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1c:T11f6,こんにちは。大阪大学工学部に通うものです。

私も高校時代、同じことで悩んでいました。基礎問題はある程度できるのに、応用問題になると急に歯が立たなくなる。「基礎ができていないのかな？」と不安になることもありましたが、結論から言うと、これは普通のことです。むしろ、今の時点で「基礎は7～8割理解できている」と思えているなら、伸びしろしかないですよ！


応用問題が解けるようになるには、ただの「練習」ではなく、【質の高い練習】が必要になります。以下に、私の経験を交えながら、具体的にどうすればいいかを説明していきます。


【1. 応用問題が解けない理由を知る】

まず、応用問題が解けない原因は、大きく分けて以下の3つに分類できます。

① 基礎の運用ができていない
　→ 解法を知っているだけで、それを適用する力が足りていない

② 問題の本質を見抜く力がない
　→ 目の前の問題を「知っている解法のパーツ」に分解できない

③ 試行錯誤の経験が不足している
　→ すぐに答えを見てしまい、思考を深める経験が少ない

実は、この3つのうち「基礎の運用」さえある程度できていれば、応用問題は練習次第で確実に解けるようになります。


【2. 質の高い練習方法】

では、どうやって応用問題に対応できるようになるのか。私が実践し、効果があった方法を紹介します。

① 1問に対して「思考の過程」を記録する
応用問題に取り組むとき、すぐに答えを見るのではなく、まずどこまで考えられたかを記録することをおすすめします。具体的には、

「これは○○の公式が使えそうだと思った」
「ここまではできたけど、次のステップが思いつかなかった」
「別の方法で考えてみたけどダメだった」

こういう【思考の流れ】を書き出すことで、自分がどこで詰まるのかが明確になります。私はこれを続けることで、「問題を解くときの自分の癖」がわかり、徐々に応用問題でも戦えるようになりました。

② 「部分解決法」を鍛える
応用問題は、大きな一問を解くというよりも、複数の基本事項を組み合わせる作業です。そのため、「この部分だけなら解ける」「ここまでは誘導できる」という練習が大切になります。

例えば、数学の問題なら、

・前半部分だけを解く
・途中式を与えられた状態で、その続きだけを考える
・解答の途中までを見て、次の展開を考える

こういった形で「部分的な思考」を鍛えると、一気に応用問題が身近になります。

③ 「間違え方の分析」をする
間違えた問題を復習するとき、私は次の2つのことを意識しました。

・「自分がどこで間違えたのか」を言語化する
・「同じタイプの問題を3日後に解き直す」

「なぜ間違えたのか」を考えないまま、ただ解き直しても効果は薄いです。

私はこの方法を取り入れてから、「同じようなミスを繰り返す回数」が減り、応用問題への対応力が少しずつ上がっていきました。


【3. 応用問題を解けるようになるためのマインドセット】

最後に、私が一番大切だと感じたのは、「応用問題は最初から解けなくて当然」という考え方です。

解けない問題があるときに「自分には無理だ」と諦めるのではなく、「これは自分が成長するチャンスだ」と思うことが大事です。


【4. まとめ】

2年で応用問題を解けるようになるのか、不安になる気持ちはよくわかります。でも、今の時点で「基礎は7～8割理解している」なら、確実に可能です。ポイントは以下の3つだと思います。

・解けなくても思考の過程を記録する
・部分的な解法を身につける
・間違えた問題を分析し、3日以内に解き直す

この3つを意識して練習すれば、確実に「応用問題を自力で解ける」レベルに到達できます。焦らず、でも着実に、積み上げていきましょう！

頑張ってください！応援しています！1d:Tc1d,こんにちは。難問を解くとき、括弧でくくるとか、補助線を引くとか、解くきっかけとなる閃きがなかなか思いつかないのですね。

私も数学は大の苦手で、解き方がわからず解法を見たら、なぜそんなこと思いつくんだ、というような解き方をしていて、愕然とすることがよくありました。

こればっかりは、基礎を習った直後に自分の頭でゼロから生み出すのは難しいと思います。多くの人は、初めてみる問題は解けませんが、その解法を学び本質の理解が進み、次に見たとき解けるようになっていくものです。ですから問題にたくさん触れて、その解き方を覚えていくというのが良いのかと思います。

出題する側も、全く新しい問題パターン！なんてものは作ることはできず、大体誰かが作ったことのあるお決まりの出題方法、型があり、後はそこにちょっとアレンジするくらいしかできません。

後はその出題者側の意図を見抜いて、このパターンだけど普通とちょっと違ってこんな工夫がされてるのね！と答えてあげればいいわけです。


いわゆる問題集にはよく出題されるパターンが網羅されてますから、それをまず押さえるのが良い勉強方法かなと思います。パターンを見抜けるようになればあとは工夫に対応です。
個別の工夫があるので見抜くのは結構大変ですが、まず基本形をイメージしてみます。工夫がされているため、そのままだとうまく解けないですが、そこからどう条件をずらせば都合よくなるかなーと考えれば、答えはもうすぐです。
作者側も、これは解けねえだろうガハハ！というのではなく、こんな工夫をしてますから、こーやってやればきれいに解けるでしょ？と、理解を問う問題を作っています。ですから数々の演習で問題の本質を見抜けるようになってきていれば、良い解法が見えてくるはずです。

最後の方はふわふわした回答になってしまいましたが、以上が私の考える回答です。

閃きは急に降ってくるものではなく、関連する訓練をしっかり行なっているからこそ、生まれるものです。
たくさんの問題に触れてパターンを覚えるとともに、出題者の意図を読み取ることを意識してみてください。
このパターンですが、こんな工夫してみてますよ。どうですか？どうやったらきれいに解けるかわかりますか？
という出題者のメッセージが込められています。それにきちんと答えられれば、大変気持ちがいいです。
まるで国語ですが笑

ぜひ問題を通じた対話を成立させる喜びを、わかってもらえればと思います。

少しでも参考になれば幸いです。
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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"応用問題の解き方"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは、はじめまして。\n東工大二年のたかゆーといいます。\n\n僕自身、高一の頃は進研模試の数学で60点とかを連発していましたが、高3の頃では東工大オープンで数学が10番代という結果を残せたのである程度参考になるかと思います。\n\n質問者さんの「どうやったら応用問題を解けるようになるのか」ということですが原因は主に２つあると考えられます。\n\n①基本的な考え方(フォーカスやチャート)の問題を完璧にできていない\n②問題を解く時になんとなくで解いてしまっている\n\n①に関しては、ほとんどの受験生ができていないように思われます。全部解けるのはもちろんのこと、なぜそのような解き方、考え方をするのかというところまで理解しましょう。\n僕はフォーカスしか使ったことがありませんが、文系の方でしたら例題の星4は完璧にしなくても大丈夫だと思われます。\n具体的にどのようにフォーカスやチャートを使っていくかは僕自身のブログでまとめておりますのでそちらをご覧ください。\n\n②に関しては、①とかぶるところがありますが問題を解く時に使った考え方や解き方を「なぜ選んだか」という理由を自分なりに考えながら問題演習をしていきましょう。最初は難しいかと思いますが、自分なりに考えて量を積んでいくと見たことのない問題でもある程度方針を絞ることができます。\nこのトレーニングの積み方としては「入試数学の掌握」という参考書がすごく役に立ちます。\nですが、この参考書はあくまでも読み物として使いましょう。\n\n入試数学において、解法の本質は30個程度しかないことに加え、問題を分析すればそのうちの２つ程度に絞られます。\nこの領域に達するのは難しいですが、僕が述べた方法で勉強していけば必ずたどり着く日がきます。\n\n拙い文章ですが最後まで読んでいただきありがとうございました。\n応援してます、頑張ってください"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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