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Teaching Abacus and Mathematical Thinking

Time: 2020-3-26 13:55:21 Access: 863

Chen Gaomu

The mathematics curriculum standards propose that the core literacy of mathematical thinking includes number sense, symbol awareness, space concept, geometric intuition, data analysis concept, computing ability, reasoning ability, model thinking, application awareness, innovation awareness, etc.

Mathematical thinking literacy must be emphasized in the teaching of abacus and mental arithmetic.

To cultivate the core literacy of mathematics, we must do the following four sentences: let students go through the process of learning mathematics, find a way to learn mathematics, realize the ideas of mathematics, and internalize into a mathematical wisdom.

How to cultivate students' mathematical thinking literacy in teaching mental arithmetic? Let us explore together.

The concepts and terminology of mathematics are scientific and rigorous. Mathematical concepts and terminology should be used in the teaching of abacus and mental arithmetic to guide students to master basic knowledge and basic skills.

First, the number of cognitive teaching.

The teaching of abacus and mental arithmetic, like the teaching of mathematics, starts from the understanding of numbers, and establishes the sense of numbers and signs.

"Knowledge of 1" is the starting course of the teaching of number recognition, which can produce assimilation and adaptability to subsequent teaching. Please see the two teachers take the same lesson with different results.

Mr. A:

(1) Guide students to observe textbook illustrations.

1. What is this? (This is a pen)

2. Look at the picture on the right. What do you see? (A child holding a pen in his hand; there is a small tree on the left and a small tree on the right; a butterfly is flying in the sky.)

3. Do you still think of objects that represent 1? (A plane, a boat ... etc.).

(2) It is expressed by abacus. These items representing 1 can be represented by a lower bead.

(3) Guide students to dial 1 and dial 1. What does this 1 mean? (Let the child imagine it again).

(4) An article can be represented by an abacus. What symbol is used to record it?

(5) Reveal the number "1" and ask: What can this 1 represent? (Let the children look at beads and think about numbers; look at numbers and think about beads).

(6) Bead practice. (Single gear, double gear, third gear, full range, two-handed practice; real dial, empty dial, want to pull practice).

(7) Guide writing. The book is empty, then the description, and finally "1" is written independently.

(8) Summary. What did children learn today?

Mr. B:

(1) Let the children open the book. The teacher said that the children watched and listened. There is a pencil on the left and a child on the right holding a pen in his hand. There is a butterfly in the upper left corner and a tree below each. These "one" objects can be dialed into 1 abacus to represent.

(2) Have students dial 1 and dial 1. This 1 can be written as the number 1.

(3) Lead the children to dial the beads, and the first, second and third gears will dial in the beads 1.

(4) Ask the children to write "1". From top to bottom like a skimming.

(E) Summary. Today I knew "1" and learned to dial 1 and dial 1. Have you learned it?

After reading these two lessons, teacher Ms. Le Yulan from Fuzhou, Jiangxi said, "Teacher A is based on students, and cultivates students' ability to think actively, observe carefully, and operate hands-on. Teaching. " Many teachers agree.

It is true that Teacher A's teaching starts from knowing things > knowing abacus >knowing numbers. Allow students to recognize objects that indicate "1", a pen, a book, an airplane, a warship, etc., which can be represented by a bead on the abacus, which represents any "1" object To record an object or abacus that represents "1", you can use the number "1" to represent it. The process of "things >beads> numbers" here is a process from concrete "things" >semi-concrete and semi-abstract "beads" > abstract "numbers". The process of diffuse thinking >concentrated thinking brings a qualitative leap to students' mental arithmetic. Here, the number sense and symbol awareness required by the mathematics curriculum standards are also reflected.

Second, the teaching of counting.

The calculation of numbers is a prominent link in the teaching of abacus and mental arithmetic. Improving the computing ability is the main direction of abacus and mental arithmetic teaching. There is no doubt about improving the computing ability. However, in the teaching of abacus and mental arithmetic, there is still a lot of work to cultivate students' core mathematical literacy. We see that the two teachers A and B have different approaches to the teaching of "5 + 9".

Teacher A:

First, show that there are 5 balls outside the box and 9 balls inside the box.

Second, ask students to observe the diagram and learn to speak three sentences.

The first sentence describes the specific problem: "There are 5 balls outside the box, 9 balls in the box, and a total of 14 balls."

The second sentence translates a specific problem into a mathematical problem: "Five and nine together are fourteen."

The third sentence transforms a mathematical problem into a mathematical formula: 5 + 9 = 14.

Next, talk about the calculation method: put 1 ball outside the box into the box, make up 10 balls with 9 balls, plus 4 balls outside the box, it is 14 balls, so 5 plus 9 equals 14 .

On the basis of this clear arithmetic algorithm, guide students to calculate the bead: dial 5, add 9, add this file is not enough, 9 and 1 make 10, dial 1, how to dial? (Dial 4 and dial 5), dial 1 to ten digits (also known as "into 1"), 5 plus 9 equals 14.

Then, ask the students to simulate the beading, transform the operation skills into mental skills, and achieve the intention in the mind, which is the "bead mental arithmetic".

Finally, through single gear practice, alternate gear practice, empty dial practice and other methods, students are proficient in mastering the "5 + 9" dial calculation.

Teacher B:

First, review the question: talk about making up 10 numbers. (1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5).

What is the complement of 9? How to dial 1 + 9?

Second, an example question: 5 + 9.

Next, discuss how to calculate the bead? (Dial in 5, add 9 and the complement of this file is 1, 9, can you dial 1 directly and enter 1 to the tens?).

Can't dial 1 directly, the teacher tells you: "When you add 9, you can't dial 9's complement 1 directly, you can use" climb 9 into 1. " (Dial 4 and dial 5, call Climb 9). "

Have students use the method of "add 9 and climb 9 into 1" and be proficient in "5 + 9".

The teaching methods of the above two teachers have caused a lot of controversy.

Some teachers think that Teacher B's teaching method can enable students to master the method of "breaking five rounds and adding" quickly (adding a few climbs and entering 1).

Some teachers think that Teacher A's teaching method is good. Not only allow students to master arithmetic algorithms, but more importantly, never forget to cultivate students' mathematical thinking literacy. Let students go through the process of learning mental arithmetic, starting with practical problems, turning into mathematical problems, and then into mathematical formulas, analyzing and finding a method of learning mental arithmetic, realizing mathematical ideas, and internalizing it into wisdom of mental arithmetic . Abacus mental arithmetic is an effective choice.

Many teachers often use "make up five numbers" to guide students to learn the calculation of "full five plus, break five minus", use "subtract one plus" to guide the calculation of round plus, use "return one plus" Guide the calculation of abduction reduction. However, the use of these concepts or terminology adds trouble and burden to primary school students in learning mathematics. Attempting to use mathematical concepts or terminology to guide bead calculations can be more reasonable and appropriate, and experiments have proved feasible.

Elementary mathematics, which talks about "composition and decomposition of 5," 1 and 4, 2 and 3, 3 and 2, 4 and 1 are all composed of 5. 5 can be divided into 1 and 4, 2 and 3, 3 and 2, 4 and 1. Use "5 components" to guide students in the calculation of "full five plus". For example: 1 + 4, dial 1, add 4, add 4 if the next bead is not enough to make 5, you can dial 5 and dial 1. (Because dialing 5 adds "1", so you need to dial 1. Here is a clear explanation of the theory.) Calculate by dialing beads such as 2 + 4, 3 + 4, 4 + 4, etc. 4, if the next bead is not enough, dial 5 and dial 1 ".

5-4, dial 5 and subtract 4, reduce the number of beads is enough, 4 and 1 make up 5, and dial 5 first, subtract 1 more, then dial 1. (For smooth and convenient dialing, you can dial 1 and dial 5). According to the calculation of 6-4, 7-4, 8-4 and other ball dialing calculations: "Every ball is not enough to reduce 4 is dialed into 1 (5 with the group of 4), and 5".

The composition and decomposition of 5 are used to guide students' calculations of "full five plus five breaks", which is consistent with the teaching of elementary school mathematics, and is conducive to training students "one look" (observation) > "two thoughts" (thinking) Power, judgment) > "three dials" (hand operation ability). Let the mind point to the operation, shining the spark of wisdom.

In elementary school mathematics, the addition of the "ten methods" and the reduction of the "ten methods" are also applicable to mental arithmetic teaching.

2 + 9, dial 2, add 9, add 10 to the digits, 9 and 1 make up 10, dial 1 to the digit, and dial 1 to the ten digits (that is, a 10).

5 + 9, dial 5, add 9 to the full ten, 9 and 1 make up 10, dial 1 for the single digit (to dial 5 for 4), and dial 1 for the ten digits (that is, a 10).

11-9, dial 11 and minus 9, if you do n't get 9 less than the number of digits, subtract 9 from one of the ten digits, and 1 more. If you dial 1, 1 minus 9 equals 2.

14-9, dial 14 and subtract 9, and 9 is not enough to reduce the number of digits. First, subtract 9 from 10 of the ten digits, and add 1 to the number of digits. Go to 1).

The organic combination of the beading process and the arithmetic algorithm, thinking penetrates into the process, which is more important than the calculation result! Corrected the phenomenon of focusing on the results and not the process, why not?

Multi-digit addition and subtraction can be counted from the high and low digits. They are calculated in the same way: "add (subtract) numbers in the same digit".

Multi-digit multiplication can start from the previous digit, or from the last digit (or any digit), because the multiplication rule is the same: "Which digit is multiplied, and the end of the product is aligned with which . "

The above different algorithms reflect the diversity of algorithms, which is conducive to the flexibility and diversity of thinking, and meets the new mathematics curriculum standards.

Abacus division and division in mathematics are both "commercial divisions", which are consistent.

Abacus and mental arithmetic have not yet formed an independent discipline. Primary school mathematics teachers are happy to incorporate abacus and mental arithmetic into mathematics teaching. They are determined to relax their mental thinking and let them enter the mathematics classroom and never lose it.

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