angularjs data binding with button not working

I am trying to make the same functionality with the google form, which is when user choose different question type, it will show different style for data input, such as text, paragraph text, multi-choice.

Here is the link of my code:

My problem is when I choose one of the question type, it does not work, goes back to the last state.

I don't know why.

Here is part of my code:

<tr>
    <th>
        <label class="question_label">Question Type</label>
    </th>
    <td>
        <select class="question_dropdown" ng-model="question.type">
            <option value= "text">Text</option>
            <option value= "paragraph">Paragraph Text</option>
        <option value= "radio">Multiple Choice</option>
        <option value= "checkbox">Checkboxes</option>
        <option value= "list">Choose from a list</option>
        </select>
    </td>
</tr>


</tbody>
</table>
<div class="question_typeContainer" ng-switch="question.type">
    <div class="question_typeText" ng-switch-when="text">
    <input class="question_textfield disabled" value="Their answer" disabled>
</div>
    <div class="question_typeText" ng-switch-when="paragraph">
    <input class="question_textfield disabled" value="Their answer" disabled>
</div>
</div>