mathematics

Abstract Purpose: The main aim of the present study was to find out the possible effect of executive functions and academic emotions on pupils' academic performance in mathmatics. Methodology: In this study, the structural equation modeling, type of non-experimental method was implemented. Using sampling method based on the structural equation modeling, 400 (100 girls and 100 boys) in fifth and sixth grade elementary school pupils in Education regions of North, Central, and South of Tehran were reandomly selected. The research data were collected by using standard tests and questionnaires. Structural equation modeling findings showed significant relationships among the executive functions of the elementary school pupils, academic emotions and their mathematics performance. Findings: Moreover, there was significant relationship between academic emotions of the elementary pupils and their academic performance in math subject. Discussion: It is concluded that executive functions and academic emotions can affect pupils' academic performance in mathmatics, requiring more atension to these two influential varaiables while teaching math.

Identifying the contributors to students’ academic performance and progress creates an approach for planning, developing, and perfecting educational programs. The present study aimed to investigate the effectiveness of flipped teaching and problem-solving methods on the sense of responsibility and problem-solving ability in mathematics among female high school students in Ahvaz. The research method was quasi-experimental with a pre-test and post-test design and a control group. The statistical population included all female high school students in Ahvaz in 2019. Using the convenience sampling method, 75 students were selected and randomly divided into two experimental groups (flipped teaching and problem-solving method) and a control group (n= 25 per group). The control group received the traditional teaching method. The research instruments included the Responsibility Questionnaire and Problem-Solving Style Questionnaire. Analysis of covariance was used to analyze the data. The results showed that there was a significant difference between the experimental and control groups in productive and unproductive problem-solving styles among the students (p < 0.01). Also, the flipped teaching and problem-solving methods increased the sense of responsibility in the students, compared to the traditional method. According to the results, the effectiveness of flipped teaching was more effective compared to problem-solving methods on the productive and unproductive problem-solving styles and sense of responsibility. Consequently, the flipped teaching and problem-solving methods can be used to promote problem-solving styles and a sense of responsibility among students.

There are at least three elemental parts in Brouuer's philosophy ef mathematics that mqy have their origin in Kant. These three parts are (1) the intuition ef time, (2) the synthetic a priority of mathematical kn01vledge, and (3) the inter-suf?jectiviry ef mathematical constructions. Brouwer borrowed the notion ef the movement eftime as an a priori intuition ef time, explicit!J expressed, from Kant. In Brouuer's philosophy ef mathematics, the intuition ef time is the on/y a priori notion, on wbicb the whole ef mathematics is built. Houeuer, their notions o] the "intuition eftime" are not the same in the genealogy ef mind As far as the second item is concerned, Brouwer believes that all ef mathematical kn01vledge is a priori and synthetic. His arguments are differentfrom Kant's arguments. The concept of ''inter-suf?jectiviry" ef mathematics in Brotouer's philosophy is very involved, and there is no reference to Kant in this respect. One mqy interpret it f?y the Kantian transcendental subject or even the Husserlian transcendental phenomenology. Both interpretations seem to be consistent. My suggestion is to read Brauner ry himse!f.

Purpose: This research was conducted with the aim of identifying effective factors on educational reform at the level of national and regional supports for high school mathematics. Methodology: The present study in terms of purpose was applied and in terms of implementation method was qualitative, which was performed in two stages of synthesis research and content analysis. The research environment in the synthesis research stage were all reference texts about recognizing the needs of the high school mathematics curriculum in the period of 2007 to 2020 years, which number of 47 sources were selected as a sample by purposeful sampling method. The research environment in the content analysis stage were all reference texts of educational reform of the high school mathematics curriculum and national and regional support in the period of 2010 to 2020 years, which number of 7 sources were selected as a sample by purposeful sampling method. The content validity of the data was confirmed by 5 experts in the field of curriculum and education of mathematics and their reliability was obtained by the agreement coefficient method between the two coders 0.88. Data were analyzed by synthesis research and content analysis methods via deductive. Findings: The results of synthesis research showed that for the effective factors on educational reform were identified 5 components and 12 subcomponents, which the components included the need to review the curriculum, preparation of teachers to change the curriculum, the need for teacher training, supervision of the education system on the teachers' performance and providing curriculum implementation arrangements. Also, the results of content analysis showed that for the effective factors on educational reform were identified 2 components and 7 subcomponents, which the components included preparation teachers to change the curriculum and providing curriculum implementation arrangements. Finally, the diagram of the effective factors on educational reform at the level of national and regional supports for high school mathematics was drawn. Conclusion: According to the results of this study, planning to improve the education of high school mathematics is essential through the use of effective factors on educational reform.

This study aimed to examine the effect of educational software on 3rd-grade elementary-school students’ mathematical problem-solving skill. This was a quasi-experimental, pretest-posttest, controlled study. The statistical population comprised all 3rd-grade elementary-school male students in District 4 of Karaj (Iran) in the academic year 2018-2019. A sample was selected via convenience sampling, and the participants were randomly assigned to two experimental and control groups (20 each). On pretest, two tests of “numerical analysis” and “attention and concentration” (Wechsler test) and a researcher-made problem-solving skill test were administered. Then, the experimental group received eight 40-minute sessions of software training, while the control group received the class’s routine education. Finally, both groups took the posttest. The data were analyzed via univariate analysis of covariance and independent samples t-test. After the experimental intervention, the two groups demonstrated a significant difference (p < 0.001) at three levels of “problem-solving speed”, “attention and concentration”, and “numerical analysis”. The two groups also showed a significant difference at the level of “problem-solving strategy identification” (p < 0.05). Accordingly, the role of educational media, and especially educational software, can be highlighted in promoting students’ learning and mathematical problem-solving skill.

In the Critique of Pure Reason Immanuel Kant said that cognition (objective perception) is acquired in the unity of sensibility (the receptivity of the mind to receive empirical representations of things, which yields intuitions) and the understanding (in which concepts – general representations of things – arise), and is mediated by the imagination. Here, it is shown that numbers, either pure or denominate, are cognized in the synthesis of intuition and mathematical concept, and that the phenomenal world of the cognizer is shaped accordingly. Any number can be related to any other number through a general mathematical formula conceived by the cognizer for the purpose. The judgment of the cognizer is manifest in the specifics of the mathematical relationship established between the two numbers in cognition. If the cognized number is the numerical value of a physical constant then in the (consistent) phenomenal world it will always have been of the value found in cognition, which explains why the universe seems to be fine-tuned for life. If the cognized number is the numerical value of a physical variable, then the number will be subject to change in accordance with physical laws. Symmetry is a recurrent feature of the phenomenology. A mathematical formula conceived by the cognizer may also relate, one to one, the numerical values of quantities in one set with the numerical values of quantities of different dimensionality in another set, which suggests that physical laws are human inventions and that causality is a pure concept of the understanding.

The architectonic is key for situating Kant’s understanding of science in the coming century. For Kant the faculty of reason turns to ideas to form a complete system. The coherence of the system rests on these ideas. In contrast to technical unity which can be abstracted a posteriori, architectonic ideas are the source of a priori unity for the system of reason because they connect our reasonable pursuit to essential human ends. Given Kant’s focus on mathematics, in the architectonic and his critical philosophy more generally, we must have some sense of the architectonic idea of mathematics. In this paper, I argue for the key principles of the architectonic idea of mathematics: 1) because mathematics is grounded in a priori intuition, it is a peculiarly human activity; 2) the method of mathematics is one of a priori construction, a method only mathematics can employ and: 3) the objects of mathematics are extensive magnitudes. Given these principles, we can use the architectonic idea to have some clarity about how mathematics has dealt with historical development.