Abstract: Embodiments of the invention disclose a virtual manipulative to facilitate math learning. The virtual manipulative comprises a user interface to progressively form one on more columns to hold partial sums or number decompositions to assist a learner in computing a sum.

Abstract: The HTML/XML tree synchronization module synchronizes a document with a view or multiple views, after a change has been made to the document. First, the tree synchronization module receives a document change from an application program. An update processor converts the tree data of the document to a character string, and receives document change information from one or more application program interfaces. The update processor utilizes the document change information to update the document tree data character string. The document change information is then sent to one or more application program interfaces to determine the scope and content of the document views. A log generator receives the view change information, and creates record logs for each changed document view. These logs are played by a log player to each view, and each view data tree is updated with the view changes contained in the change logs.

Abstract: The HTML/XML tree synchronization module synchronizes a document with a view or multiple views, after a change has been made to the document. First, the tree synchronization module receives a document change from an application program. An update processor converts the tree data of the document to a character string, and receives document change information from one or more application program interfaces. The update processor utilizes the document change information to update the document tree data character string. The document change information is then sent to one or more application program interfaces to determine the scope and content of the document views. A log generator receives the view change information, and creates record logs for each changed document view. These logs are played by a log player to each view, and each view data tree is updated with the view changes contained in the change logs.

Abstract: A downloading facility for downloading data while rejection of its use may be overridden is provided. In a preferred embodiment, the downloading facility receives a request to retrieve and use an identified body of data. In response, the facility initiates the retrieval of the identified body of data. At a time during its retrieval, use of the identified body of data is automatically rejected. In response to this rejection, the facility provides a user interface for authorizing the use of the identified body of data. During the provision of this user interface, retrieval of the identified body of data proceeds. When the provided user interface is used to authorize the use of the identified body of data, the facility uses the retrieved identified body of data in accordance with the request.

Abstract: Data requests (e.g., for a hyper text markup language document) made from a client application on a client computer connected to a computer network (e.g., the Internet) are often large. The data received by a client application is often received at a very slow rate due to network congestion and other factors. In addition, the data received may have references to embedded graphical images. If the data received does not contain the display dimensions of the embedded graphical images, then the data cannot be properly displayed until the dimensions of the embedded graphical images are known. When a data request is made, the data transfer rate is monitored. When the receive data transfer rate is slow, and the data contains an embedded graphical image of unknown dimensions, a small placeholder image is automatically displayed for the user instead of the actual data.

Abstract: A graphic user interface for a computer is provided in which representations of application programs can be placed on the display in a specified area reserved for such a purpose in which area they could not be so readily obscured and forgotten, and which includes a facility for controlling the placement of such representations within the reserved area. The graphic images are guided into specific locations, or "docks" in the reserved area, and their removal from the docks is restricted to prevent accidental withdrawal.