Teaching Mathematics Based on Graphic Management in Problem Solving Topics

Problem solving is a very important skill in mathematics that students need to master. These skills require logical thinking, deep understanding, mastery of concepts and making connections with existing knowledge. This study aimed to determine the effectiveness of graphic management -based mathematics teaching in problem-solving topics. This study uses a qualitative research approach with a case study design involving one study participant. Participants of the study were randomly selected among year 3 students with a moderate level of Mathematics proficiency. To collect data, graphic management of “Four Corners and A Diamond” and semi -structured interview sessions were conducted. Data collection from graphics management was analyzed descriptively and these interviews were analyzed inductively to obtain specific themes based on the transcripts. Findings of the study show that with this graphic management, students can organize information from questions in the form of appropriate graphics and facilitate their understanding. The implication of this study is that students can solve mathematical problems through the arrangement of information correctly based on the graphic management of "Four Corners and A Diamond". This study can also encourage teachers to use graphic management in helping students to solve non-routine mathematics problems more conceptually.

Role of Figures in Mathematics Problems in Slovak Testing T9

Besides providing information to pupils, their parents, teachers, and school founders about the achieved level in mathematics, the pupils’ results in mathematics at international or national testing can also be used for other purposes. In our research, the results of Slovak national testing T9 (success rate of pupils and difficulty of individual thematic areas and test items) seem to us to be a reasonable source for identification of critical areas in school mathematics. Based on the findings of such areas, we target more at these areas in the preparation of future teachers of mathematics. The special group of problems, so-called problems with figures, seems to be one of the critical areas. In the assignment of these problems, a part of the input information is not of a purely textual character, and in the process of solving the solver has to read information about objects appearing in the problem and relations between objects from figures (e. g. scheme, graph, chart, table, picture or map). The paper focuses on success rates of pupils in solving problems of this type and on various roles and functions of figures in problems with figures from the testing T9.

Students’ mathematical reasoning ability in solving PISA-like mathematics problem COVID-19 context

This study aims to use the Pendidikan Matematika Realistik Indonesia (PMRI) approach to measure the mathematical reasoning ability of grade VII students in answering PISA-like mathematics problems on number content in the context of COVID-19. This study employs descriptive research with 34 participants from a junior high school in Palembang, Indonesia. Tests, interviews, and observations were utilized to collect data. The method of analysis adopted is descriptive. Google Meet is used to facilitate learning. Learning the PMRI technique was accomplished in this study by assigning sharing and jumping tasks. That is, assignments for students to discuss with each other have different levels of difficulty, followed by two exam questions. In the context of COVID-19, the test questions are PISA-like maths problems. The results show that students’ average mathematical reasoning skill is 63,037, with mathematical manipulation a common indicator. Most students have exhibited indications for presenting conjectures. However, only a few students have put down indicators for drawing logical conclusions, so drawing logical conclusions is an indicator that students rarely see. Overall, grade VII students' mathematical reasoning skills in answering PISA-like mathematics questions on number material in the context of COVID-19 utilizing the PMRI approach is good since students are used to modeling contextual problems such that mathematical manipulation indicators occur.

The development of mathematics teacher professional competencies through social media

One of the competencies for mathematics teachers that needs to be developed continuously is professional competence. However, even if efforts for developing teachers’ competencies have been made formally by the government, it seems still lacking. This study, therefore, aims to develop mathematics teacher professional competencies through an informal development model using social media. This research used a qualitative method, a case study design, involving 19 mathematics teachers from various regions in Indonesia in the informal development process in the range of 2019-2021. The informal approach was carried out using question-and-answer techniques and guided discussions on mathematical problems. From the teacher development processes, 30 mathematics problems and their solutions were collected. As an illustration of this development process, this article presents five problems and their solutions, including solutions for two mathematics problems on conceptual understanding and three mathematics problems on problem-solving. We conclude that this informal approach is fruitful in helping mathematics teachers solve mathematics problems. This study implies that the teacher development process carried out in this study can be used as a model for informal teacher development by other higher education academics in their respective places.

Problems to Ponder

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to [email protected]. If published, the authors of problems will be acknowledged.

Students’ Intuition in Solving Mathematics Problems: The Case of High Mathematics Ability and Gender Differences

Students are required to find their appropriate strategies to solve mathematics problems so that intuition is needed. Male and female students have different intuition on mathematical problem-solving. Thus, gender is influencing how to obtain mathematical knowledge. This descriptive qualitative study aimed to analize the intuition differences of male and female students who have high-level mathematical abilities at secondary school in solving mathematics problems. Data was collected through tests of mathematical problem-solving and interviews then analysed through data reduction, data presentation, and conclusion. This study found that: (1) There are differences in the characteristics of male and female intuition in mathematical problems solving, (2) The intuition of male and female in mathematical problems solving based on Polya's steps is different in re-checking the answers, (3) There are differences in intuition when students solve linear equation system problems. There are differences in intuition between male and female students with high matematical abilities in each material. Students with problem-solving abilities have affirmative intuition to understand problems, anticipatory intuition for problem-solving plans and solutions, and conclusive intuition to re-examine problems.

The Beauty of Mathematics: Learning Mathematics by Questioning

Mathematics problems may seem to have no real use in life, but this could be further from the truth. The use of mathematics is everywhere in our daily lives and, without discovering it; we apply mathematics ideas, as well as the skills we learn from executing mathematical challenges every day. Unfortunately, mathematics feedback at national examinations is deficient. A mean of between 23 to 29 percent for 5 years in a row from 2014 to 2018 is a clear indication that the training of students today for tomorrow’s workplace with concept development in context, problem solving through interactive experiences and understanding through application is missed. Over this period, the evaluation of the outcome has also shown a standard deviation almost equal to the mean or even greater than the mean for instance 2016 for paper 2 (refer to Kenya National Examinations Council Report) is a clear sign that there is a big disparity from the mean and a likelihood of a number of students scoring zeros or below 10 percent. This dismal performance in national examinations particularly in mathematics demonstrates that contextual curricula and instructions that encourage numerous structures of learning like relating, transferring, applying, experiencing and collaborating are not achieved. Therefore, this article looks into different contexts in which students learn and how they broaden their abilities to make connections, enjoy discovery, and apply the knowledge learnt. These are abilities they will need throughout their daily lives and careers. Being able to do arithmetic is of little ultimate use to an individual unless he or she can apply it. Each arithmetic operation is explored in detail for its applications in the real world problems. Real life challenges motivate ideas and provide additional settings for practice.

Students' Thinking Level in Solving Mathematics Problems Based on SOLO Taxonomy as Viewed from the Mathematics Anxiety

The SOLO (Structure of Observed Learning Outcome) taxonomy is an educational taxonomy suitable for organizing various types of learning. The SOLO taxonomy categorizes students' thinking into five levels: pre-structural, uni-structural, multi-structural, relational, and extended abstract. The purpose of this study was to describe the level of students' thinking in solving mathematics problems based on the SOLO taxonomy with high, medium, and low levels of mathematics anxiety. This type of research is descriptive qualitative research. This research was conducted in one of the junior high schools in Tulungagung City, East Java, Indonesia. The instruments used were a mathematics anxiety questionnaire, test based on the SOLO taxonomy, and interview guidelines. The data analysis used the Miles and Huberman model, which consists of three stages, namely data reduction, data presentation, and conclusion drawing or verification. The results showed that subjects with high mathematics anxiety had a uni-structural level of thinking. Second, subjects with moderate mathematics anxiety had a multi-structural level of thinking. Third, subjects with low mathematics anxiety have an extended abstract thinking level.

Problems to Ponder

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to [email protected]. If published, the authors of problems will be acknowledged.