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Teacher knowledge is one of the main factors in the quality of mathematics learning. Many mathematics teachers have difficulty using proportional reasoning. Proportional reasoning is one of the essential aspects of the middle school mathematics curriculum to develop students' mathematical thinking. Teachers should realize that developing proportional reasoning is not an easy task. In this study, we investigated how teachers give proportional reasoning about the concept of proportional and nonproportional situations, especially in making sense of them. The research subjects were mathematics teachers who had taught proportional-related material. Data was collected using task-based interviews outside the teacher's working hours. Data analysis and interpretation were completed using a framework meaning-based approach. The results of the data analysis showed that the teacher is careful in understanding information, is aware of multiple meanings, and knows key information in understanding the contextual structure of proportional and non-proportional situations. Furthermore, they are also able to identify additive and multiplication relationships, have flexibility in understanding proportional and non-proportional situations separately or collectively, and understand problem-solving systematics in detail.

Purpose: Metacognitive awareness plays an important role in assisting students to solve problems because it affects their reasoning in assessing their thinking results. This research aims to investigate students' metacognitive awareness failures about solving absolute value problems in Mathematics Education. Methodology: It is qualitative research with 38 subjects of the fifth-semester students of Mathematics Education at the State Islamic University of Maulana Malik Ibrahim Malang. The materials included designing a Metacognitive Awareness Scale, a math assignment sheet related to the absolute value problem and a semistructured interview sheet. Findings: It was found that there was a significant failure, and 3 students were sampled from who had experienced different metacognitive awareness failures in solving absolute value problems. The study also proved students' inability to be aware of mistakes in determining problems, algebraic process, and their inability to know that what they carried out was wrong. Implications for Research and Practice: This research has implications for teachers, lecturers, and students to utilize the findings of the study in understanding students' metacognitive awareness failures in solving mathematical problems, especially in working on absolute value problems. This is also a reference for teachers on how to teach absolute value problems so that students do not experience metacognitive awareness failure when solving problems.

This study aims to explain the thinking process of students in solving combination problems considered from assimilation and accommodation frameworks. This research used a case study approach by classifying students into three categories of capabilities namely high, medium and low capabilities. From each of the ability categories, one student was chosen as a research subject. The results of this research showed that the student in high ability category, in understanding, planning, implementing and checking the problem solving used assimilation thinking process and they also used accommodation thinking process in solving a problem. The student in the category of medium ability, in understanding, planning, implementing and rechecking problem solving used assimilation thinking process. The student in the category of low ability, in understanding, planning and implementing problem solving used incomplete assimilation thinking process, and in rechecking the results of problem solving he was not able to do the thinking process of assimilation and accommodation.

This article was written based on the results of a study evaluating students' errors in problem solving of permutation and combination in terms of problem solving steps according to Polya. Twenty-five students were asked to do four problems related to permutation and combination. The research results showed that the students still did a mistake in understanding the problems related to permutation and combination, the students still made a mistake in planning problem solving related to permutation and combination, and the students still had a mistake in rechecking the problems given. Besides, there were some students who did the combination problem by using the permutation problem.

This research aims to explore elementary teachers noticing in stimulating students' critical and creative thinking abilities. This exploratory qualitative research focuses on the main aspects of teacher noticing (attending, interpreting, and responding) in stimulating students' critical and creative thinking abilities. Research findings on every aspect of elementary school teacher attention show sufficient evidence of stimulating students' critical and creative thinking abilities. In the aspect of attendance, the teacher highlights students' thinking in solving problems through writing. In the interpretation aspect, the teacher interprets students' thinking to understand more deeply the details of students' thinking strategies through two-way communication to expand students' understanding of the thinking strategies used. Based on the results of the interpretation, the teacher decides the student's needs and determines the response that should be given based on the student's level of understanding. The response given was in the form of providing suggestions about new thinking strategies and new learning strategies to expand students' critical and creative thinking. [ABSTRACT FROM AUTHOR]

The concept of fractions given in learning is the concept of part of whole and part of unit. The development of student's concepts of fractions can be built through fraction schemes. A partitive fraction scheme is a scheme that estimates the size of the fraction in the form of non-units to the whole that is not partitioned. The concept of fractions using a partitive fraction scheme uses a strong understanding of the concept of the part unit and part-whole fractions. This study aims to photograph the process of developing students' mental actions in constructing the concept of fractions using a partitive fraction scheme. This research method uses a qualitative approach with a case study type on students who are able to express partitive fraction schemes. The stages of data analysis consist of three stages, namely; (1) the results of task 1 data are corrected and determined by students who can solve fraction problems with part-whole and partitive unit fraction schemes, (2) students who can complete task 1 are selected as participants (3) students complete task 2 to see their problem-solving abilities fractions using a partitive fraction scheme, (3) students who can use a partitive fraction scheme were interviewed to see the mental action processes used in solving problems. The participants of this study were 35 students of fifth-grade elementary school who already understood the concept of part-whole and part of unit. The results showed that students used two types of mental action processes in the partitive fraction scheme: direct and indirect. [ABSTRACT FROM AUTHOR]

Teacher knowledge is one of the main factors in the quality of mathematics learning. Many mathematics teachers have difficulty using proportional reasoning. Proportional reasoning is one of the essential aspects of the middle school mathematics curriculum to develop students' mathematical thinking. Teachers should realize that developing proportional reasoning is not an easy task. In this study, we investigated how teachers give proportional reasoning about the concept of proportional and nonproportional situations, especially in making sense of them. The research subjects were mathematics teachers who had taught proportional-related material. Data was collected using task-based interviews outside the teacher's working hours. Data analysis and interpretation were completed using a framework meaning-based approach. The results of the data analysis showed that the teacher is careful in understanding information, is aware of multiple meanings, and knows key information in understanding the contextual structure of proportional and non-proportional situations. Furthermore, they are also able to identify additive and multiplication relationships, have flexibility in understanding proportional and non-proportional situations separately or collectively, and understand problem-solving systematics in detail. [ABSTRACT FROM AUTHOR]

Distance learning is a learning system that does not take place in one room and there is no face-to-face interaction between the teacher and the learner. This study aims to determine the impact of implementing distance learning in Indonesia from a commognitive point of view. This research is a descriptive type of research with a total of 543 participants who come from high school students in Pasuruan district, Indonesia. Data collection using a questionnaire. After the questionnaire is collected, it is analyzed using the Miles and Huberman method through reduction, display data, and conclusion, then it will be studied based on the commognitive theory. The results show that based on commognitive studies, students are more likely to still need a visual mediator as a visible object to be used as a communication medium, its realization depends on the material context. Students need to communicate to ask questions related to material that has not been understood. So it can be said that visual mediator is important during distance learning. [ABSTRACT FROM AUTHOR]

While a pandemic is currently sweeping the world, technology becomes a necessity in almost the entire aspects of life, particularly in learning activities. One of conventional learning-based platforms that adopt online system is Moodle Learning Management System. This study explored the argumentation skills of prospective teachers based on commognitive approach using the LMS. This qualitative research used online-based semi-structured questionnaire and interview during a discussion group via LMS platform. The subjects of this study were 38 prospective teachers. The research instrument was a questionnaire with eight items. It was initially assessed with Cronbach's alpha test in which the value indicated the questionnaire was reliable (0.852). The findings of this study indicate the argumentation skills of prospective teachers correlate with the commognitive framework, including claim with endorsed narratives; data with visual mediators; warrant with routine, word use, and endorsed narratives; and backing with endorsed narratives. [ABSTRACT FROM AUTHOR]

Distance learning is a learning system that does not take place in one room and there is no face-to-face interaction between the teacher and the learner. This study aims to determine the impact of implementing distance learning in Indonesia from a commognitive point of view. This research is a descriptive type of research with a total of 543 participants who come from high school students in Pasuruan district, Indonesia. Data collection using a questionnaire. After the questionnaire is collected, it is analyzed using the Miles and Huberman method through reduction, display data, and conclusion, then it will be studied based on the commognitive theory. The results show that based on commognitive studies, students are more likely to still need a visual mediator as a visible object to be used as a communication medium, its realization depends on the material context. Students need to communicate to ask questions related to material that has not been understood. So it can be said that visual mediator is important during distance learning. [ABSTRACT FROM AUTHOR]