Introduction
One of the urgent tasks of education modernization is the orientation of the educational process toward the implementation of a competency-based approach. It means the formation of crucial competencies based on students’ readiness to use the learned knowledge and methods of activity in real life to solve practical issues. This approach defines the attitude toward knowledge, skills, and abilities as means and tools for the integral formation and development of a child’s personality. In the federal component of the state educational standard of general education, it is noted that the school’s priority is the formation of general academic skills, the level of mastery which largely predetermines the success of the entire education. In this regard, the responsibility of teachers and school leaders increases not only to ensure the high quality of curricular knowledge and skills but furthermore to test students’ general learning skills.
Mathematics is one of the core subjects that supports the study of other disciplines. Practical mathematical skills are necessary for the job and vocational training and are especially important for improving the quality of life. The main goal of teaching mathematics is to ensure that students firmly and consciously master the system of mathematical knowledge. They must strengthen the skills necessary in everyday life and work activities of every member of modern society, sufficient for studying related disciplines and continuing education.
Furthermore, one of the essential structural elements of each lesson of mathematics and the whole process of learning, in general, is a test of the knowledge and skills of students. It is always a focus of attention because it indicates learning results. Students often feel deeply moved by this test; they may feel satisfied with their work, proud when they get a high assessment, or, on the contrary, lose confidence in their abilities and sometimes their interest in learning. To a large extent, the result and its competent interpretation depend on the construction of the test program. Therefore, the FSA Math program exists to assess the nature of students’ learning, but its evaluation results show both positive and negative aspects of its content.
Evaluation Results
First of all, it is essential to designate that the program is created following the goal of the mathematics course to provide subject preparation for students, sufficient for the acquisition of comprehensive mathematical education. Moreover, it contributes to the creation of didactic conditions for mastering universal learning activities (personal, cognitive, regulatory, and communicative) in the process of learning the subject content (Callan & Cleary, 2018). The program can check the level of formation of cognitive interest in the subject and the level of development of spatial imagination, needs, and abilities for intellectual activity. Components of the program contribute to checking the status of mastering the subject content generalized types of training: analysis, comparison, and classification of mathematical objects (numbers, values, numerical expressions). It is undoubtedly an important factor indicating the correlation between the goals and results of the program and the effectiveness of its implementation as a mandatory component of education in the state.
The focus of the mathematics program on the formation of methods of mental activity allows the methodological level to implement a system-activity approach in the teaching practice. It should focus on the components of learning activities and create didactic conditions for mastering universal learning activities (personal, cognitive, regulatory, communicative), which must be considered a holistic system. The origin and development of each action are determined by its relation to other types of learning actions, including mathematical ones.
The peculiarity of the program is the logic of constructing its content and testing knowledge. Its components are divided by levels and thematic principles. Each subsequent topic is organically linked to the preceding ones, allowing for the repetition of previously learned concepts and ways of action in the context of the new content in practice. It contributes to forming students’ ideas about the relationship between the studied issues (Callan & Cleary, 2018). It helps them realize what knowledge and activities they need to master and which are still too early. It has a positive impact on the cognitive motivation of students and purposefully prepares them to accept and understand new learning tasks.
At the same time, the FSA Math Program usually consists of many tasks designed to test certain qualities of test-takers. Each classification reflects this idea of the variety of test item forms and therefore suffers from a certain degree of one-sidedness. However, this phenomenon can be defined as a legitimate pattern because these classifications are artificial. They are based on an attribute of practical importance for determining specific objectives (Grigg et al., 2018). At the same time, not the most essential and practically important attributes are chosen as the basis for division in several categories of tests. Moreover, some of the existing classifications are not always subject to all the rules of division of the volume of the concept. Therefore, such types do not adequately fulfill their main task – to facilitate the process of checking the degree of knowledge assimilation and do not provide an opportunity to quickly find patterns that determine the causes of students’ lack of assimilation.
Recommendations for Improving the Program
Parents, learners, and educators should strive to maximize the effect of the program’s objectives. Each type of program assignment is most effective under certain conditions. A standard appointment that fits most material and questions is the multiple-choice one. For detailed factual information related to the content of the terms, a practical and compact test should be provided by the type of matching and alternative assignments. Alternative tasks are beneficial for testing comprehension of the material presented in the question (Bernacki & Walkington, 2018). On this basis, there is a need for all types of items, although the program does not need to contain the same number of items of each type. In addition, a variety of things is likely to make the test less monotonous for test-takers, which, in turn, will contribute to less fatigue, which often serves as a source of errors.
The problem itself should be contained in the central part of the task and not taken out in detail with choices, which should be as brief as possible. Both of these points relate to the rule about the requirement of simplicity. The central part should include only what is necessary for a clear and precise problem formulation (Boulton et al., 2018). In addition, it is not necessary to use tasks with negations in the central part because this leads to contradictions. Moreover, negative values are not as important as positive ones. It is also necessary to consider students’ capabilities in the assimilation of scientific concepts in the formation of the components of the program. The content of learning focuses on constructing a scientific-theoretical style of thinking and dialectical generalization of knowledge and contributes to the formation of students’ positive motivation (Rakoczy et al., 2019). It should be aimed at mastering the scientific picture of the world, the general ways of scientific knowledge, and available methods of action for such knowledge.
Therefore, the content of each topic should be deeply motivated, not only by creating a momentary soon passing interest or references to practical relevance in future life. The components must be such that the content was aimed at solving severe problems of scientific-theoretical cognition of phenomena and objects of the world around, at mastering the methods of such understanding (Rakoczy et al., 2019). Only in this case will students create a prospect for further study of familiar, constantly observed phenomena, which will make the basis for forming meaningful motives for learning activities. It requires more frequent testing of knowledge and skills of students to help them systematize the obtained knowledge, highlight the main thing, see their weaknesses, and focus on them not to have difficulties with them in the future.
FSA helps the teacher to provide timely assistance to the student and, if necessary, to adjust the curriculum. Therefore, teacher involvement is significant both during and after the program to adapt the curriculum. Moreover, because of the increased level of discomfort due to insufficient time to complete the program, it is recommended to improve it. This way, students will concentrate on the quality of the performance rather than on the number of minutes remaining. In general, it can be concluded that the program meets the educational standards, but some interventions would help provide a more flexible approach to meet the needs of the students.
Strategic Goal of the Mathematics Program and Assessment of the Achievement
Checking and evaluating students’ knowledge, skills, and abilities is meant to identify and compare the results of learning activities at a particular stage of education with the requirements set by the curriculum. In the ’60s of the last century, the theory of optimization of the learning process, which covers almost all the problems of didactics at that time, was developed. The place and importance of testing students’ knowledge in the learning process were determined in developing this theory (Luttenberger et al., 2018). It can be considered a link in the learning process, consisting of specific cycles. The last, the sixth link of each cycle, involves obtaining information about the learning results in the rotation and identifying unresolved learning objectives and the causes of student failure.
It is followed by the teacher and students’ analysis of their performance, discussion of these results, and the teacher’s determination of the baseline for the new cycle of the learning process. These actions contribute to making the new cycle of the learning process higher in level and more advanced and lead to a spiral development of the cycles of the learning process themselves. The approach described above should be the foundation of the mathematics program, but according to the survey, significant problems in learning and testing can still be noted. The main ones are the children’s lack of understanding of the program’s instructions and the lack of parental awareness of ways to overcome academic problems. Any program should have three obligatory parts: indicative, executive, and control (Griffith et al., 2020). The meaningful element establishes the character of the upcoming activities and operations employing which this action is to be carried out and the conditions of these operations’ application.
The executive part consists of performing the planned operations in compliance with all requirements. The controlling element provides operational monitoring of the process of acting to obtain the desired results. In this part, a discrepancy between the planned operations and the results can be found, which makes it possible to carry out the correction of the stages of action performance (Luttenberger et al., 2018). However, as a result of the program assessment, it is possible to conclude that these three components do not correlate holistically. Due to this, especially during the pandemic, students’ lack of understanding of the order of the program and the process of preparation for it increased. Thus, despite the positive aspects, we cannot call the program’s goal fully accomplished, especially in times of distance learning.
The Role of the Program in the Acquisition of Knowledge
Knowledge is the result of understanding reality, tested by socio-historical practice and certified by logic; its adequate reflection in the human mind in the form of ideas, concepts, judgments, and theories is one of the elements of education content. By checking students’ knowledge, the Program and its creators narrow the results of mastering this content. Full-value knowledge of students, acquired by them in the process of learning activity, is characterized by several qualities: completeness, depth, efficiency, flexibility, concreteness and generalization, coherence and deployment, systematicity, and awareness. The grade of knowledge of students depends, first, on the features of the cognitive activity in which they are included, and secondly, on the breadth of inclusion of this knowledge in various activities. Thus, the ability is inextricably linked to the skills of students.
The position on the inseparable connection between knowledge and skills has long been reflected in the theory of pedagogy in the form of levels of knowledge assimilation. The basis for allocating these levels is based on the content of the activity in which the acquired knowledge should be used. Each realized skill is the application of knowledge in practice. From this comes the need for a clear division of the Program into levels, each of which should correspond to the content (Tafawak et al., 2018). This approach lies at the heart of the Program, increasing its quality and effectiveness.
The learning goals set the types of cognitive activities. Sometimes the student must memorize some information to be learned. In this case, the assimilation test should be carried out by the ability to reproduce the knowledge. However, if the pupil coped with it, this is graded “excellent.” Nevertheless, more often, it is necessary to use wisdom when performing different kinds of tasks. The creators should decide in advance on which tasks students should be able to apply the learned knowledge, and it is necessary to determine what skills should be taught when mastering knowledge (Tafawak et al., 2018). Thus, the assessment of student performance consists of two components: knowledge of the content and the ability to apply knowledge in different situations. The essence of any knowledge check consists of the correspondence of the results obtained to the planned levels of assimilation. To solve the problem of testing knowledge is vital to find an objective way to correlate the results
Further Ways to Develop the Program Concerning its Functions
As part of the learning process, testing students’ knowledge performs several functions. First, the primary specific function of testing knowledge is to identify the state of students’ wisdom and skills provided by the programs at a given stage of training and guide the teacher and students in the results of their joint educational work. The second distinct operation of testing knowledge consists of fostering and strengthening students’ sense of responsibility for their academic work, promoting discipline, and the habit of a conscientious attitude to the performance of academic tasks (Xu, 2018). Lack of testing disorganizes students and lowers their consciousness of responsibility. The prospect of testing, on the contrary, makes students more responsible for their academic work. Since the program is a particular part of the learning process, it fulfills in it not only its special functions but also many general functions inherent in the learning process as a whole.
Since all functions are interconnected, the central part is distinguished by the dominant goal of testing knowledge. It turns out that “testing,” in terms of these goals, acquires the meaning of method – a way of learning and achieving the goals of education, development, and education (Xu, 2018). Then the considered functions of testing knowledge, as they coincide with the goals of education, development, and upbringing, will be the main functions of the learning process and the primary ones of the program.
The major didactic function of the mathematics program should be to provide feedback between the teacher and students. It should focus on identifying deficiencies in the flow of the learning process and gaps in students’ knowledge to determine the degree of mastery of the learning material in mathematics. The primary purpose of the FSA Program should be to determine the quality of student’s mastery of the educational material and their mastery of knowledge, skills, and abilities of the curriculum (Yu et al., 2021). The task of testing is also to measure the degree of responsibility of each student for the results of his studies and the level of his skills to gain knowledge independently.
Systematic completion of the mathematics curriculum is one of the main conditions for improving the quality of learning. The teacher’s skillful possession of various forms of knowledge control promotes students’ interest in the study of mathematics, prevents lag, and ensures students’ activity in the classroom (Yu et al., 2021). Therefore, modifications must be connected with the need to adjust the content of the subsequent stages of training in a given subject area and the intensity of teaching the material. Secondly, the specification of the main goal of the revision should correspond with learning pupils’ methods of mutual control and self-control, forming the need for both.
Conclusion
Thus, an evaluation of the FSA Mathematics Program leads to the conclusion that it has both weaknesses and strengths. Of course, the main power of the Program is that it follows the goal of measuring student outcomes in order to improve student outcomes further. The Program is also multi-component and has several levels of complexity, indicating a comprehensive approach to its creation. At the same time, the evaluation found that not all students are satisfied with the Program, are stressed by it, and are insufficiently educated on the issues of passing and preparation. There are other significant shortcomings, but small changes can help eliminate them and improve the Program’s results in a short period.
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