これは教えている東大志望の生徒に聞かれた質問です。
教科書範囲の理解から、チャートという流れは一般的ですが、
その先、つまり「次何すればいいか？」というのは人によって意見が分かれるところです。
そこで、今回は、ある程度数学の基礎学習を終えた生徒が
どんな風にステップアップしていけばいいか？
その具体的なロードマップと、演習の注意点についてお話ししていこうと思います。
まずは、目的を確認する
どの参考書をやればいいか？というのも大事なことですが、
何のためにその参考書をやるのか？目的を持つことも非常に重要です。
チャートがある程度解けるようになった生徒の状態は
基礎的な問題は解けるが、応用問題は解けない・慣れていない・解いたことがない
という状態でしょう。
そして、最終的な目標と言えば、志望校、具体的には東大の問題を解けるようになることです。
つまり、現状生徒に必要なのは、基礎レベルから、東大レベルへの橋渡し。
具体的には応用・実践型の問題集を解いてさらに数学の基礎力を高めること
になりそうです。
では、これを読んでいるあなたが「応用・実践型の問題集を解いてさらに数学の基礎力を高める」必要がある生徒という前提で、
どんな問題集を解いて行ったらいいかお伝えします。
また、紹介する参考書は自分の経験だけでなく、受験生時代に受かった友人が使っていたものや、東大に入って周りから教えてもらったものを含むようにしてあります。
基礎から東大へ！オススメ参考書３選
・松田の数学IAIIB 典型問題type100（東進ブックス）
受験に必要な典型問題を100題まとめた参考書です。私自身これを解いていたのですが、「無駄がなく、簡潔」な印象を受けました。紹介されている解法も東大レベルまで使えるほど応用力・汎用性に優れたものが多いです。チャートを終えた生徒は是非やってみることをオススメします。
・文系数学の良問プラチカ（河合出版）
先ほどのtype100よりは難易度が一段階上がります。が、難関大受験生に必須な問題が多く取り上げられており、これをしっかり解き進めることで、かなり実戦的なレベルまで数学の力を高めることができます。
・１対１対応の演習（東京出版）
同じく、プラチカとほぼ同レベルの参考書です。全部でⅠ・A・Ⅱ・B・Ⅲの5冊あります。個人的にはレベル帯がかぶっているので、プラチカか１対１対応はどちらか1つ好きな方でいいかなという印象です。私が受験生の頃はプラチカを解いていましたが、現在指導している東大志望の生徒は１対１対応の演習を解いています。
問題を解く際の注意点
こういった実戦問題を解いていく上で1つ注意していただきたいことがあります。
しかも、これは多くの受験生が陥りやすい行為です。
それは、答えを出すだけで満足しない、ということです。
数学の問題なので、はっきりわかる形で巻末に答えが載ってあります。
しかし、実際に東大入試で評価されるのは答えだけではありません。
答えに至るプロセスや論理展開、東大はそうした思考の部分を重視しています。
これは実際の数学の解答用紙です。
答えだけを重視しているなら、このような形にはしないでしょう。
東大は解答だけでなく、解答に至る受験生の思考を観察しているのです。
なので、途中経過はもちろん、適宜説明を加えたりすることを普段からやっておくことを強くお勧めします。
確かに、答えだけを見たくなる気持ちも分かります。パッと見て答えがあっていると嬉しいですし、逆に間違ったら悔しい気持ちになりますよね。
しかし、そこで一喜一憂しても受験には全く関係ありません。試験で何点取れたか、が全てなわけですから…
問題はそこで解いた問題や、解くことで得た知恵やノウハウをどう入試に活かすかという部分です。
受験勉強は突き詰めてしまえば、どう試験（本番）に活かす勉強（準備）をしてきたかが全てなのです。
逆に本番で活かせない、再現性のない勉強ばかりしていても多くは自己満足になってしまうわけです。
なので、演習段階から、解く手順を数学記号や文字で説明したり、解答とは直接関係ない部分も書くようにしましょう。
もっと欲を言えば、普段の演習の解答を東大生や、学校の先生に添削してもらうと、より良い解答作りができるようになります。
「ここの数学記号の使い方はおかしいんじゃないかな」
「ここは説明を入れたほうがいいね」
「ここ論理が飛躍してるよ」
など、自分で解答を書いていても、なかなか解答の作り方のミスは気づきにくいものです。
なので、もし、そうした環境があれば、是非添削を受けてもらいつつ演習を進めたほうが良いでしょう。
冒頭でも言いましたが、実践型の演習の目的は基礎レベルから、東大レベルへの橋渡しをすることです。
この演習の後には東大の過去問が待っています。今はまだ歯が立たなくても、歯がたてるような準備を今から進めることが重要です。
なので、漫然と参考書を解くのではなく、目的意識をはっきりさせて参考書に取り組みましょう。
こうした少しの意識を持つだけで勉強の成果は大きく変わるはずです。
まとめると
さて、今日のお話をまとめると、
チャートなどの基礎が終わった受験生は東大レベルまでの橋渡しをするためにオススメの実践型の問題集を解いていくと良いでしょう。
そして、演習時には答えを出すことで満足せず、
本番を見据えて過程や説明を書くようにして、できれば東大生や学校の先生に見てもらうようにすると良いということでした。
数学の日々の学習に役立ててほしいなと思います。
また読んでいただけたら幸いです。
もし、
・数学の学習法についてもっと詳細を聞きたい
・自分の勉強法が正しいのか不安に感じている
・実際に東大生・東大卒の先輩に勉強の相談をしたい
こんな悩みを抱えているのであれば、
1ヶ月、あなたの勉強を東大生や東大卒の先輩に見てもらいませんか？
Smart Studyでは東大をはじめとする難関大学を志望する高校生・高卒生を対象に
オンラインで、1対1のコーチングを行うことで、あなたの勉強の舵取りをする、そんなサービスです。
もし、少しでも興味があれば、是非公式サイトを覗いてみてくださいね！
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