ฝึกพูดภาษาอังกฤษด้วยเทคนิค Shadowing จากวิดีโอ: Addition and Subtraction of Small Numbers

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62 ประโยค
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1
Hey it’s Professor Dave; let’s talk about addition and subtraction.
2
As we have just come to understand, math never started out as a bunch of seemingly arbitrary operations meant to confuse and frustrate students.
3
It is simply that our understanding of math has become extremely sophisticated over the past few hundred years, and the fact that all of this existing and sometimes difficult math must be learned before anyone can contribute to the field is what is responsible for the way that so many people despise this subject.
4
But let’s remember that math began very simply as part of our language, a set of models and symbols that helped us to communicate ideas and describe our surroundings.
5
Mathematical innovations arose by necessity, and they still do, it’s simply that the frontier of today’s math lies in an abstract place that very few can understand.
6
By the end of this series, maybe we can all get there, but for now, let’s start at the very beginning.
7
What was the first kind of math that was developed by the human race?
8
That would undoubtedly be arithmetic.
9
Shortly after humans were able to count, we needed symbols to represent those counting numbers, as well as methods to manipulate those numbers in ways that represent real-life concepts.
10
How many people are in the tribe?
11
Two kids were just born, how many are there now?
12
How many years has the tribe’s wisest elder been alive?
13
Once civilizations formed and we began to trade goods with one another, we needed to be able to keep track of inventory, price items appropriately, and so forth.
14
How many apples are in the basket?
15
How many do you want, and how many are now left?
16
Being that we like to count on our fingers, and we have ten of them, many counting systems were based on a system of ten.
17
There were others based on twenty, or even sixty, but the one we use today is based on ten, so rather than diving into the anthropology of arithmetic, let’s keep our study focused on what can be readily applied.
18
Presently, our conceptualization of the number ten as the basis for our numerical system is so ingrained in our collective logic that we sometimes forget that this number is completely arbitrary.
19
If we had only eight fingers, things would be totally different.
20
But ten is what we went with, and it works just fine.
21
Getting back to the apples, the basic operations we will learn first are addition and subtraction.
22
Addition is the most basic arithmetic operation, and it represents the combination of two numbers to become a single number, or a sum.
23
If you get two apples from one vendor, and then three from another, how many apples did you get?
24
Of course we can easily count the resulting pile and see that there are five.
25
But how do we represent this mathematically?
26
Using the symbols that are common of today, we would put the number two, then the addition or plus symbol, and then the number three, followed by an equals sign and then the number five.
27
This is an equation, which is a statement of equality.
28
The expression on the left is numerically equivalent with the expression on the right.
29
This particular equation reads, “two plus three equals five”, with the word plus essentially meaning “and”, and the equals sign meaning “is”.
30
Two and three is five, so five is the sum of this additive operation.
31
The next operation that became necessary was subtraction, which is the inverse, or opposite of addition, in that it doesn’t find the sum of two numbers, it finds their difference.
32
You bring all five of your apples home and you eat one of them.
33
If one apple has been subtracted, how many are left?
34
Again, it is easy to count and see that there are four left.
35
But this result can also be calculated, which is much different from counting.
36
We can write another equation with a five, then the minus symbol, followed by a one, then the equals sign, and the number four.
37
This reads, “five minus one equals four”, which essentially means five less one is four, so four is the difference between one and five.
38
On a number line, this is the distance between the two numbers, and this is an excellent way to visualize subtraction.
39
Fourteen minus eleven is three, because three is the difference between the two numbers.
40
It takes three to get from eleven to fourteen.
41
Now that we have become familiar with the symbolic representation of these simple operations, we should discuss some applicable properties of numbers.
42
Addition is commutative, in that the order in which numbers are added does not matter.
43
Two plus three equals five, and three plus two also equals five.
44
Subtraction is not commutative.
45
It does indeed matter which number is being subtracted from the other.
46
Three minus two is not the same as two minus three.
47
Addition is also associative.
48
This means that if performing two successive additions, the order in which they are performed does not matter.
49
Two plus three plus four will be nine no matter which numbers we add first.
50
We can add the first two to get five, and then add that to four, or we can add the latter two to get seven, and then add that to two.
51
The result is the same.
52
Subtraction is not associative.
53
If we write down five minus three minus two, we could do five minus three first.
54
That gives us two, and subtracting the other two, we get zero.
55
If instead we do the three minus two first, we get one, and five minus one is four.
56
So we can see that subtraction is not associative.
57
We will learn all about the order of operations later, as well as other ways in which these kinds of properties become less obvious yet very important.
58
No matter how far we choose to go with math, and no matter how complicated equations appear to be, with symbols like square roots and logarithms and integrals, we must always remember that these symbols mean something concrete.
59
They are rooted in the physical world, even if in a way that is more difficult to immediately conceptualize than the plus symbol.
60
One goal of this series will be to make all the other mathematical operations as intelligible and relatable as addition and subtraction.
61
Once you intimately understand what mathematical constructs represent, they no longer seem arbitrary and infuriating, but instead powerful, as their utility becomes apparent.
62
So let’s move forward and learn some more arithmetic, but first, let’s check comprehension.

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คำศัพท์และข้อสังเกตด้านการพูดสำหรับบทเรียนนี้

วิดีโอนี้มี 62 ประโยค และ 1107 คำ สำหรับฝึกพูดตาม ช่วงที่มีเสียงพูดยาว 7:37 ผู้พูดพูดด้วยความเร็วสม่ำเสมอ ประมาณ 145 คำต่อนาที เหมาะกับการฝึกพูดตาม 86% ของคำอยู่ใน 3,000 คำที่ใช้บ่อยที่สุดในภาษาอังกฤษ ส่วนที่เหลือควรดูไว้ก่อนเริ่มฝึก

คำศัพท์สำคัญในวิดีโอนี้

คำที่พบไม่บ่อย 15 คำจากวิดีโอ พร้อมคำอ่านและความหมาย:

  • minus /ˈmaɪ.nəs/ — ลบ. Made less or reduced by (followed by an expression of number or quantity).
  • symbol /ˈsɪmbəl/ (คำนาม) — สัญลักษณ์. A character or glyph representing an idea, concept or object.
  • mathematics /mæθ(.ə)ˈmæt.ɪks/ (คำนาม) — คณิตศาสตร์. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
  • equation /ɪˈkweɪ.ʒən/ (คำนาม) — สมการ. The act or process of equating two or more things, or the state of those things being equal (that is, identical).
  • arbitrary /ˈɑː.bɪ.tɹə.ɹi/ (คำคุณศัพท์) — ดุลยพินิจ. Based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random.
  • finger /ˈfɪŋɡɚ/ (คำนาม) — นิ้ว. A slender jointed extremity of the human hand, (often) exclusive of the thumb, and the corresponding part, irrespective of including a thumb, in many other…
  • complicated /ˈkɑm.plɪˌkeɪ.tɪd/ (คำคุณศัพท์) — ซับซ้อน. Difficult or convoluted.
  • innovation /ˌɪn.əˈveɪ.ʃən/ (คำนาม) — นวัตกรรม. The act of innovating; the introduction of something new, in customs, rites, etc.
  • equality /ɪˈkwɑ.lɪ.ti/ (คำนาม) — ภาวะเท่ากัน. The fact of being equal.
  • abstract /ˈæbˌstɹækt/ (คำนาม) — บทคัดย่อ. An abridgement or summary of a longer publication.
  • dive /daɪv/ (คำกริยา) — ดำ. To swim under water.
  • basket /ˈbæskɪt/ (คำนาม) — ตะกร้า. A lightweight woven container, generally round, open at the top, and tapering toward the bottom.
  • civilization /ˌsɪv.ɪ.laɪˈzeɪ.ʃən/ (คำนาม) — อารยธรรม. An organized culture encompassing many communities, often on the scale of a nation or a people; a stage or system of social, political, or technical…
  • necessity /nɪˈsɛsəti/ (คำนาม) — ความต้องการ. The quality or state of being necessary, unavoidable, or absolutely requisite.
  • calculate /ˈkælkjʊleɪt/ (คำกริยา) — คำนวณ. To determine the value of something or the solution to something by a mathematical process.

การออกเสียงที่ควรระวัง

  • เสียง “th”: mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, anthropology /ˌænθɹəˈpɑləd͡ʒi/, arithmetic /æɹɪθˈmɛtɪk/, logarithm /ˈlɑ.ɡə.ɹɪ.ð(ə)m/
  • เสียง “sh” และ “zh”: equation /ɪˈkweɪ.ʒən/, essentially /ɪˈsɛnʃəli/, shortly /ˈʃɔɹtli/, representation /ˌɹɛp.ɹə.zɛnˈteɪ.ʃən/, innovation /ˌɪn.əˈveɪ.ʃən/
  • คำยาว — ลงเสียงหนักให้ถูกพยางค์: mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, arbitrary /ˈɑː.bɪ.tɹə.ɹi/, essentially /ɪˈsɛnʃəli/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/

วิธีฝึกกับวิดีโอนี้

  1. ฟังวิดีโอให้จบหนึ่งรอบโดยยังไม่ต้องพูด แล้วจดคำที่ยังไม่รู้จัก
  2. พูดตามทีละประโยคด้วยความเร็วปกติ ทำซ้ำแต่ละประโยคจนจังหวะของคุณตรงกับผู้พูด
  3. อัดเสียงตัวเองแล้วเทียบกับต้นฉบับ โดยสังเกตคำอย่าง minus, symbol, mathematics เป็นพิเศษ

ไวยากรณ์ในวิดีโอนี้

โครงสร้างที่ผู้พูดใช้บ่อยที่สุด พร้อมคำพูดจริงจากวิดีโอ:

โครงสร้างในวิดีโอ
Passive voice be + กริยาช่อง 3 — เน้นสิ่งที่เกิดขึ้น ไม่ใช่ผู้กระทำmust be learned · was developed · were just born
Present perfect have/has + กริยาช่อง 3 — เหตุการณ์ในอดีตที่ยังเกี่ยวข้องกับปัจจุบันhave just come · has become · has been subtracted
Relative clauses who / which + อนุประโยค — ข้อมูลเพิ่มเติมเกี่ยวกับคนหรือสิ่งของequation, which is · subtraction, which is · calculated, which is

เทคนิค Shadowing คืออะไร?

Shadowing เป็นเทคนิคการเรียนรู้ภาษาที่ได้รับการรับรองทางวิทยาศาสตร์ พัฒนาขึ้นสำหรับการฝึกนักแปลมืออาชีพ วิธีการนี้เรียบง่ายแต่ทรงพลัง: คุณฟังเสียงภาษาอังกฤษจากเจ้าของภาษาและพูดตามทันที — เหมือนเงาที่ตามผู้พูดด้วยช่วงเวลาห่าง 1-2 วินาที การวิจัยแสดงว่าเทคนิคนี้ปรับปรุงความแม่นยำในการออกเสียง ทำนองเสียง จังหวะ การเชื่อมเสียง การฟังเข้าใจ และความคล่องแคล่วในการพูดได้อย่างมีนัยสำคัญ

เทคนิค shadowing: อ่านคู่มือฉบับเต็มทีละขั้นตอน →