New Twiddle

components.array-experiment.js

import Ember from 'ember';

export default Ember.Component.extend({
  nativeArrayItems: Ember.computed(() => []),
  emberArrayItems: Ember.A(),
  
  actions: {
    addItemInEmberArrayUsingPushObject() {
      this.get('emberArrayItems').pushObject(Math.random());
    },
    
    addItemInNativeArrayUsingSet() {
      const items = this.get('nativeArrayItems');
      this.set('nativeArrayItems', [...items, Math.random()]);
    },
    
    addItemInNativeArrayUsingPush() {
      this.get('nativeArrayItems').push(Math.random());
    }
  }
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend();

templates.application.hbs

{{array-experiment}}

templates.components.array-experiment.hbs

<button {{action 'addItemInNativeArrayUsingSet'}}>
  Add a new item in the native Array using `set`
</button> <em>(triggers)</em>

<br>

<button {{action 'addItemInNativeArrayUsingPush'}}>
  Add a new item in the native Array using `push`
</button> <em>(does not trigger)</em>

<h2>Native array items {{nativeArrayItems.length}}</h2>
<ul>
  {{#each nativeArrayItems as |item|}}
    <li>{{item}}</li>
  {{/each}}
</ul>

<hr>

<button {{action 'addItemInEmberArrayUsingPushObject'}}>
  Add a new item in the Ember Array using `pushObject`
</button> <em>(triggers)</em>

<h2>Ember array items {{emberArrayItems.length}}</h2>
<ul>
  {{#each emberArrayItems as |item|}}
    <li>{{item}}</li>
  {{/each}}
</ul>

twiddle.json

{
  "version": "0.12.1",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.12.0",
    "ember-template-compiler": "2.12.0",
    "ember-testing": "2.12.0"
  },
  "addons": {
    "ember-data": "2.12.1"
  }
}