A trigonometric function display clock includes a clock face that has a center aligned with a central axis, axial markings aligned with an x-axis and a y-axis, and a secondary circle having a diameter equal to a radius of the axial markings. A first point on the secondary circle is aligned at the center of the central axis, and the secondary circle is configured to be rotatable about the first point. The secondary circle is configured to overlap and align with at least a portion of the axial markings as the secondary circle rotates about the first point.

A method and system for using a natural language generator for automatic assessment item generation is disclosed. The natural language generator includes a document structure generator that produces an abstract document specification defining a structure for an assessment item based on user input. The abstract document specification is input into a logical schema generator, which produces a logical schema specification that creates a more detailed specification for an assessment item. Finally, a sentence generator receives the logical schema specification and creates natural language for the assessment item based on the variables defined in the logical schema specification.

A method and system for using a natural language generator for automatic assessment item generation is disclosed. The natural language generator includes a document structure generator that produces an abstract document specification defining a structure for an assessment item based on user input. The abstract document specification is input into a logical schema generator, which produces a logical schema specification that creates a more detailed specification for an assessment item. Finally, a sentence generator receives the logical schema specification and creates natural language for the assessment item based on the variables defined in the logical schema specification.

Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface finishes, such as color, shading, cross-hatching or real or apparent texture.

Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface finishes, such as color, shading, cross-hatching or real or apparent texture.

A mathematical learning device and method comprising a plurality of puzzle grids (60), each of which displays four digits (12) in a grid pattern of two rows and two columns. These four digits (12) are in a relationship to one another predetermined according to a rule defined mathematically and logically. Each puzzle grid (60) also has its own solution grid (70) not displayed with the same puzzle grid (60), in which solution grid (70) valid substitute values (42), according to the same rule, for each of one of the four digits (12) of the puzzle grid (60), or any multiplier (22, 32) defined in the predetermined rule, are shown as a solution to this same puzzle grid (60).

A trigonometric function display clock includes a clock face that has a center aligned with a central axis, axial markings aligned with an x-axis and a y-axis, and a secondary circle having a diameter equal to a radius of the axial markings. A first point on the secondary circle is aligned at the center of the central axis, and the secondary circle is configured to be rotatable about the first point. The secondary circle is configured to overlap and align with at least a portion of the axial markings as the secondary circle rotates about the first point.

Some embodiments of the present disclosure include a method for simultaneously teaching math and providing physical exercise in a unique manner in which the physical exercise promotes easier learning and retention of math skills and the kinesthetic learning of math encourages physical exercise, while improving balance and core body strength. The method includes assigning body stances and movement to correspond to numbers; assigning body stances and movement to mathematical operations; assigning body stances and movement to equation elements; allowing a Sender and a Receiver to spar, wherein sparring includes the Sender performing an equation through assigned stances and movements; the Receiver providing an answer using the assigned stances and movements; and the Sender confirming whether the answer is correct using an assigned movement; and repeating the sparring allowing the original Receiver and Sender to switch roles; and scoring each sparring round.

Some embodiments of the present disclosure include a method for simultaneously teaching math and providing physical exercise in a unique manner in which the physical exercise promotes easier learning and retention of math skills and the kinesthetic learning of math encourages physical exercise, while improving balance and core body strength. The method includes assigning body stances and movement to correspond to numbers; assigning body stances and movement to mathematical operations; assigning body stances and movement to equation elements; allowing a Sender and a Receiver to spar, wherein sparring includes the Sender performing an equation through assigned stances and movements; the Receiver providing an answer using the assigned stances and movements; and the Sender confirming whether the answer is correct using an assigned movement; and repeating the sparring allowing the original Receiver and Sender to switch roles; and scoring each sparring round.

An apparatus for teaching statistics concepts includes a simulation module that generates a simulation of subject elements moving from a first portion of a simulated space to a second portion of the simulated space, where the simulated space has a treatment path and a non-treatment path. A propensity module utilizes one or more propensity inputs to the simulation module to affect a propensity of the subject elements to move on the treatment path to have treatment functions applied. A treatment module applies the treatment functions to the subject elements moving on the treatment path, where the treatment functions are configured to affect at least one output measure of the subject elements. A display module displays the simulation of the subject elements having the propensity inputs applied, application of the treatment functions, and the at least one output measure.