Laravelのoldのoptionを見てselectedを変えたい

現在『更新』画面を作成中なのですが、お聞きしたいことがあります。

Laravel Framework 6.0.3

optionがoldに対応して、selectedされない

様々なサイトを見たりして、同じように書いていますが、どうもうまく行きません。

Laravel
1// index.blade.php
2@extends('layouts.app')
3
4@section('content')
5<div class="container">
6    <div class="row justify-content-center">
7        <div class="col-md-8">
8            <div class="card">
9                <div class="card-header">全ての思い出</div>
10
11                <div class="card-body">
12                    @if (session('status'))
13                        <div class="alert alert-success" role="alert">
14                            {{ session('status') }}
15                        </div>
16                    @endif
17                    @foreach ($memories as $memory)
18                        <div class="card mb-3">
19                            <div class="card-body">
20                                <h5 class="card-title">{{ $memory->title }}</h5>
21                                <p class="card-text">
22                                    カテゴリー：<a href="{{ route('memories.index', ['category_id' => $memory->category_id])}}">{{ $memory->category->category_name }}</a>
23                                </p>
24                                <p class="card-text">{{ $memory->content }}</p>
25                                <a href="{{ route('memories.show', $memory->id) }}" class="btn btn-primary">詳細</a>
26                                <a href="{{ route('memories.edit', $memory->id) }}" class="btn btn-primary">編集</a>
27                                <form action="{{ route('memories.destroy',  ['memory' => $memory]) }}" method="POST">
28                                        @csrf
29                                        @method('DELETE')
30                                    <button type="submit" class="btn btn-danger">削除</button>
31                                </form>
32                            </div>
33                        </div>
34                    @endforeach
35                </div>
36            </div>
37        </div>
38    </div>
39</div>
40@endsection
41

laravel
1
2// edit.blade.php
3@extends('layouts.app')
4
5@section('content')
6<div class="container">
7    <div class="card">
8        <div class="card-header">思い出</div>
9        <div class="col-6">
10            <div class="card-body">
11                @if ($errors->any())
12                    <div class="alert alert-danger">
13                        <ul>
14                            @foreach ($errors->all() as $error)
15                                <li>{{ $error }}</li>
16                            @endforeach
17                        </ul>
18                    </div>
19                @endif
20                @if (session('status'))
21                    <div class="alert alert-success" role="alert">
22                        {{ session('status') }}
23                    </div>
24                @endif
25                <div class="card mb-3">
26                    <div class="card-body">
27                        <form method="POST" action="{{ route('memories.update',  $memory->id) }}">
28                            @csrf
29                            @method('put')
30                            <div class="form-group">
31                                    <label>いつの思い出ですか？</label>
32// ここら辺です。
33                                    <select class="form-control" name="category_id">
34                                      <option value="1" @if( old('category_id')=='1') selected @endif>中学生</option>
35                                      <option value="2" @if( old('category_id')=='2') selected @endif>高校生</option>
36                                      <option value="3" @if( old('category_id')=='3') selected @endif>大学生</option>
37                                    </select>
38                                </div>
39                                <div class="form-group">
40                                  <label for="exampleInputEmail1">memories title</label>
41                                  <input type="text" class="form-control" value="{{ old('title') ?: $memory->title }}" name="title">
42                                  <small class="form-text text-muted">title</small>
43                                </div>
44                                <div class="form-group">
45                                  <label>memories</label>
46                                  <textarea class="form-control" rows="3" name="content">{{ old('content') ?: $memory->content }}</textarea>
47                                </div>
48                                <button type="submit" class="btn btn-light">更新</button>
49                        </form>
50                    </div>
51                </div>
52            </div>
53        </div>
54    </div>
55</div>
56@endsection
57

laravel
1// MemoryControllor.php
2
3    public function edit($id)
4    {
5        $memory = Memory::find($id);
6
7        return view('memories.edit', [
8            'memory' => $memory,
9        ]);
10    }
11
12    
13    public function update(MemoryRequest $request, $id)
14    {
15        $memory = Memory::find($id);
16       
17        if (\Auth::id() === $memory->user_id) {
18            $memory->category_id = $request->category_id;
19            $memory->title = $request->title;
20            $memory->content = $request->content;
21            dd($memory);
22            $memory->save();
23        }
24        return redirect('/');
25    }
26

laravel
1// web.php
2
3
4Auth::routes();
5
6Route::get('/', 'MemoryController@index')->name('memories.index');
7Route::resource('/memories', 'MemoryController', ['except' => ['index']]);
8