「才能がなくてもできる方法」がある

104 Comments

今学期は授業数が多くて、生活のペースを掴むのになかなか苦労しています。ラボメンバーもまた増えて、ある程度のサイズの研究室で研究しながら、授業を両立する初めての学期ともいえるので、はやく慣れて軌道に乗せたいところです。

授業をやりつつ、いろんな国出身の学生を見ながら思ったことです。例えば  \( \int_{-1}^{1} y^2 \sqrt{1-y^2} \) を手計算でやるようなスキルって、どの国の学生も高校で習うわけではないようです。日本だと高校２・３年生くらいで習う、偶関数・奇関数、置換積分、三角関数の微分積分などと思います。こういうのができるかどうかは、練習したことがあるかないかで決まるだけなので、それができるからクリエイティブだというものではありません。一方で、練習の有無によって、できる子とできない子にはっきりと分かれます。

一方、大学２・３年向けの工学系の授業を教えながら感じたことですが、上記のような地道な計算を練習したことのある学生は、新しい概念を教えたときに飲み込みが早いし、計算に戸惑って大きな文脈を見失うことも少ないのかな、とも思いました。これは自分が勉強してきたときの感覚とも合致しますが、授業をしつつ、自分以外の人にもその傾向があるんじゃないかと思いました。

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ボストンに留学していた時のことです。日本人仲間で集まって数学について話す「数学談義」という会合がありました。MIT の理工学系の博士課程の人が面白い問題を持ち寄って解き合うというクセのある集まりでしたが、とても楽しかったです。私は工学部の研究室にいましたが、紙と鉛筆を使うような研究はしていなかったので、いつもは使わない頭の使い方をするのが新鮮でした。

その集まりの団長とも言える方が、ある問題の解法を説明するのに「この問題には才能がなくても解ける方法がある」と言っていました。それがとても味わい深い表現で、今でも記憶に残っています。自分なりにその言葉の意味を説明するならば「何故その方法を思い付いたのか、他の人では想像できないような、天才的ひらめきによる解き方がある一方で、最低限の理屈からスタートすることで、誰でも理解できるような解き方もある」ということなのだと思います。

一方で、ファインマン物理学にこんな発言があるようです。

Where did we get that [Schrödinger’s equation] from? It’s not possible to derive it from anything you know. It came out of the mind of Schrödinger.

The Feynman Lectures on Physics

ファインマン博士がシュレーディンガー方程式を評するコメントですが、これも味わい深いのではないでしょうか。この方程式が生まれたのは、シュレーディンガーのひらめきによるものだ、とファインマンが言っているのです。ドラゴンボールの世界で戦闘力のインフレが起こったように、果てしない「才能」のインフレーションが起こっています。

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では「才能」のない人が何かをできるようにするにはどうしたら良いのでしょうか。「才能」に見えているものは、一体何なのでしょうか。

これは自分の経験を踏まえているのですが、「数学的・物理的直感」みたいな「才能」について言えば、自分のその類の才能は数学・物理に造詣の深い研究者のレベルに遠く及びません。ボストンの「数学談義」仲間の話を聞くにつけ「世の中をこんな視点で見る人がいるんだ」と驚いたものです。その一方で、大学の初級クラスで使用するような物事の捉え方、例えば「この表面にかかる力を積分して計算する」とか「この３次元空間に圧力場がこんな感じで広がっている」みたいな感覚は、高校生の時に、微分・積分のような地味な計算を繰り返した経験が、イメージを持つ一助になっています。最初の自分の授業での経験に戻りますが、「高校数学の技術的なこと」に慣れていると、イメージしやすいことがあるようです。そして、そういった経験がない人からみたら、そういったことができるのも「才能」に見えるのかもしれません。

ひとつ思うのは、世の中の多くの事柄に関して、「才能」とは相対的なものだということです。「才能」とされる部分にも「積み上げられる部分」と「積み上げられない部分」があるのだと思います。一般的に「積み上げられない部分」とされるものが形になると、周囲が「クリエイティブだ」「天才だ」と評するのでしょう。しかし数学談義の団長が示唆したように、「積み上げられる部分」は我々が思っているよりも大きいように思います。そしてそういった才能を積み上げる方法は、私が興味のある文脈（研究とか教育です）で言えば、実際の例に触れることと、地道に手を動かすことなのかなあと思います。

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最後に少し大きな話を投げかけます（少し前に流行った AMEMIYA という芸人と同じパターンです）。果たして、日本の教育カリキュラムはどう評価するべきなのでしょうか。理工系の高校生のカリキュラムに限れば、上記のような、問題演習とパターンに慣れるようなプロセスが無駄かと言えば、私は無駄どころか優れているとさえ思います。まあ、高校理科について言えば、実験とか、ビデオを見たりとか、そういうのがもう少し増えれば良いとは思います。

大学院教育ですとどうでしょうか。「アメリカの大学院生は、社会との繋がりがあり起業することも多い。それに比べて日本の大学院生は研究室に閉じこもり・・・」などの言説は聞き飽きましたが、少なくともアメリカの博士課程においては、Qualification Exam と呼ばれる学術知識の試験があり、それに合格しなければ退学ですから、学術知識を持つことを軽視しているわけではないようです。

「日本の教育は遅れている、大まかな流れを理解することが大事であり、瑣末な計算は計算機を使えば良い」みたいなのは一理ありそうに見せて、やや誤解を招く考えだとも思います。計算機を使って意味のあることをできる「才能」を持つには、ある程度の手計算による慣れが必要だと思うからです。そう思う理由は上記に述べました。もしこの部分を省いてしまうとどうなるか、というのは面白い社会実験ですが、それをしたことで必要な人材が育たなくなってしまうと困ります。比較する対象は、諸外国の教育カリキュラムにもあるでしょうから、それらの事例などを参考にして、慎重な判断がされることを望みます。

偏見を承知で言いますが「日本の教育は知識重視で考える力が足りない」「金太郎飴のような同じ人材を作っている」のような言説を用いる大人に対しては、ご本人が深く知識を積み重ねて学習したこともなければ、クリエイティブですらないだろう、というようなステレオタイプを持っています。そう考えてしまうのは、彼ら、彼女らが発言する内容に独自性や面白みがないからです。「プログラミングを勉強しよう」「インターネットを使った学習」「留学」「3D プリンタ」など、世界中の教育機関で言われていることの繰り返しであり、スティーブ・ジョブズやイーロン・マスクの名言の引用であり、自分の言葉で語らないからです。「日本の教育ではクリエイティブになれない」のようなことを言ってる大人の発言が、さしてクリエイティブに聞こえない事実はとても示唆的です。他方、日本の教育を受けてクリエイティブである人をたくさん知っていることも付け加えておきますし、そういう人は私のようにベラベラと無意味なことを喋りません。グローバルな若い人には、大人のポジショントークに煽られないようにしてもらいたいです。

小さいものをコツコツ積み上げることは役に立つと思います。以前の自分の指導教官、同僚や、友人知人の研究者などには、クリエイティブであり「才能」がある人がたくさんいます。知識が豊富な上で、大きな文脈を見て、さらに突飛なアイデアを出してくる人たちです。そういう人は、知識の積み重ねや、細部へのこだわりを持っている人で、私にとって良いロールモデルです。クリエイティブになりたいし、才能を磨きたい私は、これからもそういう方向性で頑張りたいと思います。

 

104 thoughts on “「才能がなくてもできる方法」がある”

  1. こんにちは、現在工学系の学部一年生です。
    私は現在家庭教師をしていて、教え子の女の子に「数学ってなんの役に立つの」とよく聞かれるので非常に興味深いポストだなあと感じました。多少の面白みを見出したが、大学受験に必要であり周囲からの評価を獲得するために勉強した私からは、ただ「パターンを覚えて、論理的に考える（つながりを見出す）練習だよ」としか言いようがなかったのですが。
    私は才能とは「面白みを見出して情熱を持てる力」だと考えています。数学が嫌いな教え子は演劇がとても好きであり、一方の私はどんなに真剣に演劇を見てもそこに面白みを見いだすことはできませんでした。そうした情熱を持つことは、子どもにしかできないことなのでしょうか。それとも、深く知ることで情熱を失う構造になっているのでしょうか。
    才能よりも情熱について考えてしまうことが多いです。

    Reply

    1. ありがとうございます。工学系の学部ならば、これから数学が役に立つことは多そうですね。どんどん具体例に触れて、説得力を持って高校生に教えられるようになると思いますし、楽しみですね。

      ええ、「面白みを見出して情熱を持てる力」も才能の１つなのでしょうね。上記のようなことを書きながら、単調な計算の練習が面白みを見出すのを阻害しかねない、という指摘もわからなくはないところです。ですから、まだまだ大学以降でも、高校まででも、カリキュラムの改良の余地はあると思います。

      Reply

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