Development of assessment and forecasting skills in high school students using the SWOT methodology in solving applied problems



The development of students’ research skills is one of the most common goals in pedagogy today. It is clear that it appeared for a reason: the life requirements for the skills and competencies of a modern person determine this choice. A high school graduate should not just possess a certain amount of knowledge or a set of skills. He must be able to compare facts, analyze, contrast, generalize, draw conclusions. Speaking in templates: “the ability to learn” is more important than the teaching itself. The experience of working with graduates in the classroom shows that elements of research skills are developed directly in the process of teaching mathematics. So, let's say, in addition to special efforts. In mathematics, when faced with an unfamiliar problem, a student in any case will look for a solution, analyze, compare, draw a conclusion. The most difficult thing for students is the ability to solve applied problems. This skill requires research skills, and in fact, the very process of solving problem-search problems contributes to the development of research skills. Experience shows that, having learned to determine the type of problem, students apply the already known algorithm. And then — the matter of the correctness of the calculations. But it is precisely at the first stage — parsing the condition of the problem that the student most often has difficulties: determine the type of problem, build three components: what is given, what to find, how to build a mathematical model, a solution, at what stage errors are possible… It is necessary to teach the student to make a forecast and assessment when familiarizing himself with the problem: a familiar problem or an absolutely new one, what type of problems it can be attributed to, what is known about such problems, what is its labor intensity, the approximate time spent on solving this problem, what is the forecast and assessment of the possible correct solutions. For example, a differential equation or a geometric model or a derivative is required... Of course, the student should make such a forecast and assessment as quickly as possible in order to make a decision (if we talk about any type of exam), to solve this problem now, or to postpone it for the last, or (which may also be) not to take on it at all.

The teacher is interested in the situation: the student has a forecast and assessment as a means of successfully solving practical problems. It is clear that prediction and assessment skills are considered exploratory thinking skills. In the process of forming a forecast and assessment, the student relies on the lowest mental operations: knowledge, understanding, analysis, synthesis — after that he can only draw a conclusion and give an assessment.

A professional task has almost been formulated: it is required to develop the skill of forecasting and assessment when working with applied problems. — after that he can only make a conclusion and give an assessment. A colleague and I discussed this problem with our students and invited them to conduct joint research in action using the «action research» method.

It was necessary to find a tool to clearly understand the mechanism of influencing the problem. First decided what you need to get? In order for the student to develop clear structures of the approach to solving an applied problem, he can assess its complexity for him personally, understand whether he has enough knowledge to solve this problem and what steps can be taken. To do this, he must be able to ask questions, look for answers and, depending on the answers, make a decision. In fact, it is necessary to develop the skill of assessment and forecasting, which is necessary for the student in literally all areas of educational activity and not only. This skill is vital: you always need to be able to assess the situation and make a forecast for your further actions. A literature review helped to find the SWOT analysis method most suitable for such a professional task. The abbreviation SWOT stands for: Strengths, Weakness, Opportunities, Threats.

In fact, SWOT analysis is an analysis of strengths and weaknesses when considering an issue, as well as opportunities and threats from the external environment. SWOT analysis helps to compose a description of a specific situation, based on this description, a conclusion is made. This allows you to make correct and informed decisions. The methodology needs to be adapted for the school educational process. When solving mathematical problems, there are no external and internal factors. Students will apply the four components of analysis to solve applied, problem-search problems.

So, in the first lesson of the section «Solving applied problems by means of integration and differentiation», the students were asked to perform a SWOT analysis of the finished problem solution. There were three problems, each student received a solution to one of them. After voicing some of the answers, discussing the solution, the students began to independently solve the problems. Moreover, for an independent solution, a problem was offered to choose from: either similar to the one that was given with a ready-made solution or similar to the one whose solution the student did not see, but listened to the analysis of this problem by other students. Thus, the student was given the opportunity to solve by analogy or try to solve a problem of a different type. It was noted that all students decided to choose a different type of problem. At the stage of independent decision, we conducted observation, some students needed a leading question, support. Reconciliation of the answers showed that seven out of twenty students could not complete the tasks in the allotted time. The tables for the SWOT analysis records were on one sheet. After checking the answers, the students carried out a repeated analysis, highlighting the strengths and weaknesses of an independent solution, naming opportunities and threats. After that, it was proposed to check the analysis performed on the ready-made solution and after the independent solution. The students named among the strengths:

– step-by-step solution with a clear algorithm;

– the same equation for typical tasks;

– accurate and clear algorithm;

– clear order of actions, logical transition...

Weaknesses include:

– computational errors;

– ignorance of the properties of the logarithm;

– scheduling a step-by-step solution takes a lot of time;

– it is difficult to compose a differential equation on your own...

Opportunities:

– easy to apply to this kind of tasks;

– use a calculator;

– understanding everyday processes (teapot cooling):

– solving any problems...

Threats:

– if you do not understand the algorithm, the solution will be chaotic;

– errors during integration;

– get confused and waste time;

– to decide, but decide wrong...

The students are participants in the study, and they themselves expressed that understanding the algorithm is an important condition for the successful solution of the problem. It was required to independently write down the algorithm for solving the problems considered. Observing the implementation of this stage showed that some students (those who could not solve the problems on their own) were unable to compose an algorithm. This circumstance and the analysis of the collected cards with the students' records of the analyzes performed required careful consideration of how to construct the following lessons. After reading carefully the students' sheets, we noticed that all the students analyzed the content of the problems: solutions, algorithm, some stages: knowledge — ignorance of the properties of logarithms, the ability to integrate... But no one analyzed their own attitude or their actions. Therefore, in the next lesson (topic «Problem solving with the help of a derivative»), students were asked to conduct a SWOT analysis immediately after reading the problem statement. Without discussing the algorithm, without considering the solution to a similar problem. The students were asked to analyze their own actions when approaching the solution of the problem.

Many students had two out of four components blank or the words «no», «nothing», dashes were written. It turned out that it is difficult for students to determine what opportunities such a task gives them and what threats. This is a direct indicator that prognosis and assessment are skills to be developed. Pupils do not think, do not know how to pose such questions as “what will it give me? what does it threaten me with? " Therefore, when planning the third lesson, we planned to use SWOT analysis in such a way as to «force» students to pose questions to assess the content of the problem, their actions in solving it, and predict possible risks and consequences. And most importantly, you need to find a tool for assessing and measuring these skills. Repeated reading of the students' answers shows that almost all students perform the four components of the analysis superficially: «a clear algorithm», «solve problems», «get confused in calculations» and the like... What kind of work to offer students in order to create a situation where the student will have to analyze the condition, evaluate the content, make a forecast and make the right decision, and without spending a lot of time?

The first and second lessons were based on individual work. In the third lesson, training group work was planned. In each group there will be students who have done SWOT analysis in detail and thoughtfully and those who have done it superficially. This division will allow mutual learning in the process of joint work. Pupils will be given a new type of problem (a problem on the rate of change), after joint discussion each group will have to name one criterion for all four components of the analysis. At this stage, the Carousel strategy will be applicable: each group will add one of the weaknesses, strengths, opportunities and threats without repeating itself. A total of three for each item. Thus, in the team, those students who could not or did not want to conduct a thoughtful analysis will be immersed in this process. In any case, they will be able to listen to the arguments of the students of their group, and look for other strengths, weaknesses, opportunities and threats in solving the problem, so as not to repeat the analysis of the previous group. Yes, it is possible that some «extra» words will sound, invented in connection with the need to say something. But this is exactly what we need: there must be different opinions that the student must accept or not accept, argue — this is the process of developing the skill of assessment and forecasting.

As an assessment of the results of teaching work and a skill test, students will be offered an assignment from two tasks of a different type.

You are given a cylinder whose radius is three times smaller than its generatrix. The radius changes at a speed of 0.5 m / s. Find the rate of change in the volume of the cylinder when the radius of the cylinder is 2.5 m.

A container with a hot liquid is cooled in a room with a temperature of C. In 6 minutes the container cooled down from C to C. How long will it take to cool the container from C to C?

In each group, students discuss the problems, together they make up some semblance of a specification. They do not write down the algorithm, but the descriptors, that is, they name the steps for solving the problem, for which the score is given, determine the total number of points for the problem and the approximate time for solving the problem.

This type of work solves three educational tasks: students learn to predict and assess through the distribution of points, mutually learn through argumentation in the process of discussion, and in fact, the skill of solving applied problems is improved. In addition, the tasks of this section require the use of intersubject connections. Pupils, having different preferences and specialized additional training, made a lot of explanations in the group, asked questions. So, the problem of heat transfer requires the application of knowledge of physics (observing the work in groups, we heard the words «the coefficient in this equation is» lambda «in physics»), the problem of the rate of change is solved using the formulas of geometry. The last step is to solve these problems and check the answers.

The lesson showed that the teaching group work, work with the compilation of descriptors was performed according to the plan, but took a little more time. After checking the answers, it turned out that two students, with the correct algorithm, performed incorrect calculations in the first problem. And the other two students did not have time to complete the solution of the second problem.

The conclusion of the research based on the three lessons learned: SWOT analysis for the development of forecasting and assessment skills is best used when working in a group, individual work can be planned after the group, when students already have an understanding of the importance of these skills and clearly understand how and why it should be done.

In the next lesson, the students were given a selection of five different types of problems. For each of the tasks, the students, working in groups, determined the type of task, discussed the specifics of solving such tasks, possible errors, determined the “cost” of the task in points, and justified. After which an exchange of views was held between the groups.

For the solution, the students chose two problems out of five. We encouraged students to choose those tasks that the students would find difficult for themselves. The stage of independent decision, but within the group, students could ask for help. The observation showed that there were a minimum of questions to each other and they were of a specific nature: «why did the coefficient turn out to be negative?", «Should we round up intermediate answers?" and others. After an independent decision, a discussion was held: did the forecast and assessment of the work coincide with the tasks and if not, then why. The ability to name your mistakes is an important part of learning. Almost all students received the correct answers, all students had the right way to solve problems.

Focusing on the levels and directions of the assessment of pedagogical methods offered by A. A. Gin: relevance, novelty, manufacturability, accessibility, support in professional growth, it can be concluded that the SWOT analysis technique is not laborious, simple and understandable, but at the same time, relevant, allows you to modify it without changing the main essence — to teach a critical attitude to information, task, phenomenon...

References:

1. Poya D., «Mathematical discovery», Moscow, «Science», 1979.
2. Gin AA, «Methods of pedagogical technique», Moscow, «Vita», 6th edition, 2005.
3. Savenkov A. I. «Content and organization of research education for schoolchildren», Moscow, September, 2003.