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1c:Tc25,まずはどの科目にも言えることですが、基礎をしっかり理解し、解けるようにしてください。

基本問題を解き、わからないところは教科書や参考書に立ち返り復習する癖をつけましょう。
そして解法パターンを身につければ、応用問題も怖くありません。

数学はとにかく問題を解けばいい、と思っていませんか？
実はわたしもそう思っていました。
なので理論もわからず、とにかく問題集（私は青チャートを使っていました）を解き、間違える日々。

しかしこの勉強法は間違っている、と浪人してからやっと気付きました。

数学には定型パターンがあります。
高校数学を難しく感じるのは、そのパターンが非常に多いためです。
なので、まずはお決まりのパターンをしっかり覚えるようにしてください。

こういう問題がきたら、この公式だな、ってすぐに思いつくレベルまでもっていくのです。

以下、具体的な方法です。

私は青チャートを使っていたので、青チャートをイメージしてお答えしますが、ご自身の使っている問題集に置き換えて参考にしてみてください。

1.まずは一通り例題を解き、公式の使いどころを覚える。（基本問題）
→数学には解法パターンがあります。こういう問題が来たら、こういう方法で解く、というのが反射的にわかる、身につく、というところまでもっていきます。
この時、公式がわからない、理解できないときは教科書を開いて理解するようにしましょう。

2.例題の下にある問題を解く（標準問題）
→わからなくてもすぐに答えなどみずに、10分は考えるようにしましょう。この時色々な公式や解法が頭に浮かべば、知識は身についている証拠です。
逆に標準問題で手も足も出ないなら、教科書に立ち返りましょう。
ここまでできれば、定期テストや模試である程度の得点は見込めます。（青チャートなら国立大やマーチレベル）

3.章末問題を解く（応用、発展問題）
→数学を得点源にしたい人、難関国立大や早慶を狙う人は最終的に解けるようにしましょう。
このレベルだとさまざまな公式を合わせて使う、複合タイプの問題になります。
この問題をやるときは、「自分がどこまでわかっていて、どこからがわからないのか」をしっかり把握するようにしてください。復習するときはできないところの例題などを見返し、できるようにしましょう。
これが解ければ模試の大問もほぼ完投できます。


このように、大事なことはとにかく、
理論を理解する
ことです。
闇雲にやって量をこなすのではなく、丁寧に時間をかけて勉強してください。
1d:T11fd,初めまして。

大学数学を理解していないと解けない問題とはどんな問題を指しているのでしょうか？私は受験生時代東北大の数学も13年分ほど解きましたが、そのように感じられる問題はなかった記憶です。

もちろん数3では高校範囲だと証明できないものがあります（中間値の定理等）。また、例えば「x>0のとき、不等式sinx>x-x^3/6を示せ」という問題であれば、不等式の右辺はどこから出てきたのだろうと思うことはあるかもしれません。

ですが総じて大学範囲を理解しなければならないことは問題にするほど多くないと思います。

私自身はこれまで数学にかなり没頭してきましたが、高校範囲で「受験勉強」として取り組んだ内容は無駄になったとは感じていません。少なくとも現在学んでいる微分積分学は数3をもっと厳密に、拡張したような話が多いですし、線形代数学は行列という新しい分野ですが、ところどころベクトルのときに学んだことが役立っているように感じます。

ですが、質問者様のように受験がそういったゲームのようになっているというのも分かります。昔中国では科挙という試験が実施されていましたが、その試験では漢詩を始めとした非常に多くのことを暗記して挑む試験でした。そして、その試験にさえ合格すれば将来は安泰どころか裕福に暮らせたようです。

現行の受験制度もある種そうなっているのでは無いでしょうか。ハッキリ言えば、高校生の勉強の受験ぐらいで上手くいかない人は「学問の学ぶ姿勢」を追求したところで自信で学び切ることは出来ないという根本的な考えがあるのだと思います。当然高校の勉強は出来なかったけど天才的な研究や発見をする人もいるのかもしれませんが、母数として多くないのは明白でしょう。

「たくさんの科目に手を出していることで、学問の本質を見失っている」という指摘については、私の意見としては「まだその指摘をするには早い」という感じですね。もちろん私がその指摘をするにもまだ早いです。大袈裟に言えば我々が寿命を迎えるときにはじめて「あの勉強はいらなかった」と思うことが出来ます。

結局この教育の根幹を作った人たちは、「幅広く学ばせて、どれかが当たればいいな」みたいな発想なのでしょう。

回答作成中に思ったことですが、数学より理科（物理、化学）の方が大学範囲を黙認することが多いですね。解く上で黙認すると言うよりは、その定義自体に黙認があったり。そもそも高校で学ぶ特に理系科目というのは、非常に限られた都合のいい場合のみ扱います。数学の条件付き極値問題であれば三角関数を使ったり線形計画法を使って上手く解けるような変数の次数になっていたり、物理の公式であればその厳密な証明が大学範囲の微分積分だったり、化学では条件が綺麗すぎたり。

学問というのは具体から始まると考えています。例えば物理学の、ニュートンの運動方程式は実験事実です。つまり実験（具体）を通して一般的に正しい（抽象）とされました。数学であれば、有名なフェルマーの最終定理がありますが、あの問題は初めからn一般について示された訳ではなく、まずはn=3,4,5と示されたのです。化学でいえば、周期表は具体→抽象の一例ではないでしょうか。

そういう観点で高校の学習を振り返ってみると、限られた場合にしか出来ないような解法、考え方であっても、今後「学問」を修めるにあたって抽象化するときに役に立つことでしょう。

以上。少々まとまりがない形になってしまい申し訳ありません。このような疑問をもてる質問者様は素晴らしいと思います。もしかしたら何かやりたい研究等があるのでしょうか。であれば私と同じですね。是非受験をパスしてやりたい学問に取り組み、貢献して欲しいですね。頑張ってください。応援しています。1e:Tbd9,東北大学薬学部のヒロです。勉強における基礎とは何か、そして応用が解けるようになるためのアドバイスを教えます。参考になれば幸いです。

まず、問題を解くためには2段階の能力が必要で、一つ目は「知る」こと、そして二つ目は「使える」ことです。

一つ目の「知る」こととは、（当然ですが）教科書で公式や物質、単語について学ぶことであり、身につけることが必要な知識のことです。ただ、多くの人、というよりほぼ全員が勘違いしているのですが、「知る」ことは公式暗記や単語暗記ではありません。例えば簡単な例で言うと、二次方程式ax^2+bx+c=0を「完璧に」場合分けして答えられるか、英語で「3年がたった」を3通りで言えるか、酸化剤としての過マンガン酸カリウムの酸性条件と塩基性条件での変化とその理由など。もちろんこれらはほんの一例であり、すべての科目、すべての知識において前提条件や関連項目があります。

二つ目の「使える」こととは、実際に「知る」ことができた知識を使い、応用問題に対応できる力のことをいいます。どれだけ単語や公式を知っていたとしても、応用問題で「使える」ことができなければ意味がありません。「知る」段階で条件などを細かく学んだ人は、本当に「使える」人です。

「知る」ことは、公式や単語の丸暗記ではありません。受験生のほとんどは丸暗記することで「知る」ことができたと誤認して、いざ応用問題に手を出すと全く解けない状態に陥ります。逆に応用問題をすらすら解く受験生は、「知る」段階にて条件や公式の意味を本当の意味で「知る」人です。もしも先ほどの例を知らないのならば、そのかさんは本当に「知る」ことができていない状態です。でも、がっかりする必要はありません。今はまだ基本問題を解いているのであれば、今からでも遅くありません。使えないのに応用問題に手を出す方がよっぽど危険です。基本問題を解きながら、なぜこの公式なのか、他の答えだと不正解なのかなど、きちんと条件などを確認して、自信を持って「知る」ことができると言えるようになりましょう。

話をまとめると、基礎ができるとは、公式や単語を覚えることではなく、「使える」ようになるために「知る」ことなのです。それを意識して勉強していけば、必ず「使える」状態になります。大変かもしれませんが、本当の意味で「使える」状態になれば、周りの受験生とぶっちぎりの差が生まれます。受験勉強頑張ってください！応援しています！2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=YVJTj4ABTqPwDZPuV3I-","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"公式の証明"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",9,") コメント(",2,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"5/4 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\n国語、数学、英語\n\n地方公立高校出身、入学直後のテストは下から4番目。\n塾･予備校に通わず、参考書とスタサプで現役合格できました！\n計画に重きを置いています！ぜひ、ホームを参考にしてみてください🙌\n\n特に、同じような境遇で頑張ろうとしている人、頑張っている人、どうしても現役合格したい人に少しでも貢献したいです！！"}]}],["$","div",null,{"children":["$","$L7",null,{"href":"https://ck.jp.ap.valuecommerce.com/servlet/referral?sid=3364577&pid=884970531&vc_url=http%3A%2F%2Fshingakunet.com%2F%3Fvos%3Dnrmnvccp0000100","rel":"nofollow","target":"_blank","children":["$","$L8",null,{"src":"/images/document_request_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink パンフレットバナー画像","className":"mt-4 rounded"}]}]}],["$","div",null,{"className":"pt-4","children":["$","$L17",null,{"id":"adsbygoogle-init-under-advice"}]}]]}],["$","div",null,{"className":"flex justify-between","children":[["$","h1",null,{"className":"text-xl 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"数学の解法暗記"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんばんは。\r\n\r\n高校の数学は、おっしゃる通り、中学までの数学と比べると、様々か角度からのアプローチができるようになります。ですが、（少し厳しいことを書くかもしれませんがお許し下さい）名古屋大学を受験するにあたって、解法を一つしかわかっていないようでは、合格への道はかなり遠いと思います。\r\n\r\nといいますのも、名古屋大学の数学の入試は文系理系問わず、試験当日全員に、問題冊子、解答用紙に加えて、数学公式集が配布されます。（もちろん公式集には全ての公式が掲載されているわけではありませんが）数学の入試で、公式集が配布されるということは、つまり、「ただ単に、公式に代入して、答えが求められる」ことのできる人を大学が求めているわけではないでしょうし、そのような人が有利な採点はなされないという大学側からのメッセージではないかと思います。\r\n\r\nこのように考えますと、解法を何通り覚えたかではなく、なぜその公式・定理を使うのかということの方が大切だと思います。ただし、いきなりなぜその公式・定理を使うのかということを意識するとハードルが高すぎる可能性もありますので、まずは、複数解法のある問題に関しては、どの解法が最も計算が楽かや、どの解法が最もミスをしにくいかというような意識で、最終的には「解き方を暗記する」のではなく「なぜその公式・定理を使うのか」というような意識で数学を学習していくといいのではないかと思います。\r\n\r\nまだ３年生の5月です。現段階で、駿台模試でC判定をお持ちであれば、このままの調子で勉強していけば、合格できると思いますよ。頑張ってください。\r\n"}],["$","div",null,{"className":"flex 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"共通テスト　数学参考書"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは！東北大学文学部のkitaです！\n僕も共通テスト型の問題は苦手で、本番もとても足を引っ張りました😅\nその経験からお答えさせて頂きます！\n\nおっしゃる通り、基礎はかなり大切です。\nただ、おそらく分野によって様々だと思います。ですので、分野別に勉強することをおすすめします！\n\n具体的には、共通テストだと思考力などかなりめんどくさいので、まずはセンターの過去問を1年か2年解いてみてください。\nこの時は、時間は気にせず、自分の今の実力でどこまで行けるか、を計測します。\nそして、すんなり解けたり、時間をある程度かけたら解けたりした分野は、それなりに基礎はできています。\nしかし、全くできなかった分野は基礎が出来ていません。\nその見極めをしてください🙌\n\nその後、基礎がある程度できている分野は、まずはセンターの過去問でいいので、時間を意識して解きましょう。共通テストの過去問や、実戦問題集でもいいですが、共通テスト特有の思考力というより、まずは基礎を時間内にとくために、センターをオススメします。\n\n\nまた、基礎が全くできていない、と感じた分野に関しては、教科書をおすすめします。\n基礎ができていないと感じる人の多くは、教科書の理解がしっかりとしていません。\nまずは、教科書を固めましょう。\n\nただ、教科書でも理解が難しかったりなど、分野によってはあるでしょう。\n\nそういう場合は、\n\n高校の数学I・Aが1冊でしっかりわかる本、のような入門レベルの参考書や、\n改訂版 坂田アキラの 2次関数が面白いほどわかる本、の様な分野別の参考書をオススメします！\n\nこれらの参考書で理解が出来たら、上記のようにセンターで対策しましょう。\nまた、ある程度できてきたなと感じたら、実戦問題集などで共通テスト形式に移行しましょう！\n\n偉そうに書きましたが、僕も数学は本番全くとれませんでした😅\nですが、受験は総合点数の勝負です！\n苦手教科は、平均や6割など志望校の最低ラインまで持っていき、得意教科で安定して高得点をとる事も大事ですよ😉\n\n\n数学の様な、理系科目は中々すぐには結果が出ません。しかし、コツコツやっていれば必ず報われる教科でもあります！\n辛いかもしれませんが、絶対に諦めないでください🙌🙌\n\nでぃあんさんの、目標が達成されることをお祈りしています。頑張ってください！！\n"}],["$","div",null,{"className":"flex mb-1","children":[["$","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":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 2-2-.9-2-2 .9-2 2-2m0 10c2.7 0 5.8 1.29 6 2H6c.23-.72 3.31-2 6-2m0-12C9.79 4 8 5.79 8 8s1.79 4 4 4 4-1.79 4-4-1.79-4-4-4zm0 10c-2.67 0-8 1.34-8 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"定石を定着させる"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは！\n\n\n典型問題がよく出る大学と参考書を紹介します！\n\n過去問\n神戸大学\n神戸大学の数学は典型問題が多く、定石を覚えるのにいいと思います。あくまで過去問なので、分野もバラバラでハンドブックのように扱うのには向いてません。\n参考書\n青チャート　新数学スタンダード演習\n特にスタンダード演習についてですが、この参考書は難関大志望者が「これは定石」と言いたい問題集のようなものなのでとてもオススメです！\n\n余計なお世話かもしれませんが、質問を見て気になったことを話します。\n定石を覚えるのは大事ですが、問題への向き合い方も大事で、質問者さんは後者が疎かになっていませんか？\n後先考えないで式を作ったり、最終的にどうしたいのかわかっていないとおっしゃっているのでそのように感じました。それだと時間を無駄にしてしまう可能性があるので問題への向かい方を変えた方がいいです。具体的には問題を見てすぐ解くのではなく、3分くらいはどう解くかの方針を立てた方がいいということです。\n僕は数学で方針を立ててから解くことで成績が伸びました。\n\n頑張って下さい！\n応援しています！\n京大で待ってます！！！\n\nこの解答がいいなぁと思ったらファンになって頂けると幸いです。高評価もよろしくお願いします！"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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