Word problems and ways to solve them
I asked pupils and students many times: What do they think about their own word problem solving skills? The answers usually surprise. In primary school, they generally have no problems solving them. The problem comes later, in junior high school and high school. By analyzing the reasons for this state of affairs, you can come to the conclusion, that in primary school, a student solves simple tasks, and the math process results directly from the content of the task. Complex tasks appear in the senior grades of primary school, the solution of which requires the recognition of more complex relationships, meanwhile, the student is not prepared to solve them. Maybe the teacher in grades 1-3 and senior grades of primary school had neglected something, concentrating too much on simple tasks, apart from tasks that are more difficult to interpret and teach, as S.. Stay, "Properly folded", which, in accordance with the new core curriculum, have been moved to the higher grades of primary school. However, I see the main reason behind this, that in lessons you solve tasks, and does not learn problem solving methods. That is why it is worth paying attention to this aspect of mathematical education, which is learning by the student the structure of a text problem and various methods of solving. It is connected with frequently asking questions about the way of arriving at the result, why the student chooses such a solution, and no other and justifying the choice of method. It is necessary to pay attention to the verification of the solution, both the accounting result and the adequacy of the result to the content of the task. You can reflect on this, since word problems are so difficult for students, why not give them up? Gustaw Treliński answers briefly: We solve the tasks, because they constitute the content and meaning of mathematics. Introducing most of the math concepts, not only in the beginning classes, is done through word problems. This is also reflected in the core curriculum.
The core curriculum assumes, that a student completing the first grade:
• can cope with life situations, which must be added or subtracted to be successful;
• they write down the solution of the task with the content presented in words in a specific situation, using digital record and action signs;
A student completing class III:
• Solves single-action word problems (including differential comparison tasks, but without quotient comparison);
• performs easy monetary calculations (price, quantity, value) and copes with everyday situations that require such skills;
A student in grades 1-3 is to master the ability to solve the simplest word problems. However, you have to remember, that most math situations, e.g.. introducing successive natural numbers, monetary calculations, calendar and clock situations are related to the situations described in the form of word problems.
The methodological suggestions presented here do not exhaust the issues and the knowledge of solving word problems in grades 1-3 should be deepened, using the rich literature.
Solving word problems consists in finding answers to the questions contained in the tasks. In task:
There was on the plate 7 pears and a few apples. How many apples were there, if all the fruits were there 15?
The question is about the number of apples. The answer can be found, spreading the fruit on the plate, that is, laying 7 pears, then adding apples, so that all the fruits should be 15. Now it is enough to count the added apples and we have the answer to the question in the problem. Instead of natural fruits, you can use cut out of paper or just cut circles or buttons, sticks or other so-called. alternates. The task has been solved, but without the use of mathematical operations. The task can also be solved, taking e.g.. 15 buttons (that was all the fruit), then put it back 7 – it's pears. Now you just need to count the remaining buttons, which are the counterparts of apples.
When solving tasks using the so-called. alternates – buttons, sticks, that is, counters, we say, that we solve a problem by simulating a task situation, simulation of activities, be a simulation model. This way of solving problems is especially useful in the early stages of developing word problem solving skills. The simulation can be applied there, where there is an objective difficulty in solving the task on real objects. Simulation is associated with the so-called. manipulative methods of solving tasks, mentioned when discussing operations on natural numbers.