Once the child has written part of the number table, he or she can induce : “It is possible to move from one multiple of 8 to another by going down one row, and then left two columns." When stated he same way for multiples of 4, it is also possible to induce"It is possible to move from one multiple of 4 to another by going down one row, and then left two columns."
Then, considering “why it is possible to make this simple statement" and "whether or not it is still possible to state this for numbers over 99, and why this is the case is deductive thinking.
Next, consider what to base an explanation of this on. One will realize at this point that it is possible to base t on how the number table is dreated. This is also deductive thin Bind and is based on the following.
Since this number table has 10 numbers in each row, "going one position to the right increases the number by 1, and going one position down increases the number by 10.”
Based on this, it is evident that going down one position always adds 10, and going left two positions always subtracts 2. Combining these two moves always results in an increase of 8(10 – 2 = 8).
Therefore, if one adds 8 to a multiple of 4(or a multiple of 8), the result l always be a multiple of 4(8). This explains what is happening.
By achieving results whit one’s own abilities in this way, it is possible to gain confidence in the correctness of one’s conclusion, and to powerfully assert this conclusion. Always try to explain the truth of what you have induced, and you will feel this way. Also, think about general explanations based on clear evidence (the creation of the number table). This is dedauctive thinking.
Example 2. Deductive thinking is used not just in upper grades but also in lower grades.
Assume that at the start of single-digit multiplication in third grade, the problem "how many sheets of paper would you need to hand out 16 sheets each to children?" is presented. When the children respond with “8×16 (in Japanese 16×8).” The teacher could run with this response and say: "All right, let's consider how to find the answer to this."
This is not adequate, however. The students must be made to thoroughly understand the fundamental reasoning behind the solution. It is important that the students independently consider why this is the way the problem is solved.
The child will probably explain the problem by saying that: "In this problem, eight 16s are added: 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16." This is based on the meaning of multiplication (repeated addition of the same number), and is a deduction that generally explains why multiplication is the way to solve the problem.
Furthermore, the response to "let's think about how to perform this calculation” will probably be "the answer when you add eight 16s is 128." When the child is asked for the reason, the answer will probably be: “This multiplication is the addition of eight 16s.
Deductive thinking is used to explain this calculation and the foundation of it.
Important aspect about teaching deductive thinking
Establishing this needs to attempt to think deductively is more one's own abilities to discover solutions through analogy or induction. Through this, children will gain the desire to assert what they have discovered, and especially to think deductively and appreciate the benefits of thinking deductively.
Once the child has written part of the number table, he or she can induce : “It is possible to move from one multiple of 8 to another by going down one row, and then left two columns." When stated he same way for multiples of 4, it is also possible to induce"It is possible to move from one multiple of 4 to another by going down one row, and then left two columns." Then, considering “why it is possible to make this simple statement" and "whether or not it is still possible to state this for numbers over 99, and why this is the case is deductive thinking. Next, consider what to base an explanation of this on. One will realize at this point that it is possible to base t on how the number table is dreated. This is also deductive thin Bind and is based on the following. Since this number table has 10 numbers in each row, "going one position to the right increases the number by 1, and going one position down increases the number by 10.”Based on this, it is evident that going down one position always adds 10, and going left two positions always subtracts 2. Combining these two moves always results in an increase of 8(10 – 2 = 8).Therefore, if one adds 8 to a multiple of 4(or a multiple of 8), the result l always be a multiple of 4(8). This explains what is happening. โดยบรรลุผลลัพธ์ออกหนึ่งของความสามารถในทางนี้ เป็นไปได้ได้รับความเชื่อมั่นในความถูกต้องของข้อสรุป และ powerfully ยืนยันรูปนี้สรุป พยายามที่จะอธิบายความจริงของสิ่งที่คุณได้เกิด และคุณจะรู้สึกแบบนี้ ยัง คิดคำอธิบายทั่วไปตามหลักฐานที่ชัดเจน (การสร้างตารางตัวเลข) นี่คือความคิด dedauctiveตัวอย่างที่ 2 ใช้ deductive คิด ในระดับบนไม่เพียง แต่ ในระดับล่าง สมมุติว่าที่จุดเริ่มต้นของการคูณเลขหลักเดียวในชั้นที่สาม ปัญหา "จำนวนแผ่นของกระดาษจะต้องแจก 16 แผ่นเด็ก" นำเสนอ เมื่อเด็กตอบ ด้วย "8 × 16 (ในญี่ปุ่น 16 × 8)" ครูสามารถทำงานนี้ตอบและพูด: ",ลองพิจารณาวิธีการหาคำตอบนี้ได้" นี้ไม่เพียงพอ อย่างไรก็ตาม นักเรียนต้องทำอย่างละเอียดเข้าใจหล้กการแก้ปัญหาพื้นฐาน เป็นสิ่งสำคัญที่นักเรียนได้อย่างอิสระพิจารณาเหตุผลนี้เป็นวิธีที่แก้ปัญหาเด็กคงจะอธิบายปัญหานี้ ด้วยการพูดที่: "ในปัญหานี้ เพิ่ม 16s แปด: 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 " ซึ่งตามความหมายของการคูณ (เพิ่มซ้ำหมายเลขเดียวกัน), และจะหักซึ่งโดยทั่วไปอธิบายทำไมคูณเป็นวิธีแก้ปัญหาFurthermore, the response to "let's think about how to perform this calculation” will probably be "the answer when you add eight 16s is 128." When the child is asked for the reason, the answer will probably be: “This multiplication is the addition of eight 16s. Deductive thinking is used to explain this calculation and the foundation of it. Important aspect about teaching deductive thinking Establishing this needs to attempt to think deductively is more one's own abilities to discover solutions through analogy or induction. Through this, children will gain the desire to assert what they have discovered, and especially to think deductively and appreciate the benefits of thinking deductively.
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