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Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not necessarily be able to explain the solution well. Cognition and communication by the students will greatly affect the subsequent learning process. The aim of this study is to describe students' commognition of routine aspects in understanding derivative tasks for heterogeneous groups of cognitive styles-field dependent and independent. This qualitative study involved six third-semester mathematics education students in the city of Palu, Indonesia. We divided the subjects into two groups with field-independent (FI) and field-dependent (FD) cognitive styles. The first group consisted of two FI students and one FD student, and the second group consisted of two FD students and one FI student. Moreover, the subjects also have relatively the same mathematical ability and feminine gender. Data was collected through task-based observations, focused group discussions, and interviews. We conducted data analysis in 3 stages, namely data condensation, data display, and conclusion drawing-verification. The results showed that the subjects were more likely to use routine ritual discourse, namely flexibility on the exemplifying category, by whom the routine is performed on classifying and summarizing categories, applicability on inferring category, and closing conditional on explaining category. The result of ritual routine is a process-oriented routine through individualizing. This result implies that solving the questions is not only oriented towards the correct answers or only being able to answer, but also students need to explain it well.

This study describes the metacognition profile of female and male mathematics' education students in understanding the concept of integral calculus in the category of classifying and summarizing. This research method was an explorative method with the qualitative approach. The subjects of this study were mathematics education students at the University of Halu Oleo, totalling 47 students consisting of 12 male and 35 female. The process of selecting research subjects began with the provision of a mathematical ability test to 47 students taken from the question bank for the college entrance test. From the results of the test, selected 1 male and 1 female each have a high mathematical ability. The results of this study were as follows: There is no difference of metacognition profile between male and female mathematics education students in understanding the indefinite integral concepts in category classifying and summarizing. There was difference of metacognition profile between male and female mathematics education students in understanding the definite Integral concepts in category classifying and summarizing.

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.)

Previous research shows that speed is one of the most difficult in the upper grades of primary school. It is because students must take into consideration two variables; distance and time. Nevertheless, Indonesian students usually learn this concept as a transmission subject and teacher more emphasizes on formal mathematics in which the concept of speed given as "distance by time" rigorously. A sequence of learning activities with toy cars context was designed based on students' development and Realistic Mathematics Education (RME) principles which are guided reinvention, didactical phenomenology and emergent modelling. Using their own models, students are able to explain a proportion among distance and time in speed as well the relationship of it.

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a given area, there are many possibilities of perimeter and vice versa. When student are not aware of this relation they might be confused about the concept in their continuation of the learning process. This research was conducted to study if it would support students' understanding of the concept of perimeter and area if we let them explore the relation between perimeter and area in the very first phase of the learning process. Design research was chosen as the method to study this issue and the three basic principles in The Realistic Mathematics approach were applied in this study to support the learning process of perimeter and area. Real life context such as picture frames was chosen in developing a sequence of learning line to reach the learning goal of perimeter and area. The partipants of this research were students and mathematics teachers of grade 3 in one of the elementary school in Surabaya. Two classes were taken to involve in the first cycle and second cycle respectively. The teaching experiment shows that the class activities such as making photo frame, measuring photo paper with sticky paper and arranging shapes with wooden matches are activities which can be used to reveal the relation of perimeter and area. From those activities students build their own understanding that in fact area and perimeter are not in one to one correspondence, they found that for the given area they might find different perimeter or vice versa. They also found the reason why they multiply length and width to count the area of rectangular or square shape from sticky paper activity. Somehow some students were found to still struggle with their understanding of area and perimeter. They often simply count the area and perimeter but when it comes into comparing the area or perimeter they still struggle to differentiate between area and perimeter.

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]

In teaching proportion, the teachers usually give the students a formal formula, such as cross-multiplication, without providing them the meaning of proportionality. Thus, the students just apply it in order to solve proportional problems. However, it does not connote that they understand what proportionality means. In this paper, the authors attempt to explore how the informal proportional reasoning can be developed to a more formal level. The development of student's proportional reasoning is described in three levels since the representations of students' reasoning are different. In order to support them, several instructional activities were designed which were based on the heuristic of Realistic Mathematics Education (RME) within a learning trajectory. In this case, design research was chosen as an approach in investigating how the design works in the classroom. The result shows that the designed students' activities could help students learn about proportion and develop their proportional reasoning.

This study aims to identify research trends related to mathematical understanding and research gaps using the Systematic Mapping Study (SMS) method of data collection through Publish or Perish (PoP) software to search the initial database on Scopus. Furthermore, the initial data obtained is analyzed using VOSviewer software. The number of published articles we selected according to research objectives is 23, and we reviewed them using VOSviewer. The level of education in the articles we have reviewed starts from elementary, junior high, high school, prospective teachers, and teachers. There are 4 clusters of research on mathematical understanding. In cluster 3, there is still space to conduct research related to the growth of mathematical understanding in junior high school students because, based on the results of the bibliometric analysis, there has not been much research related to the growth of mathematical understanding in junior high school students. [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 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.)