listen to understand the problem. Therefore, when raising a problem, teachers need to pay attention to factors that are appropriate to the cognitive level, communication skills and language development of students.
Step 2: Restate the problem you just heard.
After students have listened and understood what they have heard, teachers need to create opportunities for students to present the problem again with their own arguments. Teachers can ask questions that require students to present the problem again, such as: Can you repeat how your friend did it? How did you do it? By presenting the problem they just heard, students will understand the problem better and teachers can assess the level of listening and understanding of students. At the same time, while presenting the problem they just heard, students must remember, think, and reason to connect the problems, and choose words to express according to their own understanding. This will help students not only develop their language but also contribute to the development of thinking.
Step 3: Comment on your idea and present your solution to the problem.
Teachers create opportunities and encourage students to express their opinions about their friends' ways of doing things and present their own solutions to problems. Teachers ask questions such as: Do you agree with your friends' opinions?, Why?, Do you have a different answer? The questions are designed to help students develop their reasoning skills, encourage them to continue thinking and participating, thereby helping them understand knowledge faster and connect mathematical knowledge together. Students have many opportunities to argue and present their ideas and perspectives in their studies. For students with limited cognitive and expressive abilities, teachers need to guide them to know how to comment on opinions and present simple problems.
Step 4: Comment and evaluate ideas
After students give their solutions to the problem, the teacher summarizes all the opinions and asks students to comment to find the optimal solution for the problem. When commenting to find the optimal solution for the problem, students must think and analyze all the solutions given. Therefore, students must think positively to have accurate comments, thanks to which students' thinking and language are developed. After students give their comments, the teacher is the one to conclude the problem, comment on each solution and encourage students in their studies.
c) Notes when implementing measures
- While practicing the first 3 steps of the method, there is usually no clear separation, but the steps are repeated in the process of finding ways to solve the problem. For simple problems, the first 3 steps are mainly implemented, step 4 is just the teacher's comments and evaluations of the students' answers.
- Organizing students to discuss in groups or participate in speaking to build lessons also contributes to developing listening and speaking skills.
- When developing listening and speaking skills for students in learning mathematics, teachers need to establish and maintain a respectful and supportive environment, ensuring that all students can participate equally in discussion groups, focusing on solving mathematical problems.
- When dividing into groups for pair discussion, teachers should not pair a weak student with a good student. Because then the discussion will end soon when the good student has solved the problem but the weak student has not. Even if the good student tries to explain his solution to the weak student, the weak student still will not understand.
- Teachers should encourage students to express their mathematical ideas in front of the whole class when talking about mathematical problems.
- Teachers ask questions for students to think directly and assign tasks for students to think and find solutions, then present them to the class or discussion group.
d) Illustrative example
Example 1: Developing listening and speaking skills when guiding students to solve exercises (Math 1, p.103)
Connect the points to get a zigzag line including:
a) Two line segments. B C | b) Three line segments A C |
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B
A D
To develop listening and speaking skills for students when solving this exercise, teachers can organize the following activities:
- The teacher organizes students to work in pairs to complete idea a.
- The teacher organizes students to work in groups of 4 to complete part b. After the group work is finished, the teacher organizes students to work in the whole class.
Step 1. Train students to listen and understand the problem being heard.
The teacher asks group 1 to present the results of the group discussion. Then group 1 has
B
can give the following results:
A
D
C
Group 1 presents the operation of connecting points to get a zigzag line:
+ Connect point A with point B.
+ Connect point B with point C.
+ Connect point C with point D.
Then we get the broken line ABCD consisting of 3 line segments AB, BC, CD.
Step 2 : Restate the problem heard.
The teacher calls on a student from another group to repeat the operations of group 1 to get the broken line ABCD. If the student cannot repeat it, the teacher asks the student to look at the broken line of group 1 and asks open-ended questions to help the student understand the problem being heard.
Step 3 : Review ideas and present the group's solution to the problem.
Teacher asks: Comment on the discussion results of group 1? Which group has different results?
Then, for example, group 3 commented that group 1's results were correct. In addition,
Group 3 also had the following other results:
A B
C D
Group 3 presents the operation of connecting points to get the broken line ACBD: connecting point A with point C, connecting point C with point B, connecting point B with point D. Then the broken line ACBD consists of 3 line segments AC, CB, BD.
The teacher asks students in the class to repeat the implementation of group 3 (repeat step 2)
The teacher asks for comments on the results of group 3 and presents the group's results (repeat step 3).
In case the groups have no other results, the teacher can give students more time to discuss and find other results or the teacher can give suggestions to the students.
Possible results found may be:
A B A
C DC
BB
A A
D
C C
B
D
A B
D
DC
Step 4: Comment and evaluate ideas
The teacher organizes for students to comment on the results. From there, students can see that through 4 points, many bends can be connected, including 3 straight lines.
Example 2: Develop listening and speaking skills when guiding students to solve the problem "The top row has 7 oranges, the bottom row has 5 oranges. How many more oranges does the top row have than the bottom row?" (Math 3, page 12)
Teachers organize the following activities to develop students' listening and speaking skills.
- The teacher lets students discuss in pairs to summarize the problem. Students can summarize using a line diagram, a model, or words. The teacher asks students to look at the diagram presenting the problem content.
- The teacher organizes students to discuss in small groups with the requirement to answer the question: How many more oranges are there in the row above than in the row below? After the discussion, the teacher lets students work as a whole class. Students present their answers.
For example, students in group 1 propose a plan to draw 7 oranges in the top row and 5 oranges in the bottom row. From the picture, students will see that the top row has 2 more oranges than the bottom row. The teacher asks 1 student to repeat the way their friend solved the problem. Then the teacher asks a representative of group 2 to comment on their friend's solution and present their group's solution. The teacher asks students to present group 2's solution again... The above process is repeated until all groups have presented their solutions to the problem. The next options could be:
+ Match the first orange in the top row with the first orange in the bottom row, the second orange in the top row with the second orange in the bottom row, … the fifth orange in the top row and the fifth orange in the bottom row. Students will see that there are two extra oranges in the top row. Students find the answer: the top row has two more oranges than the bottom row.
+ Subtract 7 – 5 = 2. The top row has 2 more oranges than the bottom row.
- After students present how to find the answer, the teacher calls on students to comment and present their friends' way of doing it. For incorrect solutions, the teacher asks questions for students to explain why they did the addition. Then the teacher explains to students so they can understand and correct themselves. The teacher asks students to comment on which of the above solutions is the fastest.
- The teacher guides students to present the solution. Ask students to express the solution. Other students comment and state their solution. Students state the calculation and answer to the problem.
After students have presented their solutions, teachers can ask students to ask other questions about the problem to develop their language and expression skills. Questions students may ask include:
+ Ask how many fewer oranges are there in the bottom row than in the top row?
+ Ask how many oranges are there in both rows?
+ If the row above has how many oranges less, then the number of oranges in the two rows will be equal?
+ Ask how many oranges are added to the row below so that the number of oranges in both rows is equal?
+ Ask the row above to transfer how many oranges to the row below so that the number of oranges in both rows is equal?
With the above activities, students develop the skills of listening and understanding what others say, and knowing how to express themselves so that others understand what they are saying.
Example 3 : Developing listening and speaking skills when teaching the lesson "Subtraction of numbers 17 - 7" (Math 1, page 112)
Step 1: Train students to listen and understand the problem being heard.
The teacher talked and did the operation with the counting sticks, took 17 counting sticks then separated 7 counting sticks leaving 10 counting sticks. Students listened and did the operation on the counting sticks. When students did the operation correctly, it meant that they understood the problem being heard.
Step 2 : Restate the problem you just heard.
The teacher asks students to describe the operations they have just performed in spoken language so that others can hear and understand. For example, students can describe as follows: At first there were 17 counting sticks, I separated 7 counting sticks, leaving 10 counting sticks.
Step 3 : Comment on your idea and present your solution to the problem.
The teacher asks students to comment on their friend's presentation and describe their own activities with the counting sticks. After students have accurately described the activities with the counting sticks, the teacher can guide students to describe the mathematical content more concisely and accurately. For example, "17 divided by 7 is 10", "17 minus 7 is 10" or "17 minus 7 is 10".
The teacher leads the students to do the calculation 17 - 7. The teacher asks the students to repeat how to do the subtraction 17 - 7 and the above process is repeated.
Step 4 : Comment and evaluate ideas
Teachers comment and evaluate students' presentations after each process takes place.
Measure 2: Develop reading and writing skills for students in learning math
a) Purpose of the measure
Measures to help students:
- Read and understand mathematical symbols and terms, mathematical documents such as textbooks, exercise books and situations related to mathematics.
- Use NNTH fluently and accurately when solving problems, present solutions in a concise and logical manner in written language.
- Develop reading and writing skills in Vietnamese, contributing to the development of TD.
b) Content and implementation of measures
Reading and writing are two processes that occur simultaneously in learning mathematics. Reading involves recognizing words, understanding their meanings, and connecting words to thoughts. Writing is a very effective feedback channel for teachers. When writing, students must think, remember mathematical symbols and terms to express ideas, organize them logically, and ensure accuracy when solving problems.
Writing skills need to be developed more. If reading only requires students to understand the message of a math problem or document, writing requires students to understand what they write and present it so that the reader can understand.
To develop reading and writing skills for primary school students, teachers can follow these steps:
Step 1: Read and understand the math content
In this step, teachers not only practice for students to read accurately, read aloud the mathematical content but also have to understand the content they have just read. For grade 1, teachers practice for students to read mathematical content through observing visual images, students observe the picture, understand the mathematical content that the picture conveys. Then teachers ask students to read aloud the mathematical content they have just perceived. For grades 2 and 3, teachers organize students to read silently and then read aloud the mathematical content. The initial reading process helps to memorize the mathematical content in the mind and reproduce related knowledge. Then teachers use a system of questions to help students understand the mathematical content they have just read.
Step 2: Rewrite the math content you just read
At first, the teacher asks students to rewrite the mathematical content by filling in additional information. After students are familiar with rewriting what they read, the teacher asks them to write down the complete mathematical content they have read using mathematical symbols and terms. The mathematical content written must ensure mathematical accuracy and be understandable to others. Rewriting the mathematical content they have just read helps students practice logical thinking, reasoning ability, and presenting scientific issues accurately.
Step 3: Write a problem-solving outline and present your solution.
In this step, the teacher organizes students to discuss in pairs or small groups to find a way to solve the problem or the teacher prepares a system of guiding questions for students. The teacher asks students to write a sketch of the steps to solve the problem on a draft to serve as a basis for presenting the solution.
To help students use NNTH to present solutions accurately and concisely, teachers need to practice students presenting simple problems, then gradually increase the level. When writing, students are required to mobilize knowledge and thinking to present problems in a way that is
coherent, clear, ensuring understanding of what is written and writing for others to understand. Thereby training students to be careful and contributing to the development of TD.
Step 4: Comment and evaluate the solution
Teachers organize for students to comment and evaluate their friends' work. Commenting on their friends' work will help students express their own opinions and at the same time contribute to language development. In addition, for exercises with many solutions, teachers can use questions such as: Do you have another way to do it? Can you present the solution in another way? ... to help develop students' language and thinking.
c) Notes when implementing measures
- When doing step 2 and step 3, the teacher asks students to write quickly in their notebooks. In step 2, it is necessary to help students use mathematical symbols fluently.
- Teachers need to flexibly apply teaching methods such as differentiated teaching, problem-solving and discovery teaching, cooperative learning, etc. to develop students' reading and writing skills.
- Through developing reading and writing skills, teachers can detect students' mistakes in learning math and find ways to correct them.
- Student writings are an effective information channel to help assess students' understanding of lessons in general teaching and in math teaching in particular.
d) Illustrative example
Example 1: Developing reading and writing skills for students when solving the exercise "Create a math problem based on the summary, then solve that problem" (Math 3, page 129)
Summary: 4 cars: 8520 bricks.
3 cars: … bricks?
Step 1: Read and understand the math content
The problem is summarized in words, so when looking at the summary, students are required to read and understand the mathematical content contained in it. Teachers ask questions to test students' reading and understanding of the mathematical content. Questions can be:
+ How many bricks can 4 trucks carry? (8520 bricks)
+ 8520 bricks are arranged evenly in how many carts? (4 carts)
+ What does the problem say? (8520 bricks are arranged evenly in 4 carts)