In AngularJS an isolated scope does not inherit properties from its parent scope, unlike a child scope. However, a property of an isolated scope in a directive can be bound to an attribute, which in turn can be bound to a property on the controller scope, making it possible for the isolated scope to access specified properties on the parent scope.

Example
HTML

    <div my-directive
         text="Hello {{ parentProperty2 }}!"
         attribute-for-one-way-bind="parentProperty1"
         attribute-for-two-way-bind="parentProperty2">
    </div>

Script

    angular.module("myApp",[])
            .directive("myDirective", function () {
                return {
                    restrict: "A",
                    scope: {
                        text: "@",                                       // Attribute name is optional if attribute has same
                        oneWayBoundProperty: "&attributeForOneWayBind",  // name as property on isolated scope.  (If you do
                        twoWayBoundProperty: "=attributeForTwoWayBind"   // specify the name, remember to camelCase it.)
                    },
                    link: function (scope) {
                        var tmp = scope.oneWayBoundProperty(); // A one-way bound property has to be called as a function
                        scope.twoWayBoundProperty = "Jenny";  // This will also change parentProperty2
                    },
                    template: 'My text is "{{ text }}" <br> My oneWayBoundProperty is "{{ oneWayBoundProperty() }}" <br> My twoWayBoundProperty is "{{ twoWayBoundProperty }}"'
                };
            }).controller("myController", function ($scope) {
                $scope.parentProperty1 = "World";
                $scope.parentProperty2 = "User";
            });

Output

My text is "Hello Jenny!" 
My oneWayBoundProperty is "World" 
My twoWayBoundProperty is "Jenny"

Reference
AngularJS documentation on What are Scopes?
AngularJS documentation on Creating Custom Directives
AngularJS Directives, Using Isolated Scope with Attributes

Gist
index.html