AngularJS: $scope.watch not working

I have an element a that stores the number of checked check boxes. It is updated in my partial. I have access to element in my controller, however, I need to make it global since it will be used by most of my controllers. I have used a $rootScope variable and have tried to set it to the value of the a everytime it is updated using $scope.watch, however, this is not working.

Partial:

<p>You have selected: {{ a =(categories | filter:{checked: true }).length }} JOSCOS</p>

    <ul class="a">
    <li ng-repeat="item in categories" >
      <input type="checkbox" class="chk" ng-model = "item.checked">{{item.info.ct}}
      </input>
      </li>
     </ul>
<a href = "#x1" ng-click = "al()">Start the test</a>

My angular controllers:

myApp.controller('OneController', ['$scope', '$http', function($scope, $http) {
  $http.get('js/data/JOSCO.json').success(function(data) {
    $scope.categories = data;
  });
 $scope.a = 0
    $rootScope.cat = $scope.a;
    $scope.$watch('$scope.a',function () {
      $rootScope.cat = $scope.a;
   });
   $scope.al = function(){
      alert($scope.a); //outputs properly
   };
}]);

Second controller(I have a different partial for this):

myApp.controller('DetailsController', ['$scope','$rootScope' ,function($scope, $rootScope) {

  $scope.catno = $rootScope.cat;
  alert($scope.catno);  //outputs as '0'
}]);