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1a:Te57,僕の学校も東大2~3人、京大5~10人くらい毎年出していて、同じように数学がずば抜けている人がいました。その人の考えとかを真似たらかなり僕も数学が得意になった(駿台模試で偏差値75、進研模試で83程度。最初はどちらも60くらいでした)ので、完全にこれが答えだ！となる訳ではありませんが、説明させてもらいます。

まず1つに、数学が好きだとか、常日頃から数学的に考えることが得意であることが挙げられます。勉強以外のところですね。多くの人は数学の問題を見たら、1~2つの視点くらいからしか解答を考えることができないとおもいますが、こういう人達は常日頃から物事を無意識のうちに数学的に見ているからか、3つも4つも視点を持って物事、問題を見ることができています。

数学に置き換えてみましょう。例えば図形の問題に遭遇したとします。もしみなさんが三角比を勉強したばかりであれば、多くの人は三角比を使って(正弦定理や余弦定理など)問題を解こうとする、つまり問題を深くは見ることなく1つの視点に絞って解こうとするでしょう。

しかし、抜群に数学が得意な人は違います。三角比はもちろんですが、幾何学的に解けないか(幾何学的に、というのは、円周角の定理など図形的な視点から見ることです)、高2になっていればベクトルは使えないか、また、座標に置き換えて関数のように見れないか、など、様々な視点から見るようにしているのです。1つがダメであれば他の視点に切り替えられる要領の良さを持っていると言ってもいいでしょう。

はっきり言ってこういうのは先天的、つまり持っている人はポテンシャルで持っていることが多いです。またこういう人たちは数学の勉強をしていないという訳ではなく、勉強のやり方としてはみなさんとあまり大差ないでしょう。しかし、1問1問考えるときの思考の幅広さが違うため差が出てきてしまっています。

ちなみに最初に出てきた僕の友人の数学がずば抜けていた子は、最初からこうではありませんでした。つまり、このポテンシャルを後天的に(後から)身につけたのです。

この子はどうしたかというと、とにかく恐ろしい量の問題数を解き、あらゆる解法を頭の中に入れていました。どのぐらいかというと、高1の秋には早くも数3までの履修を終え、高2の夏までには阪大の過去問を30年分解き終えていたそうです。すごすぎますね。おそらく阪大の演習をしているときにこの視野の幅広さ、切り替えの速さを身につけたのだと思います。つまりは量がものをいうのです。余談ですが、この子は最終的に京大工学部に首席で合格しました。

つまり、この様なポテンシャル、才能を今から日常的に取り入れるのは厳しいので、まずは基本的な解法を頭に入れる。そして量をこなす時にとにかく視点を広く、多く持って切り替えられるようにしていく。これの繰り返しでしたかないです。質問者さんの学校にいる方はこの部分が日常的なところから鍛えられていたのでしょう。

正解かはわかりませんが参考になれば幸いです。2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=iBa8IWsBTqPwDZPuCCUe","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"数学を極める"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",35,") コメント(",0,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"6/4 18:04"}]]}],["$","div",null,{"className":"coach-mark 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mb-4","children":[["$","div","advice-part-0",{"children":[null,"こんにちは！\nこうしんと申します！\n極め方によるかな〜って感じですね。僕の中では二種類の人間がいて、天才的な（発想で乗り切るタイプの）極め方と、凡人的な（数学を沢山経験することによって受験数学に強くなるタイプ）極め方があります。極め方といっても、数学の勉強としてはこのどちらかで、僕は後者でした。さて、タイプ別に極め方を言うと\n前者のタイプは、数学オリンピック重視の勉強をするのが良いでしょう。参考書では、「秋山仁」先生の本が有名で、相当難しいですが（受験数学レベルは確実に超えます）これにかじりついてやれば、かなり力がつくと思います。というのは、考え方の手法別に問題が分類されており、その分類に沿って学習することで発想の根幹となる考え方を学習することができるからですね。\n後者のタイプは、数学が得意な人の多くが属しているタイプ（だと僕は思う）で、数学を解いた経験を次の問題に生かすことで問題を解いている人たちです。これが得意な人は、無意識のうちに経験をインプットしています。多分、数学が好きな人が多いから、その手法におーって思って頭に記憶が残るのだと思います。この過程を意識的に故意に発動させることが、このタイプの学習法ですね。僕がやっていた方法を言うと、\n1 手頃な問題集の解答を見て、その解答のポイントを抽出し、問題の特徴別に分類する。\n2 そのポイントを頭に入れて問題を解く。\n（この時、ポイントをどのように解答に描くのかを考えてください！論証は大丈夫？流れは？これができれば、全部書かなくておkです）\n3 暗記するまで何周もする（暗記＝体が反応することです！）\nこうして、いろいろな問題集を網羅的に演習してました！問題集は、チャートとかフォーカスゴールドとかとかなんでも構いません！こうして得たポイントを試験前に眺めれば、すぐに何十問と言った復習ができるのも強いです！\n後者のタイプの勉強法は、他の教科でも効く幅広い汎用性もあります！ぜひ試してみてください！"]}]]}],["$","div",null,{"className":"mb-4","children":["$","$L16",null,{"adviserImageUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_95092571A51B439899B1063D8D6D50D9.jpg?alt=media&token=585f4249-0d2a-4a92-a02e-2826ddba651b","adviserName":"こうしん","adviserDepartment":"京都大学理学部","adviceId":"iBa8IWsBTqPwDZPuCCUe","numberOfFan":216,"clipsAvg":37.82954545454545,"adviceRateAvg":4.721739130434782,"profile":"駿台で一浪して合格しました！\nよろしくお願いします！\n自分の経験が何かの役に立てれば幸いです！\n現在、京都大学で物理専門で勉強しています〜\nついでに、登山 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mb-1","children":"僕も現役時代は数学が伸び悩んでいました。しかし、基本的な問題が解けなければ何もできないと思い、チャート式をひたすら周回しました。そこから得た結論としては質問者さんが話している「暗記的な」学習が正解だったということです。何が言いたいのかというと、数学の問題を解く道筋というのは何も無いところから自力で編み出せるわけではありません。それができるのは一部の天才だけです。大切なのは自分が使える解法にいかに落とし込めるかです。入試本番ではみんなが解ける問題をしっかり解ければ合格できます。今までにないパターンの新しいタイプの問題というのは数学だけにかけてる人が辛うじて解けるかどうかといった感じなのです。そのような類の問題を解けるようになるよりは、しっかり土台になる部分を完成させて手堅く点数を稼いでいきましょう。質問者さんが取り組もうとしている勉強法はとても力になるものなので、頑張って継続できれば自然と点数は上がっていきまよ。頑張ってくださいね。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 0h24v24H0V0z","children":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 2-2-.9-2-2 .9-2 2-2m0 10c2.7 0 5.8 1.29 6 2H6c.23-.72 3.31-2 6-2m0-12C9.79 4 8 5.79 8 8s1.79 4 4 4 4-1.79 4-4-1.79-4-4-4zm0 10c-2.67 0-8 1.34-8 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mb-1","children":"こんばんは、はじめまして。\n東工大二年のたかゆーといいます。\n\n僕自身、参考書のみで東工大に現役合格したのである程度参考になるかと思います。\n\n一言で数学の難問といっても、実は二種類あって\n①合否に関係してくる難易度の問題\n②合否に関係してこない難易度の問題\nが、実は存在します。\n\n②に関しては、本当に直感にたよる必要があります(まあ本当は頼らなくても解けるのですが、そこまで数学を極める必要はないかと)が、①に関してはきちんと正しく数学を勉強すれば解けるようになります。\n\nよく巷では「受験数学は暗記じゃ対応できない」みたいな事を言われていますが、僕は一切そう思いません。\n\n入試数学で暗記すべきことは、実はせいぜい30通りくらいです。\n\nその中からどれを選ぶのか見極める力をつければ、2、3通りに絞られるので後はそれらを試すだけです。\n\nでは、どのようにして勉強していくのかというと、序盤に関してはフォーカスやチャートなどの例題をとにかく極める必要があります。\n\nまずは、量をこなして数学に対する土台を作っていきましょう。フォーカスの使い方に関しては、僕自身の過去の回答、またはブログから探してみてください。\n\nとにかく、「どうしてそのような解き方を選ぶのか」という事を考えながら何回も解いていきましょう。\n\n次のステップとしては、入試数学の掌握という参考書を使っていきましょう。こちらは早くても高3が始まるくらいで大丈夫です。\n\nこの参考書は、控えめにいって難しすぎるので、問題は読み物として使っていきます。この参考書で特に役に立つのが、受験数学の鉄則？的なやつです。これを覚えていくうちに、入試数学に対する考え方がわかるようになってきます。\n\n最後に、応用問題が解けないからといって数学が苦手だと思わないでください。それは、確実に演習量が足りないだけです。僕自身も、高一の頃は平均点くらいしか取れない時代がありましたが、フォーカスゴールドを7周くらいしたら、学年でもトップクラスの成績まで成長しました。\n\n他にもわからないことがあれば気軽にメッセージ送っていただければ(・∀・)"}],["$","div",null,{"className":"flex 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応用問題で多くの人にとって初見\n\nまず、①について\n基本問題の演習を繰り返し、基礎固めをしてください。\n具体的な方法は下に書いておきますね。\n\n次に、②について\n応用問題は基本問題の組み合わせです！\nなので、身についた基礎をどの場面でどう使うか考える練習をしましょう！\nこれも具体的な方法を下に書きますね。\n\n\n上の①②に対応する\n数学の『オススメ教材』と『オススメ勉強法』について紹介します。\n\nまず、『オススメ教材』ですが\n全範囲を満遍なくカバーし、数学の基礎力向上に最適な教材として\n・青チャート1A2B\nをオススメします！\n\n解答解説がしっかりしていて、\nなおかつ、問題を解くときの考え方まで紹介しているので、基礎固めはこの教材を何周もすれば十分です！\n\n基礎がしっかりできていれば、\n全国の受験生が受ける模試であれば\n偏差値60〜65程度は到達可能です。\n\n青チャートを完璧にすると\n模試の時にどれが基本問題でどれが応用問題かわかるようになりますよ！\n\n次に、青チャートが終わったならば\n今度は身についた基礎を使う練習\nつまり、応用問題を解くために基礎をどの場面でどう使うかを練習しましょう！\n\nこの演習用として\n・1対1対応の数学\n・プラチカ\n・やさしい理系数学\nなどがオススメです！\n\n次に『オススメ勉強法』ですが\n青チャートを使うかどうかに関わらず、\n問題の考え方や解答を理解した後に解答を見ずに\n最初から最後まで自力で再現してみることが大切です。\n\nここで、再現できないようであれば、\nまだまだ理解が足りてないということです。\n\nつまり、\n問題を解く\n↓\n考え方と解説を理解する\n↓\n解答を見ずに、自力で再度解く\n\nこの3つのことを繰り返すことで飛躍的に数学力が上がります！\n\nぜひ、実践してみてください！"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"数学の勉強法"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"学習の指針をざっくりと示していきます。\n\nまずは学校の教科書に載っている問題を100%全て解けるようにし、各分野の基本中の基本を固めます。余裕があれば公式も全て証明しておきましょう。\n\n次に網羅系の参考書(フォーカスゴールド・青or黄チャート・一対一対応の演習などから1つ好きなもの)を使用し、典型問題の解法を頭に叩き込みます。間違えた問題には必ず日付と間違えた原因をメモし、全ての問題を必ず「問題を見た瞬間に解法が頭に思い浮かんで手が勝手に動く」レベルまで仕上げましょう。悩むようではダメです。\n\nここまで仕上がっていればかなりの数学力がついています。『やさしい理系数学』『ハイレベル数学Ⅰ・A・Ⅱ・Bの完全攻略』『ハイレベル数学Ⅲの完全攻略』などの難易度の高い問題集に手を出して実力をつけましょう。\n\nあとは直前期には必ず過去問を時間を計って解くようにしましょう。過去問を分析してどんな問題が出やすいか、最低何問解くべきかなどは絶対に調べた方が良いです。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 0h24v24H0V0z","children":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"数学の勉強法"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"まず、①と②どちらが良いかという質問ですが、私は②をお勧めします。\n\n①のやり方に関して、このやり方でうまくいく人は限られていると思います。その理由として、2つあります。1つ目は、圧倒的な応用力が必要だということです。教科書併用の問題集では、基本を確認する問題が多く含まれ、実戦に近い問題が少ないです。そのため、基本的なことを理解することができても、応用力が身に付きづらいです。もし、応用力に自信がなければ、共通テストは解けたとしても、過去問は頭を抱えることになります。過去問と問題集のレベルの差が大きいと、そこを埋めるのにも時間が必要になってくるので、効率が悪い勉強方法だと感じます。\n\n②のやり方では、共通テストや過去問とのレベル差が他の問題集に比べ少ないように感じます。そのため、青チャートを完璧にすることで、共通テストや過去問に取り組みやすくなります。私の受験勉強でも、青チャートを愛用しており、過去問と同時並行で進めていました。青チャートを完璧にすれば、どこの大学でも戦えるようになると思いますよ。\n\nおすすめの勉強法としては、①はおすすめはしないものの、共通テストや過去問には、少しは手を付けておいた方が良いと思います。その中で確認することとしては、「自分の得意不得意はなにか」「解くスピードは受験に足りているか」を特に注目しておきましょう。\n\n「自分の得意不得意を把握する」ことに関しては、もちろん苦手がない方が良いからです。さらに、これらを把握することで、点数を伸ばしやすくなるためでもあります。何ができて何ができないのかを正確に把握することで、演習を行う分野や、時間配分を的確に認識でき、効率的に演習を進めることができます。\n\n「解くスピードは受験に足りているか」に関してでは、共通テストが時間内に解き終わるかどうかで判断できます。共通テストよりも時間が厳しい過去問はあまりみたことがないです。そのため、共通テストが時間内に解くことができれば、解くスピードは十分であるといえます。もし、時間が足りない場合は、時間配分を自分で調整するなどをし、工夫してみましょう。演習面では、問題を見てから、解法を思いつくまでのスピードや、計算のスピードを意識して問題を解いてみましょう。目標をもって問題を解くと、演習の質が上がりますよ。ぜひ、参考にしてみましょう。\n健闘を祈ります。頑張ってください！"}],["$","div",null,{"className":"flex 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