Abstract: A map control module receives a stream of map data characterizing a geographic region proximal to a vehicle and outputs a moving map, and the moving map is divisible into a matrix of cells. A map item control receives a stream of point of interest (POI) data characterizing a plurality of POIs within the boundary and categorizes each of the plurality of POIs to define a set of categories. The map item control determines a display location of a map item within the matrix of cells for each of the plurality of POIs and determines an importance for each POI within a same category. The map item control forms a set of clusters of map items. Each map item in a given cluster of map items has a same cell and a same category. The map item control selects a top-item for each cluster of map items.

Abstract: A computer-implemented method and system for representing and solving at least one of an algebraic problem, a proportions problem, and a linear growth problem. A graphical user interface has a symbolic section and a pictorial section. The symbolic section includes a symbolic representation of the mathematical problem and the pictorial section includes a pictorial representation of the mathematical problem. An input is received from a user. The input is associated with one of the symbolic section and the pictorial section. In response to the input, the other of the symbolic section and the pictorial section is modified such that the symbolic section and the pictorial section track each other. The user solves the mathematical problem by interacting with at least one of the symbolic section and the pictorial section.

Abstract: A map control module receives a stream of map data characterizing a geographic region proximal to a vehicle and outputs a moving map, and the moving map is divisible into a matrix of cells. A map item control receives a stream of point of interest (POI) data characterizing a plurality of POIs within the boundary and categorizes each of the plurality of POIs to define a set of categories. The map item control determines a display location of a map item within the matrix of cells for each of the plurality of POIs and determines an importance for each POI within a same category. The map item control forms a set of clusters of map items. Each map item in a given cluster of map items has a same cell and a same category. The map item control selects a top-item for each cluster of map items.

Abstract: One example includes a radar image interface system. The system includes an image processor configured to receive synthetic aperture radar (SAR) image data associated with a region of interest and to generate a radar image of the region of interest based on the SAR image data. The image processor can be further configured to divide the radar image into a plurality of sequential units corresponding to respective zones of the region of interest. The system also includes a display system configured to display zoomed sequential units corresponding to respective zoomed versions of the sequential units of the radar image to a user. The system further includes an input interface configured to facilitate sequentially indexing through each of the zoomed versions of the sequential units on the display system in response to an indexing input provided by the user.

Abstract: A computer-implemented method and system for representing and solving at least one of an algebraic problem, a proportions problem, and a linear growth problem. A graphical user interface has a symbolic section and a pictorial section. The symbolic section includes a symbolic representation of the mathematical problem and the pictorial section includes a pictorial representation of the mathematical problem. An input is received from a user. The input is associated with one of the symbolic section and the pictorial section. In response to the input, the other of the symbolic section and the pictorial section is modified such that the symbolic section and the pictorial section track each other. The user solves the mathematical problem by interacting with at least one of the symbolic section and the pictorial section.

Abstract: An instructional system and method for representing and solving algebraic problems. A computer-implemented method of representing and solving mathematical problems comprises providing a graphical user interface for displaying an instructional system. The instructional system comprises a primary cog having a plurality of primary cog teeth and a secondary cog having a plurality of secondary cog teeth. The secondary cog is linked to the primary cog such that a rotation of the secondary cog causes a rotation of the primary cog. The method comprises representing a mathematical problem on the graphical user interface using the instructional system. The method includes receiving an input from a user and rotating the secondary cog based on the input to cause the primary cog to also rotate. The mathematical problem is solved when a particular tooth of the plurality of primary cog teeth reaches a predefined location.

Abstract: A system to implement a dynamically stylable open graphics library is disclosed. The system includes a memory configured to store machine readable instructions and data and a processing unit. The machine readable instructions and data include a view configuration file that defines view format areas of a graphical user interface where the elements of the graphical user interface are placeable, a layout configuration file that defines a layout of the elements within an area described by the view configuration file on a screen display, a style configuration file that defines a style of the elements, a graphical user interface engine configured to process the style configuration file, the layout configuration file, and the view configuration file and render the elements onto the screen display, and an interface that allows changes to be made to the configuration files by editing a language representative of the format of the configuration files.

Abstract: An instructional system and method for representing and solving algebraic problems. A computer-implemented method of representing and solving mathematical problems comprises providing a graphical user interface for displaying an instructional system. The instructional system comprises a primary cog having a plurality of primary cog teeth and a secondary cog having a plurality of secondary cog teeth. The secondary cog is linked to the primary cog such that a rotation of the secondary cog causes a rotation of the primary cog. The method comprises representing a mathematical problem on the graphical user interface using the instructional system. The method includes receiving an input from a user and rotating the secondary cog based on the input to cause the primary cog to also rotate. The mathematical problem is solved when a particular tooth of the plurality of primary cog teeth reaches a predefined location.

Abstract: A tile instructional system for presenting a linear growth problem and for allowing the linear growth problem to be solved comprises an input tray having at least a first tile and a second tile. The first tile has a first marking and the second tile has a second marking. Each of the first tile and the second tile is configured to selectively expand in accordance with its respective marking. The system includes a tile bed comprising a plurality of tile slots. Each of the plurality of tile slots is configured to receive a tile. The linear growth problem is solvable by situating in the tile bed at least one of the first tile and the second tile and by causing each tile situated in the tile bed to expand in accordance with its respective marking to fill the tile bed.

Abstract: A liquid flow instructional system for presenting a proportions problem and for allowing the proportions problem to be solved comprises an input container and a plurality of output containers selectively and fluidly coupled to the input container. The system has an adjustable valve having a plurality of configurable regions. Each of the plurality of configurable regions corresponds to one of the plurality of output containers. An activable switch is provided for initiating flow of liquid from the input container to the plurality of output containers in accordance with a user configuration of the plurality of configurable regions. The proportions problem is solvable by filling each of the plurality of output containers to capacity without spillage. The correspondence between the plurality of configurable regions and the plurality of output containers is indicated by a visible indicator.

Abstract: A tile instructional system for presenting a linear growth problem and for allowing the linear growth problem to be solved comprises an input tray having at least a first tile and a second tile. The first tile has a first marking and the second tile has a second marking. Each of the first tile and the second tile is configured to selectively expand in accordance with its respective marking. The system includes a tile bed comprising a plurality of tile slots. Each of the plurality of tile slots is configured to receive a tile. The linear growth problem is solvable by situating in the tile bed at least one of the first tile and the second tile and by causing each tile situated in the tile bed to expand in accordance with its respective marking to fill the tile bed.

Abstract: A liquid flow instructional system for presenting a proportions problem and for allowing the proportions problem to be solved comprises an input container and a plurality of output containers selectively and fluidly coupled to the input container. The system has an adjustable valve having a plurality of configurable regions. Each of the plurality of configurable regions corresponds to one of the plurality of output containers. An activable switch is provided for initiating flow of liquid from the input container to the plurality of output containers in accordance with a user configuration of the plurality of configurable regions. The proportions problem is solvable by filling each of the plurality of output containers to capacity without spillage. The correspondence between the plurality of configurable regions and the plurality of output containers is indicated by a visible indicator.

Abstract: A method for adaptively teaching content to a user comprises providing a plurality of teaching topics. The method includes sequentially associating a lead problem and a plurality of secondary problems with each of the plurality of teaching topics. Each of the lead problems and the plurality of secondary problems is an open-ended puzzle having a range of solutions and a difficulty rank. The range of solutions for each of the lead problems and the plurality of secondary problems has an optimal solution and a plurality of secondary solutions. A teaching topic is selected and a corresponding lead problem is presented to a user. User provides answer data via a physical input device having enmeshed gears. The user is provided another secondary problem in the selected teaching topic if the answer data matches one of the secondary solutions. The user is provided another lead problem if the answer data matches the optimal solution.

Abstract: A method for adaptively teaching content to a user comprises providing a plurality of teaching topics. The method includes sequentially associating a lead problem and a plurality of secondary problems with each of the plurality of teaching topics. Each of the lead problems and the plurality of secondary problems is an open-ended puzzle having a range of solutions and a difficulty rank. The range of solutions for each of the lead problems and the plurality of secondary problems has an optimal solution and a plurality of secondary solutions. A teaching topic is selected and a corresponding lead problem is presented to a user. User provides answer data via a physical input device having enmeshed gears. The user is provided another secondary problem in the selected teaching topic if the answer data matches one of the secondary solutions. The user is provided another lead problem if the answer data matches the optimal solution.