In essence, the position of science is to facilitate human life. Likewise with mathematics which is classified as a science. The birth of mathematics is none other than to provide convenience and overcome various life problems. Philosophy is a science that seeks the truth value of the essence of a problem. Philosophy and mathematics have no doubt that from the past until now these two fields of knowledge are very closely related. Philosophy of mathematics is a branch of philosophy that examines the philosophical assumptions, foundations and effects of mathematics. The aim of the philosophy of mathematics is to provide a record of the nature and methodology of mathematics and to understand the place of mathematics in human life. The position and relevance of philosophy in learning mathematics can be seen in epistemology, mathematical ontology, mathematical methodology, and mathematical logic.

One of the factors that can improve learning outcomes is the use of learning media. Today, there are many choices of media to be used in the teaching and learning process. The use of ICT-based media is one option that is currently being widely used. One technology that can be taken into account is the use of Augmented Reality (AR) media. Augmented Reality (AR) is a technology that integrates two-dimensional or three-dimensional objects into a real environment. The use of AR in learning can make learning more interactive. The purpose of this study is to describe Augmented Reality (AR) learning media in learning. The method used in this study is the method of literature review or literature study as a source of data. After tracing the data, it was found that Augmented Reality (AR) had a positive effect on spatial abilities and mathematical problem solving abilities. Therefore, the use of this media can be an option for educators in conveying materials related to geometry.

The background of this research is the Implementation of the Independent Curriculum (IKM) as a result of curriculum changes, it is rumored that the Implementation of the Independent Curriculum (IKM) is less effective, because there has not been maximum preparation in terms of outreach, implementers in the field, as well as teachers, as well as various supporting infrastructure. The implementation of the Independent Curriculum (IKM) is all wrapped up in four indicators of readiness, including: physical condition, mental condition, emotional condition, needs (motivation) and knowledge. Therefore, researchers have the desire to test the level of readiness for the Implementation of the Independent Curriculum (IKM), because schools are required to be oriented towards changing the existing curriculum in order to achieve the ideals of the nation. The research method used was the survey method, with the instrument used, namely a questionnaire, which was distributed to 60 teachers from 13 schools at the high school level (SMA) randomly in North Nias Regency. Based on the results of research on the level of learning readiness at the senior high school (SMA) level in the Implementation of the Independent Curriculum (IKM) in North Nias district, the 4 indicators studied were in the fairly prepared category.

This study aims to determine the category of mathematics teacher's ability to build the ability to understand concepts and instill mathematical problem solving abilities on student learning outcomes. This research was conducted at SMA Negeri 1 Alasa, and the sample was taken randomly as many as 272 students. The research instrument used a questionnaire, and data analysis used descriptive analysis. Based on the results of the analysis it can be concluded that the ability of mathematics teachers to build understanding of concepts and instill mathematical problem solving abilities on student learning outcomes in the moderate category.