НЕКОТОРЫЕ МЕТОДЫ ПРЕПОДАВАНИЯ РЕШЕНИЯ СЛОВЕСНЫХ МАТЕМАТИЧЕСКИХ ЗАДАЧА В ПЕРВОМ КЛАССЕ
Нгуыен Тхи Чау Гианг1, Тхи Нга2, Пхам Тхи Хаи Чâу3
1Винх Университет, Вьетнам, 2начальная школа Бинх Яуои Таы, Хо Чи Минх Сити, Вьетнам, 3Винх Университет, Вьетнам
НЕКОТОРЫЕ МЕТОДЫ ПРЕПОДАВАНИЯ РЕШЕНИЯ СЛОВЕСНЫХ МАТЕМАТИЧЕСКИХ ЗАДАЧА В ПЕРВОМ КЛАССЕ
Аннотация
Статья описывает фундаментальные аспекты преподавания решения словесных математических задача в начальной школе. Автор выдвигает ряд мер для совершенствования навыка решения словесных математических задача в первом классе.
Ключевые слова: дети, Вьетнам, умение решать задачи, преподавание умения решения задач.
Dr. Nguyen Thi Chau Giang1, Le Thi Nga2, Ms. Pham Thi Hai Châu3
1Vinh University, VietNam, 2Binh Quoi Tay Elementary School, Ho Chi Minh City, VietNam, 3Vinh University, VietNam
SOME MEASURES TO TEACH SKILLS AT MATH WORD PROBLEMS SOLVING IN THE 1ST GRADE
Abstract
This article refers to the fundamental matters of teaching skills at math word problem solving in the elementary grade. The author proposed a number of measures to teach skill at math word problem solving in the 1st grade.
Keywords: children, Vietnam, problem-solving skill, to teach the problem-solving skill.
Elementary is the first stage of the education system in Vietnam, forming the basis for the higher grades.
Mathematics is a very important especially in the life and the science. It contributes to educate the perfect, dynamic and creative people for the science and technology development in the new innovative age. Math teaching in elementary grade and math word problem solving in the 1st grade is to help children to apply math learning, to practice math skills under the diverse and various requirements. Children have opportunities to learn and develop brainstorm, reasoning skills and practice for being qualified.
In the 1st grade, math word problem solving is not too hard in term of getting calculation and answer. In term of planning the way to solve the problem, it is very difficult to teach children on finding the good and appropriate answer. Within this article, we would like to propose a number of measures to teach skills at math word problem solving in the 1st grade to help children to overcome difficulties in math problem.
- To teach skill at problem-solving in the 1st grade
1.1. Problem-solving skill
"Problem-solving skills include skills of apply mathematical knowledge to solve math problems (by inference rules and proof methods)" [4] covering: knowledge, method and approach. It should be noted that depending on the learned math, children is required to practice various skills in term of: Math study, math in other subjects, and in life as well.
1.2. To teach the problem-solving skill in the 1st grade
The teachers should pay attention to the following matters:
+ Problem understanding.
+ Used math language.
+ The ability to read.
The teachers should study and well understand the teaching methods to choose, categorize, and apply the appropriate and effective methods. They must also keep learning and improving their understanding of math word problem solving, not just solving problem in the teacher book but always having sense of collecting, creating, strengthening the problem-solving skills among at “Pupil-focus".
- The current teaching the problem solving skills in the 1st grade
2.1. The context
The math teaching in elementary grade is currently paid much attention by the Ministry of Education and Training of Vietnam, schools, teachers and parents. So the strategy of math skill teaching for the 1st grade is placed on top priority. The academic year of 2014-2015 is critical to implement the strategy for the 1st grade, particularly Mathematics. And it is found that:
- It was the high ratio of being bad at Math for the previous years.
- Children do not realize the various forms of exercises.
- Children can not make practice by them self but with the teacher help.
- Children can not study in team, support and help each other in discussion.
- Children can not make their own test of study and practice.
- Children are still satisfied at their work, with the already given way.
2.2. The current teaching the problem-solving skills in the 1st grade
The learning forms are monotonous. Meanwhile the good pupils can not show their strength and capacity, the not good ones are likely lack of knowledge, do not actively learn, even rely on the teacher guidance.
Teachers do not give effective guidance on finding the ways but often show the answers for time saving.
Teachers are not really dynamic, creative but dependent on the available documents. Pupils are not interested in math learning.
As the teachers pay less attention on training skills of understanding, analyzing the problem, pupils are not really aware of problem solving approach.
Teachers just request pupils to solve specific problems without extension, time for any similar mathematical problems developed and solved by pupils themselves.
As the teachers provide pupils few of math languages, it was difficult for pupils to identify the data and to develop the similar problems in life.
Teachers use materials (textbooks, teacher books, lectures,) in the rigid manner, without creative selection.
Due to children starting with problem solving (explanation, calculations, answer,) their thinking is mainly intuitive. On the other hand, at this stage, pupils can not fluently read and write. Even reading the questions many times, some pupils can not understand the problem. So pupils did wrong....
As solving math problem, pupils are still passive. They just solve the problem in the mechanical manner at the request of teacher. Pupils just solve the specific problems. They do not know how find the common between various problems. Therefore pupils have difficulty in identifying the common forms.
Due to the low ability of problem analyzing, pupils are stymied in problems of indirect data. Without the routine of checking, pupils get low marks.
- Some measures to teach the problem solving skills in the 1st grade
3.1. To teach the skills of math problem analyzing, interfering for understanding the problem and finding solution
For math problem-solving, it is difficult to understanding the problem and finding way. Pupils have to identify the problem, in case of familiar form (or easy to restate the problem in the familiar form), and then pupils use the learned knowledge to plan the way to solve the problem. In case of unfamiliar form, pupils should learn the questions, understand the given data, the unknown , find the relationship between them, to analyze, to make inference for approach and solution, Also in analysis and reasoning, pupils are trained in terms of thinking, as the result, the brainstorm skill is developed. Teachers should use two forms of inference: reasoning and inference (rational inference).
Each problem has three basic elements: The given data, the unknown (in question) and conditions which present the relationship between the data and the unknown.
Steps of problem analysis.
Step 1. To understand
Step 2. To summarize
Step 3. To make inference
* To make it familiar. I.e. to make the problem (strange, unfamiliar) familiar. To do this, teachers should instruct pupils to mobilize the accumulated knowledge and skills to understand the problem or put the problem in the familiar form for seeking solution.
* Using the linear method to find the way to solve the problem with straight lines instead of the number (the given, the unknown) in the condition of problem so that pupils can find the way to solve the problem.
* Using the method of calculating backwards
Teachers give the guidance of backwards calculations. The flowcharts can be used to restate the problem of which the successive circles show the condition, a calculation sign among the circle shows the relationship between the given data and conditions. The flowchart is used to let pupils understand the entire process of problem solving in the most intuitive manner.
* To use alternative method to find way
For some problems of two or more unknowns, teachers can guide pupils to use alternative methods to temporarily replace one of the unknowns. By this way, the problem has only one unknown. As solving this problem, pupils step-by –step find one unknown, then the remaining unknowns by the above temporary replacement.
As the pupils are stymied in the unknown problem, teachers should prompt pupils to use the learned knowledge to think of the solution.
Example 1: After the problem summary, the pupils are suggested to analyze the problem for seeking the solution. So, at this stage, teachers should use the methods of analysis and synthesis, proposing the way of understanding, analyzing the problem in the simple diagram form: What can you get from the problem?/ What is the problem about?/ What do you need to know?/ Do you know this one yet?/ How about this?/ What do you rely on to find the unknown?/ How?
With the guidance of make the analysis and synthesis upward, pupils understand better and solve the problem by themselves.
As knowing the pupils’ frequent mistakes, teachers spend more time to carefully teach pupils math skills and present a lot of samples.
After helping pupils to understand the math problem by indentifying the given data and the unknown, the teachers should prompt pupils with appropriate calculations: + To select "subtraction" if problem says "subtract" or "find the remaining" or "taken out"
+ To select "addition" if problem says "more".
* Note: To give math problems which says “more” without addition but subtraction, for example: "Lan has 9 flowers and Hong has 6 flowers. So how many more flowers does Lan have than Hong has?"
3.2. To teach skills of expression, presenting solution
There are some steps as follows:
- To present a sample and analyze some noting points as presenting the solution.
- To give the solution of unreasonable steps for pupils making comment and doing the right steps
- To give math problem with the suggested main steps for pupils completing the solution.
Upon the analysis, teachers can give some hints for pupils making the detail steps, completing the problem solution.
In teaching problem solving, after giving instruction of presentation, teachers should make a similar or more difficult problem for pupils finding the solution and getting presentation skills. Teachers can ask the class or each team group or each pupil to do that. While pupils are doing exercises, teachers control the class.
Thus, by having pupils follow the given steps of problem solving, teachers help the pupils expressing solutions in a strict and smart manner. Consequently, the pupils are trained of logical thinking.
Example: The question: How many chickens left does Ha have”
The answer: "The number of chicken left is"
For one math problem, pupils can have various ways to solve it. So for each type of problem, teachers should let pupils think, discuss it in groups, teams for finding out the correct & proper answer.
However the teachers should teach the best way (brief, understandable, appropriate). Other ways should be recognized as correct and proper but must be chosen for the best one.
It is the requirement to teach pupils to present the answer in the fine manner. To do this, the teacher must follow the guidance on presentation.
First, to write the Question "Question 1" (to align it left and underline it), then to summarize the question, to express the answer. The word "Answer" is placed in the center of page (underlined), the content is placed with the left indent of 2 cm and the first uppercase letter, a colon (:) at the end. The calculation is indented of 2 cm from the answer, the unit is written in bracket. The answer is indented to the right (underlined), then a colon and the calculation result and unit (not be written in bracket again). * Note: In any case, the teachers always have to use the ruler to underline and repeatedly request the pupils to give up their bad habit of: underlining by hand.
Along with the guidance of steps, teachers should present the sample on the board and ask pupils to look at, to comment on the presentation so that pupils get acquainted with the answer presentation. They should mark and correct the pupil mistakes, to praise and ask the pupils with correct and clear presentation to the board for presenting the answer so that others can follow.
3.3. To teach skills of evaluating the solution
For teaching and learning, test - assessment are extremely important. It aims at training the pupils about the responsibility, self-criticism, self-evaluation, independent, critical thinking and creative thinking.
Teachers can teach skills of test and evaluation with the following steps:
Step 1: Too thoroughly read and well understand the question.
Step 2: To check all steps.
- Check the answer right or wrong?
- Any errors?
If the answer is incorrect: Where? How to correct it?
- To check the answer, comparing with the checklist results (prepared by teachers).
Step 3: To find errors, omissions; mark the knowledge lacked, to seek the cause. Step 4: To evaluate method, steps, time: Is the solution reasonable yet? Is there any other solution? Is it necessary to adjust steps?
Step 5: To mark, to learn experience and show new approach for problem solving. With such steps, teachers will evaluate the whole process of problem solving, from the analysis to indentifying and finding the solution, to present calculation and words. Thereby teachers will teach skill of problem-solving.
Based on the review of problem solving process, pupils can see their mistakes of calculations; find the unreasonable explanation for their own experience. After pupils solve the problem, teachers ask pupils to confirm the results. So examining, checking are compulsory and taken as learning habit for solving math problem.
Moreover, teachers always prompt, train the pupils with skills at writing – in the correct and nice form. The combination of nice writing and right presentation is also a factor contributing to the success in solving the math word problem.
The inspection, evaluation that is well performed by pupils in the problem solving will encourage pupils to accumulate the learning for math problem solving. This makes them more confident in solving math problem.
- Conclusions
Math word problem solving can help pupils to apply math to life. The math word problems are important in connecting moths to the real life. It is a good foundation for the developing the mathematical thinking. Let pupils be happy with solving math problems in life by mathematical tools.
References
- Ministry of Education and Training (2007), Methods of Teaching Mathematics in Elementary grade - Materials for Teacher Training, Education Publisher
- G.Polya (1975), How to solve it, the Education Publisher, Hanoi.
- Do Trung Hieu, Do Dinh Hoan, Vu Duong Thuy, Vu Quoc Trung (1995), Methods of Teaching Mathematics in Elementary grade, Publishing House, Hanoi National University of Education
- Nguyen Ba Kim (2006), Methods of Teaching Mathematics, Publishing House, Hanoi National University of Education