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1b: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:Tc97,私も数学が苦手な人間でした。

そういう意味でこんな問題解けるようになるのか？と不安になった記憶があります。


数学や英語は成績が上がるまでに時間がかかる科目です。

基礎を積み上げて盤石にし、その上で標準レベルの問題(模試や入試等でよく出てくる典型的な問題)を解けるようにしていく必要があります。その訓練がある程度形になると、おそらく数学への苦手意識は解消されると思いますので、このレベルまで持ち上げられるように努力しましょう。


基礎を固めることに置いては、まずは教科書の例題を参考にどういった動きをしているのか、何をしようとしているのかを1つ1つ丁寧に追って理解します。

その上で、同じレベルの練習問題などを、上で理解したことを参考にしながら自力で答えに持っていくことができるか試します。教科書の練習問題や参考書に載っているようなその単元におけるごく簡単な問題をまずはスラスラ解けるように何度も繰り返してください。


その後、上で理解した知識を駆使した基礎を少し発展させたような問題を解く練習をします。


ここまでできて、基礎は完成です。


続いて、標準問題です。
入試までに発展レベルを解けるようにならなくては！と焦る受験生は多くいますが、本質は違います。

案外、この標準レベルの問題がきちんと解けるか否かで変わってくるものです。

いろいろな参考書や模試、本番の入試でよく見る問題が多いために軽視されがちですが、ここをきちんと満点もらえる答案を作れるか、これが合否を左右するといっても過言ではありません。



では、それはどの問題か？と聞かれると表現しにくいですがおそらく参考書では「標準」とか「★★(発展問題が★★★だった場合)」みたいな表現をされていると思います。教科書で言えば、章末問題の後半にあるような問題です。


このレベルの問題は、与えられた条件から基礎で理解した知識を使って、分かっていること(条件から言えること)を書き出します。その上で、基礎で演習したような動きを繰り返して解いたり、他の単元の知識を使って解法を編み出していくことになります。


はじめは動けないと思うので、解答を見ながらでも構いません。問題から与えられた条件をどのように読み取り、それをどのように噛み砕いていくのか、その動きを追って何をしているのかを理解してください。



その理解が済んだら、自分できちんとノートに記述して実際に答案を作ってみてください。


この繰り返しです。




数学が苦手ですと、勉強するのも嫌になってくると思います。それでも、諦めずに1つ1つ丁寧にこなしていってくださいね！








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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"応用力"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"入試の数学の問題には2パターンあると思っています。\n\n1° パターン化された問題(典型問題)\n2° パターン化されていない問題\n\nです。そんなに難しくない問題を出題する大学では、1°の場合が多く、1°の対策としては解法を覚えてしまうという手段があります。\nしかし、いわゆる難関大は1°よりも2°を出題しないと受験生間で差がつきません。よって2°を出題します。\n\n2°の問題は解法を覚えても意味がありません。では2°を解くためにはどのようなことをすればいいのか？\n\n数学の問題を解く際、\n問題を理解→解くための計画→計画したことを実行→自分の答えを見直す\nという流れで問題を解いていきます。\n\n1°の問題では暗記している場合、\n覚えていることを実行→自分の答えを見直す\nという解き方をしているため、2°に太刀打ちできません。\n\n2°の問題を解くには\n問題を理解→解くための計画\nをする練習が必要です。\n\nそのためには、\nまずチャート式などの数学の基本事項が分かっている、理解している必要があります。\n\nそれを2°タイプの問題を解いて練習を積み重ね、思いつく手段を実行し、基本事項を組み合わせて問題を解いていきましょう。\n\n数学は暗記する部分もありますが、それだけでは難関大には対応できません。頑張ってください。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"数学の応用問題について"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"少し命題からはずれますが、問題の大半は解けるが、あと一歩先に進めないという悩みですよね。\n当たり前のことですが、模試や本番の入試において問題集で扱った問題がそのまま数字を変える程度で出題されるというケースはほとんどありません。なので、いくら問題集の量をこなそうがそこまでの進歩はあまり期待できないかもしれません。\nでは、どうすればその壁を超えられるのか。ここからは私自身の経験談ですが、数学という科目に関して言えば、大問1つの設問には必ずなんらかのつながりがあるという前提をたてて問題を解くことを心がけていました。つまり(1)〜(3)までが独立した問題ではなく、すべてが1つの問題の中に出てくる一部の答えだ、という風に考えていたのです。(3)の部分点しかもらえないということは、その小問にこだわるあまり、全体の問題の流れを捉えられていないのかもしれません。特に国公立大学の数学ではほとんどすべての問題が記述問題であるためこのような流れが顕著に見える問題というのが多くなっています(ちなみに1番顕著なのはセンター試験)。まだ赤本等に手を出すのは早いと思うので、問題集を解く時からこのような流れを意識すると完答により近づけるようになると思います。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"数学問題集の付き合い方"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"まず、他の参考書をやる前に教科書を完璧にしよう。まず、例題を解いて、そのあと章末問題。大まかにはこんな感じで各単元を進めていけばいいと思う。応用ができないのは基礎ができてないから。数学は基礎基本がとても重要な科目。1aでつまづくとそれより先は何やってるのか全然わからないということになる。特に二次関数は高校数学の要。全ての根幹をなす分野であるから、絶対に完璧に理解し、使えるようにすること。また、理系に進むなら数学はできて当たり前の世界だし、文系でもそれなりの大学を受ける気なら数学は必要。文系で数学ができるのは本当に強い。なぜなら国英地歴よりも数学で一番差が開くから。数学ができることによって受けられる大学の幅も広がるし、レベルを上げることだってできる。だから、数学から逃げずに真摯に向き合って下さい。頑張ってね。"}],["$","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 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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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