Research And Exploratory Activities For The Intellectual Development Of Primary School Students

Let us consider examples of tasks and typical mistakes of fifth-graders

Task 1. Forty kilograms of pears were brought to the store. All pears were put equally into two boxes and a quarter of all pears from one box were sold. How many kilos of pears were sold? Students needed to choose and note the correct answer from the suggested answers: 5 kg, 10 kg, 16 kg, 20 kg. About 60% of students solved the task correctly - received the answer “5 kg”. Students who noted incorrect answers could do so for the following possible reasons:

- they are not ready to analyze the proposed practical situation. They considered that the quarter was from the whole quantity rather than from from the half, and chose the answer “10 kg”;

- they could not perform the reasoning. They limited themselves to performing only one action – finding half of all pears – and chose the answer “20 kg”;

- didn't control themselves. Those who gave the answer “16 kg” did not correspond it to the proposed situation: sold a quarter – an insignificant portion – from the half (from twenty kilograms), so 16 kg could not be sold.

Obviously, mistakes could be made for other reasons: not all the conditions of the problem are identified, the student replaced the question of the problem (calculated the remainder instead of the part of the amount), replaced a part of the number with a number, etc. Note that during further individual discussion, the vast majority of students who made a mistake did not find it difficult to answer such questions: “How do you understand the words “half of a number”, “part of a number”? How to calculate a part of the number? Is it possible to check if the part of a number is correctly found?” This suggests that students have sufficient subject knowledge to solve the problem, however, they are not able to apply it.

Let us consider the task of a higher level of difficulty. Complexity in this case is driven by an implicitly represented price-quantity-cost relationship, discovered by the student independently, based on the experience of life or applying mathematical reasoning.

Task 2. “15 fifth-graders and 20 fourth-graders came to the chess museum. All students bought tickets at the same price. For tickets for fourth graders they paid 300 rubles more than for tickets for fifth-graders. What is the ticket price? Write down the answer, make a numeric expression to answer the task question.”

The assignment was offered repeatedly within the framework of the monitoring of achievements of fourth graders (2016, 2017), in the analysis of mathematical level of competence of fifth-graders for basic school education (2017-2020). These studies were organized by the Center for Quality Assessment of the Institute for Strategy of Education Development of the Russian Academy of Education (led by G.S. Kovaleva) with the participation of the staff of the Laboratory of General Primary Education (led by prof. N.F. Vinogradova)

On average, about 40% of students received the correct answer when performing this and identical tasks, and only 20 -25% of them were able to write down a numerical expression that demonstrated their reasoning skills in the language of mathematical science. In this case, the numeric expression “300:(20-15)” contains two steps of reasoning. To make it, the student analyzes the data, draws a logical conclusion that 300 rubles were paid for the number of tickets that is the difference between the number of tickets purchased for the fourth grade and the number of tickets purchased for the fifth grade. In case of difficulty, the conclusion could be “seen” using the task model – the skill of the student and his experience should suggest him this auxiliary step. The model can be described as follows: in the upper row of 20 cells – “tickets”: in the lower row – 15, the cells of the upper and lower row are placed one under the other; five “extra” cells of the upper row are circled and under them the entry “300 rubles” is made. On the model one can immediately see that 5 tickets cost 300 rubles, which allows to answer the question of the task quickly.

The study revealed that it was easier for schoolchildren to get the correct answer (“60 rubles”), than to explain it using a mathematical record – a numeric expression. It should also be noted that in many cases children who received the answer do not take steps and efforts to explain it, prove it, even if it is required and evaluated separately. This occurs primarily because of the lack of ability of the student to exercise self-control. This ability is underdeveloped due to the lack of clear instructions in textbook assignments, or special explanations by the teacher. For example, as a rule, students take into account conditions of a task, but do not understand whether the explanation should be brief or detailed.

Participation of Russian junior schoolchildren in the international comparative study on evaluation of mathematical and natural science literacy (TIMSS-2011, 2015) demonstrated that fourth graders easily cope with tasks for the application of knowledge in situations which are familiar, worked in the lesson or periodically encountered in everyday life, but it is difficult for them to use basic knowledge when solving new educational or practical problems (Mezhdunarodnoe issledovanie po ocenke kachestva matematicheskogo I estestvennonauchnogo obrazovanija, 2016). The same research notes the lack of readiness of schoolchildren to build and make out reasoning in the process of solving non-standard problems. This is relevant to a group of tasks classified as “reasoning” by the authors of the study on types of cognitive activities (Mullis, Martin, Foy, & Hooper, 2016).

Features of participation of a junior school student in the research and exploratory activities

Let us present some features of tasks and exercises that will help identify them as research or the research and exploratory:

- the existence of a problem or a problem issue;

- lack of an obvious answer;

- mandatory assessment of one's own knowledge and lack of knowledge;

- possibility of different points of view, methods of solution or design;

- provocation to the discussion (the occasion is a conflict of knowledge, presentation of different opinions);

- construction of a summarized solution, joint making of conclusions compelling for all.

The research and exploratory activity of the junior school student (experiments, discussion of the problem, choice of alternative, etc.) begins with the formulation of the goal of solving the educational problem (Universal'nye uchebnye dejstvija kak rezul'tat obuchenija v nachal'noj shkole:…, 2016). Understanding the goal gives the student the opportunity to carry out the basic research steps:

–analysis of the situation and construction of the assumption regarding the research progress;

–identification of the information needed to achieve the goal and its use to construct reasoning – the course of the decision;

–control and self-control of the progress of work.

As part of front work, it is extremely difficult to organize research and exploratory work of younger schoolchildren, so it is advisable to carry out pair and group work from first grade, enabling the training of children in a more comfortable situation (a small group, the opportunity to speak out, the need for action on an equal footing with all, getting the help of participants of the training team if necessary).

Examples of tasks for the development of the student's research and exploratory activities.

As part of the research work, younger schoolchildren were offered tasks for the development of intellectual skills, discourse and reasoning, methods of self-control. Let us consider the specific exercises for each of these three task groups.

• Exercises on analysis of conditions, making and checking assumptions, solving logical problems.

Assignment 3. (Mullis, Martin, Ruddock, O’Sullivan, & Preuschoff, 2014)

Misha has cards like this with numbers

8 4 9 1 5 3

What is the smallest three-digit number he can make up of them? Each card can only be used once. Write down the answer and his explanation.

It is advisable to organize the work on this task in pairs or groups in the third grade. The work can be organized according to the model of the research and exploratory work. Each student can make a guess about the answer. For example, Student A said it was the number 985 and Student B said it was 134. In the next stage of discussion, everyone will try to prove their point based on the analysis of conditions. As a result, children will conclude that the answer has the following properties: a three-digit number, the smallest of the three-digit, each digit used 1 time. A model can be made as a workpiece containing spaces for three characters (such as a rectangle divided into three parts) and the words “smallest”, “numbers do not repeat”, or similar. Next, there is a discussion or reasoning on the choice of numbers for each place, starting with the first (with hundreds). During the discussion, Student A will come to the conclusion that his hypothesis had a mistake, since in his number of 9 hundred, any number with another number of hundreds will be less. The hypothesis of Student B is confirmed: the smallest number on the place of hundreds, the smallest of the remaining ones after the record of hundreds and units.

Task 4. Example of verbal logical tasks.

Situation 1. Each is preparing for winter in its own way. Here is the restless squirrel collecting nuts, mushrooms, cashing them in the hollows of trees, into chaps of wood. And squirrel looks at the hedgehog, which by autumn became completely lazy, and will conceive in foliage and nap. - Why are you a hedgehog completely fazed, - asks squirrel. - Why do you not prepare for winter, cashing the food. In winter, there will be nothing. At least you could collect the mushrooms. The hedgehog laughed and quietly answered the squirrel. What did the hedgehog say to the squirrel?

Situation 2. The mole dug his underground passages to the carrot bed and rejoiced: the carrots were ripe and sweet. The hostess pulled a carrot, and saw the mole hanging on it. Is there any errors in the text. Explain.”

As you can see, each verbal logical problem contains a specific problem, the solution of which requires knowledge of the peculiarities of animal life. In the first task, children should notice two contradictions: the hedgehog does not stock food for the winter, because he sleeps in the wintertime, cozily settling in the fallen leaves, and eats nothing. And in response to the proposal of the squirrel to collect mushrooms the hedgehog answered with a smile, as he does not eat vegetable food and mushrooms, he is a predator. The second verbal problem is solved correctly if the students are surprised that the mole has decided to eat a carrot. Children will notice this error in the text: the mole is a predator and will not eat carrots. Answering the task questions, children word a statement with reasoning, which contributes to the development of this difficult type of speech.

• Exercises on building an algorithm, reasoning.

Task 5. (Vinogradova & Kalinova, 2019, p.40) “Finish the statement: Man studies the cosmic space for ______”. The exercise helps to test the ability of third-graders to create judgments, establish causation. During the discussion of the results of the task performed individually or in a pair, the student himself or together with the classmate will be able to substantiate his point of view, to make arguments supporting his thesis.

Assignment 6. (Vinogradova & Kalinova, 2019) “Draw pictographs and explain the properties of water using them. Discuss your work with classmates. Supplement it if you need to” (p.41).

Performing this and similar exercises involves pair or group work of schoolchildren who combine their ideas about the studied subjects (in this case, the properties of water) and present a solution in the requested format. Obviously, during the work the fourth graders will discuss the properties of water, the coding of information using pictograms, as well as how to picture the summarized knowledge. The picture will reflect the development and result of the reasoning made by children, and the logic of the plot will demonstrate the willingness to interpret knowledge with the help of a self-selected topic (e.g., the picture “Seasons”, which reflects the properties of water in seasonal natural phenomena). Mistakes will prompt the teacher to carry out the group discussions of the work done and establish the cause of the mistakes.

• Exercises to control the activities.

The self-control ability is a component of learning activities. Attention to its development contributes to the gradual formation of reflexive abilities of a personality. The development of self-control in primary school is assisted by the use of special tasks or additional problem questions that encourage the child to control and correct actions, make corrections, etc. in the course of conducting an educational search or analysis of the results obtained. Self-control in research and exploratory activities assumes that the student asks himself questions: “Is this step needed in the decision?”, “How to rationally execute an action?”, “Is the question answered?”, “What is the cause of the difficulty?” (Funkcionalnaya gramotnost mladshego shkolnika…, 2018).

Let us give an example of an exercise based on the material of a mathematics task, which was successfully done by about 50% of Russian fourth graders in the international comparative study TIMSS in 2011. The task required to specify the correct answer. During the study conducted on the problem presented in this article, different groups of fourth graders of the same class were asked to explain one of the wrong solutions.

Assignment 7. Petya solved the task: “Sonya has 12 pieces of wire, 40 round beads and 48 flat beads. She uses 1 piece of wire, 10 round beads and 8 flat beads to make 1 bracelet. If Sonia makes the same bracelets, how many bracelets will she be able to make? A) 40, B) 12, C) 5, G) 4.” Petya chose the answer “12". Assume what difficulties Petya could face while working on the task.

Performing such a task in the group will create conditions for discussion of different points of view. The students are required not only to say that the answer “5” can be obtained by dividing 40 by 8, but also to explain what might have led to the mistake (which was made by more than 25% of fourth graders during the international study test). Probably, Petya worked through the task as follows. First he read the text (step 1), then found out what each number means (step 2), then correlated pairs of numbers - the available number of parts (wire, round bead, flat bead) and the quantity of parts per bracelet (step 3). The next step (step 4), should have been to figure out and check the answer. Obviously, Petya made a mistake in step 3 or step 4. In step 3, it was necessary to correlate three pairs of numbers – 1 and 12, 40 and 10, 48 and 8. Selecting the answer “12" is possible if only the first pair of numbers is correlated and the following conclusion is made: “If one piece of wire is required for one bracelet, 12 pieces will be enough for 12 bracelets.” A partial solution in step 3 resulted in the choice of the wrong answer in step 4. If Petya checked himself, asked the question “How many different parts do you need on 12 bracelets?”, he probably would spot the mistake (12 bracelets need 120 round beads and 96 flat ones), corrected it, and chose the correct answer “4”. Similar tasks with comments for teachers are presented in modern mathematics manuals for Russian primary school (Rydze & Krasnyanskaya, 2019).

As part of the study of the topic “What unites different nations?” at the lesson of the world around us for group work, students can be invited to present their perspective on the thesis “universal values that unite religions” (Okruzhayushhij mir: 4 klass…, 2017). While working through the task, the children will discuss ideas presented in different religions. For that, children will apply intellectual universal actions, such as comparison, analysis, generalization, classification. Activities of schoolchildren will include reading and discussion of textbook texts; discussion of the problem; statement of assumptions; design of a common response scheme. The information received by each participant will be evaluated, adjusted, supplemented and corrected.

The result of search and research actions of the student to solve the educational problem is the ability of the junior student to carry out transfer of knowledge to a new situation (in the lesson, or out of hours). The student begins to use languages of different subjects as means of describing reality, which allows him to see the situation, analyze it in terms of known facts, skills, ways of action in a new way, rather than only in a domestic context.

The above universal actions and examples illustrating them, which are increasingly used in the educational process of primary school, help the student to be an active participant in learning, develop his desire to expand the scope of his activities, to look beyond the boundaries of specific educational situations and known social roles (“I am a first-grader”, “I am a member of the class group”, etc.)