School geometry course has always been and remains one of the problematic “points” of teaching mathematics methods. At different times, various opinions were expressed about geometry and its place in the school system. Undoubtedly, the development of logic and intuition, which students observe in geometry, makes this discipline unique and necessary to study. One of the main goals of studying geometry in school is knowledge. However, it should be recognized that this goal concerning geometry is secondary since most school geometric knowledge is not in demand either in the practical life of a person or in scientific activity. The primary goal of studying geometry is that science is considered a phenomenon of universal human perception. Some theorems of geometry are among the most ancient monuments of world culture

The task of updating the school geometry course is to make it modern, enjoyable, taking into account the inclinations and abilities of each student, based on the level of geometric education achieved by the national school. In this case, the study of geometry depends on which textbook is used to teach geometry. A geometry manual should not be limited to building a geometric theory. The authors of all school primers try to make the presentation of the material as evidence-based as possible.

When teaching geometry in high school, it is necessary to pay attention to the formation of basic knowledge of the solid geometry course. At the same time, it is essential to find an opportunity to restore the basic understanding of the planimetry course. When studying geometry, it is crucial to increase the clarity of teaching, pay more attention to the issues of depicting geometric shapes, the formation of constructive skills and abilities, and apply geometric knowledge to solving practical problems.

## Problem Description

It is possible to highlight the main problem that students face when studying geometry. In the study of geometry, the theory is critical. However, knowing theory alone is not enough to fully immerse oneself in a geometry course (Chan & Clarke, 2017). Often students, without hesitation, memorize the formulation of a theorem and its proof, but at the same time, they find it challenging to apply it. Inability to build a drawing, since it is a well-constructed drawing, is the key to success in solving a problem.

According to their drawing, schoolchildren try to make assumptions about any figure properties that are not specified in the assignment. For example, they build an isosceles triangle and start the solution, beginning from its properties, although there is no such condition in the task. Some schoolchildren cannot make a chain of logical reasoning that will lead to the solution of the study. It is also necessary to consider the peculiarities of the psychological development of schoolchildren of this age. Now, more than ever, an alternative school needs a balanced, well-thought-out system of geometric education.

The problem with geometry in high school is that students do poorly in readiness for the Unit 1. Such conclusions were made when evaluating students according to the preliminary test. The data was collected at the beginning of the Modular Lesson on September 8, 2021. Problem with geometry test results occurs at Annapolis Road Academy. Traditional assessment tests do not provide sufficient information about the student’s inner abilities. They emphasize accurate information, including those procedures and review skills, that do not have an in-depth discussion.

## Statement of Project Objective

It is necessary to turn the class into a “math community” and not a gathering of people. The correct solution will encourage students to rely on their logic and mathematics since the training does not provide a straightforward solution for each task. It is essential to allow students to use their judgments and mathematical reasoning in place of memorization procedures. Moreover, it will enable students to reflect and be creative instead of asking only for the “correct” answer. Combining different aspects and rules with many mathematical positions is crucial instead of supporting the view that science is a system of separate concepts and skills.

Moreover, when using the assessment method exclusively, there is a tendency to distort the results to favor a specific group of students. At the same time, testing does not provide an objective assessment of the abilities of others. Practical testing aimed at assessing the level of knowledge of a large group of students requires a large number of documented technologies for collecting information on competency indicators. On the other hand, knowledge assessment is an integral part of the school curriculum. Simultaneously, learning is becoming more open and sensitive to distinctive features. It reflects any broad and accurate understanding that students have.

The model program for improving the quality of education is based on adequate consulting support. It aims to stimulate the professional growth of management and teaching staff in schools with low learning outcomes. The essential condition for improving the quality of education in geometry classes in Alternative schools with expected learning outcomes is developing a multi-level system of comprehensive support.

Moreover, the model program for improving the quality of education is based on interschool partnerships and networking of schools with different levels of quality of learning outcomes. Its goal is to provide conditions for achieving comparable educational results by educational organizations in the region, primary schools with low learning outcomes, based on interschool partnerships and network interaction of schools with different levels of quality of learning outcomes. Teachers with a high level of professional competence can lead author’s schools and creative laboratories. Educators who experience difficulties organizing the educational process, who have a low level of special training, will satisfy their professional needs by becoming listeners of an inter-municipal counseling center.

Knowledge assessment is an integral part of the learning process and pedagogy; systematic training is impossible without assessment. Nowadays, attention has begun to be paid not only to assessments focused on the final product but also to alternative assessments, which focus on the learning process (Yeo, 2017). The presentation of such authentic assignments as real-life situations increases the interest of students. The intellectual challenge provides competent data on individual learning and allows you to test various skills, including those necessary for a fulfilling life in modern society. They represent an antithesis to the prevailing assessment methods, which were considered insufficient, especially by professionals.

Traditional grading can be seen as the result of a “culture of testing,” while alternative grading can be considered a “culture of evaluation.” The classical assessment method is a traditional exam, which does not adapt to teaching methods (Ilany & Shmueli, 2021). Since the educational process involves attending full-time lectures, the exam aims to assess the material that students have memorized. However, the relationship between classroom learning and grade is not considered.

Special mention should be made of the relationship between geometry and the computer as a tool to increase the positive impact on the study of geometry. A laptop is a handy tool in geometric research. With its help, students can experimentally discover new interesting geometric facts. The person remains the most critical role to prove these facts. At the same time, from the point of view of mathematics, schoolchildren and the solid and weak technicians and humanities can be included in geometric activities using computers. The primary science, which is geometry, received a new impetus for development as an educational subject and as a science, thanks to the most modern computer technologies.

## Methodology

After taking measures to improve the teaching and teaching of geometry, research improvements in understanding the subject should be carried out, and statistics should be collected. This research is to be conducted among 150 students in grades 10, 11, and 12 during their high school geometry courses, and the application of the study must take place in three phases. The research is carried out in the Alternative School and asks not only students but also teachers.

The first part of the study consists of three questions on geometry, regarded as a straightforward question, a simple question, and a difficult question. Students are given three different time frames to answer each question: easy, too easy, and challenging. Students should solve a “too easy” question in 4 minutes, an “easy” question in 6 minutes, and a “hard” question in 7 minutes, and they should suggest different ways of solving each question as much as possible. Each question in this app is designed so that students can imagine other ways of solving the questions.

The first question belongs to the category of simple questions and consists in finding the angle on a geometric figure. The task for students is also to find the answer in as many ways as possible. At the second stage of the study, a survey of 6 questions was applied. This review asked to explore their views on mathematics and mathematical issues and the various ways they used to address these issues. Students were asked to answer the questions by choosing the following appropriate options: 1: strongly agree, 2: agree, 3: disagree: 4: strongly disagree.

The last stage consists of a test of 20 questions, which are given 20 minutes. The test should be to identify students’ ability to solve problems on spatial perception. Students with a spatial ability score above 11 are coded as students with high spatial knowledge. In contrast, students with a spatial ability score equal to or below 11 are coded as students with low spatial ability.

Statistics are collected based on calculating student grades and giving out a total score for each quality. The study results should show the level of improvement that students and teachers demonstrated in teaching and mastering geometry.

## Benefits of solving the problem

It will benefit geometry students if problems are identified and teachers know how to use the data, then they can help achieve the goal of improving student achievement. For teachers, the knowledge gained from the data analysis will be used to plan and deliver training. The teacher includes the standard in lesson plans and has proof of student progress in student work. The school’s goals are to include a commitment that promotes the following: a structured and predictable learning environment that minimizes unnecessary trauma; focuses on building positive and supportive relationships between students, teachers, staff. It should take a balanced and refreshing approach to conflict and conflict resolution through skills development.

## References

Chan, M. C. E., & Clarke, D. (2017). Structured Affordances in the Use of Open-Ended Tasks to Facilitate Collaborative Problem Solving. *ZDM—Mathematics Education*, 49, 951-963.

Ilany, B. & Shmueli, N. (2021). “Three-Stage” alternative assessment. *Creative Education*, *12*(7), 26-44.

Yeo, J. B. (2017). Development of a framework to characterize the openness of mathematical tasks. *International Journal of Science and Mathematics Education*, 15, 175-191.