・東大を目指したいけど数学が苦手
・問題集を解いたり予備校の授業は受けてるけど、あまり得意にならない
・どう数学を勉強すれば東大レベルの力がつくのか分からない
もし、あなたがこのような悩みを抱えているとしたら、この記事はきっとあなたの役に立てると思います。
今回は数学の勉強法に関して
0から東大までのロードマップについてお話ししようと思います。
これを読めば、数学のどの部分い取り組んだら良いか分かるようになるはずです。
その前に…
以前受験対策ピラミッドを紹介しました。
受験生のパフォーマンスは大枠このようになっており、
それぞれのフェーズにあった勉強の仕方が必要、というものです。
そして、これを数学で当てはめるとこうなります。
まずはこの図を頭に入れることが大事です。
この図を思い浮かべながら、「自分は今どのフェーズにいるのか？」現在地を見失わないようにしましょう。
では、それぞれのフェーズについて見ていきましょう。
フェーズ１：教科書範囲
まずは教科書範囲の理解を徹底することが大事です。
ただし、注意していただきたいのは
教科書範囲の理解≠教科書範囲の問題を解けること
です。
教科書範囲の問題を解けるようになることは非常に重要ですが、
どちらかといえば、公式の導き方とか、基礎的な概念（対数ってどういう考え方なのか？etc）を理解しておく方が重要です。
というのも、この基礎の段階で解法暗記的な手法を取ってしまうと、後に解く応用問題でつまづいてしまったり、やり直すことになったりと応用が効かなくなるからです。
逆にこのフェーズで公式の導き方や概念を理解していれば、後々難しい問題が出てきても基礎に立ち返ることができます。
そのため、理解がスムーズになったり、上達が早くなったりします。
あと、もう1点。
公式の導き方や概念を理解するためには「良い先生の授業を受ける」というのがかなり効果的です。
自分で参考書を読みながら進めるのも悪くはないのですが、
・受験で聞かれるポイントを流し読みしてしまう
・逆に枝葉末節に気を取られてしまう
・自分の理解が本当に正しいのか確かめにくい
このようなリスクがあるため
基礎の段階は良質な先生の良質な授業を受けるなどして
正しい理解に努めることが非常に重要だと私は思います。
フェーズ２：応用問題集
基礎の学習が終わったら、教科書＋αくらいの応用問題集に取り組むことが重要です。
応用問題集に取り組む目的は
・教科書範囲の理解がきちんと理解できているかの確認
・受験問題の基礎の習得
の主に2つです。
教科書範囲の確認はもちろんのこととして
より重要なのは「受験問題の基礎の習得」です。
東大の問題は小難しい公式をたくさん使ったり、高度な知識が必要な問題は意外にも少ないです。
むしろ、基礎的な考え方や、受験の基礎的な問題の組み合わせで成り立っていることがほとんど。
そのため、まずは基礎的な問題単体を速く、そして正確に解けるようになることが重要です。
具体的には「青チャート」や「Focus Gold」といった網羅系の問題集を解くと良いでしょう。
目安としては全ての問題を5分以内にサッと解答を導けるようになると良いと思います。
余談ですが、この教科書範囲から受験基礎の習得までをいかに早く完成できるか
これが東大受験生にとって非常に重要なポイントの1つです。
早く完成させればさせるほど、その分実戦問題集や過去問に長い時間をかけることができます。
なので、できればここまでは高2のうちに完成させておきたいところです。
フェーズ３：実戦問題集
さて、ここまでくれば、あと一息です。
ここではもう少しレベルをあげた問題集に取り組みます。
より実戦に近い問題を解くことで
・基礎力をさらに上げること
・難しい問題に対する考え方を学ぶこと
・確率漸化式やベクトルの外積などやや高度な内容も解けるようにしておくこと
が目的です。
特に、「確率漸化式」に関しては文理問わず東大では頻出のテーマなので
是非この段階で押さえておけると良いと思います。
最後のフェーズ４は過去問です。
実際に東大の過去問を解いて仕上げをすると良いでしょう。
まとめると
さて、今日のお話をまとめると
・まずは教科書範囲をしっかり押さえる
・次に教科書＋αの応用問題集を解く
・実戦でさらに実力を積み上げていく
ことが重要ということでした！
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！
覗いてみる
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