizes both quantitative and qualitative research methods. A linear regression test was used to determine the effect of middle school students' beliefs on their metacognitive knowledge. The results of the quantitative research analysis were followed up with a qualitative research approach to describe the metacognitive knowledge of students who have high and low confidence in solving geometric problems. This research involved 352 middle school students in the Tarakan area. Based on the results of linear regression, it is known that the beliefs of middle school students have a positive effect on their metacognitive knowledge when solving geometric problems. In addition, it was found that students with different beliefs could solve a given geometry problem, but the approach to solving it varied among subjects. Middle school students have diverse beliefs, but these variations do not affect their capacity to apply their metacognitive knowledge at every stage of solving mathematical problems. [ABSTRACT FROM AUTHOR]

Background: The derivative is an important concept in mathematics and therefore understanding the derivative concept play an essential role. However, it has been found that students' understanding of derivative is still below expectation. The reason is that they cannot explain parts that has not been understood. They has just stated that they forgot or did not understand without any detail explanation. This shows that the provided explanation which is given by students does not support the cognitive process. To overcome this situation, we need to understand how the cognitive processes that lead to such understanding. One simple tool that allows for this purpose is the theory of commognition. Objectives: This study aims to describe how the fieldindependent students understand the derivative concept viewed from the perspective of commognition theory. Design: This type of research is descriptive with a qualitative approach. Setting and Participants: Three participants were selected from 41 students of an undergraduate mathematics education program in a state university through a cognitive style test. Data collection and analysis: Task-based interviews and a focused group discussion were used for data collection. Results: The analysis results show that not all commognitive were arising during the students' understanding process. The Keywords Subject arise in the use objective phase. Writing symbols, mentioning symbols and showing symbols with hand movements are all as the visual mediators. Definition and theorem of limit as well as definition and theorem of derivative are used in routine procedures. Students tend to use ritual routines instead of exploration routines discourse. On the other side, deeds routines do not appear. Furthermore, the forms of commognition, such as gestures and semiosis, are figured out. Conclusions: The exploring the subject's cognition and communication during the discussion is a challenge in this research. Further research is needed to develop this kind of research. [ABSTRACT FROM AUTHOR]

Background: The derivative is an important concept in mathematics and therefore understanding the derivative concept play an essential role. However, it has been found that students' understanding of derivative is still below expectation. The reason is that they cannot explain parts that has not been understood. They has just stated that they forgot or did not understand without any detail explanation. This shows that the provided explanation which is given by students does not support the cognitive process. To overcome this situation, we need to understand how the cognitive processes that lead to such understanding. One simple tool that allows for this purpose is the theory of commognition. Objectives: This study aims to describe how the fieldindependent students understand the derivative concept viewed from the perspective of commognition theory. Design: This type of research is descriptive with a qualitative approach. Setting and Participants: Three participants were selected from 41 students of an undergraduate mathematics education program in a state university through a cognitive style test. Data collection and analysis: Task-based interviews and a focused group discussion were used for data collection. Results: The analysis results show that not all commognitive were arising during the students' understanding process. The Keywords Subject arise in the use objective phase. Writing symbols, mentioning symbols and showing symbols with hand movements are all as the visual mediators. Definition and theorem of limit as well as definition and theorem of derivative are used in routine procedures. Students tend to use ritual routines instead of exploration routines discourse. On the other side, deeds routines do not appear. Furthermore, the forms of commognition, such as gestures and semiosis, are figured out. Conclusions: The exploring the subject's cognition and communication during the discussion is a challenge in this research. Further research is needed to develop this kind of research. [ABSTRACT FROM AUTHOR]

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

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

The aim in study was to analyze the characteristics and levels of mathematical communication of students in solving mathematical problems. This study used a qualitative descriptive study with 6 of prospective teacher, 3 students from STIKIP Bangkalan and 3 prospective teacher students from STIKIP Al Hikmah Surabaya, Indonesia. Research data collection techniques through documentation of teaching preparation assignments, and video recordings during learning to obtain verbal mathematical communication. The comparison method is still used to analyze the data through the stages of data condensation, data display, conclusion drawing, and verification. The results show that the characteristics of mathematical communication consist of accurate, complete, smooth, and systematic. Each subject has different characteristics. The prospective teacher students with high-level communication can explain accurately, completely, fluently, and systematically facts, concepts, procedures, operations, and principles. For prospective teacher students with intermediate levels of mathematical communication can explain accurately, fluently, and systematically facts, concepts, procedures, operations, and mathematical principles. Whereas for low-level prospective teacher students, they can explain mathematics accurately. [ABSTRACT FROM AUTHOR]

A person's reasoning can be seen through his or her way in solving a problem. A person's reasoning can be explored in systematic ways. This study aimed at exploring student reasoning at the stage of understanding the problem and looking back in terms of gender differences. The sample of this study were one male and one female students at Halu Oleo University Kendari, Indonesia. This research was a qualitative research. Student reasoning data were obtained using the main instruments namely the researcher and supporting instruments namely mathematics ability tests, problem solving tests, information form, and interview guidelines. Subject selection was based on a gender questionnaire analysis. The data obtained were analyzed qualitatively. The results showed that there were differences in the reasoning of male and female student teachers, in which at the stage of understanding the problem, the answers given by the male student was more detailed than those by the female one. Whereas in looking back stage, both male and female performed the steps in the same way both in terms of checking the problem solving and calculation steps. [ABSTRACT FROM AUTHOR]

An ordered list of binary words of length n is called a distance-preserving 〈 m, n〉-code, if the list distance between two words is equal to their Hamming distance, for distances up to m. A technique for constructing cyclic 〈 m, n〉-codes is presented, based on the standard Gray code and on some simple tools from linear algebra. [ABSTRACT FROM AUTHOR]