シャドーイング練習: Addition and Subtraction of Small Numbers - 動画で英語スピーキングを学ぶ
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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.
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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.
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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.
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By the end of this series, maybe we can all get there, but for now, let’s start at the very beginning.
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What was the first kind of math that was developed by the human race?
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That would undoubtedly be arithmetic.
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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.
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How many people are in the tribe?
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Two kids were just born, how many are there now?
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How many years has the tribe’s wisest elder been alive?
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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.
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How many apples are in the basket?
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How many do you want, and how many are now left?
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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.
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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.
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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.
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If we had only eight fingers, things would be totally different.
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But ten is what we went with, and it works just fine.
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Getting back to the apples, the basic operations we will learn first are addition and subtraction.
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Addition is the most basic arithmetic operation, and it represents the combination of two numbers to become a single number, or a sum.
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If you get two apples from one vendor, and then three from another, how many apples did you get?
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Of course we can easily count the resulting pile and see that there are five.
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But how do we represent this mathematically?
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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.
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This is an equation, which is a statement of equality.
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The expression on the left is numerically equivalent with the expression on the right.
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This particular equation reads, “two plus three equals five”, with the word plus essentially meaning “and”, and the equals sign meaning “is”.
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Two and three is five, so five is the sum of this additive operation.
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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.
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You bring all five of your apples home and you eat one of them.
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If one apple has been subtracted, how many are left?
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Again, it is easy to count and see that there are four left.
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But this result can also be calculated, which is much different from counting.
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We can write another equation with a five, then the minus symbol, followed by a one, then the equals sign, and the number four.
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This reads, “five minus one equals four”, which essentially means five less one is four, so four is the difference between one and five.
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On a number line, this is the distance between the two numbers, and this is an excellent way to visualize subtraction.
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Fourteen minus eleven is three, because three is the difference between the two numbers.
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It takes three to get from eleven to fourteen.
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Now that we have become familiar with the symbolic representation of these simple operations, we should discuss some applicable properties of numbers.
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Addition is commutative, in that the order in which numbers are added does not matter.
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Two plus three equals five, and three plus two also equals five.
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Subtraction is not commutative.
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It does indeed matter which number is being subtracted from the other.
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Three minus two is not the same as two minus three.
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Addition is also associative.
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This means that if performing two successive additions, the order in which they are performed does not matter.
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Two plus three plus four will be nine no matter which numbers we add first.
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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.
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The result is the same.
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Subtraction is not associative.
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If we write down five minus three minus two, we could do five minus three first.
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That gives us two, and subtracting the other two, we get zero.
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If instead we do the three minus two first, we get one, and five minus one is four.
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So we can see that subtraction is not associative.
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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.
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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.
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They are rooted in the physical world, even if in a way that is more difficult to immediately conceptualize than the plus symbol.
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One goal of this series will be to make all the other mathematical operations as intelligible and relatable as addition and subtraction.
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Once you intimately understand what mathematical constructs represent, they no longer seem arbitrary and infuriating, but instead powerful, as their utility becomes apparent.
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So let’s move forward and learn some more arithmetic, but first, let’s check comprehension.
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このレッスンの語彙とスピーキングのポイント
この動画には、シャドーイング用の文が62文、単語が1107語あります。 音声の長さは7:37です。 話す速さは1分あたり約145語で安定しており、シャドーイングしやすいペースです。 単語の86%は英語の頻出3,000語に含まれます。残りは練習の前に確認しておきましょう。
この動画の重要語彙
動画に出てくるやや難しい単語15語を、発音と意味つきで紹介します。
- minus /ˈmaɪ.nəs/ — 引く. Made less or reduced by (followed by an expression of number or quantity).
- symbol /ˈsɪmbəl/ (名詞) — 記号, 符号. A character or glyph representing an idea, concept or object.
- mathematics /mæθ(.ə)ˈmæt.ɪks/ (名詞) — 数学. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
- equation /ɪˈkweɪ.ʒən/ (名詞) — 方程式. 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/ (形容詞) — 恣意的な. Based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random.
- finger /ˈfɪŋɡɚ/ (名詞) — 指. 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/ (形容詞) — 複雑な. Difficult or convoluted.
- concrete /ˌkɑnˈkɹit/ (形容詞) — 実際の, 具体的. Real, actual, tangible.
- contribute /kənˈtɹɪb.jut/ (動詞) — 貢献する. To give something that is or becomes part of a larger whole.
- apparent /əˈpæɹənt/ (形容詞) — 目に見える, 瞭然の. Capable of being seen, or easily seen; open to view; visible to the eye; within sight or view.
- innovation /ˌɪn.əˈveɪ.ʃən/ (名詞) — イノベーション, 革新. The act of innovating; the introduction of something new, in customs, rites, etc.
- utility /juːˈtɪlɪti/ (名詞) — 有用, 有用性. The state or condition of being useful; usefulness.
- equality /ɪˈkwɑ.lɪ.ti/ (名詞) — 平等, 均等. The fact of being equal.
- communicate /kəˈmjuːnɪkeɪt/ (動詞) — 伝える. To impart or transmit (information or knowledge) to someone; to make known, to tell.
- abstract /ˈæbˌstɹækt/ (名詞) — 概要, 要約. An abridgement or summary of a longer publication.
動画に出てくる句動詞
- count on /kaʊnʌn/ (動詞) — ...に 頼る, 当てにする. To rely on, trust, or expect.
- write down (動詞) — 書き留める, 記す. To produce or set (something) down in writing; to record something.
注意したい発音
- 「th」の音: mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, anthropology /ˌænθɹəˈpɑləd͡ʒi/, arithmetic /æɹɪθˈmɛtɪk/, logarithm /ˈlɑ.ɡə.ɹɪ.ð(ə)m/
- 「sh」と「zh」の音: equation /ɪˈkweɪ.ʒən/, essentially /ɪˈsɛnʃəli/, shortly /ˈʃɔɹtli/, representation /ˌɹɛp.ɹə.zɛnˈteɪ.ʃən/, innovation /ˌɪn.əˈveɪ.ʃən/
- 長い単語（アクセントの位置に注意）: mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, arbitrary /ˈɑː.bɪ.tɹə.ɹi/, essentially /ɪˈsɛnʃəli/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/
この動画での練習方法
- まず声を出さずに動画を最後まで聞き、知らない単語をメモします。
- 通常の速度で一文ずつシャドーイングし、話し手のリズムに合うまで繰り返します。
- 自分の声を録音して元の音声と比べます。minus, symbol, mathematicsなどの単語に特に注意しましょう。
この動画の文法
話し手がよく使っている文型を、動画の実際の表現とともに紹介します。
| 文型 | 動画での表現 |
|---|---|
| 受動態 be + 過去分詞 — 誰がするかより、何が起きるかに焦点を当てる | must be learned · was developed · were just born |
| 現在完了形 have/has + 過去分詞 — 過去の出来事が今も関係している | have just come · has become · has been subtracted |
| 関係詞節 who / which + 節 — 人や物について情報を加える | equation, which is · subtraction, which is · calculated, which is |
シャドーイングとは？英語上達に効果的な理由
シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。