下面是代码的一个工作示例的样子（带有注解中建议的一些更改）。我基本上保持了原始代码的原样，但更改了脚本中的位置和顺序。
将html和php分开是您应该始终追求的目标之一。一旦把所有的php代码放在一起，就删除重复的或不必要的内容（包括对最后插入的id的superflous select查询）。
我添加了一些注解以作额外解释。其余的大部分都没有动过

<?php

// first - all code that should always be executed,
// this will later be used in the html output.
$showAllClasses = "SELECT * FROM class";
$showClassesResult = $mysqli->query($showAllClasses) or die ('Error finding Classes');

// now the code that should only be executed on POST request
if (isset($_POST['submit'])) {

    // we only want things to happen if all queries are successful,
    // otherwise we end up with quizzes without class connections.
    $mysqli->begin_transaction();

    //Get POST variables
    $quizTitle = '"' . $mysqli->real_escape_string($_POST['quizTitle']) . '"';
    $description = '"' . $mysqli->real_escape_string($_POST['description']) . '"';

    //Question query
    $quizCreationQuery = "INSERT INTO quiz (quizTitle, description) VALUES($quizTitle, $description)";
    $mysqli->query($quizCreationQuery) or die($mysqli->error . __LINE__);

    // The $mysqli instance knows the last inserted id, so we can just use that.
    $insertedQuizId = $mysqli->insert_id;

    foreach ($_POST['check_box'] as $classID) {
        $ClassQuizQuery = "INSERT INTO quiz_class(classID, quizID) VALUES ('$classID', $insertedQuizId)";
        $mysqli->query($ClassQuizQuery) or die($mysqli->error . __LINE__);
    }

    // Everything should have worked so we can now commit the transaction
    $mysqli->commit();
}

// now that we are done with everything, we start with the html output.
// since we have done all the complicated stuff above, all we have to care
// about, is the html output and iterating over our classes to create the html table.
?>

<form method="post" action="#">
    <p>
        <label>Quiz Title: </label>
        <input type="text" placeholder="Insert Quiz Title here" name="quizTitle" class="form-control"/>
    </p>
    <p>
        <label>Quiz Description: </label>
        <input type="text" placeholder="Insert Quiz Description here" name="description" class="form-control"/>
    </p>

    <table border='1' cellpadding='10' align='center'>
        <tr><th></th><th>Class ID</th><th>Class Name</th><th>Class Description</th></tr>
        <?php while ($row = $showClassesResult->fetch_object()): ?>
            <tr>
            <td><input type='checkbox' id='<?= $row->classID ?>' name='check_box[]' value='<?= $row->classID ?>'></td>
            <td><?= $row->classID ?></td>
            <td><?= $row->className ?></td>
            <td><?= $row->classDesc ?></td>
            <td><button type='button' name='add' id='add' data-toggle='modal' data-target='#questionType' class='btn btn-success'>Edit Students</button></td>
            </tr>
        <?php endwhile ?>
    </table>
    <div align="center">
        <input type="submit" name="submit" value="Submit" class="btn btn-info"/>
    </div>
</form>